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

Numerical solution of the pressing devices shape optimization problem in the glass industry

Petr Salač (2018)

Applications of Mathematics

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In this contribution, we present the problem of shape optimization of the plunger cooling which comes from the forming process in the glass industry. We look for a shape of the inner surface of the insulation barrier located in the plunger cavity so as to achieve a constant predetermined temperature on the outward surface of the plunger. A rotationally symmetric system, composed of the mould, the glass piece, the plunger, the insulation barrier and the plunger cavity, is considered....

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,...

Closed surfaces with different shapes that are indistinguishable by the SRNF

Eric Klassen, Peter W. Michor (2020)

Archivum Mathematicum

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The Square Root Normal Field (SRNF), introduced by Jermyn et al. in [5], provides a way of representing immersed surfaces in ℝ 3 , and equipping the set of these immersions with a “distance function" (to be precise, a pseudometric) that is easy to compute. Importantly, this distance function is invariant under reparametrizations (i.e., under self-diffeomorphisms of the domain surface) and under rigid motions of ℝ 3 . Thus, it induces a distance function on the shape space of immersions, i.e.,...

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...