restricted ornstein uhlenbeck process and applications in neuronal models with periodic input signals restricted gauss markov processes are used to construct inhomogeneous leaky integrate and fire stochastic models for single neurons activity in the presence of a lower reflecting boundary and periodic input signals the first passage time problem through a time dependent threshold is explicitly developed numerical simulation and asymptotic results for firing densities are provided

tuning to resonances with iterative time reversal this paper considers a distributed wave based sensing system that probes a scene consisting of multiple interacting idealized targets each sensor is a collocated transmit receive pair that is capable of transmitting arbitrary wideband waveforms we address the problem of finding the space time transmit waveform that provides the best target detection performance in the sense of maximizing the energy scattered back into the receivers our approach is based on earlier theoretical work that showed for an idealized infinite half space geometry that the solution could be constructed by an iterative time reversal tr process in this paper we give a more realistic example involving a two sensor time domain system we show that for this system the iterative tr process can be used to tune automatically to all the target resonances that are within the bandwidth of the interrogating radar system we show that although obtaining eigenvalues and hence resonances of the scattering operator is in general unstable using the iterative tr process to obtain the resonances is a stable process moreover we show that these resonance frequencies are connected to the poles of the singularity expansion method

first passage time statistics of brownian motion with purely time dependent drift and diffusion abstract systems where resource availability approaches a critical threshold are common to many engineering and scientific applications and often necessitate the estimation of first passage time statistics of a brownian motion bm driven by time dependent drift and diffusion coefficients modeling such systems requires solving the associated fokker planck equation subject to an absorbing barrier transitional probabilities are derived via the method of images whose applicability to time dependent problems is shown to be limited to state independent drift and diffusion coefficients that only depend on time and are proportional to each other first passage time statistics such as the survival probabilities and first passage time densities are obtained analytically the analysis includes the study of different functional forms of the time dependent drift and diffusion including power law time dependence and different periodic drivers as a case study of these theoretical results a stochastic model of water resources availability in snowmelt dominated regions is presented where both temperature effects and snow precipitation input are incorporated

music imaging and electromagnetic inverse scattering of multiple scattering small anisotropic spheres the foldy lax equation is used to derive a multiple scattering model for the multiple scattering small anisotropic spheres by this model if the number of the non zero singular values of the multistatic response msr matrix is smaller than the number of the antennas the range space of the msr matrix is found to be spanned by the background green s function vectors corresponding to the and components of the electric and magnetic dipoles induced in each scatterer which indicates that the multiple signal classification music method could be implemented to obtain the locations of the scatterers after estimating the positions of the scatterers a non iterative analytical method is proposed for retrieving the polarization strength tensors as well as the orientations of the principle axes of each scatterer two numerical simulations show that the music method and the non iterative method are efficacious for the nonlinear inverse scattering problem of determining the locations and polarization strength tensors of multiple scattering small anisotropic spheres such methods could also be applied to the inversion of small isotropic spheres or extended to the inversion of small bianisotropic spheres

hamilton jacobi equations on a manifold and applications to grid generation or refinement in this paper we consider hamilton jacobi equations on a manifold typically on the graph of some previously computed function z x y and we show how the corresponding level set method allows us to generate and or to refine a mesh in regions where this function z has large derivatives such as it is the method needs to be strongly improved and accelerated but the principle is awfully natural and in principle the method is fully automatic similar ideas are also useful in image processing in particular for the active contours method

adaptive zoning for singular problems in two dimensions abstract winslow s method for the automatic generation of computation meshes is extended to adaptively vary the zone sizes and orthogonality of grid lines in the resulting mesh through simple analysis and numerical examples the adaptive mesh is shown to give significant increases in accuracy in the computation of singular problems

multistatic response matrix of spherical scatterers and the back propagation of singular fields in view of the development of multiple signal classification type non iterative imaging procedures based on the singular value decomposition of the multistatic response msr matrix of a collection of inclusions the full 3 d electromagnetic case with arbitrary contrasts of permeability and permittivity including perfectly electric conducting or perfectly magnetic conducting limit cases is studied the structure of the msr matrix of a single inclusion or a set of well separated ones is analyzed emphasis is on a far field situation in which one considers an electric dipole array operated in the transmit receive mode at a single frequency back propagated electric and magnetic fields associated to the singular vectors of the msr matrix for a single spherical inclusion or again for well separated ones are given in closed form and their leading order values are exhibited numerical illustrations cross sectional maps of back propagated fields computed from a singular value decomposition of the msr matrix are presented for one and two inclusions to illustrate this behavior as a function of the geometric and electromagnetic parameters of the configuration in a possibly noisy case

