finite element analysis of axisymmetric radomes a two step technique for the analysis of axisymmetric radomes is presented initially an axisymmetric finite element approach is employed together with an absorbing boundary condition for mesh truncation to determine the near fields scattered by an empty radome illuminated by a distant source next the reciprocity theorem is invoked to determine the far field pattern of an antenna encased by the radome by computing the interaction between the current distribution on the antenna and the near field data determined in the first step the details of the formulation are presented along with numerical results for two different arrays enclosed by radomes of varying permittivities

fluctuations in the lattice gas for burgers equation the langevin equation for the biased random hopping of particles onto unoccupied sites of a lattice is obtained from the master equation for finite systems by invoking a limit theorem due to kurtz for a weakly asymmetric process with diffusive scaling the continuum limit of this equation yields a deterministic equation that is equivalent to burgers equation the stochastic equation for the leading lattice corrections is derived and the approach to the continuum limit is illustrated with simulations

multidimensional reflected brownian motions having exponential stationary distributions on considere la distribution stationnaire d un mouvement brownien reflechi dans un domaine d dimensionnel g on etudie deux classes de processus de ce type

fast and efficient analysis of radome enclosed antennas in receiving mode by an iterative based hybrid integral equation modified surface integration method an iterative based hybrid method which combines the volume surface integral equation vsie and the modified surface integration msi method is presented to analyze the radome enclosed antennas in receiving mode compared with the previously published hybrid approaches this method improves computational accuracy by including the effects of shaded wall of the radome and the mutual interactions between antennas and radome during the numerical solution of the vsie in an iterative manner by embedding different parts of the antenna radome structure ars into three distinct oct trees the multilevel fast multipole algorithm mlfma is used to accelerate both the vsie solution and the surface volume integrations in the msi stage the new method obtains more accurate results than its original version within less cpu time and keeps good accuracy with much less memory usage and computational time when compared with the mlfma accelerated full wave vsie solution for the entire ars

a stochastic lattice gas for burgers equation a practical study we continue our investigation of stochastic lattice gases as a highly parallel means of simulating given pdes in this case burgers equation in one dimension the lattice dynamics consists of stochastic unidirectional particle displacement and our attention is turned toward the reliability of the model i e its ability to reproduce the unique physical solution of burgers equation lattice gas results are discussed and compared against finite difference calculations and exact solutions in examples which include shocks and rarefaction waves

on the diffusion approximation to two parallel queues with processor sharing a two dimensional queuing model is considered in which the server in the second queue helps the server in the first queue during periods when the second queue is empty the system is analyzed in the heavy traffic limit and explicit approximate solutions are obtained to the resulting diffusion equations using singular perturbation methods approximate asymptotic formulas are obtained for the stationary distribution of the number of customers as well as for some first passage time problems associated with the busy period it is shown that these formulas reduce to the asymptotic expansions of the exact solutions when the latter are available

equilibria for diffusion models of pairs of communicating computers symmetric case the steady state queueing behavior of interacting computers is basic to computer network theory equilibrium properties are determined for the diffusion model for the special case of a symmetrically disposed pair of communicaling computers in the mathematical model arrivals to the system can represent the presentation of programming jobs and each service represents the completion of a stage of processing the exogenous arrivals and the services during the busy period are permitted to be arbitrary renewal processes computer interaction arises as follows when each stage of processing is completed a certain probability exists that the entire job is complete however with the complementary probability the job is input to the other computer for an additional stage of processing in the space of all systems we find an infinite set of curves whereon the joint equilibrium density reduces to a very simple form for the general case a direct formal infinite series representation of the joint equilibrium density is found using conformal mapping the moment generating function is obtained rational expressions for the mean queue size and delay are given the mean queue size for poisson arrivals is interpreted a simple expression for the tail exponent for the queue size marginal is found the nature of the joint density in the neighborhood of the origin is delineated the connection to delay equilibria is mentioned extensions to a larger class of communicating computer pairs is indicated

oblique derivative boundary conditions and the image method the image method of solving boundary value problems is extended to oblique derivative boundary conditions on plane boundaries for a class of equations including the wave equation the heat equation and laplace s equation this generalizes the recent result of gilbarg and trudinger elliptic partial differential equations of second order springer verlag berlin 1977 for laplace s equation the usefulness of the method is illustrated by solving with it both the wave equation and the heat equation in a half space with an initial point source and an oblique derivative boundary condition in both cases a surface wave is found for the wave equation there is a region near the boundary where the surface wave is the first arrival for the heat equation the surface wave is the largest wave in this region for small values of the time

