Optimal design of an optical lens

We wish to construct an optimal optical lens, in the sense that it focuses all rays from a given source onto a given focal point. The construction can be reduced mathematically to a global study of a system of two nonlinear functional differential equations. We prove that this system has precisely two analytic solutions.     

Study on the Collapse of Pin-Reinforced Foam Sandwich Panel Cores

New fabrication technologies now allow for hybrid sandwich structures, known as X-core, to be manufactured. The X-core panels consist of a pin reinforced polymer foam core with carbon fiber face sheets. Carbon fiber or metallic (Titanium/Steel) pins are inserted into the foam core in the out-of-plane direction and extend from face sheet to face sheet. The through thickness three-point simply supported bending behavior of these panels is used to evaluate the collapse characteristics of the panels. Explicit experimental observations are used to calibrate analytical energy balance models describing the panel collapse as a function of geometry and properties. The mechanical response of X-core sandwich panels is compared to current sandwich materials for material selection.     

Uniform Convergence for Approximate Traveling Waves in Linear Reaction–Diffusion–Hyperbolic Systems

In this paper we study linear reaction–hyperbolic systems of the form , (i = 1, 2, ..., n) for x > 0, t > 0 coupled to a diffusion equation for p ₀ = p ₀(x, y, θ, t) with “near-equilibrium” initial and boundary data. This problem arises in a model of transport of neurofilaments in axons. The matrix (k _ij ) is assumed to have a unique null vector with positive components summed to 1 and the v _j are arbitrary velocities such that . We prove that as the solution converges to a traveling wave with velocity v and a spreading front, and that the convergence rate in the uniform norm is , for any small positive α.     

Jet impingement cooling of a discretely heated portion of a protruding pedestal with a single round air jet

The influence of a protruding pedestal on impinging jet heat transfer is investigated. A discretely heated portion of a protruding pedestal is exposed to a single circular impinging air jet with Re=10,000–30,000. Jet exit diameters of 3.5, 9.5 and 21 mm are positioned at jet exit-to-surface distances of 2–5 diameters. The nondimensional heat transfer over the discretely heated portion of the pedestal is compared to a flat plate design to gauge the effects of Reynolds number, jet diameter and jet exit-surface spacing. In all cases, the presence of the protruding pedestal downstream is found to increase heat transfer.     

Cybernetic optimization by simulated annealing: Accelerating convergence by parallel processing and probabilistic feedback control

The convergence of the simulated annealing algorithm is accelerated by a probabilistic feedback control scheme. This scheme uses two or more parallel processors to solve the same or related combinatorial optimization problems and are coupled by a probabilistic measure of quality (PMQ). The PMQ is used to generate an error signal for use in feedback control. Control over the search process is achieved by using the error signal to modulate the temperature parameter. Other aspects of control theory, such as the system gain and its effects on system performance, are described. Theoretical and experimental results show that such a scheme increases the steadystate probability of the globally optimal solutions.     

Calculation of infrared-divergent Feynman diagrams with zero mass threshold

Two-loop vertex Feynman diagrams with infrared and collinear divergences are investigated by two independent methods. On the one hand, a method of calculating Feynman diagrams from their small momentum expansion [1] extended to diagrams with zero mass thresholds [2] is applied. On the other hand, a numerical method based on a two-fold integral representation is used [3], [4]. The application of the latter method is possible by using lightcone coordinates in the parallel space. The numerical data obtained with the two methods are in impressive agreement. Received: 22 April 1997 / Published online: 20 February 1998     

Partially Coherent Waves in Nonlinear Periodic Lattices

We study the propagation of partially coherent (random-phase) waves in nonlinear periodic lattices. The dynamics in these systems is governed by the threefold interplay between the nonlinearity, the lattice properties, and the statistical (coherence) properties of the waves. Such dynamic interplay is reflected in the characteristic properties of nonlinear wave phenomena (e.g., solitons) in these systems. While the propagation of partially coherent waves in nonlinear periodic systems is a universal problem, we analyze it in the context of nonlinear photonic lattices, where recent experiments have proven their existence.