## 2018 |

Gradoni, Gabriele; Arnaut, Luke; Creagh, Stephen; Tanner, Gregor; Baharuddin, Mohd Hafiz; Smartt, Christopher; Thomas, David WP Wigner-function-based propagation of stochastic field emissions from planar electromagnetic sources (Journal Article) IEEE Transactions on Electromagnetic Compatibility, 60 , pp. 580-588, 2018, ISSN: 1558-187X. @article{Gradoni2018, title = {Wigner-function-based propagation of stochastic field emissions from planar electromagnetic sources}, author = {Gabriele Gradoni and Luke R. Arnaut and Stephen C. Creagh and Gregor Tanner and Mohd Hafiz Baharuddin and Christopher Smartt and David WP Thomas}, url = {http://ieeexplore.ieee.org/abstract/document/8046114/}, doi = {10.1109/TEMC.2017.2738329}, issn = {1558-187X}, year = {2018}, date = {2018-01-06}, journal = {IEEE Transactions on Electromagnetic Compatibility}, volume = {60}, pages = {580-588}, abstract = {Modeling the electromagnetic radiation from modern digital systems-acting effectively as extended stochastic sources as part of a complex architecture-is a challenging task. We follow an approach here based on measuring and propagating field-field autocorrelation functions (ACFs) after suitable averaging. From the modeling side, we use the Wigner transform of the ACFs to describe random wave fields in terms of position and direction of propagation variables. An approximate propagator for the components of the radiated magnetic field is constructed for these ACFs based on a linear flow map. Field-field ACFs at the aperture level are obtained from scanning measurements of complex sources. Distance and spatial resolution of the scanning plane is less than a wavelength from the source plane to capture the imprint of evanescent waves in the near-field ACFs. Near-field scanning and efficient near-to-far-field propagation is carried out and compared with measurements. Results of this study will be useful to assist far-field predictions, source reconstruction, and emission source microscopy.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Modeling the electromagnetic radiation from modern digital systems-acting effectively as extended stochastic sources as part of a complex architecture-is a challenging task. We follow an approach here based on measuring and propagating field-field autocorrelation functions (ACFs) after suitable averaging. From the modeling side, we use the Wigner transform of the ACFs to describe random wave fields in terms of position and direction of propagation variables. An approximate propagator for the components of the radiated magnetic field is constructed for these ACFs based on a linear flow map. Field-field ACFs at the aperture level are obtained from scanning measurements of complex sources. Distance and spatial resolution of the scanning plane is less than a wavelength from the source plane to capture the imprint of evanescent waves in the near-field ACFs. Near-field scanning and efficient near-to-far-field propagation is carried out and compared with measurements. Results of this study will be useful to assist far-field predictions, source reconstruction, and emission source microscopy. |

## 2017 |

Gradoni, Gabriele; Ramapriya, Deepthee Madenoor; Creagh, Stephen; Tanner, Gregor; Baharuddin, Mohd Hafiz; Nasser, Hayan; Smartt, Christopher; Thomas, David WP Near-field scanning and propagation of correlated low-frequency radiated emissions (Journal Article) IEEE Transactions on Electromagnetic Compatibility, 99 , pp. 1-9, 2017, ISSN: 1558-187X . @article{Gradoni2017b, title = {Near-field scanning and propagation of correlated low-frequency radiated emissions}, author = {Gabriele Gradoni and Deepthee Madenoor Ramapriya and Stephen C. Creagh and Gregor Tanner and Mohd Hafiz Baharuddin and Hayan Nasser and Christopher Smartt and David WP Thomas}, url = {http://ieeexplore.ieee.org/abstract/document/8231199/}, doi = {10.1109/TEMC.2017.2778046}, issn = {1558-187X }, year = {2017}, date = {2017-12-20}, journal = {IEEE Transactions on Electromagnetic Compatibility}, volume = {99}, pages = {1-9}, abstract = {Electromagnetic radiation from complex printed circuit boards can occur over a broad frequency bandwidth, ranging from hundreds of megahertz to tens of gigahertz. This is becoming a critical issue for assessment of EMC and interoperability as electronic components become more and more integrated. We use emissions from an enclosure with a single-slot aperture and equipped with operating electronics to exemplify and model such sources. Spatial correlation functions obtained from two-probe measurements are used both to characterize the source and to propagate the emissions. We examine emissions in the submicrowave frequency range, where evanescent decay dominates the measured correlation function at the distances measured. We find that an approximate, diffusion-like propagator describes the measured emissions well. A phase-space approach based on Wigner functions is exploited to develop this approximation and to provide enhanced understanding of the emissions.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Electromagnetic radiation from complex printed circuit boards can occur over a broad frequency bandwidth, ranging from hundreds of megahertz to tens of gigahertz. This is becoming a critical issue for assessment of EMC and interoperability as electronic components become more and more integrated. We use emissions from an enclosure with a single-slot aperture and equipped with operating electronics to exemplify and model such sources. Spatial correlation functions obtained from two-probe measurements are used both to characterize the source and to propagate the emissions. We examine emissions in the submicrowave frequency range, where evanescent decay dominates the measured correlation function at the distances measured. We find that an approximate, diffusion-like propagator describes the measured emissions well. A phase-space approach based on Wigner functions is exploited to develop this approximation and to provide enhanced understanding of the emissions. |

Maricar, Mohamed Ismaeel; Bahar, Ahmad; Greedy, Steve; Smartt, Chris; Phang, Sendy; Gradoni, Gabriele; Cross, Richard; Creagh, Stephen; Tanner, Gregor; Thomas, David WP Design and characterization of a diamond-shaped monopole antenna (Journal Article) Microwave and Optical Technology Letters, 59 (10), pp. 2695-2698, 2017. @article{amdBahar2017, title = {Design and characterization of a diamond-shaped monopole antenna}, author = {Mohamed Ismaeel Maricar and Ahmad Bahar and Steve Greedy and Chris Smartt and Sendy Phang and Gabriele Gradoni and Richard Cross and Stephen C Creagh and Gregor Tanner and David WP Thomas}, url = {http://onlinelibrary.wiley.com/doi/10.1002/mop.30790/full}, year = {2017}, date = {2017-10-01}, journal = {Microwave and Optical Technology Letters}, volume = {59}, number = {10}, pages = {2695-2698}, abstract = {We report a new planar antenna design in the shape of a diamond. The performance of the antenna design is initially obtained through simulation, then fabricated, and its performance evaluated through experiment. Experimental characterization of the diamond-shaped monopole antenna shows good agreement with simulation. In comparison with a simple monopole antenna, our diamond-shaped monopole antenna features smaller geometric footprint and displays a higher bandwidth at millimeteric wave frequencies.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We report a new planar antenna design in the shape of a diamond. The performance of the antenna design is initially obtained through simulation, then fabricated, and its performance evaluated through experiment. Experimental characterization of the diamond-shaped monopole antenna shows good agreement with simulation. In comparison with a simple monopole antenna, our diamond-shaped monopole antenna features smaller geometric footprint and displays a higher bandwidth at millimeteric wave frequencies. |

Chronopoulos,; Droz,; Apalowo,; Ichchou,; Yan, WJ Accurate structural identification for layered composite structures, through a wave and finite element scheme (Journal Article) Composite Structures, 2017. @article{Chronopoulos2017, title = {Accurate structural identification for layered composite structures, through a wave and finite element scheme}, author = {D Chronopoulos and C Droz and R Apalowo and M Ichchou and WJ Yan}, url = {http://www.sciencedirect.com/science/article/pii/S0263822317321803}, year = {2017}, date = {2017-09-22}, journal = {Composite Structures}, abstract = {The increased use of composite materials in modern aerospace and automotive structures, and the broad range of launch vehicles’ operating temperature imply a great temperature range for which the structures has to be frequently and thoroughly inspected. A thermal mechanical analysis is used to experimentally measure the temperature-dependent mechanical properties of a composite layered panel in the range of −100 ℃ to 150 ℃. A hybrid wave finite element/finite element computational scheme is developed to calculate the temperature-dependent wave propagation and interaction properties of a system of two structural waveguides connected through a coupling joint. Calculations are made using the measured thermomechanical properties. Temperature-dependent wave propagation constants of each structural waveguide are obtained by the wave finite element approach and then coupled to the fully finite element described coupling joint, on which damage is modelled, in order to calculate the scattering magnitudes of the waves interaction with damage across the coupling joint. The significance of the panel’s glass transition range on the measured and calculated properties is emphasised. Numerical results are presented as illustration of the work.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The increased use of composite materials in modern aerospace and automotive structures, and the broad range of launch vehicles’ operating temperature imply a great temperature range for which the structures has to be frequently and thoroughly inspected. A thermal mechanical analysis is used to experimentally measure the temperature-dependent mechanical properties of a composite layered panel in the range of −100 ℃ to 150 ℃. A hybrid wave finite element/finite element computational scheme is developed to calculate the temperature-dependent wave propagation and interaction properties of a system of two structural waveguides connected through a coupling joint. Calculations are made using the measured thermomechanical properties. Temperature-dependent wave propagation constants of each structural waveguide are obtained by the wave finite element approach and then coupled to the fully finite element described coupling joint, on which damage is modelled, in order to calculate the scattering magnitudes of the waves interaction with damage across the coupling joint. The significance of the panel’s glass transition range on the measured and calculated properties is emphasised. Numerical results are presented as illustration of the work. |

Creagh, Stephen; Blackburn, John; Gradoni, Gabriele; Hartmann, Timo; Phang, Sendy; Tanner, Gregor Fluctuation of correlation within enclosures (Conference) IEEE , 2017. @conference{Creagh2017, title = {Fluctuation of correlation within enclosures}, author = {Stephen C. Creagh and John Blackburn and Gabriele Gradoni and Timo Hartmann and Sendy Phang and Gregor Tanner}, url = {http://ieeexplore.ieee.org/abstract/document/8065548/?reload=true}, doi = {10.1109/ICEAA.2017.8065548}, year = {2017}, date = {2017-09-11}, pages = {1429-1432}, publisher = {IEEE }, abstract = {Emission from complex EM sources may be characterised by measurements of two-point correlations functions, which contain directional as well as positional information for radiated power. When such sources radiate within enclosures, the average power arising from multiple reflection can be modelled by ray tracing techniques. In this paper we describe how a bootstrapping method may be employed which exploits information gained as part of such ray-tracing simulations to provide additional information regarding fluctuation about the mean.}, keywords = {}, pubstate = {published}, tppubtype = {conference} } Emission from complex EM sources may be characterised by measurements of two-point correlations functions, which contain directional as well as positional information for radiated power. When such sources radiate within enclosures, the average power arising from multiple reflection can be modelled by ray tracing techniques. In this paper we describe how a bootstrapping method may be employed which exploits information gained as part of such ray-tracing simulations to provide additional information regarding fluctuation about the mean. |

Phang, Sendy; Vukovic, Ana; Creagh, Stephen; Gradoni, Gabriele; Benson, Trevor Parity-time symmetric metamaterial for photonics (Conference) IEEE, 2017. @conference{Phang2017, title = {Parity-time symmetric metamaterial for photonics}, author = {Sendy Phang and Ana Vukovic and Stephen C. Creagh and Gabriele Gradoni and Trevor M. Benson}, url = {http://ieeexplore.ieee.org/abstract/document/8065649/}, doi = {10.1109/ICEAA.2017.8065649}, year = {2017}, date = {2017-09-09}, pages = {1805-1808}, publisher = {IEEE}, abstract = {The paper studies the spectral properties of Parity-Time (PT) symmetric photonic structures based on circular microresonators. A semi-analytical model based on solving the Boundary Integral Equation (BIE) is used to model coupled resonators satisfying the PT-symmetric condition. Unique properties such as asymmetric transmission and a localised defect state are observed. A potential benefit of these properties is the generation of a single frequency laser source for spectroscopy or telecommunication applications.}, keywords = {}, pubstate = {published}, tppubtype = {conference} } The paper studies the spectral properties of Parity-Time (PT) symmetric photonic structures based on circular microresonators. A semi-analytical model based on solving the Boundary Integral Equation (BIE) is used to model coupled resonators satisfying the PT-symmetric condition. Unique properties such as asymmetric transmission and a localised defect state are observed. A potential benefit of these properties is the generation of a single frequency laser source for spectroscopy or telecommunication applications. |

