Related papers: Generalised Diffusion and Wave Equations: Recent A…
We discuss the derivation and the solutions of integro-differential equations (variable-order time-fractional diffusion equations) following as continuous limits for lattice continuous time random walk schemes with power-law waiting-time…
In this paper a finite difference/local discontinuous Galerkin method for the fractional diffusion-wave equation is presented and analyzed. We first propose a new finite difference method to approximate the time fractional derivatives, and…
Real data are constrained to finite sampling rates, which calls for a suitable mathematical description of the corrections to the finite-time estimations of the dynamic equations. Often in the literature, lower order discrete time…
We develop a General Fluctuation Formula for phase variables that are odd under time reversal. Simulations are used to verify the new formula.
Space time fractional nonlinear evolution equations have been widely applied for describing various types of physical mechanism of natural phenomena in mathematical physics and engineering. The proposed generalized exp expansion method…
In this paper we obtain uniform propagation estimates for systems of interacting diffusions. We adopt a general model, satisfying various conditions which ensure that the decay resulting from the internal dynamics term dominates the…
The notions of generating sets of conservation laws of systems of differential equations with respect to symmetry groups and equivalence groups are introduced and applied. This allows us to generalize essentially the procedure of finding…
Traditional elastic wavefield separation methods, while accurate, often demand substantial computational resources, especially for large geological models or 3D scenarios. Purely data-driven neural network approaches can be more efficient,…
A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…
A systematic and full description of the theory for a dissipation mechanism of wind wave energy in a spectral representation is given. As a basis of the theory, the fundamental is stated that the most general dissipation mechanism for wind…
These notes build an introduction to Convolution Quadrature techniques applied to linear convolutions and convolution equations with a bias to problems related to wave propagation. The notes are self-contained and emphasize algorithmic…
The generalized Langrangian mean theory provides exact equations for general wave-turbulence-mean flow interactions in three dimensions. For practical applications, these equations must be closed by specifying the wave forcing terms. Here…
We discuss the "generalized fluctuation-dissipation relations (theorems)" for the first time suggested by us in 1977-1984 as statistical-thermodynamical consequences of time symmetry (reversibility) of microscopic dynamics. It is shown, in…
This paper develops a general approach to the derivation of the boundary conditions for hydrodynamic equations for charged and neutral plasma components. It includes both a well-known classical case for pure diffusion, and considers the…
We consider the long time behavior of Wong-Zakai approximations of stochastic differential equations. These piecewise smooth diffusion approximations are of great importance in many areas, such as those with ordinary differential equations…
Historically and to date, the continuity equation has served as a consistency criterion for the development of physical theories. Employing Clifford's geometric algebras, a system of continuity equations for a generalised multivector of the…
Chemical waves constitute a known class of dissipative structures emerging in reaction-diffusion systems. They play a crucial role in biology, spreading information rapidly to synchronize and coordinate biological events. We develop a…
The equations of General Relativity are recast in the form of a wave equation for the Weyl tensor. This allows to reformulate gravitational wave theory in terms of curvature waves, rather than metric waves. The existence of two transverse…
This study focuses on the numerical modeling of wave propagation in fractionally-dissipative media. These viscoelastic models are such that the attenuation is frequency dependent and follows a power law with non-integer exponent. As a…
In view of the usefulness and importance of the kinetic equation in certain physical problems, the authors derive the explicit solution of a fractional kinetic equation of general character, that unifies and extends earlier results.…