Abstract. We present a solver for the 2D high-frequency Helmholtz equation in heterogeneous, constant density, acoustic media, with online parallel complexity that scales empirically as O(NP ), where N is the number of volume unknowns, and P is the number of processors, as long as P = O(N1/5). This sublinear scaling is achieved by domain decomposition, not distributed linear algebra, and improv...

We show that Fokker-Planck equation for chordal SLE process under a simple rescaling of the probability density can be traced to the minisuperspace Wheeler-de Witt equation for boundary operator in 2d Liouville gravity. Insertion of an operator, calculating SLE critical exponent, corresponds to adding matter contribution to WdW equation. This observation may be useful for understanding of why S...

We study the macroscopic scaling and weak coupling limit for a random Schrödinger equation on Z. We prove that the Wigner transforms of a large class of ”macroscopic” solutions converge in r-th mean to solutions of a linear Boltzmann equation, for any finite value of r ∈ R+. This extends previous results where convergence in expectation was established.

We prove rigorously that the one-particle density matrix of interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of the Gross-Pitaevskii equation in suitable scaling limits. The result is extended to k-particle density matrices for all positive integer k. AMS Classification Number (2000): 35Q55, 81Q15, 81T18, 81V70. Running title: Derivation of Gross-...

We obtain the exact solution for the Burgers equation with a time dependent forcing, which depends linearly on the spatial coordinate. For the case of a stochastic time dependence an exact expression for the joint probability distribution for the velocity fields at multiple spatial points is obtained. A connection with stretched vortices in hydrodynamic flows is discussed. Burgers equation [1],...

Within a phenomenological quasiparticle model, the quark mass and temperature dependence of the QCD equation of state is discussed and compared with lattice QCD results. Different approximations for the quasiparticle dispersion relations are employed, scaling properties of the equation of state with quark mass and deconfinement temperature are investigated and a continuation to asymptotically l...

This paper reviews the recent progress on stochastic PDEs arising from different aspects of the turbulence theory including the stochastic Navier-Stokes equation, stochastic Burgers equation and stochastic passive scalar and passive vector equations. Issues discussed include the existence of invariant measures, scaling of the structure functions, asymptotic behavior of the probability density f...

Based on a recent L-L framework, we establish the acoustic limit of the Boltzmann equation for general collision kernels. The scaling of the fluctuations with respect to Knudsen number is optimal. Our approach is based on a new analysis of the compressible Euler limit of the Boltzmann equation, as well as refined estimates of Euler and acoustic solutions.

We consider the stochastic Swift-Hohenberg equation on a large domain near its change of stability. We show that, under the appropriate scaling, its solutions can be approximated by a periodic wave, which is modulated by the solutions to a stochastic Ginzburg-Landau equation. We then proceed to show that this approximation also extends to the invariant measures of these equations.

An inhomogeneous nonlinear Schrödinger equation is considered, which is invariant under L scaling. The sharp condition for global existence of H solutions is established, involving the L norm of the ground state of the stationary equation. Strong instability of standing waves is proved by constructing self-similar solutions blowing up in finite time.