Gradoni, Gabriele; Arnault, Luk; Creagh, Stephen; Tanner, Gregor; Baharuddin, Mohd Hafiz; Smartt, Christopher; Thomas, David WP Wigner function based propagation of stochastic field emissions from planar electromagnetic sources (Journal Article) IEEE Transactions on Electromagnetic Compatibility, 2017. @article{Gradoni2017, title = {Wigner function based propagation of stochastic field emissions from planar electromagnetic sources}, author = {Gabriele Gradoni and Luk R Arnault and Stephen C Creagh and Gregor Tanner and Mohd Hafiz Baharuddin and Christopher Smartt and David WP Thomas}, url = {http://ieeexplore.ieee.org/document/8046114/}, year = {2017}, date = {2017-08-05}, journal = {IEEE Transactions on Electromagnetic Compatibility}, abstract = {Modelling the electromagnetic radiation from modern digital systems – acting effectively as extended, stochastic sources as part of a complex architecture – is a challenging task. We follow an approach here based on measuring and propagating field-field autocorrelation functions (ACFs) after suitable averaging. From the modelling side, we use the Wigner transform of the ACFs to describe random wave fields in terms of position and direction of propagation variables. An approximate propagator for the components of the radiated magnetic field is constructed for these ACFs based on a linear flow map. Field-field ACFs at aperture level are obtained from scanning measurements of complex sources. Distance and spatial resolution of the scanning plane is less than a wavelength from the source plane to capture the imprint of evanescent waves in the near- field ACFs. Near-field scanning and efficient near-to-far field propagation is carried out and compared with measurements. Results of this study will be useful to assist far-field predictions, source reconstruction, and emission source microscopy. Index Terms—Statistical Electromagnetics, Near-field Scan, Wigner Function, Correlation, Reverberation Chamber.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Modelling the electromagnetic radiation from modern digital systems – acting effectively as extended, stochastic sources as part of a complex architecture – is a challenging task. We follow an approach here based on measuring and propagating field-field autocorrelation functions (ACFs) after suitable averaging. From the modelling side, we use the Wigner transform of the ACFs to describe random wave fields in terms of position and direction of propagation variables. An approximate propagator for the components of the radiated magnetic field is constructed for these ACFs based on a linear flow map. Field-field ACFs at aperture level are obtained from scanning measurements of complex sources. Distance and spatial resolution of the scanning plane is less than a wavelength from the source plane to capture the imprint of evanescent waves in the near- field ACFs. Near-field scanning and efficient near-to-far field propagation is carried out and compared with measurements. Results of this study will be useful to assist far-field predictions, source reconstruction, and emission source microscopy. Index Terms—Statistical Electromagnetics, Near-field Scan, Wigner Function, Correlation, Reverberation Chamber. |

Apalowo, RK; Chronopoulos,; Ichchou,; Essa,; Escalera, Martin De La The impact of temperature on wave interaction with damage in composite structures (Journal Article) Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 231 (16), pp. 3042-3056, 2017. @article{Apalowo2017, title = {The impact of temperature on wave interaction with damage in composite structures}, author = {RK Apalowo and D Chronopoulos and M Ichchou and Y Essa and F Martin De La Escalera}, url = {http://journals.sagepub.com/doi/abs/10.1177/0954406217718217}, year = {2017}, date = {2017-08-01}, journal = {Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science}, volume = {231}, number = {16}, pages = {3042-3056}, abstract = {The increased use of composite materials in modern aerospace and automotive structures, and the broad range of launch vehicles’ operating temperature imply a great temperature range for which the structures has to be frequently and thoroughly inspected. A thermal mechanical analysis is used to experimentally measure the temperature-dependent mechanical properties of a composite layered panel in the range of −100 ℃ to 150 ℃. A hybrid wave finite element/finite element computational scheme is developed to calculate the temperature-dependent wave propagation and interaction properties of a system of two structural waveguides connected through a coupling joint. Calculations are made using the measured thermomechanical properties. Temperature-dependent wave propagation constants of each structural waveguide are obtained by the wave finite element approach and then coupled to the fully finite element described coupling joint, on which damage is modelled, in order to calculate the scattering magnitudes of the waves interaction with damage across the coupling joint. The significance of the panel’s glass transition range on the measured and calculated properties is emphasised. Numerical results are presented as illustration of the work.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The increased use of composite materials in modern aerospace and automotive structures, and the broad range of launch vehicles’ operating temperature imply a great temperature range for which the structures has to be frequently and thoroughly inspected. A thermal mechanical analysis is used to experimentally measure the temperature-dependent mechanical properties of a composite layered panel in the range of −100 ℃ to 150 ℃. A hybrid wave finite element/finite element computational scheme is developed to calculate the temperature-dependent wave propagation and interaction properties of a system of two structural waveguides connected through a coupling joint. Calculations are made using the measured thermomechanical properties. Temperature-dependent wave propagation constants of each structural waveguide are obtained by the wave finite element approach and then coupled to the fully finite element described coupling joint, on which damage is modelled, in order to calculate the scattering magnitudes of the waves interaction with damage across the coupling joint. The significance of the panel’s glass transition range on the measured and calculated properties is emphasised. Numerical results are presented as illustration of the work. |

Chronopoulos, Dimitrios; Collet, Manuel; Ichchou, Mohamed Wave sensitivity analysis for periodic and arbitrarily complex composite structures (Journal Article) Engineering Computations, 34 (5), pp. 1572-1597, 2017. @article{Chronopoulos2017b, title = {Wave sensitivity analysis for periodic and arbitrarily complex composite structures}, author = {Dimitrios Chronopoulos and Manuel Collet and Mohamed Ichchou}, url = {http://www.emeraldinsight.com/doi/full/10.1108/EC-06-2016-0200}, year = {2017}, date = {2017-07-03}, journal = {Engineering Computations}, volume = {34}, number = {5}, pages = {1572-1597}, abstract = { Purpose This paper aims to present the development of a numerical continuum-discrete approach for computing the sensitivity of the waves propagating in periodic composite structures. The work can be directly used for evaluating the sensitivity of the structural dynamic performance with respect to geometric and layering structural modifications. Design/methodology/approach A structure of arbitrary layering and geometric complexity is modelled using solid finite element (FE). A generic expression for computing the variation of the mass and the stiffness matrices of the structure with respect to the material and geometric characteristics is hereby given. The sensitivity of the structural wave properties can thus be numerically determined by computing the variability of the corresponding eigenvalues for the resulting eigenproblem. The exhibited approach is validated against the finite difference method as well as analytical results. Findings An intense wavenumber dependence is observed for the sensitivity results of a sandwich structure. This exhibits the importance and potential of the presented tool with regard to the optimization of layered structures for specific applications. The model can also be used for computing the effect of the inclusion of smart layers such as auxetics and piezoelectrics. Originality/value The paper presents the first continuum-discrete approach specifically developed for accurately and efficiently computing the sensitivity of the wave propagation data for periodic composite structures irrespective of their size. The considered structure can be of arbitrary layering and material characteristics as FE modelling is used.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Purpose This paper aims to present the development of a numerical continuum-discrete approach for computing the sensitivity of the waves propagating in periodic composite structures. The work can be directly used for evaluating the sensitivity of the structural dynamic performance with respect to geometric and layering structural modifications. Design/methodology/approach A structure of arbitrary layering and geometric complexity is modelled using solid finite element (FE). A generic expression for computing the variation of the mass and the stiffness matrices of the structure with respect to the material and geometric characteristics is hereby given. The sensitivity of the structural wave properties can thus be numerically determined by computing the variability of the corresponding eigenvalues for the resulting eigenproblem. The exhibited approach is validated against the finite difference method as well as analytical results. Findings An intense wavenumber dependence is observed for the sensitivity results of a sandwich structure. This exhibits the importance and potential of the presented tool with regard to the optimization of layered structures for specific applications. The model can also be used for computing the effect of the inclusion of smart layers such as auxetics and piezoelectrics. Originality/value The paper presents the first continuum-discrete approach specifically developed for accurately and efficiently computing the sensitivity of the wave propagation data for periodic composite structures irrespective of their size. The considered structure can be of arbitrary layering and material characteristics as FE modelling is used. |

Chronopoulos, Dimitrios; Antoniadis,; Ampatzidis, Theofanis Enhanced acoustic insulation properties of composite metamaterials having embedded negative stiffness inclusions (Journal Article) Extreme Mechanics Letters, 12 , pp. 48-54, 2017. @article{Chronopoulos2017b, title = {Enhanced acoustic insulation properties of composite metamaterials having embedded negative stiffness inclusions}, author = {Dimitrios Chronopoulos and I Antoniadis and Theofanis Ampatzidis}, url = {http://www.sciencedirect.com/science/article/pii/S2352431616300487}, year = {2017}, date = {2017-04-01}, journal = {Extreme Mechanics Letters}, volume = {12}, pages = {48-54}, abstract = {Despite the fact that the concept of incorporating Negative Stiffness (NS) elements within mechanical systems was formulated and validated more than 40 years ago, it has only recently received consistent attention. In this work, the design of a layered mechanical metamaterial having implemented NS inclusions is presented and its acoustic wave propagation properties are modelled. A dedicated two-dimensional periodic structure theory scheme is developed in order to compute the frequency dependent damping loss factor of the metamaterial structure. The acoustic transmission properties through the modelled panel are computed within a Statistical Energy Analysis (SEA) scheme. It is demonstrated that the suggested layered metamaterial exhibits highly superior acoustic insulation performance close and above the acoustic coincidence range, thanks to the drastic increase of its structural damping properties implied by the NS elements. Additionally, the proposed configuration presents superior performance in a broadband frequency range when compared to a viscoelastic damping constraint layer of equivalent mass.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Despite the fact that the concept of incorporating Negative Stiffness (NS) elements within mechanical systems was formulated and validated more than 40 years ago, it has only recently received consistent attention. In this work, the design of a layered mechanical metamaterial having implemented NS inclusions is presented and its acoustic wave propagation properties are modelled. A dedicated two-dimensional periodic structure theory scheme is developed in order to compute the frequency dependent damping loss factor of the metamaterial structure. The acoustic transmission properties through the modelled panel are computed within a Statistical Energy Analysis (SEA) scheme. It is demonstrated that the suggested layered metamaterial exhibits highly superior acoustic insulation performance close and above the acoustic coincidence range, thanks to the drastic increase of its structural damping properties implied by the NS elements. Additionally, the proposed configuration presents superior performance in a broadband frequency range when compared to a viscoelastic damping constraint layer of equivalent mass. |

Bajars, Janis; Chappell, David; Hartmann, Timo; Tanner, Gregor Improved Approximation of Phase-Space Densities on Triangulated Domains Using Discrete Flow Mapping with p-Refinement (Journal Article) Journal of Scientific Computing, 72 (3), pp. 1290-1312, 2017. @article{Bajars2017b, title = {Improved Approximation of Phase-Space Densities on Triangulated Domains Using Discrete Flow Mapping with p-Refinement}, author = {Janis Bajars and David J Chappell and Timo Hartmann and Gregor Tanner}, url = {https://link.springer.com/article/10.1007/s10915-017-0397-8}, year = {2017}, date = {2017-01-09}, journal = { Journal of Scientific Computing}, volume = {72}, number = {3}, pages = {1290-1312}, abstract = {We consider the approximation of the phase-space flow of a dynamical system on a triangulated surface using an approach known as Discrete Flow Mapping. Such flows are of interest throughout statistical mechanics, but the focus here is on flows arising from ray tracing approximations of linear wave equations. An orthogonal polynomial basis approximation of the phase-space density is applied in both the position and direction coordinates, in contrast with previous studies where piecewise constant functions have typically been applied for the spatial approximation. In order to improve the tractability of an orthogonal polynomial approximation in both phase-space coordinates, we propose a careful strategy for computing the propagation operator. For the favourable case of a Legendre polynomial basis we show that the integrals in the definition of the propagation operator may be evaluated analytically with respect to position and via a spectrally convergent quadrature rule for the direction coordinate. A generally applicable spectral quadrature scheme for integration with respect to both coordinates is also detailed for completeness. Finally, we provide numerical results that motivate the use of p-refinement in the orthogonal polynomial basis.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We consider the approximation of the phase-space flow of a dynamical system on a triangulated surface using an approach known as Discrete Flow Mapping. Such flows are of interest throughout statistical mechanics, but the focus here is on flows arising from ray tracing approximations of linear wave equations. An orthogonal polynomial basis approximation of the phase-space density is applied in both the position and direction coordinates, in contrast with previous studies where piecewise constant functions have typically been applied for the spatial approximation. In order to improve the tractability of an orthogonal polynomial approximation in both phase-space coordinates, we propose a careful strategy for computing the propagation operator. For the favourable case of a Legendre polynomial basis we show that the integrals in the definition of the propagation operator may be evaluated analytically with respect to position and via a spectrally convergent quadrature rule for the direction coordinate. A generally applicable spectral quadrature scheme for integration with respect to both coordinates is also detailed for completeness. Finally, we provide numerical results that motivate the use of p-refinement in the orthogonal polynomial basis. |

Bajars, Janis; Chappell, David; Søndergaard, Niels; Chappell, David; Tanner, Gregor Transport of phase space densities through tetrahedral meshes using discrete flow mapping (Journal Article) Journal of Computational Physics, 328 , pp. 95-108, 2017. @article{Bajars2017, title = {Transport of phase space densities through tetrahedral meshes using discrete flow mapping}, author = {Janis Bajars and David J Chappell and Niels Søndergaard and David Chappell and Gregor Tanner}, url = {http://www.sciencedirect.com/science/article/pii/S0021999116305174}, year = {2017}, date = {2017-01-01}, journal = {Journal of Computational Physics}, volume = {328}, pages = {95-108}, abstract = {Discrete flow mapping was recently introduced as an efficient ray based method determining wave energy distributions in complex built up structures. Wave energy densities are transported along ray trajectories through polygonal mesh elements using a finite dimensional approximationof a ray transfer operator. In this way the method can be viewed as a smoothed ray tracing method defined over meshed surfaces. Many applications require the resolution of wave energy distributions in three-dimensional domains, such as in room acoustics, underwater acoustics and for electromagnetic cavity problems. In this work we extend discrete flow mapping to three-dimensional domains by propagating wave energy densities through tetrahedral meshes. The geometric simplicity of the tetrahedral mesh elements is utilised to efficiently compute the ray transfer operator using a mixture of analytic and spectrally accurate numerical integration. The important issue of how to choose a suitable basis approximation in phase space whilst maintaining a reasonable computational cost is addressed via low order local approximations on tetrahedral faces in the position coordinate and high order orthogonal polynomial expansions in momentum space}, keywords = {}, pubstate = {published}, tppubtype = {article} } Discrete flow mapping was recently introduced as an efficient ray based method determining wave energy distributions in complex built up structures. Wave energy densities are transported along ray trajectories through polygonal mesh elements using a finite dimensional approximationof a ray transfer operator. In this way the method can be viewed as a smoothed ray tracing method defined over meshed surfaces. Many applications require the resolution of wave energy distributions in three-dimensional domains, such as in room acoustics, underwater acoustics and for electromagnetic cavity problems. In this work we extend discrete flow mapping to three-dimensional domains by propagating wave energy densities through tetrahedral meshes. The geometric simplicity of the tetrahedral mesh elements is utilised to efficiently compute the ray transfer operator using a mixture of analytic and spectrally accurate numerical integration. The important issue of how to choose a suitable basis approximation in phase space whilst maintaining a reasonable computational cost is addressed via low order local approximations on tetrahedral faces in the position coordinate and high order orthogonal polynomial expansions in momentum space |

