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This study investigates the different novel forms of the dynamical equations of a particle orbiting a rotating asteroid and the effective potential, the Jacobi integral, etc. on different manifolds. Nine new forms of the dynamical equations…
We study the transport of active Brownian particles (ABPs) in three-dimensional (3D) oscillatory geometries, which are spatially periodic. We establish a generalized Fick-Jacobs approach, which reduces a 3D system to an effective 1D system…
The linear finite element approximation of a general linear diffusion problem with arbitrary anisotropic meshes is considered. The conditioning of the resultant stiffness matrix and the Jacobi preconditioned stiffness matrix is investigated…
Anisotropic hydrodynamics improves upon standard dissipative fluid dynamics by treating certain large dissipative corrections non-perturbatively. Relativistic heavy-ion collisions feature two such large dissipative effects: (i) Strongly…
We study the regularity of entropy solutions for quasilinear parabolic equations with anisotropic degeneracy and stochastic forcing. Building on previous works, we establish space-time regularity under a non-degeneracy condition that does…
Analytic solutions to the nonlinear radiation diffusion equation with an instantaneous point source for a non-homogeneous medium with a power law spatial density profile, are presented. The solutions are a generalization of the well known…
A theory of electromagnetic wave propagation in a weakly anisotropic smoothly inhomogeneous medium is developed, based on the quantum-mechanical diagonalization procedure applied to Maxwell equations. The equations of motion for the…
We present a new computational method for the accurate identification of the propagation modes and polarizations of elastic waves propagating in periodic solid structures and metamaterials. The method uses the eigenvectors calculated at…
We show how the basic idea of parabolic Jacobi relaxation can be modified to obtain a new class of hyperbolic relaxation schemes that are suitable for the solution of elliptic equations. Some of the analytic and numerical properties of…
A new approach was recently introduced by the authors for constructing analytic solutions of the linear PDEs describing elastodynamics. Here, this approach is applied to the case of a homogeneous isotropic half-space body satisfying…
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…
We derive upper and lower limits for the basic physical parameters (mass-radius ratio, anisotropy, redshift and total energy) for arbitrary anisotropic general relativistic matter distributions in the presence of a cosmological constant.…
Wave propagation is a common occurrence in all of physics. A linear approximation provides a simpler way to describe various fields related to observable phenomena in laboratory physics as well as astronomy and cosmology, allowing us to…
A variational principle is proposed for obtaining the Jacobi equations in systems admitting a Lagrangian description. The variational principle gives simultaneously the Lagrange equations of motion and the Jacobi variational equations for…
Electromagnetism in an inhomogeneous dielectric medium at rest is described using the methods of differential geometry. In contrast to a general relativistic approach the electromagnetic fields are discussed in three-dimensional space only.…
The structure of steady plane-parallel radiative shock waves propagating through the hydrogen gas undergoing partial ionization and excitation of bound atomic states is investigated in terms of the self-consistent solution of the equations…
We live in a world filled with anisotropy, a ubiquitous characteristic of both natural and engineered systems. In this study, we concentrate on space deformation and introduce \textit{anisotropic Green coordinates}, which provide versatile…
In the classical one-dimensional solution of fluid dynamics equations all unknown functions depend only on time t and Cartesian coordinate x. Although fluid spreads in all directions (velocity vector has three components) the whole picture…
Numerical solutions of the eikonal (Hamilton-Jacobi) equation for transversely isotropic (TI) media are essential for imaging and traveltime tomography applications. Such solutions, however, suffer from the inherent higher-order…
The numerical approximation of high-frequency wave propagation in inhomogeneous media is a challenging problem. In particular, computing high-frequency solutions by direct simulations requires several points per wavelength for stability and…