Related papers: Propagation of a Three-dimensional Weak Shock Fron…
Media composed of colliding hard disks (2D) or hard spheres (3D) serve as good approximations for the collective hydrodynamic description of gases, liquids and granular media. In the present study, the compressible hydrodynamics and shock…
We study the propagation of tension caused by an external force along a long polymeric molecule in two different settings, namely along a free polymer in 3d space being pulled from one end, and along a pre-stretched circular polymer,…
We address the problem of a front propagation in chains with a bi-stable nondegenerate on-site potential and a nonlinear gradient coupling. For a generic nonlinear coupling, one encounters a special regime of transitions, characterized by…
We show the necessity for a new approach towards comprehensive and consistent simulations of the propagation of galactic cosmic rays. Our developments are optimised for addressing the spatially 3-dimensional inhomogeneous diffusion problem…
The core focus of this research work is to obtain invariant solutions and conservation laws of the (3+1)-dimensional ZK equation, a higher-dimensional generalization of the Korteweg--de Vries (KdV) equation, which describes the phenomenon…
We establish local-in-time existence and uniqueness results for nonlocal conservation laws with a nonlinear mobility, in several space dimensions, under weak assumptions on the kernel, which is assumed to be bounded and of finite total…
A universal KP-like equation in 2+1 dimensions, which models general nonlinear wave phenomena exhibiting p-power nonlinearity, dispersion, and small transversality, is studied. Special cases include the integrable KP…
When a magnetised, thermal plasma containing a shock wave efficiently accelerates Cosmic Rays (CR) a reaction is exerted on the fluid structure. The simplest description of this process involves three conservation equations for the…
The complex interaction between shocks and plasma turbulence is extremely important to address crucial features of energy conversion in a broad range of astrophysical systems. We study the interaction between a supercritical, perpendicular…
Size-dependence of energy transport and the effects of reduced dimensionality on transport coefficients are of key importance for understanding nonequilibrium properties of matter on the nanoscale. Here, we perform nonequilibrium and…
We propose to use spin hydrodynamics, a two-fluid model of spin propagation, as a generalization of the diffusion equation. We show that in the dense limit spin hydrodynamics reduces to Fick's law and the diffusion equation. In the opposite…
Context: Cosmic ray acceleration in galaxy clusters is still an ongoing puzzle, with relativistic electrons forming radio relics at merger shocks and emitting synchrotron radiation. In the present work we perform hybrid-kinetic simulations…
Particles in turbulence live complicated lives. It is nonetheless sometimes possible to find order in this complexity. It was proposed in [Falkovich et al., Phys. Rev. Lett. 110, 214502 (2013)] that pairs of Lagrangian tracers at small…
The outward propagation of asymmetries introduced to originally axisymmetric turbulent flows is investigated, where 3D Batchelor vortices at high Reynolds numbers and with arbitrary swirl numbers are chosen as test cases. It is well known…
A thermomechanical, polar continuum formulation under finite strains is proposed for anisotropic materials using a multiplicative decomposition of the deformation gradient. First, the kinematics and conservation laws for three dimensional,…
We present and discuss a novel approach to deal with conservation properties for the simulation of nonlinear complex porous media flows in the presence of: 1) multiscale heterogeneity structures appearing in the elliptic-pressure-velocity…
We have used kinetic Monte Carlo (kMC) simulations of a lattice gas to study front fluctuations in the spreading of a non-volatile liquid droplet onto a solid substrate. Our results are consistent with a diffusive growth law for the radius…
We describe $\delta$ shock wave arising from continuous initial data in the case of triangular conservation law system arising from "generalized pressureless gas dynamics model". We use the weak asymptotic method.
We address the theory of quasi-static crack propagation in a strip of glass that is pulled from a hot oven towards a cold bath. This problem had been carefully studied in a number of experiments that offer a wealth of data to challenge the…
Crack front waves (FWs) are dynamic objects that propagate along moving crack fronts in 3D materials. We study FW dynamics in the framework of a 3D phase-field framework that features a rate-dependent fracture energy $\Gamma(v)$ ($v$ is the…