Chronopoulos, Dimitrios Wave steering effects in anisotropic composite structures: Direct calculation of the energy skew angle through a finite element scheme (Journal Article) Ultrasonics, 73 , pp. 43-48, 2017. @article{Chronopoulos2017b, title = {Wave steering effects in anisotropic composite structures: Direct calculation of the energy skew angle through a finite element scheme}, author = {Dimitrios Chronopoulos}, url = {http://www.sciencedirect.com/science/article/pii/S0041624X16301536}, year = {2017}, date = {2017-01-01}, journal = {Ultrasonics}, volume = {73}, pages = {43-48}, abstract = {A systematic expression quantifying the wave energy skewing phenomenon as a function of the mechanical characteristics of a non-isotropic structure is derived in this study. A structure of arbitrary anisotropy, layering and geometric complexity is modelled through Finite Elements (FEs) coupled to a periodic structure wave scheme. A generic approach for efficiently computing the angular sensitivity of the wave slowness for each wave type, direction and frequency is presented. The approach does not involve any finite differentiation scheme and is therefore computationally efficient and not prone to the associated numerical errors.}, keywords = {}, pubstate = {published}, tppubtype = {article} } A systematic expression quantifying the wave energy skewing phenomenon as a function of the mechanical characteristics of a non-isotropic structure is derived in this study. A structure of arbitrary anisotropy, layering and geometric complexity is modelled through Finite Elements (FEs) coupled to a periodic structure wave scheme. A generic approach for efficiently computing the angular sensitivity of the wave slowness for each wave type, direction and frequency is presented. The approach does not involve any finite differentiation scheme and is therefore computationally efficient and not prone to the associated numerical errors. |

## 2016 |

Creagh, Stephen; Gradoni, Gabriele; Hartmann, Timo; Tanner, Gregor Propagating wave correlations in complex systems (Journal Article) Journal of Physics A: Mathematical and Theoretical, 50 (4), 2016. @article{Creagh2016, title = {Propagating wave correlations in complex systems}, author = {Stephen C Creagh and Gabriele Gradoni and Timo Hartmann and Gregor Tanner}, url = {http://iopscience.iop.org/article/10.1088/1751-8121/50/4/045101/meta}, year = {2016}, date = {2016-12-23}, journal = {Journal of Physics A: Mathematical and Theoretical}, volume = {50}, number = {4}, abstract = {We describe a novel approach for computing wave correlation functions inside finite spatial domains driven by complex and statistical sources. By exploiting semiclassical approximations, we provide explicit algorithms to calculate the local mean of these correlation functions in terms of the underlying classical dynamics. By defining appropriate ensemble averages, we show that fluctuations about the mean can be characterised in terms of classical correlations. We give in particular an explicit expression relating fluctuations of diagonal contributions to those of the full wave correlation function. The methods have a wide range of applications both in quantum mechanics and for classical wave problems such as in vibro-acoustics and electromagnetism. We apply the methods here to simple quantum systems, so-called quantum maps, which model the behaviour of generic problems on Poincaré sections. Although low-dimensional, these models exhibit a chaotic classical limit and share common characteristics with wave propagation in complex structures.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We describe a novel approach for computing wave correlation functions inside finite spatial domains driven by complex and statistical sources. By exploiting semiclassical approximations, we provide explicit algorithms to calculate the local mean of these correlation functions in terms of the underlying classical dynamics. By defining appropriate ensemble averages, we show that fluctuations about the mean can be characterised in terms of classical correlations. We give in particular an explicit expression relating fluctuations of diagonal contributions to those of the full wave correlation function. The methods have a wide range of applications both in quantum mechanics and for classical wave problems such as in vibro-acoustics and electromagnetism. We apply the methods here to simple quantum systems, so-called quantum maps, which model the behaviour of generic problems on Poincaré sections. Although low-dimensional, these models exhibit a chaotic classical limit and share common characteristics with wave propagation in complex structures. |

Thomas, DWP; Smartt,; Nasser,; Baharuddin,; Greedy,; Gradoni,; Creagh, SC; Tanner, Time domain measurement of near field emissions from complex PCBs (Journal Article) Microwave Conference (EuMC), 2016 46th European, pp. 707-710, 2016. @article{Thomas2016, title = {Time domain measurement of near field emissions from complex PCBs}, author = {DWP Thomas and C Smartt and H Nasser and M Baharuddin and S Greedy and G Gradoni and SC Creagh and G Tanner}, url = {http://ieeexplore.ieee.org/abstract/document/7824441/}, year = {2016}, date = {2016-10-10}, journal = {Microwave Conference (EuMC), 2016 46th European}, pages = {707-710}, abstract = {This paper discusses how the measurements of the near-field emissions in the time domain can be used to characterize the broadband emissions from complex sources such as multifunctional Printed Circuit Boards (PCBs). The near-fields, transverse to the measurement surface, are sufficient to characterise the radiator provided the surface contains all the significant fields. For time domain measurements, the field probe is calibrated over a broad bandwidth for both amplitude and phase to provide the probe impulse response. A suitable digital filter applied with the same probe impulse response to extract the time domain magnetic field data from the probe output voltage. Results show that good agreement in the can be obtained. The measured near fields can then be used to create an equivalent model of the PCB which can be used to predict the emissions in the far field or in any environment. In this work the objective is to create an equivalent time dependent dipole array model of the DUT.}, keywords = {}, pubstate = {published}, tppubtype = {article} } This paper discusses how the measurements of the near-field emissions in the time domain can be used to characterize the broadband emissions from complex sources such as multifunctional Printed Circuit Boards (PCBs). The near-fields, transverse to the measurement surface, are sufficient to characterise the radiator provided the surface contains all the significant fields. For time domain measurements, the field probe is calibrated over a broad bandwidth for both amplitude and phase to provide the probe impulse response. A suitable digital filter applied with the same probe impulse response to extract the time domain magnetic field data from the probe output voltage. Results show that good agreement in the can be obtained. The measured near fields can then be used to create an equivalent model of the PCB which can be used to predict the emissions in the far field or in any environment. In this work the objective is to create an equivalent time dependent dipole array model of the DUT. |

Gradoni, Gabriele; Antonsen, Thomas; Ott, Ed; Anlage, Steven Random coupling model for the radiation of statistical sources inside cavities (Journal Article) Microwave Conference (EuMC), 2016 46th European, pp. 711-714, 2016. @article{Gradoni2016, title = {Random coupling model for the radiation of statistical sources inside cavities}, author = {Gabriele Gradoni and Thomas M Antonsen and Ed Ott and Steven M Anlage}, url = {http://ieeexplore.ieee.org/abstract/document/7824442/}, year = {2016}, date = {2016-10-04}, journal = { Microwave Conference (EuMC), 2016 46th European}, pages = {711-714}, abstract = {We review a statistical model, the random coupling model, that describes the high-frequency excitation of irregular cavities through arbitrary sources. The model uses wave chaos theory to describing wave mixing in terms of universal fluctuation laws. The model accounts for system specific details of the excitation through a deterministic description. We consider the scenario where a continuous statistical source operates inside an irregular cavity with losses. Discrete approximations of complex sources in terms of dipoles are available in literature. This can be exploited to construct an impedance matrix at the terminals (ports) of the dipole, and thus characterise the response of the cavity in therms of voltages and currents. In particular, upon a random current excitation, conveniently characterised in terms of correlation matrix, an ensemble average voltage-voltage correlation matrix can be found through the impedance matrices predicted by the random coupling model. Results are of interest in electromagnetic compatibility for the characterisation of multifunctional digital electronics, as well as for dense multiple-input multiple-output communication operating in reflecting environments}, keywords = {}, pubstate = {published}, tppubtype = {article} } We review a statistical model, the random coupling model, that describes the high-frequency excitation of irregular cavities through arbitrary sources. The model uses wave chaos theory to describing wave mixing in terms of universal fluctuation laws. The model accounts for system specific details of the excitation through a deterministic description. We consider the scenario where a continuous statistical source operates inside an irregular cavity with losses. Discrete approximations of complex sources in terms of dipoles are available in literature. This can be exploited to construct an impedance matrix at the terminals (ports) of the dipole, and thus characterise the response of the cavity in therms of voltages and currents. In particular, upon a random current excitation, conveniently characterised in terms of correlation matrix, an ensemble average voltage-voltage correlation matrix can be found through the impedance matrices predicted by the random coupling model. Results are of interest in electromagnetic compatibility for the characterisation of multifunctional digital electronics, as well as for dense multiple-input multiple-output communication operating in reflecting environments |

Hartman, Timo; Xie, Gang; Bajars, Janis; Chappell, David; Tanner, Gregor Vibro-acoustic energy flow through spot-welds inDynamical Energy Analysis (Journal Article) Inter-Noise, 2016. @article{Hartman2016b, title = {Vibro-acoustic energy flow through spot-welds inDynamical Energy Analysis}, author = {Timo Hartman and Gang Xie and Janis Bajars and David Chappell and Gregor Tanner}, url = {http://pub.dega-akustik.de/IN2016/data/articles/000575.pdf}, year = {2016}, date = {2016-08-18}, journal = {Inter-Noise}, abstract = {Dynamical Energy Analysis (DEA) in the form of Discrete Flow Mapping (DFM) is a fairly new mesh-basedmethod for numerically modelling structure borne sound transmission in complex structures. A key feature isthe possibility to work directly on existing finite element (FE) meshes avoiding time-consuming and costly re-modelling. Furthermore, DFM provides detailed spatial information about the vibrational energy distributionwithin a complex structure in the mid-to-high frequency range. In this work we will illustrate the methodusing a car floor structure which consists of a big panel and several rails connected by spot welds modeled inFE through Rigid Body Elements (RBE)}, keywords = {}, pubstate = {published}, tppubtype = {article} } Dynamical Energy Analysis (DEA) in the form of Discrete Flow Mapping (DFM) is a fairly new mesh-basedmethod for numerically modelling structure borne sound transmission in complex structures. A key feature isthe possibility to work directly on existing finite element (FE) meshes avoiding time-consuming and costly re-modelling. Furthermore, DFM provides detailed spatial information about the vibrational energy distributionwithin a complex structure in the mid-to-high frequency range. In this work we will illustrate the methodusing a car floor structure which consists of a big panel and several rails connected by spot welds modeled inFE through Rigid Body Elements (RBE) |

Gradoni, Gabriele; Creagh, Stephen; Tanner, Gregor Transfer operator approach for cavities with apertures (Journal Article) Electromagnetic Theory (EMTS), 2016 URSI International Symposium, pp. 682-685, 2016. @article{Gradoni2016b, title = {Transfer operator approach for cavities with apertures}, author = {Gabriele Gradoni and Stephen C Creagh and Gregor Tanner}, url = {http://ieeexplore.ieee.org/abstract/document/7571490/}, year = {2016}, date = {2016-08-08}, journal = {Electromagnetic Theory (EMTS), 2016 URSI International Symposium}, pages = {682-685}, abstract = {We describe a representation of the boundary integral equations for wave propagation in enclosures which leads to a direct description of transport and dynamical characteristics of the problem. The formalism is extended to account for arbitrary and possibly statistical sources driving a polygonal cavity problem and to account for apertures. In this approach, the boundary integral equations are encoded within a shift operator which propagates waves leaving the boundary until they return to the boundary as an incoming wave. The response of the system to non-deterministic, statistical sources characterised by correlation functions can be treated, providing a direct path to ray-tracing approaches through the Wigner function. The high frequency limit is retrieved semiclassically and provides a simple ray tracing scheme transporting densities of rays as an averaged response. Interference effects due to transport along multiple paths can also be accounted for.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We describe a representation of the boundary integral equations for wave propagation in enclosures which leads to a direct description of transport and dynamical characteristics of the problem. The formalism is extended to account for arbitrary and possibly statistical sources driving a polygonal cavity problem and to account for apertures. In this approach, the boundary integral equations are encoded within a shift operator which propagates waves leaving the boundary until they return to the boundary as an incoming wave. The response of the system to non-deterministic, statistical sources characterised by correlation functions can be treated, providing a direct path to ray-tracing approaches through the Wigner function. The high frequency limit is retrieved semiclassically and provides a simple ray tracing scheme transporting densities of rays as an averaged response. Interference effects due to transport along multiple paths can also be accounted for. |

