We study a new class of kinetic equations describing nonequilibrium macroscopic dynamics of soliton gases with elastic collisions. These equations represent nonlinear integro-differential systems and have a novel structure, which we investigate by studying in detail the class of N -component ‘cold-gas’ hydrodynamic reductions. We prove that these reductions represent integrable linearly degener...

We review recent developments in the rigorous derivation of hydrodynamic-type macroscopic equations from simple microscopic models: continuous time stochastic cellular automata. The deterministic evolution of hydrodynamic variables emerges as the "law of large numbe~s," which holds with probability one in the limit in which the ratio of the microscopic to the macroscopic spatial and temporal sc...

in this study, liquid-liquid extraction process in a kuhni extraction column was modeled and simulated. a non-equilibrium dynamic model was developed for modeling liquid-liquid extraction processes based on a rate-based model. the model equations are inclusive of partial and ordinary differential equations which were discretized in column height direction. the population balance model was used ...

in this study, a method which is based on the integration of navier-stokes and continuity equations has been used to develop the governing equations. in these equations the coriolis acceleration and the effect of wind also have been considered. the main application of the model is to solve two dimensional problems with free surface in the plane. the offshore engineering projects and the hydrody...

We present the hydrodynamic and electrohydrodynamic equations for the liquid

We present a new hydrodynamic model for the interactions between collision-free Cucker–Smale flocking particles and a viscous incompressible fluid. Our proposed model consists of two hydrodynamic models. For the Cucker–Smale flocking particles, we employ the pressureless Euler system with a non-local flocking dissipation, whereas for the fluid, we use the incompressible Navier–Stokes equations....

Thermodynamic fluctuations are significant at microscopic scales even when hydrodynamic transport models (i.e., Navier-Stokes equations) are still accurate; a well-known example is Rayleigh scattering, which makes the sky blue. Interesting phenomena also appear in non-equilibrium systems, such as the enhancement of diffusion during mixing due to the correlation of velocity and concentration flu...

Hydrodynamic type systems are systems of quasilinear equations of the first order. They naturally arise in continuum mechanics but also occur as a result of semi-classical approximations of nonlinear dispersive waves. The mathematical theory of one-dimensional hyperbolic quasilinear equations initiated by B. Riemann in XIX century has been developed into a rich and diverse area of applied mathe...

The convective hydrodynamic model of semiconductor devices is analyzed employing parallel and stabilized finite element methods. The stabilized finite element method for the two-carrier hydrodynamic equations and the parallel computational model are briefly described. Numerical results are shown for a bipolar transistor. A comparison of drift-diffusion, energy-transport and the hydrodynamic mod...

We study collisions between two strongly interacting atomic Fermi gas clouds. We observe exotic nonlinear hydrodynamic behavior, distinguished by the formation of a very sharp and stable density peak as the clouds collide and subsequent evolution into a boxlike shape. We model the nonlinear dynamics of these collisions by using quasi-1D hydrodynamic equations. Our simulations of the time-depend...