Biomedical subjects

Vlad Mitlin

Publications and source records attributed to Vlad Mitlin.

5 recordsLinked to original sources

PubMed2005

Nonlinear relaxation patterns in the Cahn-Hilliard equation: an exact solution.

We consider the 1-D Cahn-Hilliard equation with the order parameter v and derive an equation for a modified order parameter g such that g''=v'. The new equation allows for separation of variables. This yields exact solutions for v expressed in terms of generalized hypergeometric functions. These solutions have an infinite gradient at their zeros and the first three derivatives of zero at their extrema. The amplitude of these patterns decreases as the inverse square root of time. It is suggested that the phenomenon of compartmentalization of evolving structures typically observed in evolutionary models of the Cahn-Hilliard type is a manifestation of relaxation patterns similar to those derived in this paper.

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PubMed2005

The mu-derivative and its applications to finding exact solutions of the Cahn-Hilliard, Korteveg-de Vries, and Burgers equations.

A new transformation termed the mu-derivative is introduced. Applying it to the Cahn-Hilliard equation yields dynamical exact solutions. It is shown that the mu-transformed Cahn-Hilliard equation can be presented in a separable form. This transformation also yields dynamical exact solutions and separable forms for other nonlinear models such as the modified Korteveg-de Vries and the Burgers equations. The general structure of a nonlinear partial differential equation that becomes separable upon applying the mu-derivative is described.

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PubMed2005

On structural forces in thin fluid films at the critical point.

Smooth approximations for structural force in thin fluid films near the critical point are presented to facilitate the usage of formulas derived in [J. Colloid Interface Sci. 278 (2004) 173-183] in experimental studies.

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PubMed2005

A new form of the Cahn-Hilliard equation: applications to spinodal dewetting.

This paper presents a new form of the Cahn-Hilliard equation. The new equation is substantially more robust to simulating intrinsic instabilities of the spinodal dewetting process compared to the standard one.

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PubMed2004

Gradient theory for structural forces in thin fluid films near the critical point.

We consider a general form of the local gradient theory for structural forces in thin fluid films near the critical point. A complete analytical solution of this problem at separation distances substantially larger than the molecular size is presented. That is, pi= -[330Psi(-4)H(8.8923-Psi) + 384exp(-Psi)H(Psi-8.8923)]H(-Gamma)+[1134.36Psi(-4)H(8.8923-Psi + 192exp(-Psi)H(Psi-8.8923)]H(Gamma) where Gamma <0 for similar (both attractive or both repulsive) and Gamma >0 for dissimilar (one attractive, another repulsive) bounding surfaces. Here pi and Psi are the structural force and the separation distance scaled in a certain way, and H(.) is a unit step function. For binary polymer films, the results are further elaborated to include a scaling dependence of the structural force on polymerization degrees of components.

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