Hartman, Timo; Morita, Satoshi; Tanner, Gregor; Chappell, David High-frequency structure-borne sound transmission on anFE mesh for a tractor model using Dynamical Energy Anal-ysis (Journal Article) ISMA, 2016. @article{Hartman2016, title = {High-frequency structure-borne sound transmission on anFE mesh for a tractor model using Dynamical Energy Anal-ysis}, author = {Timo Hartman and Satoshi Morita and Gregor Tanner and David Chappell}, year = {2016}, date = {2016-06-17}, journal = {ISMA}, abstract = {Dynamical Energy Analysis (DEA) combined with the Discrete Flow Mapping technique (DFM) has re-cently been introduced as a mesh-based high frequency method modelling structure borne sound for com-plex built-up structures. This has proven to enhance vibro-acoustic simulations considerably by making itpossible to work directly on existing finite element meshes circumventing time-consuming and costly re-modelling strategies. In addition, DFM provides detailed spatial information about the vibrational energydistribution within a complex structure in the mid-to-high frequency range. We will present here progressin the development of the DEA method towards handling complex FEM-meshes including Rigid Body El-ements and sound radiation. In addition, structure borne transmission paths through rubber mounts and atglass-metal interfaces are considered. We present results for a tractor model and compare with measurementresults}, keywords = {}, pubstate = {published}, tppubtype = {article} } Dynamical Energy Analysis (DEA) combined with the Discrete Flow Mapping technique (DFM) has re-cently been introduced as a mesh-based high frequency method modelling structure borne sound for com-plex built-up structures. This has proven to enhance vibro-acoustic simulations considerably by making itpossible to work directly on existing finite element meshes circumventing time-consuming and costly re-modelling strategies. In addition, DFM provides detailed spatial information about the vibrational energydistribution within a complex structure in the mid-to-high frequency range. We will present here progressin the development of the DEA method towards handling complex FEM-meshes including Rigid Body El-ements and sound radiation. In addition, structure borne transmission paths through rubber mounts and atglass-metal interfaces are considered. We present results for a tractor model and compare with measurementresults |

Arnaut, Luke; Gradoni, Gabriele Probability Distribution of the Coherence Bandwidth of a Reverberation Chamber (Journal Article) IEEE Transactions on Antennas and Propagation , 63 (5), pp. 2286 - 2290, 2016. @article{Arnaut2016, title = {Probability Distribution of the Coherence Bandwidth of a Reverberation Chamber}, author = {Luke R. Arnaut and Gabriele Gradoni}, url = {http://ieeexplore.ieee.org/document/7041166/?tp=&arnumber=7041166}, year = {2016}, date = {2016-02-12}, journal = {IEEE Transactions on Antennas and Propagation }, volume = {63}, number = {5}, pages = {2286 - 2290}, abstract = {A theoretical probability distribution and associated statistics for the coherence bandwidth of an ideal mode-stirred reverberation chamber are derived. The stochastic model assumes and exploits the ergodicity of a dynamic wave chaotic cavity by expressing the coherence bandwidth in terms of the random effective excitation bandwidth and by replacing spatial averaging of transmitter-receiver locations with stir (ensemble) averaging. The theoretical model is validated through comparison with the empirical cumulative distribution function (cdf) extracted from measured S-parameter data from a real chamber, and through simulation using analytical calculations for a fictitious wall-stirred chamber. The results are particularly relevant to the improvement of transmission quality and uncertainty quantification of wireless multipath propagation.}, keywords = {}, pubstate = {published}, tppubtype = {article} } A theoretical probability distribution and associated statistics for the coherence bandwidth of an ideal mode-stirred reverberation chamber are derived. The stochastic model assumes and exploits the ergodicity of a dynamic wave chaotic cavity by expressing the coherence bandwidth in terms of the random effective excitation bandwidth and by replacing spatial averaging of transmitter-receiver locations with stir (ensemble) averaging. The theoretical model is validated through comparison with the empirical cumulative distribution function (cdf) extracted from measured S-parameter data from a real chamber, and through simulation using analytical calculations for a fictitious wall-stirred chamber. The results are particularly relevant to the improvement of transmission quality and uncertainty quantification of wireless multipath propagation. |

## 2015 |

Gagliardi, Luigi; Micheli, Davide; Gradoni, Gabriele; Moglie, Franco; Primiani, Valter Mariani Coupling Between Multipath Environments Through a Large Aperture (Journal Article) Antennas and Wireless Propagation Letters, IEEE, 14 , pp. 1463-1466, 2015. @article{Gagliardi2015, title = {Coupling Between Multipath Environments Through a Large Aperture}, author = {Luigi Gagliardi and Davide Micheli and Gabriele Gradoni and Franco Moglie and Valter Mariani Primiani}, url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?reload=true&arnumber=7057544}, year = {2015}, date = {2015-07-21}, journal = {Antennas and Wireless Propagation Letters, IEEE}, volume = {14}, pages = {1463-1466}, abstract = {A key issue in measuring the shielding of buildings against wireless communications signals is presented. We use a mode-stirred reverberation chamber (RC) to emulate the EM coupling through windows or doors. This is achieved experimentally by leaving the RC door open. The room hosting the RC is identified as an external semi-reverberant space, and thus used to generate the stochastic field exciting the internal RC through the door opening. Two methods for the transmission parameter measurement and shielding effectiveness estimation are compared: the first one consists in moving receiving antenna within a volume, the second one makes use of a rotating stirrer. The comparison confirms the interchangeability of the two techniques provided a proper averaging factor is introduced. This argument supports a quasi-ergodic hypothesis in imperfect and semi-open reverberating environments. The measured aperture SE is compared to a theoretical value given by an ideal reverberating environment.}, keywords = {}, pubstate = {published}, tppubtype = {article} } A key issue in measuring the shielding of buildings against wireless communications signals is presented. We use a mode-stirred reverberation chamber (RC) to emulate the EM coupling through windows or doors. This is achieved experimentally by leaving the RC door open. The room hosting the RC is identified as an external semi-reverberant space, and thus used to generate the stochastic field exciting the internal RC through the door opening. Two methods for the transmission parameter measurement and shielding effectiveness estimation are compared: the first one consists in moving receiving antenna within a volume, the second one makes use of a rotating stirrer. The comparison confirms the interchangeability of the two techniques provided a proper averaging factor is introduced. This argument supports a quasi-ergodic hypothesis in imperfect and semi-open reverberating environments. The measured aperture SE is compared to a theoretical value given by an ideal reverberating environment. |

Gradoni, Gabriele; Jr, Thomas Antonsen; Anlage, Steven; Ott, Edward Random coupling model for the radiation of irregular apertures (Journal Article) Radio Science, 50 , pp. 678–687, 2015. @article{Gradoni2015, title = {Random coupling model for the radiation of irregular apertures}, author = {Gabriele Gradoni and Thomas M. Antonsen Jr and Steven Anlage and Edward Ott}, url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=6565729}, year = {2015}, date = {2015-07-16}, journal = {Radio Science}, volume = {50}, pages = {678–687}, abstract = {In this paper, we propose and investigate the radiation of chaotic apertures. It is assumed that an aperture is wide and its geometry is irregular enough to infer a random behavior of the tangential field, that is expanded in chaotic modes. Particular emphasis is devoted to the calculation of the freespace aperture admittance matrix, whose element average takes a simple closed-form expression. The radiation admittance matrix is found to be purely diagonal at relatively short-wavelength, and it exhibits unusual frequency behavior. The extreme scenario of a chaotic aperture radiating inside a chaotic cavity is analyzed by the random coupling model. Transmitted power distribution is generated in various loss conditions, upon oblique planewave excitation of the aperture. It is found that cavity loss and number of aperture modes influence symmetry and fluctuation law of the transmitted power distribution. Obtained results offer a mathematical framework for the physical understanding of scattering in extremely complicated environments, mode-stirred reverberation chambers, wireless channels, radar traces, and statistical optics.}, keywords = {}, pubstate = {published}, tppubtype = {article} } In this paper, we propose and investigate the radiation of chaotic apertures. It is assumed that an aperture is wide and its geometry is irregular enough to infer a random behavior of the tangential field, that is expanded in chaotic modes. Particular emphasis is devoted to the calculation of the freespace aperture admittance matrix, whose element average takes a simple closed-form expression. The radiation admittance matrix is found to be purely diagonal at relatively short-wavelength, and it exhibits unusual frequency behavior. The extreme scenario of a chaotic aperture radiating inside a chaotic cavity is analyzed by the random coupling model. Transmitted power distribution is generated in various loss conditions, upon oblique planewave excitation of the aperture. It is found that cavity loss and number of aperture modes influence symmetry and fluctuation law of the transmitted power distribution. Obtained results offer a mathematical framework for the physical understanding of scattering in extremely complicated environments, mode-stirred reverberation chambers, wireless channels, radar traces, and statistical optics. |

Gradoni, Gabriele; Creagh, Stephen; Tanner, Gregor; Smartt, Chris; Thomas, Dave A phase-space approach for propagating field-field correlation functions (Journal Article) New J. Phys., 17 , pp. 093027 , 2015. @article{GSGCD, title = {A phase-space approach for propagating field-field correlation functions}, author = {Gabriele Gradoni and Stephen C. Creagh and Gregor Tanner and Chris Smartt and Dave W. Thomas}, url = {https://arxiv.org/pdf/1504.00507.pdf}, year = {2015}, date = {2015-07-15}, journal = { New J. Phys.}, volume = {17}, pages = {093027 }, abstract = {We show that radiation from complex and inherently random but correlated wave sources can be modelled efficiently by using an approach based on the Wigner distribution function. Our method exploits the connection between correlation functions and theWigner function and admits in its simplest approximation a direct representation in terms of the evolution of ray densities in phase space. We show that next leading order corrections to the ray-tracing approximation lead to Airy-function type phase space propagators. By exploiting the exact Wigner function propagator, inherently wave-like effects such as evanescent decay or radiation from more heterogeneous sources as well as diffraction and reflections can be included and analysed. We discuss in particular the role of evanescent waves in the near-field of non-paraxial sources and give explicit expressions for the growth rate of the correlation length as function of the distance from the source. Furthermore, results for the reflection of partially coherent sources from flat mirrors are given. We focus here on electromagnetic sources at microwave frequencies and modelling efforts in the context of electromagnetic compatibility.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We show that radiation from complex and inherently random but correlated wave sources can be modelled efficiently by using an approach based on the Wigner distribution function. Our method exploits the connection between correlation functions and theWigner function and admits in its simplest approximation a direct representation in terms of the evolution of ray densities in phase space. We show that next leading order corrections to the ray-tracing approximation lead to Airy-function type phase space propagators. By exploiting the exact Wigner function propagator, inherently wave-like effects such as evanescent decay or radiation from more heterogeneous sources as well as diffraction and reflections can be included and analysed. We discuss in particular the role of evanescent waves in the near-field of non-paraxial sources and give explicit expressions for the growth rate of the correlation length as function of the distance from the source. Furthermore, results for the reflection of partially coherent sources from flat mirrors are given. We focus here on electromagnetic sources at microwave frequencies and modelling efforts in the context of electromagnetic compatibility. |

Foulger, Iain; Gnutzmann, Sven; Tanner, Gregor Quantum walks and quantum search on graphene lattices (Journal Article) Phys. Rev, A 91 (062323), 2015. @article{Foulger2015, title = {Quantum walks and quantum search on graphene lattices}, author = {Iain Foulger and Sven Gnutzmann and Gregor Tanner}, url = {http://journals.aps.org/pra/abstract/10.1103/PhysRevA.91.062323}, year = {2015}, date = {2015-07-14}, journal = {Phys. Rev}, volume = {A 91}, number = {062323}, abstract = {Quantum walks have been very useful in developing search algorithms in quantum information, in particular fordevising of spatial search algorithms. However, the construction of continuous-time quantum search algorithmsin two-dimensional lattices has proved difficult, requiring additional degrees of freedom. Here, we demonstratethat a continuous-time quantum walk search is possible in two dimensions by changing the search topology to agraphene lattice, utilizing the Dirac point in the energy spectrum. This is made possible by making a change tostandard methods of marking a particular site in the lattice. Various ways of marking a site are shown to result insuccessful search protocols. We further establish that the search can be adapted to transfer probability amplitudeacross the lattice between specific lattice sites thus establishing a line of communication between these sites.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Quantum walks have been very useful in developing search algorithms in quantum information, in particular fordevising of spatial search algorithms. However, the construction of continuous-time quantum search algorithmsin two-dimensional lattices has proved difficult, requiring additional degrees of freedom. Here, we demonstratethat a continuous-time quantum walk search is possible in two dimensions by changing the search topology to agraphene lattice, utilizing the Dirac point in the energy spectrum. This is made possible by making a change tostandard methods of marking a particular site in the lattice. Various ways of marking a site are shown to result insuccessful search protocols. We further establish that the search can be adapted to transfer probability amplitudeacross the lattice between specific lattice sites thus establishing a line of communication between these sites. |

