Thermodynamic limit for mean-field spin models.
Bianchi, A., Contucci, P., Giardina, C. (2003)
Mathematical Physics Electronic Journal [electronic only]
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Bianchi, A., Contucci, P., Giardina, C. (2003)
Mathematical Physics Electronic Journal [electronic only]
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Zhan Chen (2016)
Molecular Based Mathematical Biology
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In this work, the existence of a global minimizer for the previous Lagrangian formulation of nonpolar solvation model proposed in [1] has been proved. One of the proofs involves a construction of a phase field model that converges to the Lagrangian formulation. Moreover, an Eulerian formulation of nonpolar solvation model is proposed and implemented under a similar parameterization scheme to that in [1]. By doing so, the connection, similarity and difference between the Eulerian formulation...
Zenon Kosowski (2007)
Applicationes Mathematicae
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We investigate a 1-dimensional simple version of the Fried-Gurtin 3-dimensional model of isothermal phase transitions in solids. The model uses an order parameter to study solid-solid phase transitions. The free energy density has the Landau-Ginzburg form and depends on a strain, an order parameter and its gradient. The problem considered here has the form of a coupled system of one-dimensional elasticity and a relaxation law for a scalar order parameter. Under some physically justified...
Zhiming Chen, Qiang Du (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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In this paper, we construct a combined upwinding and mixed finite element method for the numerical solution of a two-dimensional mean field model of superconducting vortices. An advantage of our method is that it works for any unstructured regular triangulation. A simple convergence analysis is given without resorting to the discrete maximum principle. Numerical examples are also presented.
Kwaśniewski, A. K.
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Schmitt, Andreas
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Summary: We give an introduction to the Skyrme model from a mathematical point of view. Hereby, we show that it is difficult to solve the field equation even by means of the classical ansatz, the so-called hedgehog ansatz. Our main result is an extended existence proof for solutions of the field equation in the hedgehog ansatz.