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Digitale Medien

Motion by curvature in generalized Cahn-Allen models (1994)

Fife, Paul C. ; Lacey, Andrew A.

Springer

Journal of statistical physics 77 (1994), S. 173-181

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ISSN: 1572-9613

Schlagwort(e): Grain boundary ; internal layers ; motion by curvature ; Cahn-Allen model ; Allen-Cahn model ; Ginzburg-Landau functional

Quelle: Springer Online Journal Archives 1860-2000

Thema: Physik

Notizen: Abstract The Cahn-Allen model for the motion of phase-antiphase boundaries is generalized to account for nonlinearities in the kinetic coefficient (relaxation velocity) and the coefficient of the gradient free energy. The resulting equation is $$\varepsilon ^2 u_l = \alpha (u)(\varepsilon [\kappa (u)]^{{\raise0.5ex\hbox{$\scriptstyle 1$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle 2$}}} \nabla \cdot \{ [\kappa (u)]^{{\raise0.5ex\hbox{$\scriptstyle 1$}\kern-0.1em/\kern-0.15em\lower0.25ex\hbox{$\scriptstyle 2$}}} \nabla u\} - f(u))$$ wheref is bistable. Hereu is an order parameter and κ and α are physical quantities associated with the system's free energy and relaxation speed, respectively. Grain boundaries, away from triple junctions, are modeled by solutions with internal layers when ε≪1. The classical motion-by-curvature law for solution layers, well known when κ and α are constant, is shown by formal asymptotic analysis to be unchanged in form under this generalization, the only difference being in the value of the coefficient entering into the relation. The analysis is extended to the case when the relaxation time for the process vanishes for a set of values ofu. Then α is infinite for those values.

Materialart: Digitale Medien

URL: http://dx.doi.org/10.1007/BF02186837

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Digitale Medien

Numerical technique and computational procedure for isotachophoresis (1990)

Palusinski, Olgierd A. ; Su, Yu ; Fife, Paul C.

Weinheim : Wiley-Blackwell

Electrophoresis 11 (1990), S. 903-907

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ISSN: 0173-0835

Schlagwort(e): Chemistry ; Biochemistry and Biotechnology

Quelle: Wiley InterScience Backfile Collection 1832-2000

Thema: Biologie , Chemie und Pharmazie

Notizen: This paper presents a new numerical method for computation of solutions of prototypical equations of isotachophoresis. Numerical computation is complicated because the Poisson equation, which relates electrostatic potential to space charge density, contains a small parameter. This parameter is usually assumed to have the value of zero. Under this assumption the Poisson differential equation is replaced by an algebraic equation, which is often called the equation of electroneutrality, because it indeed states that the electrolyte is electrically neutral this assumption were not studied in the past. Here we propose an iterative procedure which allows for computation of solutions without the assumption of electroneutrality. The accuracy is controlled by a number of iterations and is limited by a computer round-off error only. The method is based on our previously published theory of existence and uniqueness of solutions of isotachophoretic equations. Details of the computational algorithm for prototypical equations of isotachophoresis are given. A numerical example and comparison with previously published data are also provided.

Zusätzliches Material: 4 Ill.