Böhm, Julian; Bellec, Matthieu; Mortessagne, Fabrice; Kuhl, Ulrich; Barkhofen, Sonja; Gehler, Stefan; Stöckmann, Hans-Jürgen; Foulger, Iain; Gnutzmann, Sven; Tanner, Gregor Microwave Experiments Simulating Quantum Search and Directed Transport in Artificial Graphene (Journal Article) Phys. Rev. Lett. 114, (110501), 2015. @article{Böhm2015, title = {Microwave Experiments Simulating Quantum Search and Directed Transport in Artificial Graphene}, author = {Julian Böhm and Matthieu Bellec and Fabrice Mortessagne and Ulrich Kuhl and Sonja Barkhofen and Stefan Gehler and Hans-Jürgen Stöckmann and Iain Foulger and Sven Gnutzmann and Gregor Tanner}, url = {http://journals.aps.org/pra/abstract/10.1103/PhysRevA.91.062323}, year = {2015}, date = {2015-07-13}, journal = {Phys. Rev. Lett. 114}, number = {110501}, abstract = {A series of quantum search algorithms have been proposed recently providing an algebraic speedup compared to classical search algorithms from N to N−−√, where N is the number of items in the search space. In particular, devising searches on regular lattices has become popular in extending Grover's original algorithm to spatial searching. Working in a tight-binding setup, it could be demonstrated, theoretically, that a search is possible in the physically relevant dimensions 2 and 3 if the lattice spectrum possesses Dirac points. We present here a proof of principle experiment implementing wave search algorithms and directed wave transport in a graphene lattice arrangement. The idea is based on bringing localized search states into resonance with an extended lattice state in an energy region of low spectral density---namely, at or near the Dirac point. The experiment is implemented using classical waves in a microwave setup containing weakly coupled dielectric resonators placed in a honeycomb arrangement, i.e., artificial graphene. Furthermore, we investigate the scaling behavior experimentally using linear chains.}, keywords = {}, pubstate = {published}, tppubtype = {article} } A series of quantum search algorithms have been proposed recently providing an algebraic speedup compared to classical search algorithms from N to N−−√, where N is the number of items in the search space. In particular, devising searches on regular lattices has become popular in extending Grover's original algorithm to spatial searching. Working in a tight-binding setup, it could be demonstrated, theoretically, that a search is possible in the physically relevant dimensions 2 and 3 if the lattice spectrum possesses Dirac points. We present here a proof of principle experiment implementing wave search algorithms and directed wave transport in a graphene lattice arrangement. The idea is based on bringing localized search states into resonance with an extended lattice state in an energy region of low spectral density---namely, at or near the Dirac point. The experiment is implemented using classical waves in a microwave setup containing weakly coupled dielectric resonators placed in a honeycomb arrangement, i.e., artificial graphene. Furthermore, we investigate the scaling behavior experimentally using linear chains. |

Gradoni, Gabriele; Jr, Thomas Antonsen; Anlage, Steven; Ott, Edward A statistical model for the excitation of cavities through apertures (Journal Article) IEEE TEMC, 57 (5), 2015. @article{Gradoni2015b, title = {A statistical model for the excitation of cavities through apertures}, author = {Gabriele Gradoni and Thomas M. Antonsen Jr and Steven Anlage and Edward Ott}, url = {https://arxiv.org/pdf/1502.06642v1.pdf}, year = {2015}, date = {2015-02-23}, journal = {IEEE TEMC}, volume = {57}, number = {5}, abstract = {In this paper, a statistical model for the coupling of electromagnetic radiation into enclosures through apertures is presented. The model gives a unified picture bridging deterministic theories of aperture radiation, and statistical models necessary for capturing the properties of irregular shaped enclosures. A Monte Carlo technique based on random matrix theory is used to predict and study the power transmitted through the aperture into the enclosure. Universal behavior of the net power entering the aperture is found. Results are of interest for predicting the coupling of external radiation through openings in irregular enclosures and reverberation chambers.}, keywords = {}, pubstate = {published}, tppubtype = {article} } In this paper, a statistical model for the coupling of electromagnetic radiation into enclosures through apertures is presented. The model gives a unified picture bridging deterministic theories of aperture radiation, and statistical models necessary for capturing the properties of irregular shaped enclosures. A Monte Carlo technique based on random matrix theory is used to predict and study the power transmitted through the aperture into the enclosure. Universal behavior of the net power entering the aperture is found. Results are of interest for predicting the coupling of external radiation through openings in irregular enclosures and reverberation chambers. |

Phang, Sendy; Vukovic, Ana; Creagh, Stephen; Benson, Trevor; Sewell, Phillip; Gradoni, Gabriele Parity-time symmetric coupled microresonators with a dispersive gain/loss (Journal Article) Opt. Express, 23 , pp. 11493-11507, 2015. @article{Phang2015, title = {Parity-time symmetric coupled microresonators with a dispersive gain/loss}, author = {Sendy Phang and Ana Vukovic and Stephen C. Creagh and Trevor M. Benson and Phillip D. Sewell and Gabriele Gradoni}, url = {https://arxiv.org/pdf/1501.07455v1.pdf}, year = {2015}, date = {2015-01-29}, journal = {Opt. Express}, volume = {23}, pages = {11493-11507}, abstract = {The paper reports on the coupling of Parity-Time (PT)-symmetric whispering gallery resonators with realistic material and gain/loss models. Response of the PT system is analyzed for the case of low and high material and gain dispersion, and also for two practical scenarios when the pump frequency is not aligned with the resonant frequency of the desired whispering gallery mode and when there is imbalance in the gain/loss profile. The results show that the presence of dispersion and frequency misalignment causes skewness in frequency bifurcation and significant reduction of the PT breaking point, respectively. Finally, as coupled WGM resonators are inherently lossy structures, we show that unbalancing the gain/loss in resonators is required to compensate for inherent loss of the structure and achieve improved PT properties.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The paper reports on the coupling of Parity-Time (PT)-symmetric whispering gallery resonators with realistic material and gain/loss models. Response of the PT system is analyzed for the case of low and high material and gain dispersion, and also for two practical scenarios when the pump frequency is not aligned with the resonant frequency of the desired whispering gallery mode and when there is imbalance in the gain/loss profile. The results show that the presence of dispersion and frequency misalignment causes skewness in frequency bifurcation and significant reduction of the PT breaking point, respectively. Finally, as coupled WGM resonators are inherently lossy structures, we show that unbalancing the gain/loss in resonators is required to compensate for inherent loss of the structure and achieve improved PT properties. |

## 2014 |

Gradoni, Gabriele; Creagh, Stephen; Tanner, Gregor A wigner function approach for describing the radiation of complex sources (Conference) IEEE, 2014. @conference{Gradoni2014b, title = {A wigner function approach for describing the radiation of complex sources}, author = {Gabriele Gradoni and Stephen C. Creagh and Gregor Tanner}, url = {http://ieeexplore.ieee.org/document/6899092/}, year = {2014}, date = {2014-11-20}, journal = {Electromagnetic Compatibility (EMC)}, publisher = {IEEE}, abstract = {The radiation of complex electromagnetic sources in free space is described using a propagator of field-field correlation functions. We exploit a wave kinematic analogy to predict the evolution of correlation functions in terms of the propagation of density functions in the phase space associated with ray tracing. The Wigner distribution function formalism is used to derive propagation rules for these densities. The problem is reduced to tracing ray families in phase space for near-homogeneous sources. Numerical results are presented, and the correlation spreading predicted from the Van Cittert-Zernike theorem of statistical optics is retrieved as a special case. An application of the method to evaluate mechanical stirrers used in reverberation chambers is presented and discussed. These results serve as a proof-of-principle for understanding and predicting emissions from sources in more complicated environments.}, keywords = {}, pubstate = {published}, tppubtype = {conference} } The radiation of complex electromagnetic sources in free space is described using a propagator of field-field correlation functions. We exploit a wave kinematic analogy to predict the evolution of correlation functions in terms of the propagation of density functions in the phase space associated with ray tracing. The Wigner distribution function formalism is used to derive propagation rules for these densities. The problem is reduced to tracing ray families in phase space for near-homogeneous sources. Numerical results are presented, and the correlation spreading predicted from the Van Cittert-Zernike theorem of statistical optics is retrieved as a special case. An application of the method to evaluate mechanical stirrers used in reverberation chambers is presented and discussed. These results serve as a proof-of-principle for understanding and predicting emissions from sources in more complicated environments. |

Chappell, David; Tanner, Gregor A boundary integral formalism for stochastic ray tracing in billiards (Journal Article) 2014. @article{Chappell2014, title = {A boundary integral formalism for stochastic ray tracing in billiards}, author = {David Chappell and Gregor Tanner }, url = {https://www.researchgate.net/publication/264673599_A_boundary_integral_formalism_for_stochastic_ray_tracing_in_billiards}, year = {2014}, date = {2014-07-31}, abstract = {Determining the flow of rays or particles driven by a force or velocity field is fundamental to modelling many physical processes, including weather forecasting and the simulation of molecular dynamics. High frequency wave energy distributions can also be approximated using flow or transport equations. Applications arise in underwater and room acoustics, vibro-acoustics, seismology, electromagnetics, quantum mechanics and in producing computer generated imagery. In many practical applications, the driving field is not known exactly and the dynamics are determined only up to a degree of uncertainty. This paper presents a boundary integral framework for propagating flows including uncertainties, which is shown to systematically interpolate between a deterministic and a completely random description of the trajectory propagation. A simple but efficient discretisation approach is applied to model uncertain billiard dynamics in an integrable rectangular domain.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Determining the flow of rays or particles driven by a force or velocity field is fundamental to modelling many physical processes, including weather forecasting and the simulation of molecular dynamics. High frequency wave energy distributions can also be approximated using flow or transport equations. Applications arise in underwater and room acoustics, vibro-acoustics, seismology, electromagnetics, quantum mechanics and in producing computer generated imagery. In many practical applications, the driving field is not known exactly and the dynamics are determined only up to a degree of uncertainty. This paper presents a boundary integral framework for propagating flows including uncertainties, which is shown to systematically interpolate between a deterministic and a completely random description of the trajectory propagation. A simple but efficient discretisation approach is applied to model uncertain billiard dynamics in an integrable rectangular domain. |

Foulger, Iain; Gnutzmann, Sven; Tanner, Gregor Quantum Search on Graphene Lattices (Journal Article) Phys. Rev. Lett. 112, (070504), 2014. @article{Foulger2014, title = {Quantum Search on Graphene Lattices}, author = {Iain Foulger and Sven Gnutzmann and Gregor Tanner}, url = {http://arxiv.org/pdf/1501.07543v2.pdf}, year = {2014}, date = {2014-07-25}, journal = {Phys. Rev. Lett. 112}, number = {070504}, abstract = {Quantum walks have been very useful in developing search algorithms in quantum information, in particular for devising of spatial search algorithms. However, the construction of continuous-time quantum search algorithms in two-dimensional lattices has proved difficult, requiring additional degrees of freedom. Here, we demonstrate that continuous-time quantum walk search is possible in two-dimensions by changing the search topology to a graphene lattice, utilising the Dirac point in the energy spectrum. This is made possible by making a change to standard methods of marking a particular site in the lattice. Various ways of marking a site are shown to result in successful search protocols. We further establish that the search can be adapted to transfer probability amplitude across the lattice between specific lattice sites thus establishing a line of communication between these sites.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Quantum walks have been very useful in developing search algorithms in quantum information, in particular for devising of spatial search algorithms. However, the construction of continuous-time quantum search algorithms in two-dimensional lattices has proved difficult, requiring additional degrees of freedom. Here, we demonstrate that continuous-time quantum walk search is possible in two-dimensions by changing the search topology to a graphene lattice, utilising the Dirac point in the energy spectrum. This is made possible by making a change to standard methods of marking a particular site in the lattice. Various ways of marking a site are shown to result in successful search protocols. We further establish that the search can be adapted to transfer probability amplitude across the lattice between specific lattice sites thus establishing a line of communication between these sites. |

Tanner, Gregor; Chappell, David; Löche, Dominik; Søndergaard, Niels Discrete Flow Mapping - A Mesh Based Simulation Tool for Mid-to- High Frequency Vibro-Acoustic Excitation of Complex Automotive Structures (Journal Article) SAE International, (01-2079), 2014. @article{Tanner2014, title = {Discrete Flow Mapping - A Mesh Based Simulation Tool for Mid-to- High Frequency Vibro-Acoustic Excitation of Complex Automotive Structures}, author = {Gregor Tanner and David Chappell and Dominik Löche and Niels Søndergaard}, url = {http://paginas.fe.up.pt/~eurodyn2014/CD/papers/452_MS21_ABS_1258.pdf}, doi = {10.4271/2014-01-2079}, year = {2014}, date = {2014-07-18}, journal = {SAE International}, number = {01-2079}, abstract = {A new method called Discrete Flow Mapping (DFM) has been presented recently in [1], extending existing high frequency methods for modeling the vibro-acoustic properties of mechanical built-up structures towards a mesh based approach. This makes it possible to do vibro-acoustic simulations directly on existing finite element method (FEM) meshes. It provides detailed spatial information about the vibrational energy of a whole structure of arbitrary complexity in the mid-to-high frequency range. The response of small-scale features and coupling coefficients between sub-components are obtained through local FEM models integrated into the global DFM treatment. The computational cost of DFM is largely frequency independent making it possible to get results for mid to high frequencies. This tool will be important when considering the vibrational response of a structure as a whole moving away from modelling vibrations only in sub-parts of the mechanical body. We will present here applications of DFM in the motor vehicle and ship building industry KEY WORDS: Ray tracing; Flow propagation; Ulam method; High-frequency wave asymptotics; Statistical energy analysis; Power flow analysis}, keywords = {}, pubstate = {published}, tppubtype = {article} } A new method called Discrete Flow Mapping (DFM) has been presented recently in [1], extending existing high frequency methods for modeling the vibro-acoustic properties of mechanical built-up structures towards a mesh based approach. This makes it possible to do vibro-acoustic simulations directly on existing finite element method (FEM) meshes. It provides detailed spatial information about the vibrational energy of a whole structure of arbitrary complexity in the mid-to-high frequency range. The response of small-scale features and coupling coefficients between sub-components are obtained through local FEM models integrated into the global DFM treatment. The computational cost of DFM is largely frequency independent making it possible to get results for mid to high frequencies. This tool will be important when considering the vibrational response of a structure as a whole moving away from modelling vibrations only in sub-parts of the mechanical body. We will present here applications of DFM in the motor vehicle and ship building industry KEY WORDS: Ray tracing; Flow propagation; Ulam method; High-frequency wave asymptotics; Statistical energy analysis; Power flow analysis |

