Related papers: Third order quasi-compact schemes for space temper…
The mathematical theory of a novel variational approximation scheme for general second and fourth order partial differential equations \begin{equation}\label{eq: A} \partial_t u - \nabla\cdot\Big(u\nabla\frac{\delta\phi}{\delta…
We study a turbulence closure model in which the fractional Laplacian $(-\Delta)^\alpha$ of the velocity field represents the turbulence diffusivity. We investigate the energy spectrum of the model by applying Pao's energy transfer theory.…
An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…
The tempered evolution equation describes the trapped dynamics, widely appearing in nature, e.g., the motion of living particles in viscous liquid. This paper proposes the fast predictor-corrector approach for the tempered fractional…
We investigate the role of the form of the spatial diffusion coefficient in shock acceleration of fast particles. Referring to non-classical diffusion and using the results of numerical (hybrid) simulations tailored for the downstream shock…
We propose a unified method for the large space-time scaling limit of \emph{linear} collisional kinetic equations in the whole space. The limit is of \emph{fractional} diffusion type for heavy tail equilibria with slow enough decay, and of…
Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. In this work we introduce a new fractional operator…
In the continuous time random walk model, the time-fractional operator usually expresses an infinite waiting time probability density. Different from that usual setting, this work considers the tempered time-fractional operator, which…
We conduct numerical experiments to determine the density probability distribution function (PDF) produced in supersonic, isothermal, self-gravitating turbulence of the sort that is ubiquitous in star-forming molecular clouds. Our…
A consolidated mathematical formulation of the spherically symmetric mass-transfer problem is presented, with the quasi-stationary approximating equations derived from a perturbation point of view for the leading-order effect. For the…
Using classical density functional theory (DFT) in a modified mean-field approximation we investigate the fluid phase behavior of quasi-two dimensional dipolar fluids confined to a plane. The particles carry three-dimensional dipole moments…
We extend the Wigner-Weyl-Moyal phase-space formulation of quantum mechanics to general curved configuration spaces. The underlying phase space is based on the chosen coordinates of the manifold and their canonically conjugate momenta. The…
In this paper, we provide closed form expressions for the probability density functions (PDF) of the interference power in a network whose transmitters are arranged according to the Poisson Point Process (PPP). These expressions apply for…
The Gaussian Wave-Packet phase-space representation is used to show that the expansion in powers of $\hbar$ of the quantum Liouville propagator leads, in the zeroth order term, to results close to those obtained in the statistical…
We start with a general governing equation for diffusion transport, written in a conserved form, in which the phenomenological flux laws can be constructed in a number of alternative ways. We pay particular attention to flux laws that can…
This paper outlines an approach to the approximation of probability density functions by quadratic forms of weighted orthonormal basis functions with positive semi-definite Hermitian matrices of unit trace. Such matrices are called…
Structure-induced features of the wave functions for the quantum systems on complex networks are discussed in this paper. For a quantum system on a network, the state corresponding to the eigenvalue close to the center of the spectrum is…
By means of the multifractal analysis (MFA), the expressions of the probability density functions (PDFs) are unified in a compact analytical formula which is valid for various quantities in turbulence. It is shown that the formula can…
In this paper, we develop a numerical method for the L\'evy-Fokker-Planck equation with the fractional diffusive scaling. There are two main challenges. One comes from a two-fold nonlocality, that is, the need to apply the fractional…
Steady state distribution functions can be used to calculate stability conditions for modes, radiation energy losses, and particle loss rates. Heuristic analytic approximations to these distributions can capture key behaviors of the true…