منابع مشابه
Probabilistic Analysis of Mean-Field Games
The purpose of this paper is to provide a complete probabilistic analysis of a large class of stochastic differential games with mean field interactions. We implement the Mean-Field Game strategy developed analytically by Lasry and Lions in a purely probabilistic framework, relying on tailor-made forms of the stochastic maximum principle. While we assume that the state dynamics are affine in th...
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For low dimensional systems, (i.e. 2D and, to a certain extent, 1D) it is proved that mean–field theory can provide an asymptotic guideline to the phase structure of actual systems. In particular, for attractive pair interactions that are sufficiently “spead out” according to an exponential (Yukawa) potential it is shown that the energy, free energy and, in particular, the block magnetization (...
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We consider the solidi cation of a pure material from its undercooled melt, taking into account e ects of surface tension, kinetic undercooling and crystalline anisotropy. The classical mathematical formulation consists of two heat equations coupled with boundary conditions prescribed at the moving solid-liquid interface. Analytic solutions are known only for a few special cases. Since the prob...
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We introduce unconditionally stable finite element approximations for a phase field model for solidification, which take highly anisotropic surface energy and kinetic effects into account. We hence approximate Stefan problems with anisotropic Gibbs–Thomson law with kinetic undercooling, and quasi-static variants thereof. The phase field model is given by θwt + λ %(φ)φt = ∇ . (b(φ)∇w) , cΨ a α %...
متن کاملPhase - Field Simulation of Solidification 1
W. J. Boettinger,1 J. A. Warren,1 C. Beckermann,2 and A. Karma3 1Metallurgy Division, Materials Science and Engineering Laboratory, NIST, Gaithersburg, Maryland 20899; e-mail: [email protected]; [email protected] 2Department of Mechanical and Industrial Engineering, University of Iowa, Iowa City, Iowa 52242; e-mail: [email protected] 3Department of Physics and Center for Inter...
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ژورنال
عنوان ژورنال: Progress of Theoretical Physics
سال: 1994
ISSN: 0033-068X,1347-4081
DOI: 10.1143/ptp.92.687