All Outputs (21)

Closed form expressions for the Green’s function of a quantum graph—a scattering approach (2023)
Journal Article
Lawrie, T., Gnutzmann, S., & Tanner, G. K. (2023). Closed form expressions for the Green’s function of a quantum graph—a scattering approach. Journal of Physics A: Mathematical and Theoretical, 56(47), Article 475202. https://doi.org/10.1088/1751-8121/ad03a5

In this work we present a three step procedure for generating a closed form expression of the Green’s function on both closed and open finite quantum graphs with general self-adjoint matching conditions. We first generalize and simplify the approach... Read More about Closed form expressions for the Green’s function of a quantum graph—a scattering approach.

A quantum graph approach to metamaterial design (2022)
Journal Article
Lawrie, T., Tanner, G., & Chronopoulos, D. (2022). A quantum graph approach to metamaterial design. Scientific Reports, 12(1), Article 18006. https://doi.org/10.1038/s41598-022-22265-2

Since the turn of the century, metamaterials have gained a large amount of attention due to their potential for possessing highly nontrivial and exotic properties—such as cloaking or perfect lensing. There has been a great push to create reliable mat... Read More about A quantum graph approach to metamaterial design.

A direction preserving discretization for computing phase-space densities (2021)
Journal Article
Chappell, D., Crofts, J. J., Richter, M., & Tanner, G. (2021). A direction preserving discretization for computing phase-space densities. SIAM Journal on Scientific Computing, 43(4), B884-B906. https://doi.org/10.1137/20M1352041

Ray flow methods are an efficient tool to estimate vibro-acoustic or electromagnetic energy transport in complex domains at high-frequencies. Here, a Petrov-Galerkin discretization of a phase-space boundary integral equation for transporting wave ene... Read More about A direction preserving discretization for computing phase-space densities.

Wireless power distributions in multi-cavity systems at high frequencies (2021)
Journal Article
Adnan, F., Blakaj, V., Phang, S., Antonsen, T. M., Creagh, S. C., Gradoni, G., & Tanner, G. (2021). Wireless power distributions in multi-cavity systems at high frequencies. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 477(2245), Article 20200228. https://doi.org/10.1098/rspa.2020.0228

The next generations of wireless networks will work in frequency bands ranging from sub-6 GHz up to 100 GHz. Radio signal propagation differs here in several critical aspects from the behaviour in the microwave frequencies currently used. With wavele... Read More about Wireless power distributions in multi-cavity systems at high frequencies.

Tunnelling around bends—Wave scattering in curved shell structures (2020)
Journal Article
Mohammed, N. M., Creagh, S. C., & Tanner, G. (2021). Tunnelling around bends—Wave scattering in curved shell structures. Wave Motion, 101, Article 102697. https://doi.org/10.1016/j.wavemoti.2020.102697

A ray dynamics describing wave transport on curved and smooth thin shells can be obtained from the underlying wave equations via the Eikonal approximation. We analyse mid-frequency effects near the ring frequency for curved plates consisting of a cyl... Read More about Tunnelling around bends—Wave scattering in curved shell structures.

Diffraction of Wigner functions (2020)
Journal Article
Creagh, S., Sieber, M., Gradoni, G., & Tanner, G. K. (2021). Diffraction of Wigner functions. Journal of Physics A: Mathematical and Theoretical, 54(1), Article 015701. https://doi.org/10.1088/1751-8121/abc72a

We describe the contribution of diffractive orbits to semiclassical approximations of Wigner function propagators. These contributions are based on diffractively scattered rays used in the geometrical theory of diffraction (GTD). They provide an exte... Read More about Diffraction of Wigner functions.