Chappell, David; Löche, Dominik; Søndergaard, Niels; Tanner, Gregor Dynamical energy analysis on mesh grids - a new tool for describing the vibro-acoustic response of complex mechanical structures (Journal Article) Wave Motion, 51 (589-597), 2014. @article{Chappell2014b, title = {Dynamical energy analysis on mesh grids - a new tool for describing the vibro-acoustic response of complex mechanical structures}, author = {David Chappell and Dominik Löche and Niels Søndergaard and Gregor Tanner}, url = {https://arxiv.org/pdf/1303.4249.pdf}, year = {2014}, date = {2014-07-17}, journal = {Wave Motion}, volume = {51}, number = {589-597}, abstract = {Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics, vibro-acoustics, seismology, electromagnetics, and quantum mechanics. Related flow problems based on general conservation laws are used, for example, in weather forecasting or molecular dynamics simulations. Solutions to these flow equations are often large scale, complex and high-dimensional, leading to formidable challenges for numerical approximation methods. This paper presents an efficient and widely applicable method, called discrete flow mapping, for solving such problems on triangulated surfaces. An application in structural dynamics - determining the vibro-acoustic response of a cast aluminium car body component - is presented. }, keywords = {}, pubstate = {published}, tppubtype = {article} } Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics, vibro-acoustics, seismology, electromagnetics, and quantum mechanics. Related flow problems based on general conservation laws are used, for example, in weather forecasting or molecular dynamics simulations. Solutions to these flow equations are often large scale, complex and high-dimensional, leading to formidable challenges for numerical approximation methods. This paper presents an efficient and widely applicable method, called discrete flow mapping, for solving such problems on triangulated surfaces. An application in structural dynamics - determining the vibro-acoustic response of a cast aluminium car body component - is presented. |

Gradoni, Gabriele; Arnaut, Luke Transient evolution of eigenmodes in dynamic cavities and time-varying media (Journal Article) Radio Science, 2014. @article{Gradoni2014, title = {Transient evolution of eigenmodes in dynamic cavities and time-varying media}, author = {Gabriele Gradoni and Luke R. Arnaut}, url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=6565730&newsearch=true&queryText=Transient%20evolution%20of%20eigen-modes%20in%20dynamic%20cavities%20and%20time-varying%20media}, year = {2014}, date = {2014-07-15}, journal = {Radio Science}, abstract = {In this paper, we investigate the transient evolution of the natural modes of dynamic cavities and time-varying media. The mode amplitude is modelled as a damped harmonic oscillator with time-varying coefficients, i.e., a parametric oscillator. An approximate closed-form solution is found in terms of the modified Airy function method. The solution for the Doppler shifted mode spectrum is specialized to a mode-stirred cavity. The time dependence of the coefficients is being related to the physical dimensions and the speed of a rotating perturbation (stirrer) in a deterministic way. Because of the stochastic nature of mode-stirred cavities, the effect of random Doppler shifts are also investigated, leading to a Fokker-Planck equation whose diffusion coefficient shows quadratic dependence on the mode amplitude. The analytical results obtained from this analysis are useful for comparison with other solution techniques, particularly those involving Green functions, and is of interest in continuous-time mode-stirred reverberation chambers, as well as in other fields of physics involving dynamic cavities and random media.}, keywords = {}, pubstate = {published}, tppubtype = {article} } In this paper, we investigate the transient evolution of the natural modes of dynamic cavities and time-varying media. The mode amplitude is modelled as a damped harmonic oscillator with time-varying coefficients, i.e., a parametric oscillator. An approximate closed-form solution is found in terms of the modified Airy function method. The solution for the Doppler shifted mode spectrum is specialized to a mode-stirred cavity. The time dependence of the coefficients is being related to the physical dimensions and the speed of a rotating perturbation (stirrer) in a deterministic way. Because of the stochastic nature of mode-stirred cavities, the effect of random Doppler shifts are also investigated, leading to a Fokker-Planck equation whose diffusion coefficient shows quadratic dependence on the mode amplitude. The analytical results obtained from this analysis are useful for comparison with other solution techniques, particularly those involving Green functions, and is of interest in continuous-time mode-stirred reverberation chambers, as well as in other fields of physics involving dynamic cavities and random media. |

Tanner, Gregor; Mace, Brian Special issue of wave motion—“Innovations in wave modelling” (Journal Article) Wave Motion, 51 , pp. 547–549, 2014. @article{Tanner2014b, title = {Special issue of wave motion—“Innovations in wave modelling”}, author = {Gregor Tanner and Brian Mace}, url = {http://www.sciencedirect.com/science/article/pii/S0165212514000377}, year = {2014}, date = {2014-06-13}, journal = {Wave Motion}, volume = {51}, pages = {547–549}, abstract = {The Issue focuses on the development and the application of numerical and analytical methods for the modelling of problems of acoustics, vibro-acoustics, structural dynamics and electromagnetic waves, with the emphasis on the mid-to-short wavelength limit. Wave fields in enclosures can then show a surprising amount of complexity due to multiple reflections, refraction or diffractive contributions. In the mechanical engineering community, this leads to typical mid-frequency problems, that is, in parts of a built-up structure the local wavelength is comparable to the size of the (sub)system (small or stiff components), in others it is orders of magnitudes smaller (thin, large metal sheets). In electronic engineering Electromagnetic Compatibility (EMC) is an area of research facing very similar problems. With the current clock speed of electrical devices, components on chips or printed circuit boards can become efficient short wavelength radiators which can interact and affect each other. These disturbances need to be modelled, including multiple reflection and diffraction effects in enclosures. The Special Issue addresses this important research field from the modelling side in an interdisciplinary manner. }, keywords = {}, pubstate = {published}, tppubtype = {article} } The Issue focuses on the development and the application of numerical and analytical methods for the modelling of problems of acoustics, vibro-acoustics, structural dynamics and electromagnetic waves, with the emphasis on the mid-to-short wavelength limit. Wave fields in enclosures can then show a surprising amount of complexity due to multiple reflections, refraction or diffractive contributions. In the mechanical engineering community, this leads to typical mid-frequency problems, that is, in parts of a built-up structure the local wavelength is comparable to the size of the (sub)system (small or stiff components), in others it is orders of magnitudes smaller (thin, large metal sheets). In electronic engineering Electromagnetic Compatibility (EMC) is an area of research facing very similar problems. With the current clock speed of electrical devices, components on chips or printed circuit boards can become efficient short wavelength radiators which can interact and affect each other. These disturbances need to be modelled, including multiple reflection and diffraction effects in enclosures. The Special Issue addresses this important research field from the modelling side in an interdisciplinary manner. |

## 2013 |

Creagh, Stephen; Hamdin, Ben; Tanner, Gregor In – out decomposition of boundary integral equations (Journal Article) J. Phys. A: Math. Theor. 46, (435203), 2013. @article{Creagh2013, title = {In – out decomposition of boundary integral equations}, author = {Stephen C. Creagh and H. Ben Hamdin and Gregor Tanner}, url = {http://arxiv.org/pdf/1307.3885v2.pdf}, year = {2013}, date = {2013-07-10}, journal = {J. Phys. A: Math. Theor. 46}, number = {435203}, abstract = {We propose a reformulation of the boundary integral equations for the Helmholtz equation in a domain in terms of incoming and outgoing boundary waves. We obtain transfer operator descriptions which are exact and thus incorporate features such as diffraction and evanescent coupling; these effects are absent in the well known semiclassical transfer operators in the sense of Bogomolny. It has long been established that transfer operators are equivalent to the boundary integral approach within semiclassical approximation. Exact treatments have been restricted to specific boundary conditions (such as Dirichlet or Neumann). The approach we propose is independent of the boundary conditions, and in fact allows one to decouple entirely the problem of propagating waves across the interior from the problem of reflecting waves at the boundary. As an application, we show how the decomposition may be used to calculate GoosH¨anchen shifts of ray dynamics in billiards with variable boundary conditions and for dielectric cavities. }, keywords = {}, pubstate = {published}, tppubtype = {article} } We propose a reformulation of the boundary integral equations for the Helmholtz equation in a domain in terms of incoming and outgoing boundary waves. We obtain transfer operator descriptions which are exact and thus incorporate features such as diffraction and evanescent coupling; these effects are absent in the well known semiclassical transfer operators in the sense of Bogomolny. It has long been established that transfer operators are equivalent to the boundary integral approach within semiclassical approximation. Exact treatments have been restricted to specific boundary conditions (such as Dirichlet or Neumann). The approach we propose is independent of the boundary conditions, and in fact allows one to decouple entirely the problem of propagating waves across the interior from the problem of reflecting waves at the boundary. As an application, we show how the decomposition may be used to calculate GoosH¨anchen shifts of ray dynamics in billiards with variable boundary conditions and for dielectric cavities. |

Chappell, David; Tanner, Gregor; Löche, Dominik; Søndergaard, Niels Discrete flow mapping: transport of phase space densities on triangulated surfaces (Journal Article) Proceedings of the Royal Society A, (469 2155 20130153), 2013. @article{Chappell2013, title = {Discrete flow mapping: transport of phase space densities on triangulated surfaces}, author = {David Chappell and Gregor Tanner and Dominik Löche and Niels Søndergaard}, url = {https://arxiv.org/pdf/1303.4249v2.pdf}, year = {2013}, date = {2013-07-01}, journal = {Proceedings of the Royal Society A}, number = {469 2155 20130153}, abstract = {Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics, vibro-acoustics, seismology, electromagnetics, and quantum mechanics. Related flow problems based on general conservation laws are used, for example, in weather forecasting or molecular dynamics simulations. Solutions to these flow equations are often large scale, complex and high-dimensional, leading to formidable challenges for numerical approximation methods. This paper presents an efficient and widely applicable method, called discrete flow mapping, for solving such problems on triangulated surfaces. An application in structural dynamics - determining the vibro-acoustic response of a cast aluminium car body component - is presented.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Energy distributions of high frequency linear wave fields are often modelled in terms of flow or transport equations with ray dynamics given by a Hamiltonian vector field in phase space. Applications arise in underwater and room acoustics, vibro-acoustics, seismology, electromagnetics, and quantum mechanics. Related flow problems based on general conservation laws are used, for example, in weather forecasting or molecular dynamics simulations. Solutions to these flow equations are often large scale, complex and high-dimensional, leading to formidable challenges for numerical approximation methods. This paper presents an efficient and widely applicable method, called discrete flow mapping, for solving such problems on triangulated surfaces. An application in structural dynamics - determining the vibro-acoustic response of a cast aluminium car body component - is presented. |

Waltner, Daniel; Gnutzmann, Sven; Tanner, Gregor; Richter, Klaus sub-determinant approach for pseudo-orbit expansions of spectral determinants (Journal Article) Phys. Rev. E 87, (052919), 2013. @article{Waltner2013, title = { sub-determinant approach for pseudo-orbit expansions of spectral determinants}, author = {Daniel Waltner and Sven Gnutzmann and Gregor Tanner and Klaus Richter }, url = {http://epub.uni-regensburg.de/33645/1/2013-PRE-Waltner-et-al.pdf}, year = {2013}, date = {2013-06-28}, journal = {Phys. Rev. E 87}, number = {052919}, abstract = {We study the implications of unitarity for pseudo-orbit expansions of the spectral determinants of quantum maps and quantum graphs. In particular, we advocate to group pseudo-orbits into subdeterminants. We show explicitly that the cancellation of long orbits is elegantly described on this level and that unitarity can be built in using a simple subdeterminant identity which has a nontrivial interpretation in terms of pseudo-orbits. This identity yields much more detailed relations between pseudo-orbits of different lengths than was known previously. We reformulate Newton identities and the spectral density in terms of subdeterminant expansions and point out the implications of the subdeterminant identity for these expressions. We analyze furthermore the effect of the identity on spectral correlation functions such as the autocorrelation and parametric cross-correlation functions of the spectral determinant and the spectral form factor.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We study the implications of unitarity for pseudo-orbit expansions of the spectral determinants of quantum maps and quantum graphs. In particular, we advocate to group pseudo-orbits into subdeterminants. We show explicitly that the cancellation of long orbits is elegantly described on this level and that unitarity can be built in using a simple subdeterminant identity which has a nontrivial interpretation in terms of pseudo-orbits. This identity yields much more detailed relations between pseudo-orbits of different lengths than was known previously. We reformulate Newton identities and the spectral density in terms of subdeterminant expansions and point out the implications of the subdeterminant identity for these expressions. We analyze furthermore the effect of the identity on spectral correlation functions such as the autocorrelation and parametric cross-correlation functions of the spectral determinant and the spectral form factor. |

