Strong Soret Effect in One Dimension

We consider a one-dimensional gas of two kinds of particles with different masses interacting through short range interactions. The system exhibits an extreme form of the Soret effect: when the ends of the system are in contact with thermal baths of different temperatures, there is complete separation of the species. We show how this separation can be well described in the Boltzmann approximation and discuss the origin of this odd behavior.     

Fourier acceleration of iterative processes in disordered systems

Technical details are given on how to use Fourier acceleration with iterative processes such as relaxation and conjugate gradient methods. These methods are often used to solve large linear systems of equations, but become hopelessly slow very rapidly as the size of the set of equations to be solved increases. Fourier acceleration is a method designed to alleviate these problems and result in a very fast algorithm. The method is explained for the Jacobi relaxation and conjugate gradient methods and is applied to two models: the random resistor network and the random central-force network. In the first model, acceleration works very well; in the second, little is gained. We discuss reasons for this. We also include a discussion of stopping criteria.     

Three-Dimensional Analytical Models for Virus Transport in Saturated Porous Media

Analytical models for virus transport in saturated, homogeneous porous media are developed. The models account for three-dimensional dispersion in a uniform flow field, and first-order inactivation of suspended and deposited viruses with different inactivation rate coefficients. Virus deposition onto solid particles is described by two different processes: nonequilibrium adsorption which is applicable to viruses behaving as solutes; and colloid filtration which is applicable to viruses behaving as colloids. The governing virus transport equations are solved analytically by employing Laplace/Fourier transform techniques. Instantaneous and continuous/periodic virus loadings from a point source are examined.     

Distance—Stability of Nonlinear Discrete Systems

In this paper,the distance-sability of nonlinear discrete system is investigated by meansof the Gauss-Seidel iteration method.Some algebric criteria of the distance-stability are ob-tained.Construction of Lyapunov function is avoided.     

Effect of magnetic-field-induced torsion on neutrinos and supernova collapse

Summary The neutrino emission from supernova 1987A is being studied by taking into consideration the effect of the magnetic field present in the star. The magnetic field generates an anisotropic feature in the local space-time, which in turn leads to the cancellation of the axial-vector part of the neutrino current. The interaction cross-section of these neutrinos in the course of their interaction with matter on Earth has an inverse square energy dependence. The present work presents the calculations based on this changed cross-section that relates to predictions of the expected number of events at KAMIOKANDE on the basis of the Mont Blanc signal. It might be interesting to take a look into the implications of these results. The author of this paper has agreed to not receive the proofs for correction.     

Phase dynamics of Bose-Einstein condensates: Losses versus revivals

In the absence of losses the phase of a Bose-Einstein condensate undergoes collapses and revivals in time due to elastic atomic interactions. As experiments necessarily involve inelastic collisions, we develop a model to describe the phase dynamics of the condensates in presence of collisional losses. We find that a few inelastic processes are sufficient to damp the revivals of the phase. For this reason the observability of phase revivals for present experimental conditions is limited to condensates with a few hundreds of atoms. Received: 23 February 1998 / Revised: 21 July 1998 / Accepted: 23 July 1998     

A composition law for Runge-Kutta methods applied to index-2 differential-algebraic equations

This paper presents a new composition law for Runge-Kutta methods when applied to index-2 differential-algebraic systems. Applications of this result to the study of the order of composite methods and of symmetric methods are given.     

Periodic maintenance and repair rate control in stochastic manufacturing systems

In this paper, we consider a periodic preventive maintenance, repair, and production model of a flexible manufacturing system with failure-prone machines, where the control variables are the repair rate and production rate. We use periodic preventive maintenance to reduce the machine failure rates and improve the productivity of the system. One of the distinct features of the model is that the repair rate is adjustable. Our objective is to choose a control process that minimizes the total cost of inventory/shortage, production, repair, and maintenance. Under suitable conditions, we show that the value function is locally Lipschitz and satisfies an Hamilton-Jacobi-Bellman equation. A sufficient condition for optimal control is obtained. Since analytic solutions are rarely available, we design an algorithm to approximate the optimal control problem. To demonstrate the performance of the numerical method, an example is presented.Research of this author was supported by the Natural Sciences and Engineering Research Council of Canada, Grant OGP0036444.Research of this author was supported in part by the University of Georgia.Research of this author was supported in part by the National Science Foundation, Grant DMS-92-24372.     

The diameter of a fuzzy set

In pattern recognition one often wants to measure geometric properties of imprecisely defined subsets of an image. This paper proposes definitions of intrinsic and extrinsic diameter for fuzzy subsets which reduce to the ordinary definitions when the subsets are crisp. We also define height and width for a fuzzy subset and show how they relate to the area (i.e., integral of membership). For convex fuzzy subsets the intrinsic diameter cannot exceed the extrinsic diameter, but it can be smaller. Finally, for piecewise constant convex fuzzy subsets the intrinsic diameter cannot exceed half the fuzzy perimeter, but this need not be true in the nonconvex case.