Surface Tension in Kac Glass Models

In this paper we study a distance-dependent surface tension, defined as the free-energy cost to put metastable states at a given distance. This will be done in the framework of a disordered microscopic model with Kac interactions that can be solved in the mean-field limit.Comment: 13 pages, 6 figure

Tracking Polar Mesospheric Clouds Using Unbinned Correlation Methods

We are experimenting with a correlation method that allows us to cross-correlate images that have geolocated pixels without having to bin the pixels and lose resolution. In addition to preserving resolution, this correlation method also allows us to perform transformations on the images that would be difficult to perform with other correlation methods. We are working on this correlation method in order to use cross-correlations to track polar mesospheric clouds (PMCs) using the data from the Cloud Imaging and Particle Size (CIPS) instrument on the Aeronomy of Ice in the Mesosphere (AIM) satellite

Metastable States, Relaxation Times and Free-energy Barriers in Finite Dimensional Glassy Systems

In this note we discuss metastability in a long-but-finite range disordered model for the glass transition. We show that relaxation is dominated by configuration belonging to metastable states and associate an in principle computable free-energy barrier to the equilibrium relaxation time. Adam-Gibbs like relaxation times appear naturally in this approach.Comment: 4 pages, 2 figures. Typos correcte

Analytic determination of dynamical and mosaic length scales in a Kac glass model

We consider a disordered spin model with multi-spin interactions undergoing a glass transition. We introduce a dynamic and a static length scales and compute them in the Kac limit (long--but--finite range interactions). They diverge at the dynamic and static phase transition with exponents (respectively) -1/4 and -1. The two length scales are approximately equal well above the mode coupling transition. Their discrepancy increases rapidly as this transition is approached. We argue that this signals a crossover from mode coupling to activated dynamics.Comment: 4 pages, 4 eps figures. New version conform to the published on

First steps of a nucleation theory in disordered systems

We devise a field theoretical formalism for a microscopic theory of nucleation processes and phase coexistence in finite dimensional glassy systems. We study disordered $p$-spin models with large but finite range of interaction. We work in the framework of glassy effective potential theory which in mean-field is a non-convex, two minima function of the overlap. We will associate metastability and phase coexistence with the existence of space inhomogeneous solution of suitable field equations and we will study the simplest of such solutions.Comment: 31 pages, 4 figures. Content revised, typos correcte

A note on the Guerra and Talagrand theorems for Mean Field Spin Glasses: the simple case of spherical models

The aim of this paper is to discuss the main ideas of the Talagrand proof of the Parisi Ansatz for the free-energy of Mean Field Spin Glasses with a physicist's approach. We consider the case of the spherical $p$-spin model, which has the following advantages: 1) the Parisi Ansatz takes the simple ``one step replica symmetry breaking form'', 2) the replica free-energy as a function of the order parameters is simple enough to allow for numerical maximization with arbitrary precision. We present the essential ideas of the proof, we stress its connections with the theory of effective potentials for glassy systems, and we reduce the technically more difficult part of the Talagrand's analysis to an explicit evaluation of the solution of a variational problem.Comment: 20 pages, 5 figures. Added references and minor language correction

Uncertainty Quantification for Linear Hyperbolic Equations with Stochastic Process or Random Field Coefficients

In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media. Two types of models are presented: The first has a time-dependent coefficient modeled by the Ornstein--Uhlenbeck process. The second has a random field coefficient with a given covariance in space. For the former a formula for the exact solution in terms of moments is derived. In both cases stable numerical schemes are introduced to solve these random partial differential equations. Simulation results including convergence studies conclude the theoretical findings

Vortices in Quantum Spin Systems

We examine spin vortices in ferromagnetic quantum Heisenberg models with planar anisotropy on two-dimensional lattices. The symmetry properties and the time evolution of vortices built up from spin-coherent states are studied in detail. Although these states show a dispersion typical for wave packets, important features of classical vortices are conserved. Moreover, the results on symmetry properties provide a construction scheme for vortex-like excitations from exact eigenstates, which have a well-controlled time evolution. Our approach works for arbitrary spin length both on triangular and square lattices.Comment: Remarks added and conclusions enlarged, version to be published in European Physical Journal