gauss markov processes in the presence of a reflecting boundary and applications in neuronal models abstract gauss markov processes restricted from below by special reflecting boundaries are considered and the transition probability density functions are determined furthermore the first passage time density through a time dependent threshold is studied by using analytical numerical and asymptotic methods the restricted gauss markov processes are then used to construct inhomogeneous leaky integrate and fire stochastic models for single neurons activity in the presence of a reversal hyperpolarization potential and time varying input signals

the transient solution of time dependent m m 1 queues the transient behavior of time dependent m m 1 queues is studied the boundary probability function pi sub 0 t which is the probability that the queue is empty at time t is shown with analyticity arguments to satisfy a volterra type integral equation the boundary integral equation is derived and a numerical algorithm is used to solve the integral equation and to find the expected queue size from pi sub 0 t the approach can be applied to many other types of time dependent queues examples are given

composite overlapping meshes for the solution of partial differential equations abstract we discuss the generation of curvilinear composite overlapping grids and the numerical solution of partial differential equations on them a composite overlapping grid consists of a set of curvilinear component grids that cover a region and overlap where they meet continuity conditions interpolation are imposed at the overlapping boundaries the principal advantage of composite grids is in the generation of grids for regions with complicated geometries the grid construction program cmpgrd is used to create composite grids with any number of component grids we describe some techniques for the solution of elliptic and time dependent pdes on composite meshes applications to the solution of the compressible navier stokes equations are presented

constructing transient birth death processes by means of suitable transformations for a birth death process n t with a reflecting state at 0 we propose a method able to construct a new birth death process m t defined on the same state space the birth and death rates of m t depend on the rates of n t and on the probability law of the process n t evaluated at an exponentially distributed random time under a suitable assumption we obtain the conditional probabilities the mean of the process and the laplace transforms of the downward first passage time densities of m t we also discuss the connection between the proposed method and the notion of similarity as well as a relation between the distribution of m t and the steady state probabilities of n t subject to catastrophes governed by a poisson process we investigate new processes constructed from i a birth death process with constant rates and ii a linear immigration death process various numerical computations are performed to illustrate the obtained results

on the sensitivity of time reversal imaging techniques to model perturbations time reversal tr techniques involve physical or synthetic retransmission of signals acquired by a set of transceivers in a time reversed fashion and can be used for a host of applications including ultrawideband imaging of obscured targets this work investigates the performance of some tr based techniques under non ideal conditions and is divided into three main parts in the first part we investigate the robustness of tr based imaging techniques via the decomposition of tr operator dort algorithm and the multiple signal classification music algorithm under clutter and additive noise in the second part we examine the effect of tr invariance breaking due to losses in the intervening media on the performance of both dort and tr based music in the third part effects of translational perturbations of the tr array are examined as a class of model perturbations these ensuing effects are then exploited in a controlled manner as a means to extract second order spatial statistics of the probed media

transient solution of an m m 1 queue with catastrophes abstract a transient solution for the system size in the m m 1 queueing model with the possibility of catastrophes at the service station is derived in the direct way asymptotic behavior of the probability of the server being idle and mean queue size are discussed steady state probabilities are also obtained

a modification of the wiener process due to a poisson random train of diffusion enhancing pulses a poisson modified wiener process is considered its conditional probability density is calculated exactly various forms of the evolution equation are derived for the case when the initial probability density is arbitrary a generalization is also treated when this equation contains a term analogous to the potential energy term in the schrodinger equation the green function of this equation is derived in the form of a functional integral which may be considered as a direct generalization of the feynman kac integral an application is suggested in the theory of quasiparticles with a non parabolic dispersion law

variational mesh adaptation ii error estimates and monitor functions the key to the success of a variational mesh adaptation method is to define a proper monitor function which controls mesh adaptation in this paper we study the choice of the monitor function for the variational adaptive mesh method developed in the previous work j comput phys 174 2001 924 two types of monitor functions scalar matrix and non scalar matrix ones are defined based on asymptotic estimates of interpolation error obtained using the interpolation theory of finite element methods the choice of the adaptation intensity parameter is also discussed for each of these monitor functions asymptotic bounds on interpolation error are obtained for adaptive meshes that satisfy the regularity and equidistribution conditions two dimensional numerical results are given to verify the theoretical findings

analysis of reflected diffusions via an exponential time based transformation let x t be a time homogeneous diffusion process with state space 0 infty where 0 is a reflecting or entrance endpoint and let z denote a random variable that describes the process x t evaluated at an exponentially distributed random time we propose a method to obtain closed form expressions for the conditional density and the mean of a new diffusion process y t with the same state space and with the same infinitesimal variance whose drift depends on the infinitesimal moments of x t and on the hazard rate function of z this method also allows us to obtain the laplace transform of the first passage time density of y t through a lower constant boundary we then discuss the relation between y t and the process x t subject to catastrophes as well as the interpretation of y t as a diffusion in a decreasing potential we study in detail some special cases concerning diffusion processes obtained when x t is the wiener ornstein uhlenbeck bessel and rayleigh process

