Related papers: Exact closed-form solutions for Lamb's problem (II…
In this paper, new representations of the Green's function for an acoustic d-dimensional half-space problem with impedance boundary conditions are presented. The main features of the new representation are: a) in addition to additive terms…
The purpose of this paper is to investigate the fundamental problem of the non-uniform subsonic motion of a point force and line forces in an unbounded, homogeneous, isotropic medium in analogy to the electromagnetic Li\'enard-Wiechert…
We explore the dynamics of the three-dimensional compressible Taylor--Green vortex from the perspective of kinetic theory by directly solving the six-dimensional Boltzmann equation. This work studies the connections between molecular-scale…
In this paper, we construct exact solutions that character three-dimensional, nonlinear trapped lee waves propagation superimposed on longitudinal atmospheric currents in the $\beta$-plane approximation. The solutions obtained are presented…
This study investigates the elastic response of a two-dimensional semi-infinite medium subjected to a moving surface load with a prescribed displacement profile. As a fundamental step, we derive analytical Green's functions for the…
Motivated by the desire to understand the causal structure of physical signals produced in curved spacetimes -- particularly around black holes -- we show how, for certain classes of geometries, one might obtain its retarded or advanced…
An analytical expression of the strain distribution due to lattice mismatch is obtained in an infinite isotropic elastic medium (a matrix) with a three-dimensional polyhedron-shaped inclusion (a quantum dot). The expression was obtained…
The Green's function method has applications in several fields in Physics, from classical differential equations to quantum many-body problems. In the quantum context, Green's functions are correlation functions, from which it is possible…
Solar oscillations can be modeled by Galbrun's equation which describes Lagrangian wave displacement in a self-gravitating stratified medium. For spherically symmetric backgrounds, we construct an algorithm to compute efficiently and…
We propose integral representations and analytical solutions for the propagator of the $1+1$ dimensional Salpeter Hamiltonian, describing a relativistic quantum particle with no spin. We explore the exact Green function and an exact…
This work comprises a detailed theoretical and computational study of the boundary value problem for transversely isotropic linear elastic bodies. General conditions for well-posedness are derived in terms of the material parameters. The…
We extend the theory of complete Bernstein functions to matrix-valued functions and apply it to analyze Green's function of an anisotropic multi-dimension\-al linear viscoelastic problem. Green's function is given by the superposition of…
The pointwise space-time behavior of the Green's function of the three-dimensional modified Vlasov-Poisson-Boltzmann system is studied in this paper. It is shown that the Green's function has a decomposition of the macroscopic diffusive…
We consider a general setting for dynamic tensor field tomography in an inhomogeneous refracting and absorbing medium as inverse source problem for the associated transport equation. Following Fermat's principle the Riemannian metric in the…
In this paper, we are concerned with a time-dependent transmission problem for a thermo-piezoelectric elastic body immersed in a compressible fluid. It is shown that the problem can be treated by the boundary-field equation method, provided…
We study the Dirac equation in 3+1 dimensions with a general combination of scalar, vector and tensor interactions with arbitrary strengths, all of them described by central Coulomb potentials acting on a particular plane of motion. For the…
We present a general phase-space kinetic model for charged particle transport through combined localised and delocalised states, capable of describing scattering collisions, trapping, detrapping and losses. The model is described by a…
We present approximate exterior and interior solutions of Einstein's equations which describe the gravitational field of a static deformed mass distribution. The deformation of the source is taken into account up to the first order in the…
An explicit high order semi-Lagrangian method is developed for solving Lagrangian transport equations in Eulerian-Lagrangian formulations. To ensure a semi-Lagrangian approximation that is consistent with an explicit Eulerian, discontinuous…
We derive exact solutions to the sine--Gordon equation describing localized structures on the background of librational and rotational travelling waves. In the case of librational waves, the exact solution represents a localized spike in…