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This study presents an extension of the corrected Smagorinsky model, incorporating advanced techniques for error estimation and regularity analysis of far-from-equilibrium turbulent flows. A new formulation that increases the model's…
We derive the transport coefficients of second-order fluid dynamics with $14$ dynamical moments using the method of moments and the Chapman-Enskog method in the relaxation-time approximation for the collision integral of the relativistic…
We investigate a second-order accurate time-stepping scheme for solving a time-fractional diffusion equation with a Caputo derivative of order~$\alpha \in (0,1)$. The basic idea of our scheme is based on local integration followed by linear…
In this paper we provide a detailed convergence analysis for an unconditionally energy stable, second-order accurate convex splitting scheme for the Modified Phase Field Crystal equation, a generalized damped wave equation for which the…
We have studied self-conjugate second-order equations with spinor wavefunctions for fermions moving in an external Coulomb field. For stationary states, the equations are characterized by separated states with positive and negative…
The classical Kramers problem of the kinetic theory is analytically solved. The Kramers problem about isothermal sliding for quantum Fermi gases is considered. Quantum gases with the velocity-dependent collision frequency are considered.…
The diffusive transport in two-dimensional incompressible turbulent fields is investigated with the aid of high-quality direct numerical simulations. Three classes of turbulence spectra that are able to capture both short and long-range…
We derive the maximum accelerated particle energy from first-order and second-order Fermi acceleration at nonrelativistic and relativistic shocks for explosions taking place in a uniform surrounding medium. Second-order stochastic processes…
We give a detailed derivation of the second-order (local) hydrodynamics for Boltzmann equation with an external force by using the renormalization group method. In this method, we solve the Boltzmann equation faithfully to extract the…
Langevin simulation provides an effective way to study collisional effects in beams by reducing the six-dimensional Fokker-Planck equation to a group of stochastic ordinary differential equations. These resulting equations usually have…
We derive the hydrodynamic limit of a kinetic equation where the interactions in velocity are modelled by a linear operator (Fokker-Planck or Linear Boltzmann) and the force in the Vlasov term is a stochastic process with high amplitude and…
Our Recent advancements in stochastic processes have illuminated a paradox associated with the Einstein model of Brownian motion. The model predicts an infinite propagation speed, conflicting with the second law of thermodynamics. The…
We sample a velocity field that has an inertial spectrum and a skewness that matches experimental data. In particular, we compute a self-consistent correction to the Kolmogorov exponent and find that for our model it is zero. We find that…
Space fractional convection diffusion equation describes physical phenomena where particles or energy (or other physical quantities) are transferred inside a physical system due to two processes: convection and superdiffusion. In this…
Exploiting a Lagrangian strategy we present a numerical study for both perturbative and nonperturbative regions of the Kraichnan advection model. The major result is the numerical assessment of the first-order $1/d$-expansion by M.…
We discuss the phenomenon of energization of relativistic charged particles in three-dimensional (3D) incompressible MHD turbulence and the diffusive properties of the motion of the same particles. We show that the random electric field…
We establish long-time and large-data existence of a suitable weak solution to three-dimensional internal unsteady flows described by Kolmogorov's two-equation model of turbulence. The governing system of equations is completed by initial…
Hyperbolic conservation laws with stiff source terms appear in the study of a variety of physical systems. Early work showed that the use of formally second-order accurate semi-implicit methods could lead to a substantial loss of accuracy,…
We theoretically explore key concepts of two-dimensional turbulence in a homogeneous compressible superfluid described by a dissipative two-dimensional Gross-Pitaeveskii equation. Such a fluid supports quantized vortices that have a size…
The stochastic properties of a Langevin-type Markov process can be extracted from a given time series by a Markov analysis. Also processes that obey a stochastically forced second order differential equation can be analyzed this way by…