Transfer operator approach to ray-tracing in circular domains (2020)
Journal Article
Slipantschuk, J., Richter, M., Chappell, D. J., Tanner, G., Just, W., & Bandtlow, O. F. (2020). Transfer operator approach to ray-tracing in circular domains. Nonlinearity, 33(11), 5773-5790. https://doi.org/10.1088/1361-6544/ab9dca

The computation of wave-energy distributions in the mid-to-high frequency regime can be reduced to ray-tracing calculations. Solving the ray-tracing problem in terms of an operator equation for the energy density leads to an inhomogeneous equation wh... Read More about Transfer operator approach to ray-tracing in circular domains.

Nearfield acoustical holography – a Wigner function approach (2020)
Journal Article
Ramapriya, D. M., Gradoni, G., Creagh, S. C., Tanner, G., Moers, E., & Lopéz Arteaga, I. (2020). Nearfield acoustical holography – a Wigner function approach. Journal of Sound and Vibration, 486, Article 115593. https://doi.org/10.1016/j.jsv.2020.115593

We propose to use Wigner transformation methods as a tool for propagating measured acoustic signals from and towards a source region. We demonstrate the usefulness of the approach both for source reconstruction purposes and as a stable numerical simu... Read More about Nearfield acoustical holography – a Wigner function approach.

Efficient Statistical Model for Predicting Electromagnetic Wave Distribution in Coupled Enclosures (2020)
Journal Article
Ma, S., Phang, S., Drikas, Z., Addissie, B., Hong, R., Blakaj, V., …Anlage, S. M. (2020). Efficient Statistical Model for Predicting Electromagnetic Wave Distribution in Coupled Enclosures. Physical Review Applied, 14(1), Article 014022. https://doi.org/10.1103/PhysRevApplied.14.014022

The random coupling model (RCM) has been successfully applied to predicting the statistics of currents and voltages at ports in complex electromagnetic (EM) enclosures operating in the short-wavelength limit. Recent studies have extended the RCM to s... Read More about Efficient Statistical Model for Predicting Electromagnetic Wave Distribution in Coupled Enclosures.

Active vibration control of thin constrained composite damping plates with double piezoelectric layers (2019)
Journal Article
Cao, X., Tanner, G., & Chronopoulos, D. (2020). Active vibration control of thin constrained composite damping plates with double piezoelectric layers. Wave Motion, 92, Article 102423. https://doi.org/10.1016/j.wavemoti.2019.102423

Vibrations and the damping behaviour of thin constrained composite plates with double piezoelectric layers are analytically explored by using Fourier transformation and classical laminated plate theory. Electric potential equations in the double piez... Read More about Active vibration control of thin constrained composite damping plates with double piezoelectric layers.

Elastodynamics on graphs: wave propagation on networks of plates (2018)
Journal Article
Brewer, C., Creagh, S. C., & Tanner, G. (2018). Elastodynamics on graphs: wave propagation on networks of plates. Journal of Physics A: Mathematical and Theoretical, 51(44), Article 445101. https://doi.org/10.1088/1751-8121/aae1d2

We consider the wave dynamics on networks of plates coupled along 1D joints. This set-up can be mapped onto an extension of wave graph systems studied in, for example, quantum graph theory. In the elastic case, different mode-types (flexural, longitu... Read More about Elastodynamics on graphs: wave propagation on networks of plates.

Uncertainty quantification for phase-space boundary integral models of ray propagation (2018)
Journal Article
Chappell, D. J., & Tanner, G. (2018). Uncertainty quantification for phase-space boundary integral models of ray propagation. Wave Motion, https://doi.org/10.1016/j.wavemoti.2018.08.010

Total photoionization cross section of planar helium: scaling laws and collision orbits (2018)
Journal Article
Lee, M.-H., Byun, C. W., Choi, N. N., & Tanner, G. (2018). Total photoionization cross section of planar helium: scaling laws and collision orbits. Journal of Physics B: Atomic, Molecular and Optical Physics, 51(18), Article 185001. https://doi.org/10.1088/1361-6455/aad8e2

The total photoionization cross section of planar helium has been calculated up to the single ionization threshold I22 of triple P states. The cross section shows chaotic fluctuations as the energy E approaches the double ionization threshold E=0. By... Read More about Total photoionization cross section of planar helium: scaling laws and collision orbits.

