A local search approach to a circle cutting problem arising in the motor cycle industry

This paper is concerned with the development of a customized circle packing algorithm for a manufacturer of sprockets for the motor cycle industry. Practical constraints mean that the problem differs somewhat from those tackled elsewhere in the literature. In particular, the layouts need to conform to a given structure. This is achieved by using a local search algorithm with an appropriate starting solution and a series of neighbourhoods designed to preserve the layout structure. Empirical evidence based on real data shows that the quality of the resulting solutions closely matches that of cutting patterns currently produced by human experts. Computation times average around 20–30?s per order as compared to several hours for an equivalent manual solution.     

Tunneling radiation of a Gibbons-Maeda dilaton black hole

We use the Parikh-Wilczek method to treat Hawking radiation as a tunneling process across the event horizon and calculate the emission rate of a Gibbons-Maeda dilaton black hole. We show that if self-gravitation is taken into account, then the radiation deviates from the purely thermal spectrum, and the corrected spectrum is consistent with an underlying unitary theory. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 151, No. 1, pp. 172–175, April, 2007.     

Asymptotic and boundary integral formulae for the computational reconstruction of small conductivity imperfections

In this paper we investigate the electrostatic problem of determining conductivity profiles from the knowledge of boundary currents and voltages. We obtain an improved estimate for the voltage potential of a two-dimensional conductor having finitely many circular inclusions and piecewise constant conductivity profile. We derive an asymptotic expansion for the voltage potential in terms of the reference voltage potential and the location, size, and conductivity of the inhomogeneities. This representation is used to formulate the nonlinear least squares problem for estimating the location and size of the inhomogeneities. Required boundary data for the voltage potential are generated numerically by solving a system of integral equations. Computational experiments are presented to demonstrate the effectiveness of our identification procedure.     

Theory of Valuations on Manifolds: A Survey

This is a non-technical survey of a recent theory of valuations on manifolds constructed in [A10], [A11], [AF] and [A12], and actually a guide to this series of articles. We also review some recent related results obtained by a number of people. Received: February 2006, Revision: June 2006, Accepted: June 2006     

Phase Shift Modulations for Stable,Oscillatory, Traveling,Strongly Nonlinear Waves

Oscillatory dispersive waves propagating in a slowly varying medium are analyzed for Klein-Gordon equations with perturbations. The method of multiple scales is extended to include two fast scales, the usual traveling-wave phase and time, in order to allow initial conditions not usually permitted. An exact wave-action equation is introduced if the traveling wave is stable, involving averages over the periodic wave as well as time. This is equivalent to an extended averaged Lagrangian principle. The equation for the slow modulations of the phase shift of the traveling wave is derived from the higher order terms in the exact action equation and is shown to be the same as in earlier more restrictive studies.     

Molecular addressing? Studies on light-induced reorientation in liquid-crystalline side chain polymers

Polarized light leads to an effective reorientation of the optic axis in the glassy state of liquid-crystalline side chain polymers containing azobenzene mesogenic groups, via a trans-cis and cis-trans isomerization. Using a combination of U V and IR dichroitic studies it is shown for copolymers consisting of chromophores (azobenzene) and non-chromophores (phenylbenzoate) that only the chromophores are reoriented by light as far as the glassy state is concerned. Individual chromophores are thus addressed by photoselection. Photoselection in the fluid nematic state, on the other hand, leads also to a reorientation of the non-chromophores.