An Exact Solution for the Optical Absorbance of Thin Films

The electric and magnetic fields within optical thin films are obtained exactly in closed form as solutions of a system of difference equations presented by Berning and utilized by Dill, Neureuther, Tuttle, and Walker in their sample program for modeling optical lithography. The solution allows an explicit closed form expression for the absorbance.     

Resonance in a Quantum Chain

A resonance of a magnetic impurity with a quantum spin-chain is studied. A Fresnel diffraction pattern is found.     

Ising Chain with Random Magnetic Moments

The Ising chain with random magnetic moments is discussed, and the thermodynamic functions are computed.     

Ising model with variable bond strength

The partition function of the two-dimensional Ising model with variable bond strength along one dimension is computed exactly.     

On the interdependence of van der waals and double layer forces

We study the effect of coupling the electrostatic and low frequency electrodynamic responses of colloidal systems. Exact results are reported for the van der Waals free energy of interaction of non-uniform electrolyte across planar dielectric and planar charged dielectric across non-uniform electrolyte. In both cases, the results depend on the double layer repulsion.     

Properties of Successive Sample Moment Estimators

Moment type estimation of characteristics of a successively sampled finite population requires finding a solution to a pair of transcendental equations. Some global properties of two structurally distinct pairs—a symmetric and an asymmetric pair—of such equations are presented. Results of a Monte Carlo experiment designed to compare the performance of estimators computed by solving these transcendental equation pairs are reported.     

Lax Pair for the Free-Fermion Eight-Vertex Model

An explicit result on the quantum Lax pair for the eight-vertex free-fermion model with external fields in both directions is exhibited. Its relation to the quantum spectral transform and its corresponding Hamiltonian—the XY model with a transverse field—is discussed. The Yang-Baxter relation is computed, and the equations of motion are solved.     

On the Ising model in the presence of magnetic field

We demonstrate that the partition function of the 2-dimensional Ising model in the presence of a magnetic field can be expressed in terms of the distributions of the prime numbers in closed form.     

A note on an exact solution for the optical absorbance by thin films

The Babu-Barouch solution of Berning's difference equation for the electromagnetic fields within optical thin films is shown to converge in the continuum limit to a solution (expressed as a converging series) of the limiting differential equation.Supported in part by the NSF Grant #ECS 8611298 and the mathematics division of AFOSR.     

The Van Der Waals Interaction Across Non-Uniform Electrolyte

The interaction of like colloidal particles separated by electrolyte is the resultant of the attractive Vander Waals force and the repulsive electrostatic forces, screened by the non-uniform electrolyte. Hitherto, these contributions have been estimated separately. In this paper, the coupling of the low frequency electromagnetic fluctuations to the static charge distribution between two planes is examined. This coupling is expressed by a pair of second order coupled differential equations, which are solved exactly. The resulting eigenvalue equation is derived and the zero frequency contribution to the Vander Waals free energy calculated.