Related papers: The mathematical theory of splitting-merging patte…
We develop a hybrid scheme based on a finite difference scheme and a rescaling technique to approximate the solution of nonlinear wave equation. In order to numerically reproduce the blow-up phenomena, we propose a rule of scaling…
Using the very basic physics principles, we have studied the implications of quantum corrections to classical electrodynamics and the propagation of electromagnetic waves and pulses. The initial nonlinear wave equation for the…
Low-frequency simulations of a one-layer model with lateral buoyancy variations (i.e., thermodynamically active) have revealed circulatory motions resembling quite closely submesoscale observations in the surface ocean rather than…
In this paper, we describe certain crucial steps in the development of an algorithm for finding the Riemann solution in systems of conservation laws. We relax the classical hypotheses of strict hyperbolicity and genuine nonlinearity of Lax.…
Anomalous kinetics of infective (e.g., autocatalytic) reactions in open, nonhyperbolic chaotic flows are important for many applications in biological, chemical, and environmental sciences. We present a scaling theory for the singular…
In this paper, we propose an adaptive high-order method for hyperbolic systems of conservation laws. The proposed method is based on a dual formulation approach: Two numerical solutions, corresponding to conservative and nonconservative…
We study the following class of scalar hyperbolic conservation laws with discontinuous fluxes: \partial_t\rho+\partial_xF(x,\rho)=0. The main feature of such a conservation law is the discontinuity of the flux function in the space variable…
We consider the numerical approximation of a system of partial differential equations involving a nonlinear Schr\"odinger equation coupled with a hyperbolic conservation law. This system arises in models for the interaction of short and…
We investigate the qualitative dynamics of smooth solutions to the radially symmetric isentropic compressible Euler equations, focusing specifically on the evolution of rarefactive and compressive wave characters across three distinct…
Theoretical studies on linear shear instabilities often use simple velocity and density profiles (e.g. constant, piecewise) for obtaining good qualitative and quantitative predictions of the initial disturbances. Furthermore, such simple…
This article deals with relaxation approximations of nonlinear systems of hyperbolic balance laws. We introduce a class of relaxation schemes and establish their stability and convergence to the solution of hyperbolic balance laws before…
Within the so-called scaled quantum theory, the standard bouncing ball problem is analyzed under the presence of a gravitational field and harmonic potential. In this framework, the quantum-classical transition of the density matrix is…
Self-propelled particles with hydrodynamic interactions (microswimmers) have previously been shown to produce long-range ordering phenomena. Many theoretical explanations for these collective phenomena are connected to instabilities in the…
For a model of nonlinear elastodynamics, we construct a finite volume scheme which is able to capture nonclassical shocks (also called undercompressive shocks). Those shocks verify an entropy inequality but are not admissible in the sense…
We present a numerical model and a set of conservative algorithms for Non-Maxwellian plasma kinetics with inelastic collisions. These algorithms self-consistently solve for the time evolution of an isotropic electron energy distribution…
Non-Hermitian systems can manifest rich static and dynamical properties at their exceptional points (EPs). Here, we identify yet another class of distinct phenomena that is hinged on EPs, namely, the emergence of a series of non-Hermitian…
The Riemann problem for the discrete conservation law $2 \dot{u}_n + u^2_{n+1} - u^2_{n-1} = 0$ is classified using Whitham modulation theory, a quasi-continuum approximation, and numerical simulations. A surprisingly elaborate set of…
Non-reciprocal interactions between scalar fields that represent the concentrations of two active species are known to break the parity and time-reversal (PT) symmetries of the equilibrium state, as manifested in the emergence of travelling…
We review recent interest in the relativistic Riemann problem as a method for generating a non-equilibrium steady state. In the version of the problem under con- sideration, the initial conditions consist of a planar interface between two…
Reaction-diffusion equations appear in biology and chemistry, and combine linear diffusion with different kind of reaction terms. Some of them are remarkable from the mathematical point of view, since they admit families of travelling waves…