reflected brownian motion in a wedge semimartingale property in this paper the object of study is reflected brownian motion in a two dimensional wedge with constant direction of reflection on each side of the wedge the basic question considered here is when is this process a semimartingale it is first shown that a related process defined by specifying the corner of the wedge to be an absorbing state rather than an instantaneous one is a semimartingale conditions for the existence and uniqueness of the process for which the corner is an instantaneous state were given by vardhan and williams brownian motion in a wedge with oblique reflection comm pure appl math to appear under these conditions it is shown that starting away from the corner the process is a semimartingale if and only if there is a convex combination of the directions of reflection that points into the wedge this equivalence is also shown to hold starting from the corner except in one unresolved case for which the wedge angle exceeds and the directions of reflection are exactly opposed

renormalization of stochastic lattice models basic formulation we describe a general method for the multiscale analysis of stochastic lattice models beginning with a lattice langevin formulation of site fluctuations we derive stochastic partial differential equations by regularizing the transition rules of the model subsequent coarse graining is accomplished by calculating renormalization group rg trajectories from initial conditions determined by the regularized atomistic models the rg trajectories correspond to hierarchies of continuum equations describing lattice models over expanding length and time scales these continuum equations retain a quantitative connection over different scales as well as to the underlying atomistic dynamics this provides a systematic method for the derivation of continuum equations from the transition rules of lattice models for any length and time scales as an illustration we consider the one dimensional 1d wolf villain wv model europhys lett 13 389 1990 the rg analysis of this model which we develop in detail is generic and can be applied to a wide range of conservative lattice models the rg trajectory of the 1d wv model shows a complex crossover sequence of linear and nonlinear stochastic differential equations which is in excellent agreement with kinetic monte carlo simulations of this model we conclude by discussing possible applications of the multiscale method described here to other nonequilibrium systems

reflected brownian motion with skew symmetric data in a polyhedral domain this paper is concerned with the characterization and invariant measures of certain reflected brownian motions rbm s in polyhedral domains the kind of rbm studied here behaves like d dimensional brownian motion with constant drift in the interior of a simple polyhedron and is instantaneously reflected at the boundary in directions that depend on the face that is hit under the assumption that the directions of reflection satisfy a certain skew symmetry condition first introduced in harrison williams 9 it is shown that such an rbm can be characterized in terms of a family of submartingales and that it reaches non smooth parts of the boundary with probability zero in 9 a purely analytic problem associated with such an rbm was solved here the exponential form solution obtained in 9 is shown to be the density of an invariant measure for the rbm furthermore if the density is integrable over the polyhedral state space then it yields the unique stationary distribution for the rbm in the proofs of these results a key role is played by a dual process for the rbm and by results in 9 for reflected brownian motions on smooth approximating domains

conformal mapping solution of laplace s equation on a polygon with oblique derivative boundary conditions we consider laplace s equation in a polygonal domain together with the boundary conditions that along each side the derivative in the direction at a specified oblique angle from the normal should be zero first we prove that solutions to this problem can always be constructed by taking the real part of an analytic function that maps the domain onto another region with straight sides oriented according to the angles given in the boundary conditions then we show that this procedure can be carried out successfully in practice by the numerical calculation of schwarz christoffel transformations the method is illustrated by application to a hall effect problem in electronics and to a reflected brownian motion problem motivated by queueing theory

non hermitian localization and population biology the time evolution of spatial fluctuations in inhomogeneous d dimensional biological systems is analyzed a single species continuous growth model in which the population disperses via diffusion and convection is considered time independent environmental heterogeneities such as a random distribution of nutrients or sunlight are modeled by quenched disorder in the growth rate linearization of this model of population dynamics shows that the fastest growing localized state dominates in a time proportional to a power of the logarithm of the system size using an analogy with a schr odinger equation subject to a constant imaginary vector potential we propose a delocalization transition for the steady state of the nonlinear problem at a critical convection threshold separating localized and extended states in the limit of high convection velocity the linearized growth problem in d dimensions exhibits singular scaling behavior described by a d ensuremath 1 dimensional generalization of the noisy burgers equation with universal singularities in the density of states associated with disorder averaged eigenvalues near the band edge in the complex plane the burgers mapping leads to unusual transverse spreading of convecting delocalized populations

on the diffusion approximation to a fork and join queueing model the use of singular perturbation methods to obtain approximate analytic solutions to the types of diffusion equations that are used to model queueing networks is shown as an example a two dimensional fork and join model is considered approximations to the stationary distribution of the number of customers in the system as well as the residual busy period are computed the formulas obtained clearly show the dependence of the solution on the variables and the parameters of the model

