Related papers: On the shock change equations
We report on the formation of a dispersive shock wave in a nonlinear optical medium. We monitor the evolution of the shock by tuning the incoming beam power. The experimental observations for the position and intensity of the solitonic edge…
The equations of continuum hydrodynamics can be derived from the Boltzmann equation, which describes rarefied gas dynamics at the kinetic level, by means of the Chapman-Enskog expansion. This expansion assumes a small Knudsen number, and as…
Brenner has recently proposed modifications to the Navier-Stokes equations that are based on theoretical arguments but supported only by experiments having a fairly limited range. These modifications relate to a diffusion of fluid volume…
A new exact solution of the Navier-Stokes equation is derived for the compressible flows which are far from equilibrium in the limit of extremely low shear viscosity and relatively large volume viscosity. The closed description of the…
The new generalized kinetic equation is offered. This equation represents a hybrid Shakhov's equation and ellipsoidal statistical Holway's equation. Equation constants are expressed through such physically significant quantities, as…
We determine the spectrum of particles accelerated at shocks with arbitrary speed and arbitrary scattering properties for different choices of the equation of state of the downstream plasma. More specifically we consider the effect of…
We obtain the full equations of motion for a wide, pivoted, slider bearing. These are used to review the choice of the optimal position for the pivot point, to discuss its response to time-dependent sliding velocity, and to determine the…
We analyze the conservation properties of various discretizations of the system of compressible Euler equations for shock-free flows, with special focus on the treatment of the energy equation and on the induced discrete equations for other…
We consider a general formulation of gradient flow evolution for problems whose natural framework is the one of metric spaces. The applications we deal with are concerned with the evolution of {\it capacitary measures} with respect to the…
This is the first of two papers examining the critical collapse of spherically symmetric perfect fluids with the equation of state P = (Gamma -1)rho. Here we present the equations of motion and describe a computer code capable of simulating…
We consider the Riemann problem of the dilute approximation equations with spatiotemporally dependent volume fractions from the full model of suspension, in which the particles settle to the solid substrate and the clear liquid film flows…
By solving a simple kinetic equation, in the relaxation time approximation, and for a particular set of moments of the distribution function, we establish a set of equations which, on the one hand, capture exactly the dynamics of the…
Partially invariant solution to (2+1)D shallow water equation is constructed and investigated. The solution describes an extension of a stripe, bounded by linear source and drain of fluid. Realizations of smooth flow and of hydraulic jump…
Hydrodynamic equations for ideal incompressible fluid are written in terms of generalized stream function. Two-dimensional version of these equations is transformed to the form of one dynamic equation for the stream function. This equation…
We consider a dilute gas of hard spheres in dimension $d \geq 2$ that upon collision either annihilate with probability $p$ or undergo an elastic scattering with probability $1-p$. For such a system neither mass, momentum, nor kinetic…
In the present work we revisit the shock wave dynamics in a granular chain with precompression. By approximating the model by an $\alpha$-Fermi-Pasta-Ulam-Tsingou chain, we leverage the connection of the latter in the strain variable…
The hydrodynamic equations for a model of a confined quasi-two-dimensional gas of smooth inelastic hard spheres are derived from the Boltzmann equation for the model, using a generalization of the Chapman-Enskog method. The heat and…
Smoothed Particle Hydrodynamics is reformulated in terms of the convolution of the original hydrodynamics equations, and the new evolution equations for the particles are derived. The same evolution equation of motion is also derived using…
In shockwave theory, the density, velocity and pressure jumps are derived from the conservation equations. Here, we address the physics of a weak shock the other way around. We first show that the density profile of a weak shockwave in a…
Smoke circle vortexes are a typical dynamic phenomenon in nature. The similar circle vortexes phenomenon appears in hurricane, turbulence, and many others. A semi-empirical method is constructed to get some intrinsic understanding about…