Transport of phase space densities through tetrahedral meshes using discrete flow mapping (2016)
Journal Article
Bajars, J., Chappell, D., Søndergaard, N., & Tanner, G. (in press). Transport of phase space densities through tetrahedral meshes using discrete flow mapping. Journal of Computational Physics, 328, https://doi.org/10.1016/j.jcp.2016.10.019

Discrete flow mapping was recently introduced as an efficient ray based method determin- ing wave energy distributions in complex built up structures. Wave energy densities are transported along ray trajectories through polygonal mesh elements using... Read More about Transport of phase space densities through tetrahedral meshes using discrete flow mapping.

Quantum walks and quantum search on graphene lattices (2015)
Journal Article
Foulger, I., Gnutzmann, S., & Tanner, G. (2015). Quantum walks and quantum search on graphene lattices. Physical Review A, 91(6), Article 062323. https://doi.org/10.1103/PhysRevA.91.062323

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 ha... Read More about Quantum walks and quantum search on graphene lattices.

Microwave experiments simulating quantum search and directed transport in artificial graphene (2015)
Journal Article
Böhm, J., Bellec, M., Mortessagne, F., Kuhl, U., Barkhofen, S., Gehler, S., …Tanner, G. (2015). Microwave experiments simulating quantum search and directed transport in artificial graphene. Physical Review Letters, 114(11), Article 110501. https://doi.org/10.1103/PhysRevLett.114.110501

A series of quantum search algorithms have been proposed recently providing an algebraic speedup compared to classical search algorithms from N to \sqrt{N}, where N is the number of items in the search space. In particular, devising searches on regul... Read More about Microwave experiments simulating quantum search and directed transport in artificial graphene.

A boundary integral formalism for stochastic ray tracing in billiards (2014)
Journal Article
Chappell, D., & Tanner, G. (in press). A boundary integral formalism for stochastic ray tracing in billiards. Chaos, 24, Article 043137. https://doi.org/10.1063/1.4903064

Determining the flow of rays or non-interacting particles driven by a force or velocity field is fundamental to modelling many physical processes. These include particle flows arising in fluid mechanics and ray flows arising in the geometrical optics... Read More about A boundary integral formalism for stochastic ray tracing in billiards.

Quantum search on graphene lattices (2014)
Journal Article
Foulger, I., Gnutzmann, S., & Tanner, G. (2014). Quantum search on graphene lattices. Physical Review Letters, 112, Article 070504. https://doi.org/10.1103/PhysRevLett.112.070504

We present a continuous-time quantum search algorithm on a graphene lattice. This provides the sought- after implementation of an efficient continuous-time quantum search on a two-dimensional lattice. The search uses the linearity of the dispersion r... Read More about Quantum search on graphene lattices.

Dynamical energy analysis on mesh grids: a new tool for describing the vibro-acoustic response of complex mechanical structures (2014)
Journal Article
Chappell, D. J., Loechel, D., Sondergaard, N., & Tanner, G. (2014). Dynamical energy analysis on mesh grids: a new tool for describing the vibro-acoustic response of complex mechanical structures. Wave Motion, 51(4), https://doi.org/10.1016/j.wavemoti.2014.01.004

We present a new approach for modelling noise and vibration in complex mechanical structures in the mid-to-high frequency regime. It is based on a dynamical energy analysis (DEA) formulation which extends standard techniques such as statistical energ... Read More about Dynamical energy analysis on mesh grids: a new tool for describing the vibro-acoustic response of complex mechanical structures.

In–out decomposition of boundary integral equations (2013)
Journal Article
Creagh, S. C., Hamdin, H. B., & Tanner, G. (2013). In–out decomposition of boundary integral equations. Journal of Physics A: Mathematical and Theoretical, 46(43), Article 435203. https://doi.org/10.1088/1751-8113/46/43/435203

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 diff... Read More about In–out decomposition of boundary integral equations.