Related papers: Microscopic shape of shocks in a domain growth mod…
This work is devoted to the study of the decay of multiscale deterministic solutions of the unforced Burgers' equation in the limit of vanishing viscosity. A deterministic model of turbulence-like evolution is considered. We con- struct the…
Energy spectrum of turbulent fluids exhibit a bump at an intermediate wavenumber, between the inertial and the dissipation range. This bump is called bottleneck. Such bottlenecks are also seen in the energy spectrum of the solutions of…
We present an analysis of stationary discrete shock profiles for a discontinuous Galerkin method approximating scalar nonlinear hyperbolic conservation laws with a convex flux. Using the Godunov method for the numerical flux, we…
This paper proves the existence of unstable shocks of the Burgers-Hilbert equation conjectured in arXiv:2006.05568. More precisely, we construct smooth initial data with finite $H^9$-norm such that the solution in self-similar coordinates…
The approach of nonequilibrium evolution thermodynamics earlier offered is developed. It helps to describe the processes of defect formation within the adiabatic approximation. The basic equations system depends on the initial defects…
This paper discusses aspects of the second order hyperbolic partial differential equation associated with the ideal lossless string under tension and it's relationship to two discrete models. These models are finite differencing in the time…
Recent work on stochastic interacting particle systems with two particle species (or single-species systems with kinematic constraints) has demonstrated the existence of spontaneous symmetry breaking, long-range order and phase coexistence…
Hall-MHD is a mixed hyperbolic-parabolic partial differential equation that describes the dynamics of an ideal two fluid plasma with massless electrons. We study the only shock wave family that exists in this system (the other…
We provide a `user guide' to the literature of the past twenty years concerning the modeling and approximation of discontinuous solutions to nonlinear hyperbolic systems that admit small-scale dependent shock waves. We cover several classes…
The memory effects on microscopic kinetic systems have been sometimes modelled by means of the introduction of second order time derivatives in the macroscopic hydrodynamic equations. One prototypical example is the hyperbolic modification…
We analyze the field theory of fully developed Burgers turbulence. Its key elements are shock fields, which characterize the singularity statistics of the velocity field. The shock fields enter an operator product expansion describing…
Dynamic response of the one-dimensional viscoelastic rod of finite length, that has one end fixed and the other subject to prescribed either displacement or stress, is analyzed by the analytical means of Laplace transform, yielding the…
In this mini-review we summarize the progress of modeling, simulation and analysis of shock responses of heterogeneous materials in our group in recent years. The basic methodology is as below. We first decompose the problem into different…
Ductile damage models and cohesive laws incorporate the material plasticity entailing the growth of irrecoverable deformations even after complete failure. This unrealistic growth remains concealed until the unilateral effects arising from…
The peridynamic model of a solid does not involve spatial gradients of the displacement field and is therefore well suited for studying defect propagation. Here, bond-based peridynamic theory is used to study the equilibrium and steady…
We analyze the relationship between the lowest energy configurations of an infinite harmonic chain of particles in a periodic potential and the evolution of characteristics in a periodically-forced inviscid Burgers equation. The shock…
The mesoscopic concept is a way to deal with complex materials with an internal structure within continuum mechanics. It consists of extending the domain of the balance equations by mesoscopic variables and of introducing a local…
We are interested in the numerical approximation of discontinuous solutions in non conservative hyperbolic systems. An extension to second-order of a new strategy based on in-cell discontinuous reconstructions to deal with this challenging…
We consider atomistic systems consisting of interacting particles arranged in atomic lattices whose quasi-static evolution is driven by time-dependent boundary conditions. The interaction of the particles is modeled by classical interaction…
We present a linear dispersive partial differential equation which manifests a number of qualitative features of dispersive shocks, typically thought to occur only in nonlinear models. The model captures much of the short time phenomenon…