In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist. The diffusion equations and their data are derived from asymptotic and layer analysis which allows general scattering kernels and general data. We apply the ha...

The scaling limit for a class of interacting superprocesses and the associated singular, degenerate stochastic partial differential equation (SDSPDE) are investigated. It is proved that the scaling limit is a coalescing, purely-atomic-measure-valued process which is the unique strong solution of a reconstructed, associated SDSPDE.

Between 0.65 K and 3.2 K, the temperature dependence of the vapor pressure P of 3He is defined by the International Temperature Scale of 1990 (ITS-90). However, the ITS-90 vapor pressure equation was not designed to be consistent with the scaling law required for the second temperature derivative of the vapor pressure in the vicinity of the liquid-vapor critical point. In this paper, two scalin...

We demonstrate a scaling method for non-Markovian Monte Carlo wave-function simulations used to study open quantum systems weakly coupled to their environments. We derive a scaling equation, from which the result for the expectation values of arbitrary operators of interest can be calculated, all the quantities in the equation being easily obtainable from the scaled Monte Carlo wave-function si...

We study the catastrophic stationary self-focusing (collapse) of a laser beam in nonlinear Kerr media. The width of self-similar solutions near the collapse distance z = zc obeys the (zc − z)1/2 scaling law with the well-known leading-order modification of loglog type ∝ (ln | ln(zc − z)|)−1/2. We show that the validity of the loglog modification requires double-exponentially large amplitudes of...

This study makes the first attempt to use the 2/3-order fractional Laplacian modeling of Kolmogorov -5/3 scaling of fully developed turbulence and enhanced diffusing movements of random turbulent particles. A combined effect of inertial interactions induced diffusivity and the molecular Brownian diffusivity is considered the bi-fractal mechanism behind multifractal scaling of moderate Reynolds ...

We study an improved three-dimensional Ising model with external magnetic field near the critical point by Monte Carlo simulations. From our data we determine numerically the universal scaling function of the magnetization, that is the equation of state. For the purpose of normalization of the scaling function we calculate the critical amplitudes of the magnetization and of the susceptibility o...

We present a review of the Symmetric Unitary One Matrix Models. In particular we compute the scaling operators in the double scaling limit and the corresponding mKdV ows. We brieey discuss the computation of the space of solutions to the string equation as a subspace of Gr (0)

Statistical properties of evolving random graphs are analyzed using kinetic theory. Treating the linking process dynamically, structural characteristics of links, paths, cycles, and components are obtained analytically using the rate equation approach. Scaling laws for finite systems are derived using extreme statistics and scaling arguments.

From the available literature, the allometric scaling laws generally exist in biology, ecology, etc. These scaling laws obey power law distributions. A possibly better approach to characterize the power law is to utilize fractional derivatives. In this paper, we establish a fractional differential equation model for this allometry by using the Caputo fractional derivatives.