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A stochastic phase-field model determined from molecular dynamics

Erik von Schwerin, Anders Szepessy (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

The dynamics of dendritic growth of a crystal in an undercooled melt is determined by macroscopic diffusion-convection of heat and by capillary forces acting on the nanometer scale of the solid-liquid interface width. Its modelling is useful for instance in processing techniques based on casting. The phase-field method is widely used to study evolution of such microstructural phase transformations on a continuum level; it couples the energy equation to a phenomenological Allen-Cahn/Ginzburg-Landau equation...

A stochastic symbiosis model with degenerate diffusion process

Urszula Skwara (2010)

Annales Polonici Mathematici

We present a model of symbiosis given by a system of stochastic differential equations. We consider a situation when the same factor influences both populations or only one population is stochastically perturbed. We analyse the long-time behaviour of the solutions and prove the asymptoptic stability of the system.

A strong invariance principle for negatively associated random fields

Guang-hui Cai (2011)

Czechoslovak Mathematical Journal

In this paper we obtain a strong invariance principle for negatively associated random fields, under the assumptions that the field has a finite ( 2 + δ ) th moment and the covariance coefficient u ( n ) exponentially decreases to 0 . The main tools are the Berkes-Morrow multi-parameter blocking technique and the Csörgő-Révész quantile transform method.

A strong mixing condition for second-order stationary random fields

Raymond Cheng (1992)

Studia Mathematica

Let X m n be a second-order stationary random field on Z². Let ℳ(L) be the linear span of X m n : m ≤ 0 , n ∈ Z , and ℳ(RN) the linear span of X m n : m ≥ N , n ∈ Z . Spectral criteria are given for the condition l i m N → ∞ c N = 0 , where c N is the cosine of the angle between ℳ(L) and ℳ ( R N ) .

A study of the dynamic of influence through differential equations∗

Emmanuel Maruani, Michel Grabisch, Agnieszka Rusinowska (2012)

RAIRO - Operations Research

The paper concerns a model of influence in which agents make their decisions on a certain issue. We assume that each agent is inclined to make a particular decision, but due to a possible influence of the others, his final decision may be different from his initial inclination. Since in reality the influence does not necessarily stop after one step, but may iterate, we present a model which allows us to study the dynamic of influence. An innovative...

A study of the dynamic of influence through differential equations∗

Emmanuel Maruani, Michel Grabisch, Agnieszka Rusinowska (2012)

RAIRO - Operations Research

The paper concerns a model of influence in which agents make their decisions on a certain issue. We assume that each agent is inclined to make a particular decision, but due to a possible influence of the others, his final decision may be different from his initial inclination. Since in reality the influence does not necessarily stop after one step, but may iterate, we present a model which allows us to study the dynamic of influence. An innovative...

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