Chappell, David; Tanner, Gregor Solving the stationary Liouville equation via a boundary element method (Journal Article) ournal of Computational Physics, (234), pp. 487-498, 2013. @article{Chappell2013b, title = {Solving the stationary Liouville equation via a boundary element method}, author = {David Chappell and Gregor Tanner}, url = {http://arxiv.org/pdf/1202.4754v1.pdf}, year = {2013}, date = {2013-06-27}, journal = {ournal of Computational Physics}, number = {234}, pages = { 487-498}, abstract = {Intensity distributions of linear wave fields are, in the high frequency limit, often approximated in terms of flow or transport equations in phase space. Common techniques for solving the flow equations for both time dependent and stationary problems are ray tracing or level set methods. In the context of predicting the vibro-acoustic response of complex engineering structures, reduced ray tracing methods such as Statistical Energy Analysis or variants thereof have found widespread applications. Starting directly from the stationary Liouville equation, we develop a boundary element method for solving the transport equations for complex multi-component structures. The method, which is an improved version of the Dynamical Energy Analysis technique introduced recently by the authors, interpolates between standard statistical energy analysis and full ray tracing, containing both of these methods as limiting cases. We demonstrate that the method can be used to efficiently deal with complex large scale problems giving good approximations of the energy distribution when compared to exact solutions of the underlying wave equation. Keywords: Statistical energy analysis, high-frequency asymptotics, Liouville equation, boundary element method }, keywords = {}, pubstate = {published}, tppubtype = {article} } Intensity distributions of linear wave fields are, in the high frequency limit, often approximated in terms of flow or transport equations in phase space. Common techniques for solving the flow equations for both time dependent and stationary problems are ray tracing or level set methods. In the context of predicting the vibro-acoustic response of complex engineering structures, reduced ray tracing methods such as Statistical Energy Analysis or variants thereof have found widespread applications. Starting directly from the stationary Liouville equation, we develop a boundary element method for solving the transport equations for complex multi-component structures. The method, which is an improved version of the Dynamical Energy Analysis technique introduced recently by the authors, interpolates between standard statistical energy analysis and full ray tracing, containing both of these methods as limiting cases. We demonstrate that the method can be used to efficiently deal with complex large scale problems giving good approximations of the energy distribution when compared to exact solutions of the underlying wave equation. Keywords: Statistical energy analysis, high-frequency asymptotics, Liouville equation, boundary element method |

Monti, Tammara; Gradoni, Gabriele Hollow-Core Coaxial Fiber Sensor for Biophotonic Detection (Journal Article) IEEE Journal of Selected Topics in Quantum Electronics, 20 (2), pp. 134 - 142, 2013. @article{Monti2013, title = {Hollow-Core Coaxial Fiber Sensor for Biophotonic Detection}, author = {Tammara Monti and Gabriele Gradoni}, url = {http://ieeexplore.ieee.org/document/6588879/}, year = {2013}, date = {2013-04-23}, journal = { IEEE Journal of Selected Topics in Quantum Electronics}, volume = {20}, number = {2}, pages = {134 - 142}, abstract = {n this paper, a photonic biosensor based on a hollow-core coaxial fiber is presented and discussed. The sensor is aimed to detect the presence of specific biomarkers in a complex human compound, e.g., serum, urine, saliva, cell lysate. The target detection occurs through a biological binding that alters the mode confinement of the Bragg structure. A generic (suboptimal) structure is designed by using the transfer matrix method. The sensor performances are shown in terms of confinement losses. For spherical protein of 5 nm, the confinement loss is increased of 1.213 dB/m. Furthermore, a parametric analysis is performed, which drives toward the possible optimization of the fiber. From a practical point of view, the joint application of selective molecular functionalization of fiber interfaces, and multilayer fiber “rolling” technique are believed to enable for the realization of the sensor.}, keywords = {}, pubstate = {published}, tppubtype = {article} } n this paper, a photonic biosensor based on a hollow-core coaxial fiber is presented and discussed. The sensor is aimed to detect the presence of specific biomarkers in a complex human compound, e.g., serum, urine, saliva, cell lysate. The target detection occurs through a biological binding that alters the mode confinement of the Bragg structure. A generic (suboptimal) structure is designed by using the transfer matrix method. The sensor performances are shown in terms of confinement losses. For spherical protein of 5 nm, the confinement loss is increased of 1.213 dB/m. Furthermore, a parametric analysis is performed, which drives toward the possible optimization of the fiber. From a practical point of view, the joint application of selective molecular functionalization of fiber interfaces, and multilayer fiber “rolling” technique are believed to enable for the realization of the sensor. |

Gradoni, Gabriele; Yeh, Jen-Hao; Xia, Bo; Jr, Thomas Antonsen; Anlage, Steven; Ott, Edward Predicting the statistics of wave transport through chaotic cavities by the Random Coupling Model: a review and recent progress (Journal Article) Wave Motion, 2013. @article{Gradoni2013, title = {Predicting the statistics of wave transport through chaotic cavities by the Random Coupling Model: a review and recent progress}, author = {Gabriele Gradoni and Jen-Hao Yeh and Bo Xia and Thomas M. Antonsen Jr and Steven Anlage and Edward Ott}, year = {2013}, date = {2013-03-26}, journal = {Wave Motion}, abstract = {https://arxiv.org/pdf/1303.6526v1.pdf}, keywords = {}, pubstate = {published}, tppubtype = {article} } https://arxiv.org/pdf/1303.6526v1.pdf |

## 2012 |

Hamdin, Ben; Tanner, Gregor Multi-Component BEM for the Helmholtz Equation - A Normal Derivative Method (Journal Article) Shock and Vibration, 19 , pp. 957-967, 2012. @article{Hamdin2012, title = {Multi-Component BEM for the Helmholtz Equation - A Normal Derivative Method}, author = {H. Ben Hamdin and Gregor Tanner}, url = {http://downloads.hindawi.com/journals/sv/2012/451785.pdf}, year = {2012}, date = {2012-07-19}, journal = {Shock and Vibration}, volume = {19}, pages = {957-967}, abstract = {We describe a multi-component boundary element method for predicting wave energy distributions in a complex built-up system with material properties changing discontinuously at boundaries between sub-components. We point out that depending on the boundary conditions and the number of interfaces between sub-components, it may be advantageous to use a normal derivative method to set up the integral kernels. We describe how the resulting hypersingular integral kernels can be regularised. The method can be used to minimise the number of weakly singular integrals thus leading to BEM formulations which are easier to handle.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We describe a multi-component boundary element method for predicting wave energy distributions in a complex built-up system with material properties changing discontinuously at boundaries between sub-components. We point out that depending on the boundary conditions and the number of interfaces between sub-components, it may be advantageous to use a normal derivative method to set up the integral kernels. We describe how the resulting hypersingular integral kernels can be regularised. The method can be used to minimise the number of weakly singular integrals thus leading to BEM formulations which are easier to handle. |

Chappell, David; Tanner, Gregor; and, Stefano Giani Boundary element dynamical energy analysis: a versatile method for solving two or three dimensional wave problems in the high frequency limit (Journal Article) Journal of Computational Physics, 231 , pp. 6181-6191, 2012. @article{Chappell2012, title = {Boundary element dynamical energy analysis: a versatile method for solving two or three dimensional wave problems in the high frequency limit}, author = {David Chappell and Gregor Tanner and Stefano Giani and}, url = {http://arxiv.org/abs/1202.4416}, year = {2012}, date = {2012-06-14}, journal = {Journal of Computational Physics}, volume = {231}, pages = {6181-6191}, abstract = {Dynamical energy analysis was recently introduced as a new method for determining the distribution of mechanical and acoustic wave energy in complex built up structures. The technique interpolates between standard statistical energy analysis and full ray tracing, containing both of these methods as limiting cases. As such the applicability of the method is wide ranging and additionally includes the numerical modelling of problems in optics and more generally of linear wave problems in electromagnetics. In this work we consider a new approach to the method with enhanced versatility, enabling three-dimensional problems to be handled in a straightforward manner. The main challenge is the high dimensionality of the problem: we determine the wave energy density both as a function of the spatial coordinate and momentum (or direction) space. The momentum variables are expressed in separable (polar) coordinates facilitating the use of products of univariate basis expansions. However this is not the case for the spatial argument and so we propose to make use of automated mesh generating routines to both localise the approximation, allowing quadrature costs to be kept moderate, and give versatility in the code for different geometric configurations.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Dynamical energy analysis was recently introduced as a new method for determining the distribution of mechanical and acoustic wave energy in complex built up structures. The technique interpolates between standard statistical energy analysis and full ray tracing, containing both of these methods as limiting cases. As such the applicability of the method is wide ranging and additionally includes the numerical modelling of problems in optics and more generally of linear wave problems in electromagnetics. In this work we consider a new approach to the method with enhanced versatility, enabling three-dimensional problems to be handled in a straightforward manner. The main challenge is the high dimensionality of the problem: we determine the wave energy density both as a function of the spatial coordinate and momentum (or direction) space. The momentum variables are expressed in separable (polar) coordinates facilitating the use of products of univariate basis expansions. However this is not the case for the spatial argument and so we propose to make use of automated mesh generating routines to both localise the approximation, allowing quadrature costs to be kept moderate, and give versatility in the code for different geometric configurations. |

## 2011 |

Chappell, David; Giani, Stefano; Tanner, Gregor Dynamical energy analysis for built-up acoustic systems at high frequencies (Journal Article) Journal of the Acoustical Society of America, 130 (1420 ), 2011. @article{Chappell2011, title = {Dynamical energy analysis for built-up acoustic systems at high frequencies}, author = {David Chappell and Stefano Giani and Gregor Tanner}, url = {https://arxiv.org/pdf/1009.3769.pdf}, year = {2011}, date = {2011-08-02}, journal = {Journal of the Acoustical Society of America}, volume = {130}, number = {1420 }, abstract = {Standard methods for describing the intensity distribution of mechanical and acoustic wave fields in the high frequency asymptotic limit are often based on flow transport equations. Common techniques are statistical energy analysis, employed mostly in the context of vibro-acoustics, and ray tracing, a popular tool in architectural acoustics. Dynamical energy analysis makes it possible to interpolate between standard statistical energy analysis and full ray tracing, containing both of these methods as limiting cases. In this work a version of dynamical energy analysis based on a Chebyshev basis expansion of the Perron-Frobenius operator governing the ray dynamics is introduced. It is shown that the technique can efficiently deal with multi-component systems overcoming typical geometrical limitations present in statistical energy analysis. Results are compared with state-ofthe-art hp-adaptive discontinuous Galerkin finite element simulations.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Standard methods for describing the intensity distribution of mechanical and acoustic wave fields in the high frequency asymptotic limit are often based on flow transport equations. Common techniques are statistical energy analysis, employed mostly in the context of vibro-acoustics, and ray tracing, a popular tool in architectural acoustics. Dynamical energy analysis makes it possible to interpolate between standard statistical energy analysis and full ray tracing, containing both of these methods as limiting cases. In this work a version of dynamical energy analysis based on a Chebyshev basis expansion of the Perron-Frobenius operator governing the ray dynamics is introduced. It is shown that the technique can efficiently deal with multi-component systems overcoming typical geometrical limitations present in statistical energy analysis. Results are compared with state-ofthe-art hp-adaptive discontinuous Galerkin finite element simulations. |

Tanner, Gregor; Chappell, David; Maksimov, DN Wave Intensity Distributions in Complex Structures (Journal Article) Acta Phys. Pol. A, 120 , pp. A172-A17, 2011. @article{Tanner2011, title = {Wave Intensity Distributions in Complex Structures}, author = {Gregor Tanner and David Chappell and DN Maksimov}, url = {http://przyrbwn.icm.edu.pl/APP/PDF/120/a120z6ap63.pdf}, year = {2011}, date = {2011-07-06}, journal = {Acta Phys. Pol. A}, volume = {120}, pages = { A172-A17}, abstract = {The vibro-acoustic response of mechanical structures can in general be well approximated in terms of linear wave equations. Standard numerical solution methods comprise the nite or boundary element method in the low frequency regime and statistical energy analysis in the high-frequency limit. Major computational challenges are posed by the so-called mid-frequency problem that is, composite structures where the local wavelength may vary by orders of magnitude across the components. Recently, a new approach towards determining the distribution of mechanical and acoustic wave energy in complex built-up structures improving on standard statistical energy analysis has been proposed. The technique interpolates between statistical energy analysis and ray tracing containing both these methods as limiting cases. The method has its origin in studying solutions of wave equation with an underlying chaotic ray-dynamics often referred to as wave chaos. Within the new theory dynamical energy analysis statistical energy analysis is identied as a low resolution ray tracing algorithm and typical statistical energy analysis assumptions can be quantied in terms of the properties of the ray dynamics. We have furthermore developed a hybrid statistical energy analysis/nite element method based on random wave model assumptions for the short-wavelength components. This makes it possible to tackle mid-frequency problems under certain constraints on the geometry of the structure. Dynamical energy analysis and statistical energy analysis/ nite element method calculations for a range of multi-component model systems will be presented. The results are compared with both statistical energy analysis results and nite element method as well as boundary element method calculations. Dynamical energy analysis emerges as a numerically ecient method for calculating mean wave intensities with a high degree of spatial resolution and capturing long range correlations in the ray dynamics}, keywords = {}, pubstate = {published}, tppubtype = {article} } The vibro-acoustic response of mechanical structures can in general be well approximated in terms of linear wave equations. Standard numerical solution methods comprise the nite or boundary element method in the low frequency regime and statistical energy analysis in the high-frequency limit. Major computational challenges are posed by the so-called mid-frequency problem that is, composite structures where the local wavelength may vary by orders of magnitude across the components. Recently, a new approach towards determining the distribution of mechanical and acoustic wave energy in complex built-up structures improving on standard statistical energy analysis has been proposed. The technique interpolates between statistical energy analysis and ray tracing containing both these methods as limiting cases. The method has its origin in studying solutions of wave equation with an underlying chaotic ray-dynamics often referred to as wave chaos. Within the new theory dynamical energy analysis statistical energy analysis is identied as a low resolution ray tracing algorithm and typical statistical energy analysis assumptions can be quantied in terms of the properties of the ray dynamics. We have furthermore developed a hybrid statistical energy analysis/nite element method based on random wave model assumptions for the short-wavelength components. This makes it possible to tackle mid-frequency problems under certain constraints on the geometry of the structure. Dynamical energy analysis and statistical energy analysis/ nite element method calculations for a range of multi-component model systems will be presented. The results are compared with both statistical energy analysis results and nite element method as well as boundary element method calculations. Dynamical energy analysis emerges as a numerically ecient method for calculating mean wave intensities with a high degree of spatial resolution and capturing long range correlations in the ray dynamics |

