Related papers: Consolidating boundary methods for finding the eig…
This paper extends the Method of Particular Solutions (MPS) to the computation of eigenfrequencies and eigenmodes of plates. Specific approximation schemes are developed, with plane waves (MPS-PW) or Fourier-Bessel functions (MPS-FB). This…
We obtain a semiclassical expression for the projector onto eigenfunctions by means of the Fredholm theory. We express the projector in the coherent state basis, thus obtaining the semiclassical Husimi representation of the stadium…
Orbits in different dispersive billiard systems, e.g. the 3 disk system, are mapped into a topological well ordered symbol plane and it is showed that forbidden and allowed orbits are separated by a monotone pruning front. The pruning front…
While many dynamical systems of mechanical origin, in particular billiards, are strongly chaotic -- enjoy exponential mixing, the rates of mixing in many other models are slow (algebraic, or polynomial). The dynamics in the latter are…
In this paper we establish a kind of bijection between the orbits of a polygonal outer billiards system and the orbits of a related (and simpler to analyze) system called the pinwheel map. One consequence of the result is that the outer…
We present a fluctuating boundary integral method (FBIM) for overdamped Brownian Dynamics (BD) of two-dimensional periodic suspensions of rigid particles of complex shape immersed in a Stokes fluid. We develop a novel approach for…
We revisit the spectral statistics of the C$_3$--symmetric billiard introduced by Dembowski [Phys. Rev. E, R4516 (2000)], which exhibits both GOE and GUE statistics depending on the symmetry block. Using high--precision Beyn's…
The billiard problem concerns a point particle moving freely in a region of the horizontal plane bounded by a closed curve $\Gamma$, and reflected at each impact with $\Gamma$. The region is called a `billiard', and the reflections are…
We study a generalized three-dimensional stadium billiard and present strong numerical evidence that this system is completely chaotic. In this convex billiard chaos is generated by the defocusing mechanism. The construction of this…
The demagnetization field in micromagnetism is given as the gradient of a potential which solves a partial differential equation (PDE) posed in R^d. In its most general form, this PDE is supplied with continuity condition on the boundary of…
The properties of energy levels in a family of classically pseudointegrable systems, the barrier billiards, are investigated. An extensive numerical study of nearest-neighbor spacing distributions, next-to-nearest spacing distributions,…
Inferring electromagnetic propagation characteristics within the marine atmospheric boundary layer (MABL) from data in real time is crucial for modern maritime navigation and communications. The propagation of electromagnetic waves is well…
The semiclassical description of billiard spectra is extended to include the diffractive contributions from orbits which are nearly tangent to a concave part of the boundary. The leading correction for an unstable isolated orbit is of the…
In this paper, we consider the scattering of a plane wave by a rigid obstacle embedded in a homogeneous and isotropic elastic medium in three dimensions. Based on the Helmholtz decomposition, the elastic scattering problem is reduced to a…
We study uniqueness of an elliptic Riemannian polyhedron using the elliptic version for Boundary Control method, which we presented in [1]. We also present interface detection criteria for hyperbolic Riemannian manifolds through…
We propose a method of measuring approximate quantum eigenfunctions in polygonalized billiard geometries, based on a quasiclassical evolution operator having a (smoothened) Perron-Frobenius kernel modulated by a phase arising from quantum…
Eigendecomposition of the Laplace-Beltrami operator is instrumental for a variety of applications from physics to data science. We develop a numerical method of computation of the eigenvalues and eigenfunctions of the Laplace-Beltrami…
A novel boundary element method (BEM) removes the classical dependence on explicit fundamental solutions and extends quasi-optimal BEM discretisations to strongly elliptic operators with variable coefficients. The approach constructs a…
In this note, we extend the results on eigenfunction concentration in billiards as proved by the third author in \cite{M1}. There, the methods developed in Burq-Zworski \cite{BZ3} to study eigenfunctions for billiards which have rectangular…
Given a random quantum state of multiple distinguishable or indistinguishable particles, we provide an effective method, rooted in symplectic geometry, to compute the joint probability distribution of the eigenvalues of its one-body reduced…