The numerical solution of the flow of a liquid crystal governed by a particular instance of the Ericksen–Leslie equations is considered. Convergence results for this system rely crucially upon energy estimates which involve norms of the director field. We show how a mixed method may be used to eliminate the need for Hermite finite elements and establish convergence of the method.
The numerical solution of the flow of a liquid crystal governed by a particular instance of the Ericksen–Leslie equations is considered. Convergence results for this system rely crucially upon energy estimates which involve (Ω) norms of the director field. We show how a mixed method may be used to eliminate the need for Hermite finite elements and establish convergence of the method.
Gramicidin A is a small and well characterized peptide that forms an ion channel in lipid membranes. An important feature of gramicidin A (gA) pore is that its conductance is affected by the electric charges near the its entrance. This property has led to the application of gramicidin A as a biochemical sensor for monitoring and quantifying a number of chemical and enzymatic reactions. Here, a mathematical model of conductance changes of gramicidin A pores in response to the presence of electrical...
In this paper we give some criteria for the existence of compactly supported -solutions ( is an integer and ) of matrix refinement equations. Several examples are presented to illustrate the general theory.
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