Related papers: Shock structures in time averaged patterns for the…
The dispersing equation was derived from system of the hydrodynamic equations that take into account the gravity, and from boundary conditions of shock front. The dispersing equation made it possible to study unstable stability of front not…
The dynamics of the multi-dimensional randomly forced Burgers equation is studied in the limit of vanishing viscosity. It is shown both theoretically and numerically that the shocks have a universal global structure which is determined by…
A shock waveform is proposed based on the mechanical mechanism of shock generation in a structure. The parameters in the shock waveform have clear mechanical meanings about the generation and development of the shock. A shock signal…
Numerical simulations of a simple reaction--diffusion model reveal a surprising variety of irregular spatio--temporal patterns. These patterns arise in response to finite--amplitude perturbations. Some of them resemble the steady irregular…
The study of pattern emergence together with exploration of the exemplar Turing model is enjoying a renaissance both from theoretical and experimental perspective. Here, we implement a stability analysis of spatially dependent reaction…
We use the Gurevich-Pitaevskii approach based on the Whitham averaging method for studying the formation of dispersive shock waves in an intense light pulse propagating through a saturable nonlinear medium. Although the Whitham modulation…
The particle density distribution emerging from the solution of the Vlasov equation for relativistic, non-interacting particles with spherically symmetric initial conditions is shown to exhibit a shell-like structure for late fixed times in…
This paper aims to investigate the diffusion behavior of particles moving in stochastic flows under a structure-preserving scheme. We compute the effective diffusivity for normal diffusive random flows and establish the power law between…
Intrinsic equations of motion of superconducting cosmic string may admit solutions in the shock-wave form that implies discontinuity of the current term \chi. The hypersurface of discontinuity propagates at finite velocity determined by…
The Kuramoto-Sivashinsky equation is a prototypical chaotic nonlinear partial differential equation (PDE) in which the size of the spatial domain plays the role of a bifurcation parameter. We investigate the changing dynamics of the…
Boundary effects in the stepwise structure of the Lyapunov spectra and the corresponding wavelike structure of the Lyapunov vectors are discussed numerically in quasi-one-dimensional systems consisting of many hard-disks. Four kinds of…
We study the motion of passive tracers in a two-dimensional turbulent velocity field generated by the Kuramoto-Sivashinsky equation. By varying the direction of the velocity-vector with respect to the field-gradient we can continuously vary…
There are many subtle issues associated with solving the Navier-Stokes equations. In this paper, several of these issues, which have been observed previously in research involving the Navier-Stokes equations, are studied within the…
Combining the results of [14] and [10], the trend to equilibrium in large time is studied for a large particle system associated to a Vlasov-Fokker-Planck equation. Under some conditions (that allow non-convex confining potentials) the…
For stochastic Hamilton-Jacobi (SHJ) equations, instability points are the space-time locations where two eternal solutions with the same asymptotic velocity differ. Another fundamental structure in such equations is shocks, which are the…
We are concerned with rigorous mathematical analysis of shock diffraction by two-dimensional convex cornered wedges in compressible fluid flow governed by the nonlinear wave system. This shock diffraction problem can be formulated as a…
We calculate the quasi-stationary structure of a radiating shock wave propagating through a spherically symmetric shell of cold gas by solving the time-dependent equations of radiation hydrodynamics on an adaptive grid. We show that this…
Phase-locked states with a constant phase shift between the neighboring oscillators are studied in rings of identical Kuramoto oscillators with time-delayed nearest-neighbor coupling. The linear stability of these states is derived and it…
Recurrence plots exhibit line structures which represent typical behaviour of the investigated system. The local slope of these line structures is connected with a specific transformation of the time scales of different segments of the…
Presented here is the mathematical model describing the phenomenon of shock waves. The underlying concept is based on the time-space model of wave propagation.