We investigate a multidimensional nonisentropic radiation hydrodynamics model. We study the local existence and the convergence of the nonisentropic radiation hydrodynamics equations via the non-relativistic limit. The local existence of smooth solutions to both systems is obtained. For well-prepared initial data, the convergence of the limit is rigorously justified by an analysis of asymptotic...

We present theoretical predictions for the equation of state of a harmonically trapped Fermi gas in the unitary limit. Our calculations compare Monte Carlo results with the equation of state of a uniform gas using three distinct perturbation schemes. We show that in experiments the temperature can be usefully calibrated by making use of the entropy, which is invariant during an adiabatic conver...

Let P be a packing of balls in Euclidean space E" having the property that the radius of every ball of P lies in the interval [l//c, k]. If G is a Schottky group associated to P , then the Hausdorff dimension of the topological limit set of G is less than a uniform constant C(k, n) < n. In particular, this limit set has zero volume.

We study the inviscid limit of the free boundary Navier-Stokes equations. We prove the existence of solutions on a uniform time interval by using a suitable functional framework based on Sobolev conormal spaces. This allows us to use a strong compactness argument to justify the inviscid limit. Our approach does not rely on the justification of asymptotic expansions. In particular, we get a new ...

We have searched the 1st-year WMAP W-Band CMB anisotropy map for evidence of cosmic strings. We have set a limit of δ = 8πGμ/c < 8.2× 10 at 95% CL for statistical search for a significant number of strings in the map. We also have set a limit using the uniform distribution of strings model in the WMAP data with δ = 8πGμ/c < 7.34 × 10 at 95% CL. And the pattern search technique we developed here...

Recent work on optimization problems in random link models has verified several conjectures originating in statistical physics and the replica and cavity methods. In particular the numerical value 2.0415 for the limit length of a traveling salesman tour in a complete graph with uniform [0, 1] edge lengths has been established. In this paper we show that the crucial integral equation obtained wi...

We work out a graph limit theory for dense interval graphs. The theory developed departs from the usual description of a graph limit as a symmetric function W (x, y) on the unit square, with x and y uniform on the interval (0, 1). Instead, we fix a W and change the underlying distribution of the coordinates x and y. We find choices such that our limits are continuous. Connections to random inte...

We give an expression for the most general input-output map associated with the members of a certain important large family of causal time-invariant linear systems. This expression is a uniform limit of a convolution. We also give a necessary and sufficient condition under which the limit can be written as a convolution, and we relate this to the concepts of an impulse response and a q-response...

We prove global existence and stability of solution to the mass-critical stochastic nonlinear Schr\"odinger equation in $d=1$ at $L^2$ regularity. Our construction starts with truncated subcritical problem. With presence truncation, we construct critical as limit solutions. then obtain uniform bounds on solutions problems that allow us remove truncation limit.

We apply the dynamical approach to the study of the second order semilinear elliptic boundary value problem in a cylindrical domain with a small parameter ε at the second derivative with respect to the variable t corresponding to the axis of the cylinder. We prove that, under natural assumptions on the nonlinear interaction function f and the external forces g(t), this problem possesses the uni...