We construct strong solutions for a nonlinear wave equation for a thin vibrating plate described by nonlinear elastodynamics. For sufficiently small thickness we obtain existence of strong solutions for large times under appropriate scaling of the initial values such that the limit system as h → 0 is either the nonlinear von Kármán plate equation or the linear fourth order Germain-Lagrange equa...

We consider the non-reactive elastic Boltzmann equation for multicomponent gaseous mixtures. We deduce, under the standard diffusive scaling, that well prepared initial conditions lead to solutions satisfying the Maxwell-Stefan diffusion equations in the vanishing Mach and Knudsen numbers limit.

We study the initial value problem (IVP) associated to some canonical dispersive equations. Our main concern is to establish the minimal regularity property required in the data which guarantees the local well-posedness of the problem. Measuring this regularity in the classical Sobolev spaces, we show ill-posedness results for Sobolev index above the value suggested by the scaling argument.

Data from direct numerical simulations (DNS) of fully-developed turbulent channel flows subjected to a constant surface heat-flux are used to explore the scaling behaviours admitted by the mean thermal energy equation. Following the framework of Wei et al. (2005) [1,2], the analysis employs a theory based on the magnitude ordering of terms in the mean thermal energy equation of wall-bounded tur...

By defining a prepotential function for the stationary Schrödinger equation we derive an inversion formula for the space variable x as a function of the wave–function ψ. The resulting equation is a Legendre transform that relates x, the prepotential F , and the probability density. We invert the Schrödinger equation to a third–order differential equation for F and observe that the inversion pro...

The string equation appearing in the double scaling limit of the Hermitian one–matrix model, which corresponds to a Galilean self–similar condition for the KdV hierarchy, is reformulated as a scaling self–similar condition for the Ur–KdV hierarchy. A non–scaling limit analysis of the one–matrix model has led to the complexified NLS hierarchy and a string equation. We show that this corresponds ...

We present an outline of how the ideas of self-similarity can be applied to wavelet theory, especially in connection to wavelets associated with a multiresolution analysis of R n allowing arbitrary dilation matrices and no restrictions on the number of scaling functions. 1. Introduction Wavelet bases have proved highly useful in many areas of mathematics, science, and engineering. One of the mo...

A statistical mechanical based equation of state has been employed to calculate the liquid density of lead, mercury, bismuth and lead-bismuth and lead-lithium eutectic alloys.The equation is basically that of Song, Mason and Ihm [Ihm G, Song Y, Mason EA. J. Chem. Phys.1991; 94: 3839] which is modified by Ghatee and Boushehri. Three temperature dependent parameters are required to use this e...

We investigate the low-temperature critical behavior of the three dimensional random-field Ising ferromagnet. By a scaling analysis we find that in the limit of temperature T → 0 the usual scaling relations have to be modified as far as the exponent α of the specific heat is concerned. At zero temperature, the Rushbrooke equation is modified to α+2β+γ = 1, an equation which we expect to be vali...