Home  Papers 
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) (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 onedimensional, linear partialdifferential equation describing convectivediffusive or, equivalently, advectivedispersive behavior with sorption, desorption (a source), or decay. The problem was formulated for a finite domain with Robin (thirdtype) 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 onedimensional transient solution he provides leads immediately and easily to a multidimensional solution (i.e., in two or three spatial dimensions). Then, the corresponding single or multidimensional steadystate problems are simpler cases of the general solution. Similarly, since the Robin (thirdtype) boundaries are the sum of a Dirichlet (firsttype) and a Neumann (secondtype) term, either of which can be identically zero, solutions for a first or secondtype boundary are also furnished as a simple corollary, as discussed in appendix in his dissertation. Applications:: The general formulation chosen furnishes a solution for masstransport in one, two, or threedimensions. 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 thirdtype 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 coauthored 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/etd1107103092611/). 


