Related papers: Anisotropic matching principle for the hydrodynami…
Bouncing cosmologies are often proposed as alternatives to standard inflation for the explanation of the homogeneity and flatness of the universe. In such scenarios, the present cosmological expansion is preceded by a contraction phase.…
Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they…
A residual error estimator is proposed for the energy norm of the error for a scalar reaction-diffusion problem and for the monodomain model used in cardiac electrophysiology. The problem is discretized using $P_1$ finite elements in space,…
In this paper, explicit method of constructing approximations (the Triangle Entropy Method) is developed for nonequilibrium problems. This method enables one to treat any complicated nonlinear functionals that fit best the physics of a…
We generalize Einstein's probabilistic method for the Brownian motion to study compressible fluids in porous media. The multi-dimensional case is considered with general probability distribution functions. By relating the expected…
The anisotropy of many one-dimensional and first-order-in-time (T$^1$) scalar wave equations (e.g., Korteweg-de Vries and Camassa-Holm) limits their physical completeness and applicability to bidirectional/high-dimensional systems. We…
A spatially-periodic longitudinal wave is considered in relativistic dissipative hydrodynamics. At sufficiently small wave amplitudes, an analytic solution is obtained in the linearised limit of the macroscopic conservation equations within…
Here we study the wave propagation and stability of general relativistic non-resistive dissipative second-order magnetohydrodynamic equations in curved space-time. We solve the Boltzmann equation for a system of particles and antiparticles…
We formulate spin magnetohydrodynamics (MHD) by including the magnetic-flux and total angular momentum conservation laws in the hydrodynamic framework. To specify the local angular momentum conservation, we choose the totally antisymmetric…
We study the hydrodynamic limit for the isothermal dynamics of an anharmonic chain under hyperbolic space-time scaling and with nonvanishing viscosity. The temperature is kept constant by a contact with a heat bath, realised via a…
The system of our interest is a dilute binary mixture, in which we consider that the species have different temperatures as an initial condition. To study their time evolution, we use the full version of the Boltzmann equation, under the…
Using the conservation laws for charge, energy, momentum, and angular momentum, we derive hydrodynamic equations for the charge density, local temperature, and fluid velocity, as well as for the spin tensor, starting from local equilibrium…
Hydrodynamics can be formulated as the gradient expansion of conserved currents in terms of the fundamental fields describing the near-equilibrium fluid flow. In the relativistic case, the Navier-Stokes equations follow from the…
We show that at any temperature, the low-energy (with respect to the chemical potential) collective excitations of the transverse components of the energy-momentum tensor and the global U(1) current in the field theory dual to the planar…
We consider fixed points of steady solutions and flow directions using the boson Boltzmann equation that is a one-dimensionally reduced kinetic equation after the angular integration. With an elastic collision integral of the two-to-two…
The recently developed framework of anisotropic hydrodynamics is generalized to describe the dynamics of coupled quark and gluon fluids. The quark and gluon components of the fluids are characterized by different dynamical anisotropy…
We establish the hydrodynamic limit of the one-dimensional Boltzmann equation with hard-sphere collisions toward Riemann solutions of the compressible Euler system. The Riemann solutions covered by our result include generic superpositions…
We present the perturbative solution of the multicomponent Boltzmann kinetic equation based on the set of observables including the hydrodynamic velocity and temperature for each component. The solution is obtained by modifying the formal…
In the context of the longitudinally boost-invariant Bjorken flow with transverse expansion, we use three different numerical methods to analyze the emergence of attractor solutions in an ideal gas of massless particles exhibiting constant…
In this paper, around a global smooth irrotational solution to the classical isentropic compressible Euler-Poisson system, we construct classical solutions to the one-species relativistic Vlasov-Maxwell-Boltzmann system on any finite time…