Related papers: On the dissipation at a shock wave in an elastic b…
We study the two-dimensional structural stability of shock waves in a compressible isentropic inviscid elastic fluid in the sense of the local-in-time existence and uniqueness of discontinuous shock front solutions of the equations of…
We consider an abstract linear wave equation with a time-dependent dissipation that decays at infinity with the so-called scale invariant rate, which represents the critical case. We do not assume that the coefficient of the dissipation…
Spherically collapsing cavitation bubbles produce a shock wave followed by a rebound bubble. Here we present a systematic investigation of the energy partition between the rebound and the shock. Highly spherical cavitation bubbles are…
The present study focuses on direct numerical simulations of breaking waves generated by a wave plate at constant water depths. The aim is to quantify the dynamics and kinematics in the breaking process, together with the air entrainment…
We present results from a systematic numerical study of structural properties of an unforced, incompressible, homogeneous, and isotropic three-dimensional turbulent fluid with an initial energy spectrum that develops a cascade of kinetic…
The behaviour of sports balls during impact defines some special features of each sport. The velocity of the game, the accuracy of passes or shots, the control of the ball direction after impact, the risks of injury, are all set by the…
In most classical fluids, shock waves are strongly dissipative, their energy being quickly lost through viscous damping. But in systems such as cold plasmas, superfluids, and Bose-Einstein condensates, where viscosity is negligible or…
In this work, a higher-order irrotational strain gradient plasticity theory is studied in the small strain regime. A detailed numerical study is based on the problem of simple shear of a non-homogeneous block comprising an elastic-plastic…
This work is concerned with the purely dissipative version of a well-established model of rate-independent strain-gradient plasticity. In the conventional theory of plasticity the approach to determining plastic flow is local, and based on…
In this paper, we study the numerical stabilization of a 1D system of two wave equations coupled by velocities with an internal, local control acting on only one equation. In the theoretical part of this study, we distinguished two cases.…
We revisit the problem of a triad of resonantly interacting nonlinear waves driven by an external force applied to the unstable mode of the triad. The equations are Hamiltonian, and can be reduced to a dynamical system for 5 real variables…
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,…
This paper deals with the energy transport properties of charged particles with time-dependent damping force. Based on the proposed nonlinear dimensionless mapping,the stability and dynamical evolution of the particle system is analyzed…
We analyze a class of linear shell models subject to stochastic forcing in finitely many degrees of freedom. The unforced systems considered formally conserve energy. Despite being formally conservative, we show that these dynamical systems…
We numerically solve the propagation of a shock wave in a chain of elastic beads with no restoring forces under traction (no-tension elasticity). We find a sequence of peaks of decreasing amplitude and velocity. Analyzing the main peak at…
Some dynamical properties present in a problem concerning the acceleration of particles in a wave packet are studied. The dynamics of the model is described in terms of a two-dimensional area preserving map. We show that the phase space is…
Presented here is a study of well-posedness and asymptotic stability of a "degenerately damped" PDE modeling a vibrating elastic string. The coefficient of the damping may vanish at small amplitudes thus weakening the effect of the…
The control of energy dissipation in non-spherical particle contact remains an unresolved problem. Unlike spherical contact, where the interaction reduces to a one-dimensional normal oscillator, both the effective inertia and the effective…
This article is concerned with the energy decay of an infinite memory wave equation with a logarithmic nonlinear term and a frictional damping term. The problem is formulated in a bounded domain in $\mathbb R^d$ ($d\ge3$) with a smooth…
This paper deals with a one-dimensional wave equation with a nonlinear dynamic boundary condition and a Neumann-type boundary control acting on the other extremity. We consider a class of nonlinear stabilizing feedbacks that only depend on…