Exactly Solvable Models, QED, and porous media: A journey through increasing dimensionality. [QED (quantum electrodynamics)]

Miscellaneous · Fri Jan 01 00:00:00 EST 1993

OSTI ID:7042336

Coker, D A

The research comprising this thesis is in three different fields of theoretical physics: Exactly Solvable Models, QED in 2+1 Dimensions and Fluid Flow in Porous Media. The first result in Exactly Solvable Models is concerned with the partition function for the inhomogeneous six-vertex model with domain wall boundary conditions on an N [times] N lattice. The authors show that the partition function may be written as the determinant of an N [times] N matrix whose elements are trigonometric functions of the spectral parameters. Next, the authors discuss the placement of integrable quantum field theories on a lattice of finite, arbitrary spacing preserving the original R-matrix and the corresponding integrable structure. This also leads to the definition of new models through use of the lattice spacing as a free parameter. The presence of a magnetic flux string in 2+1 dimensions is known to give rise to both induced charge and current densities with the total charge being a topological invariant. The authors consider the feedback effects by solving for the self-consistent charge and current densities that satisfy both the Dirac and Maxwell equations. Using g [identical to] e[sup 2]/m as a dimensionless coupling, the authors find an analytic all order solution that is exact in the limits g [much lt] 1 and g [yields] [infinity]. Results for intermediate g are also discussed. In the final subject area, the authors perform an analytic structural reliability analysis for first contact miscible, two phase flow in a one dimensional porous medium. The sensitivity of the probability for time-of-breakthrough is examined for two common models of the joint probability distribution between the porosity and the permeability of the medium: Normal-normal, normal-lognormal. The first order analysis is essentially exact for the normal-normal model. The accuracy of first order analysis for the normal-lognormal model is determined using a specific example of field data.

• Research Organization: State Univ. of New York, Stony Brook, NY (United States)
• OSTI ID: 7042336
• Resource Relation: Other Information: Thesis (Ph.D.)
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
LATTICE FIELD THEORY
PARTITION FUNCTIONS
POROUS MATERIALS
FLUID FLOW
QUANTUM ELECTRODYNAMICS
ANALYTICAL SOLUTION
DIRAC EQUATION
MANY-DIMENSIONAL CALCULATIONS
R MATRIX
DIFFERENTIAL EQUATIONS
ELECTRODYNAMICS
EQUATIONS
FIELD THEORIES
FUNCTIONS
MATERIALS
MATRICES
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM FIELD THEORY
WAVE EQUATIONS
662100* - General Theory of Particles & Fields- (1992-)