Flows involving Lifshitz solutions

Landau-Lifshitz-Slonczewski Equations: Global Weak and Classical Solutions

We consider magnetization dynamics under the influence of a spin-polarized current, given in terms of a spin-velocity field v, governed by the following modification of the Landau– Lifshitz–Gilbert equation ∂m ∂t + v · ∇m = m × (α ∂m ∂t + β v · ∇m − Δm), called the Landau– Lifshitz–Slonczewski equation. We focus on the situation of magnetizations defined on the entire Euclidean space m(t) : R3 ...

Weak Solutions of the Stochastic Landau-lifshitz-gilbert Equation

Abstract. The Landau-Lifshitz-Gilbert equation perturbed by a multiplicative spacedependent noise is considered for a ferromagnet filling a bounded three-dimensional domain. We show the existence of weak martingale solutions taking values in a sphere S. The regularity of weak solutions is also discussed. Some of the regularity results are new even for the deterministic Landau-Lifshitz-Gilbert e...

Advancements on problems involving maximum flows

Lifshitz holography

In this article we review recent progress on the holographic modelling of field theories with Lifshitz symmetry. We focus in particular on the holographic dictionary for Lifshitz backgrounds the relationship between bulk fields and boundary operators, operator correlation functions and underlying geometrical structure. The holographic dictionary is essential in identifying the universality clas...

Advection-dominated Accretion Flows: Optically Thin Solutions

General properties of advection-dominated accretion ows are discussed. Special emphasis is given to the optically thin branch of solutions, which has very high ion and electron temperatures and is thermally stable. This solution branch has been applied to a number of low-luminosity accreting black holes. The models have resolved some puzzles and have provided a straightforward explanation of th...