One-dimensional three-body Schrödinger equation is studied, with binding mediated by the power-law two-body long-range attraction V (x) = αx in superposition with a short-range repulsion V (x) = β/x (plus, possibly, further subdominant power-law components). Such an unsolvable and non-separable generalization of Calogero model (where one had L = K = 2) is shown to become separable and solvable ...

We study the first passage time (FPT) problem in Levy type of anomalous diffusion. Using the recently formulated fractional Fokker-Planck equation, we obtain an analytic expression for the FPT distribution which, in the large passage time limit, is characterized by a universal power law. Contrasting this power law with the asymptotic FPT distribution from another type of anomalous diffusion exe...

Fractional wave equations with attenuation have been proposed by Caputo [5], Szabo [27], Chen and Holm [7], and Kelly et al. [11]. These equations capture the power-law attenuation with frequency observed in many experimental settings when sound waves travel through inhomogeneous media. In particular, these models are useful for medical ultrasound. This paper develops stochastic solutions and w...

The migration of melt through the mantle of the Earth is governed by a third-order nonlinear partial differential equation for the voidage or volume fraction of melt. The partial differential equation depends on the permeability of the medium which is assumed to be a function of the voidage. It is shown that the partial differential equation admits, as well as translations in time and space, ot...

in this paper, the transient inertial viscoelastic flow around a circular cylinder is investigated numerically. a second order finite-volume method is used to increase the numerical accuracy. here, the giesekus model is used as the constitutive equation. this nonlinear model has prominent ability in describing normal stress differences and viscosity in power-law regions. the impacts of the elas...

In this paper the similarity solutions of the Prandtl boundary layer equations describing a nonNewtonian power law fluid past an impermeable flat plate, driven by a power law velocity profile ) 0 ( > = B By U σ have been investigated. It is shown that there are analytical solutions for any 2 , 0 ≠ > n n and any 0 2 / 1 < ≤ − σ . We give a method for the determination of the power series solutio...

We present a numerical study of a derivative nonlinear Schrödinger equation with a general power nonlinearity, |ψ| ψx. In the L-supercritical regime, σ > 1, our simulations indicate that there is a finite time singularity. We obtain a precise description of the local structure of the solution in terms of blowup rate and asymptotic profile, in a form similar to that of the nonlinear Schrödinger ...

A constitutive law for rock behaviors including the brittle, transient and steady-state behaviors is derived to recognize the temporal seismicity patterns on surface displacement or prior and subsequent to mainshocks, and formulated as the relaxation modulus (i.e., the ratio of stress to strain) following a temporal power-law relaxation. This constitutive law is transformable into the empirical...

Starting from a master equation, we derive the evolution equation for the size distribution of elements in an evolving system, where each element can grow, divide into two, and produce new elements. We then probe general solutions of the evolution equation, to obtain such skew distributions as power-law, log-normal, and Weibull distributions, depending on the growth or division and production. ...

Frequency-dependent attenuation typically obeys an empirical power law with an exponent ranging from 0 to 2. The standard time-domain partial differential equation models can describe merely two extreme cases of frequency-independent and frequency-squared dependent attenuations. The otherwise nonzero and nonsquare frequency dependency occurring in many cases of practical interest is thus often ...