Related papers: Spatial structure of shock formation
We study, using numerical simulations, the dynamical evolution of self-gravitating point particles in static euclidean space, starting from a simple class of infinite ``shuffled lattice'' initial conditions. These are obtained by applying…
We investigate the influence of an infinite dimensional Gaussian noise on the bubbling phenomenon for the stochastic harmonic map flow $u(t,\cdot ):\mathbb{D}^2\to\mathbb{S}^2$, from the two-dimensional unit disc onto the sphere. The…
The spatial dimensions 1 and 4 play an exceptional role for radial solutions of the pressureless repulsive Euler-Poisson equations. Namely, for any spatial dimension except 1 and 4, any nontrivial solution of the Cauchy problem blows up in…
The behavior of a class of solutions of the shallow water Airy system originating from initial data with discontinuous derivatives is considered. Initial data are obtained by splicing together self-similar parabolae with a constant…
Caustics are natural phenomena in which nature concentrates the energy of waves. Although, they are known mostly in optics, caustics are intrinsic to all wave phenomena. For example, studies show that fluctuations in the profile of an ocean…
We study the properties of spacelike singularities in spherically symmetric spacetimes obeying the Einstein equations, in the presence of matter. We consider in particular matter described by a scalar field, both in the presence of an…
In this paper we consider the isentropic compressible Euler equations in two space dimensions together with particular initial data. The latter consists only of two constant states, where one state lies on the lower and the other state on…
We study the evolution of the ultra-relativistic shock wave in a plane-parallel atmosphere adjacent to a vacuum and the subsequent breakout phenomenon. When the density distribution has a power law with the distance from the surface, there…
We study singularity formation for the pressureless Euler-Poisson system of cold ion dynamics. In contrast to the Euler-Poisson system with pressure, when its smooth solutions experience $C^1$ blow-up, the $L^\infty$ norm of the density…
We model the diffusive shock acceleration of particles in a system of two colliding shock waves and present a method to solve the time-dependent problem analytically in the test-particle approximation and high energy limit. In particular,…
We report on experimental observations of the bending of a dust acoustic shock wave around a dust void region. This phenomenon occurs as a planar shock wavefront encounters a compressible obstacle in the form of a void whose size is larger…
Using a very high precision spectral calculation applied to the incompressible and inviscid flow with initial condition $\psi_0(x_1, x_2) = \cos x_1+\cos 2x_2$, we find that the width $\delta(t)$ of its analyticity strip follows a…
Further to results in [9], pointing out the role of initial density and velocity distributions towards determining the final outcome of spherical dust collapse, the causal structure of singularity is examined here in terms of evolution of…
We use the one-dimensional steady version of the equations derived in paper I to compute the structure of shock waves. The agreement with experiment is good, especially when we retain the experimental value of the Prandtl number adopted in…
We show that the multi-dimensional compressible Euler system for isothermal flow of an ideal, polytropic gas admits global-in-time, radially symmetric solutions with unbounded amplitudes due to wave focusing. The examples are similarity…
The Lagrangian fluid description is employed to solve the initial value problem for one-dimensional, compressible fluid flows represented by the Euler-Poisson system. Exact nonlinear and time-dependent solutions are obtained, which exhibit…
We discuss the relation between three recent approaches of describing the dynamics and the spatial distribution of particles suspended in turbulent flows: phase-space singularities in the inertial particle dynamics (caustics), real-space…
The Kuramoto-Sivashinsky equation with fixed boundary conditions is numerically studied. Shocklike structures appear in the time-averaged patterns for some parameter range of the boundary values. Effective diffusion constant is estimated…
We investigate the scaling properties of the sources of crackling noise in a fully-dynamic numerical model of sedimentary rocks subject to uniaxial compression. The model is initiated by filling a cylindrical container with randomly-sized…
We find a smooth solution of the 2D Euler equation on a bounded domain which exists and is unique in a natural class locally in time, but blows up in finite time in the sense of its vorticity losing continuity. The domain's boundary is…