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The focus of our work is dispersive, second-order effective model describing the low-frequency wave motion in heterogeneous (e.g.~functionally-graded) media endowed with periodic microstructure. For this class of quasi-periodic medium…
The algebraic method enables one to study the properties of the spectrum of a quadratic Hamiltonian through the mathematical properties of a matrix representation called regular or adjoint. This matrix exhibits exceptional points where it…
Numerical methods are developed to simulate the wave propagation in heterogeneous 2D fluid / poroelastic media. Wave propagation is described by the usual acoustics equations (in the fluid medium) and by the low-frequency Biot's equations…
Caustic formation occurs within a ray skeleton as optical or acoustic fields propagate in a medium with variable refractive properties and are unphysical, their presence being an artifact of the ray approximation of the field, and methods…
Results are presented for finding the optimal orientation of an anisotropic elastic material. The problem is formulated as minimizing the strain energy subject to rotation of the material axes, under a state of uniform stress. It is shown…
A geometric approach to integrability and reduction of dynamical system is developed from a modern perspective. The main ingredients in such analysis are the infinitesimal symmetries and the tensor fields that are invariant under the given…
Numerical continuation techniques are powerful tools that have been extensively used to identify particular solutions of nonlinear dynamical systems and enable trajectory design in chaotic astrodynamics problems such as the Circular…
We analyze the equilibrium statistical mechanics of canonical, non-canonical and non-Hamiltonian equations of motion by throwing light into the peculiar geometric structure of phase space. Some fundamental issues regarding time translation…
In this study we derive a single-particle equation of motion, from first-principles, starting out with a microscopic description of a tracer particle in a one-dimensional many-particle system with a general two-body interaction potential.…
The cubic nonlinear Helmholtz equation with third and fourth order dispersion and non-Kerr nonlinearity like the self steepening and the self frequency shift is considered. This model describes nonparaxial ultrashort pulse propagation in an…
We analyze the convergence to equilibrium in a family of Kac-like kinetic equations in multiple space dimensions. These equations describe the change of the velocity distribution in a spatially homogeneous gas due to binary collisions…
We introduce the notion of pathwise entropy solutions for a class of degenerate parabolic-hyperbolic equations with non-isotropic nonlinearity and fluxes with rough time dependence and prove their well-posedness. In the case of Brownian…
This work contains a systematic treatment of single particle Synchrotron Radiation and some application to realistic beams with given cross section area, divergence and energy spread. Standard theory relies on several approximations whose…
We present a complete formulation of second-order (2+1)-dimensional anisotropic hydrodynamics. The resulting framework generalizes leading-order anisotropic hydrodynamics by allowing for deviations of the one-particle distribution function…
Case's method obtains solutions to the radiative transport equation as superpositions of elementary solutions when the specific intensity depends on one spatial variable. In this paper, we find elementary solutions when the specific…
Although the post-Newtonian Lagrangian formalism is widely used in relativistic dynamical and statistical studies of test bodies moving around arbitrary mass distributions, the corresponding general Hamiltonian formalism is still relatively…
We propose a time-domain boundary integral method to model linear wave propagation with refractive, focusing, and Doppler effects arising from medium heterogeneities and moving obstacles. In contrast to existing techniques, our method…
The classical and relativistic Hamilton-Jacobi approach is applied to the one-dimensional homogeneous potential, $V(q)=\alpha q^n$, where $\alpha$ and $n$ are continuously varying parameters. In the non-relativistic case, the exact…
Using a so-called hemispherical model we derive a general transport equation for cosmic ray and thermal particles scattered in pitch angle by magnetic inhomogeneities in a moving collisionless plasma. The weak scattering through 90 degrees…
In this article, I demonstrate a new method to derive Jacobi metrics from Randers-Finsler metrics by introducing a more generalised approach to Hamiltonian mechanics for such spacetimes and discuss the related applications and properties. I…