Maksimov, Dimitrri; Tanner, Gregor A hybrid approach for predicting the distribution of vibro-acoustic energy in complex built-up structures (Journal Article) Journal of the Acoustical Society of America, 130 (1337 ), 2011. @article{Maksimov2011, title = {A hybrid approach for predicting the distribution of vibro-acoustic energy in complex built-up structures}, author = {Dimitrri N. Maksimov and Gregor Tanner}, url = {http://arxiv.org/pdf/1009.3651v2.pdf}, year = {2011}, date = {2011-04-27}, journal = {Journal of the Acoustical Society of America}, volume = {130}, number = {1337 }, abstract = {Finding the distribution of vibro-acoustic energy in complex built-up structures in the mid-to-high frequency regime is a difficult task. In particular, structures with large variation of local wavelengths and/or characteristic scales pose a challenge referred to as the mid-frequency problem. Standard numerical methods such as the finite element method (FEM) scale with the local wavelength and quickly become too large even for modern computer architectures. High frequency techniques, such as statistical energy analysis (SEA), often miss important information such as dominant resonance behaviour due to stiff or small scale parts of the structure. Hybrid methods circumvent this problem by coupling FEM/BEM and SEA models in a given built-up structure. In the approach adopted here, the whole system is split into a number of subsystems which are treated by either FEM or SEA depending on the local wavelength. Subsystems with relative long wavelengths are modelled using FEM. Making a diffuse field assumption for the wave fields in the short wave length components, the coupling between subsystems can be reduced to a weighted random field correlation function. The approach presented results in an SEA-like set of linear equations which can be solved for the mean energies in the short wavelength subsystems.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Finding the distribution of vibro-acoustic energy in complex built-up structures in the mid-to-high frequency regime is a difficult task. In particular, structures with large variation of local wavelengths and/or characteristic scales pose a challenge referred to as the mid-frequency problem. Standard numerical methods such as the finite element method (FEM) scale with the local wavelength and quickly become too large even for modern computer architectures. High frequency techniques, such as statistical energy analysis (SEA), often miss important information such as dominant resonance behaviour due to stiff or small scale parts of the structure. Hybrid methods circumvent this problem by coupling FEM/BEM and SEA models in a given built-up structure. In the approach adopted here, the whole system is split into a number of subsystems which are treated by either FEM or SEA depending on the local wavelength. Subsystems with relative long wavelengths are modelled using FEM. Making a diffuse field assumption for the wave fields in the short wave length components, the coupling between subsystems can be reduced to a weighted random field correlation function. The approach presented results in an SEA-like set of linear equations which can be solved for the mean energies in the short wavelength subsystems. |

## 2010 |

Hein, Birgit; Tanner, Gregor Quantum search algorithms on a regular lattice (Journal Article) Rev. A 82, (012326 ), 2010. @article{Hein2010, title = {Quantum search algorithms on a regular lattice}, author = {Birgit Hein and Gregor Tanner}, url = {http://arxiv.org/pdf/1005.3676v1.pdf}, year = {2010}, date = {2010-05-20}, journal = {Rev. A 82}, number = {012326 }, abstract = {Quantum algorithms for searching one or more marked items on a d-dimensional lattice provide an extension of Grover's search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms of the level dynamics near an avoided crossing of a one-parameter family of quantum random walks. We give approximations for both the level-splitting at the avoided crossing and the effectively two-dimensional subspace of the full Hilbert space spanning the level crossing. This makes it possible to give the leading order behaviour for the search time and the localisation probability in the limit of large lattice size including the leading order coefficients. For d=2 and d=3, these coefficients are calculated explicitly. Closed form expressions are given for higher dimensions.}, keywords = {}, pubstate = {published}, tppubtype = {article} } Quantum algorithms for searching one or more marked items on a d-dimensional lattice provide an extension of Grover's search algorithm including a spatial component. We demonstrate that these lattice search algorithms can be viewed in terms of the level dynamics near an avoided crossing of a one-parameter family of quantum random walks. We give approximations for both the level-splitting at the avoided crossing and the effectively two-dimensional subspace of the full Hilbert space spanning the level crossing. This makes it possible to give the leading order behaviour for the search time and the localisation probability in the limit of large lattice size including the leading order coefficients. For d=2 and d=3, these coefficients are calculated explicitly. Closed form expressions are given for higher dimensions. |

Lee, Min-Ho; Byun, Chang Woo; Choi, Nark Nyul; Tanner, Gregor Photoionization of two-electron atoms via highly doubly excited states: Numerical and semiclassical results (Journal Article) Phys. Rev. A, 81 (043419 ), 2010. @article{Lee2010, title = {Photoionization of two-electron atoms via highly doubly excited states: Numerical and semiclassical results}, author = {Min-Ho Lee and Chang Woo Byun and Nark Nyul Choi and Gregor Tanner}, url = {http://journals.aps.org/pra/abstract/10.1103/PhysRevA.81.043419}, year = {2010}, date = {2010-04-27}, journal = {Phys. Rev. A}, volume = {81}, number = {043419 }, abstract = {The quantum regime of highly doubly excited states in two-electron atoms has, so far, been largely inaccessible both to numerical methods as well as to experiments. Recent advances in semiclassical closed orbit theory in combination with a quantum mapping approach have shown a new way into this region of high dynamical complexity. In particular, new scaling laws near the double-ionization threshold as well as the dominant semiclassical contributions to the total photoionization cross section can be identified. We will present this new approach here in all its detail. It is based on representing the photoionization cross section in terms of quantum maps. These quantum maps or quantum propagators are used as a starting point for developing an efficient numerical method for calculating cross sections. Furthermore, by writing the quantum operators in semiclassical approximations, it is possible to interpret the quantum results in terms of classical triple collision orbits and to derive threshold laws near the three-particle breakup point. Semiclassical and numerical quantum results show excellent agreement for a model system, namely collinear helium.}, keywords = {}, pubstate = {published}, tppubtype = {article} } The quantum regime of highly doubly excited states in two-electron atoms has, so far, been largely inaccessible both to numerical methods as well as to experiments. Recent advances in semiclassical closed orbit theory in combination with a quantum mapping approach have shown a new way into this region of high dynamical complexity. In particular, new scaling laws near the double-ionization threshold as well as the dominant semiclassical contributions to the total photoionization cross section can be identified. We will present this new approach here in all its detail. It is based on representing the photoionization cross section in terms of quantum maps. These quantum maps or quantum propagators are used as a starting point for developing an efficient numerical method for calculating cross sections. Furthermore, by writing the quantum operators in semiclassical approximations, it is possible to interpret the quantum results in terms of classical triple collision orbits and to derive threshold laws near the three-particle breakup point. Semiclassical and numerical quantum results show excellent agreement for a model system, namely collinear helium. |

Hein, Birgit; Tanner, Gregor Wave communication across regular lattices (Journal Article) Phys. Rev. Lett .103, (260501 ), 2010. @article{Hein2010b, title = {Wave communication across regular lattices}, author = {Birgit Hein and Gregor Tanner}, url = {https://arxiv.org/pdf/1001.0335v1.pdf}, year = {2010}, date = {2010-01-02}, journal = {Phys. Rev. Lett .103}, number = {260501 }, abstract = {We propose a novel way to communicate signals in the form of waves across a d - dimensional lattice. The mechanism is based on quantum search algorithms and makes it possible to both search for marked positions in a regular grid and to communicate between two (or more) points on the lattice. Remarkably, neither the sender nor the receiver needs to know the position of each other despite the fact that the signal is only exchanged between the contributing parties. This is an example of using wave interference as a resource by controlling localisation phenomena effectively. Possible experimental realisations will be discussed.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We propose a novel way to communicate signals in the form of waves across a d - dimensional lattice. The mechanism is based on quantum search algorithms and makes it possible to both search for marked positions in a regular grid and to communicate between two (or more) points on the lattice. Remarkably, neither the sender nor the receiver needs to know the position of each other despite the fact that the signal is only exchanged between the contributing parties. This is an example of using wave interference as a resource by controlling localisation phenomena effectively. Possible experimental realisations will be discussed. |

## 2009 |

Tanner, Gregor Dynamical Energy Analysis - determining wave energy distributions in complex vibro-acoustical structures (Journal Article) Journal of Sound and Vibration, 320 , pp. 1023-1038, 2009. @article{Tanner2009, title = {Dynamical Energy Analysis - determining wave energy distributions in complex vibro-acoustical structures}, author = {Gregor Tanner }, url = {http://arxiv.org/pdf/0803.1791v1.pdf}, year = {2009}, date = {2009-07-16}, journal = {Journal of Sound and Vibration}, volume = {320}, pages = {1023-1038}, abstract = {We propose a new approach towards determining the distribution of mechanical and acoustic wave energy in complex built-up structures. The technique interpolates between standard Statistical Energy Analysis (SEA) and full ray tracing containing both these methods as limiting case. By writing the flow of ray trajectories in terms of linear phase space operators, it is suggested here to reformulate ray-tracing algorithms in terms of boundary operators containing only short ray segments. SEA can now be identified as a low resolution ray tracing algorithm and typical SEA assumptions can be quantified in terms of the properties of the ray dynamics. The new technique presented here enhances the range of applicability of standard SEA considerably by systematically incorporating dynamical correlations wherever necessary. Some of the inefficiencies inherent in typical ray tracing methods can be avoided using only a limited amount of the geometrical ray information. The new dynamical theory - Dynamical Energy Analysis (DEA) - thus provides a universal approach towards determining wave energy distributions in complex structures.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We propose a new approach towards determining the distribution of mechanical and acoustic wave energy in complex built-up structures. The technique interpolates between standard Statistical Energy Analysis (SEA) and full ray tracing containing both these methods as limiting case. By writing the flow of ray trajectories in terms of linear phase space operators, it is suggested here to reformulate ray-tracing algorithms in terms of boundary operators containing only short ray segments. SEA can now be identified as a low resolution ray tracing algorithm and typical SEA assumptions can be quantified in terms of the properties of the ray dynamics. The new technique presented here enhances the range of applicability of standard SEA considerably by systematically incorporating dynamical correlations wherever necessary. Some of the inefficiencies inherent in typical ray tracing methods can be avoided using only a limited amount of the geometrical ray information. The new dynamical theory - Dynamical Energy Analysis (DEA) - thus provides a universal approach towards determining wave energy distributions in complex structures. |

Hein, Birgit; Tanner, Gregor Quantum search algorithms on the hypercube (Journal Article) ournal of Physics A, 42 (085303), 2009. @article{Hein2009, title = {Quantum search algorithms on the hypercube}, author = {Birgit Hein and Gregor Tanner}, url = {http://arxiv.org/pdf/0906.3094v1.pdf}, year = {2009}, date = {2009-06-17}, journal = {ournal of Physics A}, volume = {42}, number = {085303}, abstract = {We investigate a set of discrete-time quantum search algorithms on the n-dimensional hypercube following a proposal by Shenvi, Kempe and Whaley. We show that there exists a whole class of quantum search algorithms in the symmetry reduced space which perform a search of a marked vertex in time of order N−−√ where N=2n, the number of vertices. In analogy to Grover's algorithm, the spatial search is effectively facilitated through a rotation in a two-level sub-space of the full Hilbert space. In the hypercube, these two-level systems are introduced through avoided crossings. We give estimates on the quantum states forming the 2-level sub-spaces at the avoided crossings and derive improved estimates on the search times.}, keywords = {}, pubstate = {published}, tppubtype = {article} } We investigate a set of discrete-time quantum search algorithms on the n-dimensional hypercube following a proposal by Shenvi, Kempe and Whaley. We show that there exists a whole class of quantum search algorithms in the symmetry reduced space which perform a search of a marked vertex in time of order N−−√ where N=2n, the number of vertices. In analogy to Grover's algorithm, the spatial search is effectively facilitated through a rotation in a two-level sub-space of the full Hilbert space. In the hypercube, these two-level systems are introduced through avoided crossings. We give estimates on the quantum states forming the 2-level sub-spaces at the avoided crossings and derive improved estimates on the search times. |