Hypoelliptic heat kernel inequalities on Lie groups

This paper discusses the existence of gradient estimates for second order hypoelliptic heat kernels on manifolds. It is now standard that such inequalities, in the elliptic case, are equivalent to a lower bound on the Ricci tensor of the Riemannian metric. For hypoelliptic operators, the associated "Ricci curvature" takes on the value -\infty at points of degeneracy of the semi-Riemannian metric associated to the operator. For this reason, the standard proofs for the elliptic theory fail in the hypoelliptic setting. This paper presents recent results for hypoelliptic operators. Malliavin calculus methods transfer the problem to one of determining certain infinite dimensional estimates. Here, the underlying manifold is a Lie group, and the hypoelliptic operators are invariant under left translation. In particular, "L^p-type" gradient estimates hold for p\in(1,\infty), and the p=2 gradient estimate implies a Poincar\'e estimate in this context.Comment: 22 pages, 0 figures; final journal versio

Global Solvability of the Cauchy Problem for the Landau-Lifshitz-Gilbert Equation in Higher Dimensions

We prove existence, uniqueness and asymptotics of global smooth solutions for the Landau-Lifshitz-Gilbert equation in dimension $n \ge 3$, valid under a smallness condition of initial gradients in the $L^n$ norm. The argument is based on the method of moving frames that produces a covariant complex Ginzburg-Landau equation, and a priori estimates that we obtain by the method of weighted-in-time norms as introduced by Fujita and Kato

Heat kernel analysis on semi-infinite Lie groups

This paper studies Brownian motion and heat kernel measure on a class of infinite dimensional Lie groups. We prove a Cameron-Martin type quasi-invariance theorem for the heat kernel measure and give estimates on the $L^p$ norms of the Radon-Nikodym derivatives. We also prove that a logarithmic Sobolev inequality holds in this setting.Comment: 35 page

Electrodynamic induction flowmeter

Device determines velocity and electrical conductivity of a moving fluid of high electrical resistance by imposing a transverse electro-quasistatic field on the fluid. Position changes of charge accumulations induced within the fluid by the field are sensed by relative movement between fluid and sensor

Synchronous charge-constrained electroquasistatic generator

Electroquasistatic generator depends on electroquasistatic interactions to provide synchronous operation. The generator employs a moving insulating belt, with an ac electric potential source to establish positively and negatively charged regions on the belt. The field effect of the charges on the belt creates an ac output voltage

Strong solvability of regularized stochastic Landau-Lifshitz-Gilbert equation

We examine a stochastic Landau-Lifshitz-Gilbert equation based on an exchange energy functional containing second-order derivatives of the unknown field. Such regularizations are featured in advanced micromagnetic models recently introduced in connection with nanoscale topological solitons. We show that, in contrast to the classical stochastic Landau-Lifshitz-Gilbert equation based on the Dirichlet energy alone, the regularized equation is solvable in the stochastically strong sense. As a consequence it preserves the topology of the initial data, almost surely

Small Deviations for Time-Changed Brownian Motions and Applications to Second-Order Chaos

We prove strong small deviations results for Brownian motion under independent time-changes satisfying their own asymptotic criteria. We then apply these results to certain stochastic integrals which are elements of second-order homogeneous chaos.Comment: 23 page

Flexual buckling of structural glass columns. Initial geometrical imperfection as a base for Monte Carlo simulation

In this paper Monte Carlo simulations of structural glass columns are presented. The simulation was performed according to the analytical second order theory of compressed elastic rods. A previous research on shape and size of initial geometrical imperfections is briefly summarized. An experimental analysis of glass columns that were performed for evaluation of equivalent geometrical imperfections is mentioned too