Displaying similar documents to “Ising fog drip: the shallow puddle, o ( N ) deep”

Random hysteresis loops

Gioia Carinci (2013)

Annales de l'I.H.P. Probabilités et statistiques

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Dynamical hysteresis is a phenomenon which arises in ferromagnetic systems below the critical temperature as a response to adiabatic variations of the external magnetic field. We study the problem in the context of the mean-field Ising model with Glauber dynamics, proving that for frequencies of the magnetic field oscillations of order N - 2 / 3 , N the size of the system, the “critical” hysteresis loop becomes random.

Semidirected random polymers: Strong disorder and localization

Nikolaos Zygouras (2010)

Actes des rencontres du CIRM

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Semi-directed, random polymers can be modeled by a simple random walk on Z d in a random potential - ( λ + β ω ( x ) ) x ∈ Z d , where λ > 0 , β > 0 and ω ( x ) x ∈ Z d is a collection of i.i.d., nonnegative random variables. We identify situations where the annealed and quenched costs, that the polymer pays to perform long crossings are different. In these situations we show that the polymer exhibits localization.

Relaxations for Minimizing Metric Distortion and Elastic Energies for 3D Shape Matching

Daniel Cremers, Emanuele Rodolà, Thomas Windheuser (2013)

Actes des rencontres du CIRM

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We present two methods for non-rigid shape matching. Both methods formulate shape matching as an energy minimization problem, where the energy measures distortion of the metric defined on the shapes in one case, or directly describes the physical deformation relating the two shapes in the other case. The first method considers a parametrized relaxation of the widely adopted quadratic assignment problem (QAP) formulation for minimum distortion correspondence between deformable shapes....

Optimization of plunger cavity

Salač, Petr

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In the contribution we present a problem of shape optimization of the cooling cavity of a plunger that is used in the forming process in the glass in dustry. A rotationally symmetric system of the mould, the glass piece, the plunger and the plunger cavity is considered. The state problem is given as a stationary heat conduction process. The system includes a heat source representing the glass piece that is cooled from inside by water flowing through the plunger cavity and from outside...

On two fragmentation schemes with algebraic splitting probability

M. Ghorbel, T. Huillet (2006)

Applicationes Mathematicae

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Consider the following inhomogeneous fragmentation model: suppose an initial particle with mass x₀ ∈ (0,1) undergoes splitting into b > 1 fragments of random sizes with some size-dependent probability p(x₀). With probability 1-p(x₀), this particle is left unchanged forever. Iterate the splitting procedure on each sub-fragment if any, independently. Two cases are considered: the stable and unstable case with p ( x ₀ ) = x ₀ a and p ( x ₀ ) = 1 - x ₀ a respectively, for some a > 0. In the first (resp. second) case,...

Anisotropic functions : a genericity result with crystallographic implications

Victor J. Mizel, Alexander J. Zaslavski (2004)

ESAIM: Control, Optimisation and Calculus of Variations

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In the 1950’s and 1960’s surface physicists/metallurgists such as Herring and Mullins applied ingenious thermodynamic arguments to explain a number of experimentally observed surface phenomena in crystals. These insights permitted the successful engineering of a large number of alloys, where the major mathematical novelty was that the surface response to external stress was anisotropic. By examining step/terrace (vicinal) surface defects it was discovered through lengthy and tedious...

Existence of graphs with sub exponential transitions probability decay and applications

Clément Rau (2010)

Bulletin de la Société Mathématique de France

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In this paper, we recall the existence of graphs with bounded valency such that the simple random walk has a return probability at time n at the origin of order exp ( - n α ) , for fixed α ∈ [ 0 , 1 [ and with Følner function exp ( n 2 α 1 - α ) . This result was proved by Erschler (see [4], [3]); we give a more detailed proof of this construction in the appendix. In the second part, we give an application of the existence of such graphs. We obtain bounds of the correct order for some functional of the local time of a simple random...

A spatial individual-based contact model with age structure

Dominika Jasińska (2017)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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The Markov dynamics of an infinite continuum birth-and-death system of point particles with age is studied. Each particle is characterized by its location x ∈ ℝ d and age a x ≥ 0 . The birth and death rates of a particle are age dependent. The states of the system are described in terms of probability measures on the corresponding configuration space. The exact solution of the  evolution equation for the correlation functions of first and second orders is found.

The magnetization at high temperature for a p-spin interaction model with external field

David Márquez-Carreras (2007)

Applicationes Mathematicae

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This paper is devoted to a detailed and rigorous study of the magnetization at high temperature for a p-spin interaction model with external field, generalizing the Sherrington-Kirkpatrick model. In particular, we prove that ⟨ σ i ⟩ (the mean of a spin with respect to the Gibbs measure) converges to an explicitly given random variable, and that ⟨σ₁⟩,...,⟨σₙ⟩ are asymptotically independent.