A boundary integral formalism for stochastic ray tracing in billiards

Chappell, David J.; Tanner, Gregor

doi:10.1063/1.4903064

Cited by 12 publications

(4 citation statements)

References 42 publications

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“…energy leaving through Port 1 again after one or two reflections. An example of energy diffusion predicted by DEA is presented in [56]. Note also, that in the regime of low losses one finds a small deviation between RT/DEA and PWB.…”

Section: Resultsmentioning

confidence: 99%

Wireless power distributions in multi-cavity systems at high frequencies

et al. 2021

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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 wavelengths in the millimetre range (mmWave), both penetration loss and free-space path loss increase, while specular reflection will dominate over diffraction as an important propagation channel. Thus, current channel model protocols used for the generation of mobile networks and based on statistical parameter distributions obtained from measurements become insufficient due to the lack of deterministic information about the surroundings of the base station and the receiver-devices. These challenges call for new modelling tools for channel modelling which work in the short-wavelength/high-frequency limit and incorporate site-specific details—both indoors and outdoors. Typical high-frequency tools used in this context—besides purely statistical approaches—are based on ray-tracing techniques. Ray-tracing can become challenging when multiple reflections dominate. In this context, mesh-based energy flow methods have become popular in recent years. In this study, we compare the two approaches both in terms of accuracy and efficiency and benchmark them against traditional power balance methods.

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Section: Resultsmentioning

confidence: 99%

Wireless power distributions in multi-cavity systems at high frequencies

et al. 2021

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“…Stochastic propagation may be described by replacing the δ-distribution in (4) with a finite-width kernel (see for example Ref. [40]). If w i,j = 1, or more generally, if there are no dissipative terms and the initial phase space density is conserved, that is,…”

Section: Frobenius-perron Operator On a Tetrahedral Meshmentioning

confidence: 99%

Transport of phase space densities through tetrahedral meshes using discrete flow mapping

Bajars

Chappell

Søndergaard

et al. 2017

Journal of Computational Physics

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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 approximation of 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.

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“…The operator L is also referred to as the Frobenius-Perron (FP) operator [38]. The integral representation in ( 12) is useful for considering effects like absorption and mode conversion as well as uncertainty, see [39]. The ray-dynamical, or classical, analogues of equation ( 9) are now provided by…”

Section: Relation To Classical Phase Space Densitiesmentioning

confidence: 99%

Propagating wave correlations in complex systems

Creagh¹,

Gradoni²,

Hartmann³

et al. 2016

J. Phys. A: Math. Theor.

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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.

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A boundary integral formalism for stochastic ray tracing in billiards

Cited by 12 publications

References 42 publications

Wireless power distributions in multi-cavity systems at high frequencies

Wireless power distributions in multi-cavity systems at high frequencies

Transport of phase space densities through tetrahedral meshes using discrete flow mapping

Propagating wave correlations in complex systems

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