We derive an equation for the existence probability Ep for general percolation problem using an analytical argument based on exponential-decay behaviour of spatial correlation function. It is shown that the finite-size scaling function is well approximated by the error function. The present argument explain why it is universal. We use Monte Carlo simulation to calculate Ep for polydisperse cont...

This paper is concerned with the study of solutions to discrete parabolic equations in divergence form with random coefficients, and their convergence to solutions of a homogenized equation. It has previously been shown that if the random environment is translational invariant and ergodic, then solutions of the random equation converge under diffusive scaling to solutions of a homogenized parab...

We derive a mesoscopic description of the behavior of a simple financial market where the agents can create their own portfolio between two investments alternatives: a stock and a bond. The model is derived starting from the Levy-Levy-Solomon microscopic model [13, 14] using the methods of kinetic theory and consists of a linear Boltzmann equation for the wealth distribution of the agents coupl...

Using a code based on the Lattice Boltzmann Equation, we have performed numerical simulations of a turbulent shear flow. We investigate the scaling behaviour of the structure functions in presence of anisotropic homogeneous turbulence, and we show that although Extended Self Similarity does not hold when strong shear effects are present, a more generalized scaling law can still be defined. PACS...

In this paper, we consider the modified quasi-geostrophic equation ∂tθ + (u · ∇) θ + κΛθ = 0 u = Λα−1R⊥θ. with κ > 0, α ∈ (0, 1] and θ0 ∈ L2(R2). We remark that the extra Λα−1 is introduced in order to make the scaling invariance of this system similar to the scaling invariance of the critical quasi-geostrophic equations. In this paper, we use Besov space techniques to prove global existence an...

In this paper, we consider the modified quasi-geostrophic equation ∂tθ + (u · ∇) θ + κΛ θ = 0 u = ΛRθ. with κ > 0, α ∈ (0, 1] and θ0 ∈ L(R). We remark that the extra Λ is introduced in order to make the scaling invariance of this system similar to the scaling invariance of the critical quasi-geostrophic equations. In this paper, we use Besov space techniques to prove global existence and regula...

The present paper establishes the self-averaging, radiative transfer limit for the twofrequency Wigner distribution for random classical waves in the paraxial approximation. Depending on the ratio of the wavelength to the correlation length the limiting equation is either a Boltzmannlike integral equation or a Fokker-Planck-like differential equation in the phase space. When the longitudinal fl...

Starting from the concept of the pseudospinodal, the authors derive an explicit expression for the scaling equation of state applicable to liquid-gas [and universality class (3,1)] systems. The advantages of this equation over other phenomenological equations are: it has no adjustable, unphysical parameters; it is valid in the metastable region; and it can simultaneously predict PVT data and th...

In this paper we study several aspects of solitary wave solutions of the Ostrovsky equation. Using variational methods, we show that as the rotation parameter goes to zero, ground state solitary waves of the Ostrovsky equation converge to solitary waves of the Korteweg-deVries equation. We also investigate the properties of the function d(c) which determines the stability of the ground states. ...

We study turbulence in the one-dimensional Burgers equation with a white-in-time, Gaussian random force that has a Fourier-space spectrum approximately 1/k, where k is the wave number. From very high-resolution numerical simulations, in the limit of vanishing viscosity, we find evidence for multiscaling of velocity structure functions which cannot be falsified by standard tests. We find a new a...