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Note This site is maintained to facilitate access to research Dr. Golz carried out while at Louisiana State University. When this site is removed from the web, the full text of Dr. Golz's published papers will continue to be available from the permanent electronic archives of the National Sea Grant Library (NSGL) and the Los Alamos National Lab preprint server (arXiv).

William Golz

Ph.D. Louisiana State University (Click for Dissertation)

The Mathematics Genealogy Project (Click)
(Golz, Dorroh, Wall, Van Vleck, Klein, Lipschitz, Dirichlet, Fourier, Lagrange, Euler, Johann Bernoulli, Jacob Bernoulli, Leibniz, Weigel)

Theory:: Golz's doctoral dissertation resolved a very general one-dimensional, linear partial-differential equation describing convective-diffusive or, equivalently, advective-dispersive behavior with sorption, desorption (a source), or decay. The problem was formulated for a finite domain with Robin (third-type) boundary conditions which, when transformed, yielded a system of ordinary differential equations with an eigenvalue expansion that composes a uniformly convergent series of real variables. As detailed in his dissertation, the one-dimensional transient solution he provides leads immediately and easily to a multi-dimensional solution (i.e., in two or three spatial dimensions). Then, the corresponding single- or multi-dimensional steady-state problems are simpler cases of the general solution. Similarly, since the Robin (third-type) boundaries are the sum of a Dirichlet (first-type) and a Neumann (second-type) term, either of which can be identically zero, solutions for a first- or second-type boundary are also furnished as a simple corollary, as discussed in appendix in his dissertation.

Applications:: The general formulation chosen furnishes a solution for mass-transport in one-, two-, or three-dimensions. Problems may include sorption, desorption (a source), or decay (the solution remains valid when terms describing any of those phenomenon are identically zero). The furnished solution is valid for either first, second, or third-type boundary conditions. Physical problems may include surface- and ground- water pollution or the transport of therapeutic drugs across biofilm boundaries, cellular membranes, and venous walls. Dr. Golz will continue to respond to email inquiries from scientists whom need specific information regarding the way in which the solution may be adapted to a particular physical problem.

Publications:: Dr. Golz's work first appeared in a 2001 paper he co-authored with Dr. J. Robert Dorroh in Applied Mathematics Letters (http://xxx.lanl.gov/abs/math.AP/0404234) with the details more fully enumerated in his 2003 dissertation (http://etd.lsu.edu/docs/available/etd-1107103-092611/).

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