We prove the appearance of an explicit lower bound on the solution to the full Boltzmann equation in the torus for a broad family of collision kernels including in particular long-range interaction models, under the assumption of some uniform bounds on some hydrodynamic quantities. This lower bound is independent of time and space. When the collision kernel satisfies Grad’s cutoff assumption, t...

We study a family of classical string solutions with large spins on Rt×S subspace of AdS5×S background. These solutions are related to Complex sine-Gordon solitons via Pohlmeyer’s reduction. The equations of motion for the classical strings are cast into Lamé equations and Complex sine-Gordon equations. We solve them under periodic boundary conditions, and obtain analytic profiles for the close...

A stochastic Navier–Stokes equation with space-time Gaussian white noise is considered, having as infinitesimal invariant measure a Gaussian measure µν whose covariance is given in terms of the enstrophy. Pathwise uniqueness for µν-a.e. initial velocity is proven for solutions having µν as invariant measure. 1. Introduction. We are interested in the stochastic Navier–Stokes equation with a spac...

We investigate various boundary conditions in two dimensional turbulence systematically in the context of conformal field theory. Keeping the conformal invariance, we can either change the shape of boundaries through finite conformal transformations, or insert boundary operators so as to handle more general cases. Effects of such operations will be reflected in physically measurable quantities ...

The numerical approximation scheme for solving the nonlinear initial value problem ∂tb(v) = ∂xxβ(x, v) + β(x, v) with periodic boundary conditions is presented. Local existence and uniqueness of a solution and convergence of approximations is a consequence of the results of Mikula and Kačur (1996), where the anisotropic curvature driven evolution of plane convex curves is studied. The considere...

Peskin’s Immersed Boundary (IB) method is one of the most popular numerical methods for many years and has been applied to problems in mathematical biology, fluid mechanics, material sciences, and many other areas. Peskin’s IB method is associated with discrete delta functions. It is believed that the IB method is first order accurate in the L∞ norm. But almost none rigorous proof could be foun...

The generation of primate smooth pursuit eye movements involves two processes. One process transforms the direction and speed of target motion into a motor command and the other regulates the strength, or "gain," of the visual-motor transformation. We have conducted a behavioral analysis to identify the signals that modulate the internal gain of pursuit. To test whether the modulatory signals a...

Equations that follow from the Navier-Stokes equation and incompressibility but with no other approximations are “exact.”. Exact equations relating secondand third-order structure functions are studied, as is an exact incompressibility condition on the second-order velocity structure function. Opportunities for investigations using these equations are discussed. Precisely defined averaging oper...

A large number of di erential equation problems which admit traveling waves have very large (typically in nite) naturally de ned domains, with boundary conditions de ned at the domain boundary. To be able to numerically solve these problems in smaller subdomains of the original domain, arti cial boundary conditions must be de ned for these subdomains. One such arti cal boundaryconditionswhich c...