a fast volume surface integral equation solver for scattering from composite conducting dielectric objects this paper presents a fast hybrid volume surface integral equation approach for the computation of electromagnetic scattering from objects comprising both conductors and dielectric materials the volume electric field integral equation is applied to the material region and the surface electric field integral equation is applied on the conducting surface the method of moments mom is used to convert the integral equation into a matrix equation and the precorrected fft p fft method is employed to reduce the memory requirement and cpu time for the matrix solution the present approach is sufficiently versatile in handling problems with either open or closed conductors and dielectric materials of arbitrary inhomogeneity due to the combination of the surface and volume electric field integral equations the application of the precorrected fft method facilitates the solving of much larger problems than can be handled by the conventional mom

reflected brownian motion on an orthant we consider a k dimensional diffusion process z whose state space is the nonnegative orthant on the interior of the orthant z behaves like a kdimensional brownian motion with arbitrary covariance matrix and drift vector at each of the k 1 dimensional hyperplanes that form the boundary of the orthant z reflects instantaneously in a direction that is constant over that hyperplane there is no extant theory of multidimensional diffusion that applies to this process because the boundary of its state space is not smooth we adopt an approach that requires a restriction on the directions of reflection but reiman has shown that this restriction is met by all diffusions z arising as heavy traffic limits in open k station queuing networks our process z is defined as a path to path mapping of k dimensional brownian motion from this construction it follows that z is a continuous markov process and a semimartingale using the latter property we obtain a change of variable formula from which one can develop a complete analytical theory for the process z

lattice gases large deviations and the incompressible navier stokes equations we study the incompressible limit for a class of stochastic particle systems on the cubic lattice zd d 3 for initial distributions corresponding to arbitrary macroscopic l2 initial data the distributions of the evolving empirical momentum densities are shown to have a weak limit supported entirely on global weak solutions of the incompressible navier stokes equations furthermore explicit exponential rates for the convergence large deviations are obtained the probability to violate the divergence free condition decays at rate at least exp e d l while the probability to violate the momentum conservation equation decays at rate exp fe d 2 with an explicit rate function given by an hi1 norm

stochastic burgers and kpz equations from particle systems we consider two strictly related models a solid on solid interface growth model and the weakly asymmetric exclusion process both on the one dimensional lattice it has been proven that in the diffusive scaling limit the density field of the weakly asymmetric exclusion process evolves according to the burgers equation and the fluctuation field converges to a generalized ornstein uhlenbeck process we analyze instead the density fluctuations beyond the hydrodynamical scale and prove that their limiting distribution solves the non linear burgers equation with a random noise on the density current for the solid on solid model we prove that the fluctuation field of the interface profile if suitably rescaled converges to the kardar parisi zhang equation this provides a microscopic justification of the so called kinetic roughening i e the non gaussian fluctuations in some non equilibrium processes our main tool is the cole hopf transformation and its microscopic version we also develop a mathematical theory for the macroscopic equations

fluctuations in the motions of mass and of patterns in one dimensional driven diffusive systems the stochastic spreading of mass fluctuations in systems described by a fluctuating burgers equation increases ast2 3 with time as a consequence the stochastic motion of a mass front a point through which no excess mass current is flowing is shown to increase ast1 3 the same is true for the stochastic displacement of mass points and shock fronts with respect to their average drift provided the initial configuration is fixed an additional average over the stationary distribution of the initial configuration yields stochastic displacements increasing with time ast1 2

burger s model of turbulence as a stochastic process a recently proposed mesoscopic description of fluid dynamics leads to a new approach to turbulence in contrast to the classical statistical theory of turbulence the new approach introduces a probabilistic time evolution of the random velocity governed by a master equation the mesoscopic approach is explained by means of the 1 1 dimensional burger s model of turbulence by a continuous time stochastic simulation realizations of turbulent velocity fields are generated correlation functions and energy spectra are evaluated from appropriate ensemble averages

fokker planck equation for lattice deposition models an asymptotically exact fokker planck equation for the height fluctuations of lattice deposition models is derived from a van kampen expansion of the master equation using an edwards wilkinson type model as an example the solution of the equivalent langevin equation reproduces the surface roughness and lateral height correlations obtained with kinetic monte carlo kmc simulations our discrete equations of motion thereby provide an exact analytic and computational alternative to kmc simulations of these models