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A Class Of Functions That Are Quasiconvex But Not Polyconvex, Catherine S. Remus

Masters Theses

In 1991 V. Sverak [11] gave an example of a function that was invariant and quasiconvex but not polyconvex. We have generalized this example to a wide class of functions that meet certain ellipticity and growth conditions. Quasiconvexity is one necessary and sufficient condition for the existence of solutions to the minimization problem in elliptic P.D.E. theory. Invariance is frequently a requirement of the stored energy function in Calculus of Variation approaches to elasticity problems.

Computational Models For Diusion Of Second Messengers In Visual Transduction, Harihar Khanal

Doctoral Dissertations

The process of phototransduction, whereby light is converted into an electrical response in retinal rod and cone photoreceptors, involves, as a crucial step, the diffusion of cytoplasmic signaling molecules, termed second messengers. A barrier to mathematical and computational modeling is the complex geometry of the rod outer segment which contains about 1000 thin discs. Most current investigations on the subject assume a well stirred bulk aqueous environment thereby avoiding such geometrical complexity. We present theoretical and computational spatio-temporal models for phototransduction in vertebrate rod photoreceptors, which are pointwise in nature and thus take into account the complex geometry of the …

Eigenvalue Dependence On Problem Parameters For Stieltjes Sturm-Liouville Problems, Laurie Elizabeth Battle

Doctoral Dissertations

This work examines generalized Stieltjes Sturm-Liouville boundary value problems with particular consideration of self-adjoint problems. Of central importance is determining conditions under which the eigenvalues depend continuously and differentiably on the problem data. These results can be applied to various physical problems, such as constructing beams to maximize the fundamental frequency of vibration, or constructing columns to maximize the height without buckling. These problems involve maximizing the smallest eigenvalues of Sturm-Liouville equations, and the continuous dependence of the eigenvalues on the problem parameters can be used to accomplish this.

We first consider the generalized 2n-dimensional initial value problem dy …

Fractal Images Generated By Newton's Method.", Jennifer Corte

Masters Theses

We investigate the behavior of Newton's Method for finding roots applied to complex-valued functions of complex variables. This re- quires an analysis of iteration of rational functions. The fractal nature of Newton's Method in the complex plane gives us intricate and beautiful images. By investigating select functions we attempt to generalize a pattern of behavior.

An Individual- Based Model For The Toxic Algae Species Pseudo-Nitzschia Multiseries, Maria Siopsis

Doctoral Dissertations

In 1987 an outbreak of a previously unobserved disease occurred in Canada and was traced back to the toxin domoic acid produced by the diatom Pseudo-nitzschia multiseries. Since then, fisheries closures due to domoic acid have occurred worldwide. Pseudo-nitzschia species produce domoic acid under nutrient stress, including low silicon or phosphorus under high nitrogen conditions. However, it is still unclear what conditions cause the dangerously high levels that have sometimes been observed. We present an individual-based algae model detailing the physiology of an algal cell with a focus on nutrient and energy flows to delineate the causes of domoic acid …