相关论文: Bursts and Shocks in a Continuum Shell Model

This paper is concerned with the blowup phenomenon of stochastic parabolic equations both on bounded domain and in the whole space. We introduce a new method to study the blowup phenomenon on bounded domain. Comparing with the existing…

We study linear pseudoparabolic equations with unbounded and time-dependent coefficients. We solve the case which has remained open in several recent studies of pseudoparabolic equations with unbounded and time-dependent coefficients. In…

Direct numerical simulation of the strongly nonlinear stages of instability development for a non-conducting liquid with a charged free surface in a normal electric field is performed. It is demonstrated that two main stages of the…

We construct a discrete shell-model for two-dimensional turbulence that takes into account local and nonlocal interactions between velocity modes in Fourier space. In real space, its continuous limit is described by the one-dimensional…

We investigate shock formation in an asymmetric exclusion process with creation and annihilation of particles in the bulk. We show how the continuum mean-field equations can be studied analytically and hence derive the phase diagrams of the…

Hele-Shaw flow at vanishing surface tension is ill-defined. In finite time, the flow develops cusp-like singularities. We show that the ill-defined problem admits a weak {\it dispersive} solution when singularities give rise to a graph of…

We consider a two dimensional lattice model to describe the opening of a crack in hydraulic fracturing. In particular we consider that the material only breaks under tension and the fluid has no pressure drop inside the crack. For the case…

In this paper, we'll answer several abstract, formal questions about the nature of crack growth and nucleation. Bringing a field theory point of view to fracture illuminates things in what I hope will be an entertaining way. Formally, what…

The dynamical symmetry breaking associated with the existence and non-existence of breather solutions is studied. Here, nonlinear hyperbolic evolution equations are calculated using a high-precision numerical scheme. %%% First, for…

When the pressure of particles accelerated at shock waves is no longer negligible compared to the kinetic pressure of the gas, the linear theory of diffusive shock acceleration breaks down. This is expected in particular when the shock…

Stationary solutions to the equations of non-linear diffusive shock acceleration play a fundamental role in the theory of cosmic-ray acceleration. Their existence usually requires that a fraction of the accelerated particles be allowed to…

The nonlinear evolution of unstable C-type shocks in weakly ionized plasmas is studied by means of time-dependent magnetohydrodynamical simulations. This study is limited to shocks in magnetically dominated plasmas (in which the Alfven…

The full kinetic dynamics of a perpendicular collisionless shock is studied by means of a one-dimensional electromagnetic full particle simulation. The present simulation domain is taken in the shock rest frame in contrast to the previous…

In this work we study the dynamic behaviour of compound shells of revolution partially filled with an ideal incompressible fluid based on boundary-value problems. New analytical mathematical model with corresponding discrete scheme for the…

In a recent feature article in this journal, co-authored by Gert van der Heijden, I described the static-dynamic analogy and its role in understanding the localized post-buckling of shell-like structures, looking exclusively at integrable…

In mechanical systems it is of interest to know the onset of fracture in dependence of the boundary conditions. Here we study a one-dimensional model which allows for an underlying heterogeneous structure in the discrete setting. Such…

A fundamental question in fluid dynamics concerns the formation of discontinuous shock waves from smooth initial data. We prove that from smooth initial data, smooth solutions to the 2d Euler equations in azimuthal symmetry form a first…

It is stated in the main in essence new approach to mechanics of the stressed state of the solid body from statistically isotropic material and the homogeneous liquid dynamics. The approach essence is in the detected property of the…

In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions, related to the Kelvin-Voigt damping. Global existence and asymptotic stability of solutions starting in a stable set are proved. Blow up for…

Shell models of turbulence have a finite-time blowup in the inviscid limit, i.e., the enstrophy diverges while the single-shell velocities stay finite. The signature of this blowup is represented by self-similar instantonic structures…