on the reflected ornstein uhlenbeck process with catastrophes abstract the reflected ornstein uhlenbeck process in the presence of catastrophes that occur at exponential rate is considered explicit expressions for the transition probability density and for related moments are determined the first visit time to zero state is also investigated a systematic computational analysis is performed to elucidate the role played by the parameters

variational curve and surface grid generation abstract variational algorithms that control the lengths of grid lines cell areas and the orthogonality of grid lines can be used for generating boundary conforming grids on surfaces additional geometric control is provided by using a reference grid while solution adaptivity is achieved by using weights in a typical application the reference grid can be used to produce an exponential compression of the grid at a boundary while the solution adaptive weights are used to make the grid spacing inversely proportional to the gradient when the gradient is large of some solution being computed on the grid the grid is adapted on both the interior and boundary of the surface the algorithm performs these tasks with exceptional precision as demonstrated in the examples presented here

recent progress on application of hp adaptive be fe methods to elastic scattering summary several new issues related to the projcct described in references 1 3 are reported the presented problems include i sensitivity of p convergence results to geometric parametrizations and an idea of a new mesh generation for lip approximations 2 a posteriori error estimation for the coupled problem 3 a better understanding of the meaning of the asymptotic convergence a few typical numerical examples conclude the presentation

strong approximations for time dependent queues a time dependent mt mt 1 queue alternates through periods of under over and critical loading we derive period dependent pathwise asymptotic expansions for its queue length within the framework of strong approximations our main results include time dependent fluid approximations supported by a functional strong law of large numbers and diffusion approximations supported by a functional central limit theorem this complements and extends previous work on asymptotic expansions of the queue length transition probabilities

an adaptive direct variational grid generation method abstract variational grid generation techniques are now used to produce grids suitable for solving numerical partial differential equations in irregular geometries variational grid generation methods are very robust but slow the method considered here is a discrete variational method this method preserves the robustness of the variational method also it is very fast so it can be used in time dependent problems here we discuss geometry and solution adaption for the direct discrete grid generation method and some examples are presented to demonstrate its capabilities

gaussian beams and legendre polynomials as invariants of the time reversal operator for a large rigid cylinder the dort method french acronym for decomposition of the time reversal operator is an active remote sensing technique using an array of antennas for the detection and localization of scatterers this method is based on the singular value decomposition of the interelement response matrix in this paper an analytical expression of the singular vectors due to the reflection from a large rigid cylinder is provided depending on the array aperture two asymptotic regimes are described it is shown that the singular vectors correspond to hermite gaussian modes for large apertures and legendre polynomials for small ones using perturbation theory the corresponding singular values are deduced theoretical predictions are in good agreement with experimental results

on some time non homogeneous queueing systems with catastrophes computations for non homogeneous birth and death processes with catastrophes applications to queueing and population dynamics problems effect of the periodicity of the rates on the performance of systems with catastrophes non stationary queueing systems subject to catastrophes occurring with time varying intensity are considered the effect of a catastrophe is to make the queue instantly empty the transition probabilities the related moments and the first visit time density to zero state are analyzed particular attention is dedicated to queueing systems in the presence of catastrophes with periodic intensity function various applications are provided including the non stationary birth death process with immigration the queueing systems m t m t 1 and m t m t

on the construction of a special class of time inhomogeneous diffusion processes a special class of time inhomogeneous diffusion processes generated starting from gauss markov processes conditioned on the same initial state is considered this class includes many interesting diffusion processes with time dependent infinitesimal drift and variance for which the transition probability density function is explicitly determined moreover closed form results for the first passage time density through suitable time varying boundaries are obtained special cases generated starting from wiener and ornstein uhlenbeck processes are considered and widely discussed

a continuous time markov chain under the influence of a regulating point process and applications in stochastic models with catastrophes abstract we consider a continuous time markov chain n t t 0 with state space s a point process x t t 0 using a function a 0 s in the following way influences the evolution of n t whenever an event of x t occurs at time t the markov chain of interest goes immediately at state a t and evolves according to the dynamics of n t until the next event of x t and so on we study the transient and the limiting distribution of the resulting process and prove some stochastic comparison facts several examples that demonstrate the applicability of the model are also included

birth death processes and associated polynomials we consider birth death processes on the nonnegative integers and the corresponding sequences of orthogonal polynomials called birth death polynomials the sequence of associated polynomials linked with a sequence of birth death polynomials and its orthogonalizing measure can be used in the analysis of the underlying birth death process in several ways we briefly review the known applications of associated polynomials which concern transition and first entrance time probabilities and establish some new results in this vein in particular our findings indicate how the prevalence of recurrence or recurrence in a birth death process can be recognized from certain properties of the orthogonalizing measure for the associated polynomials

discretization of three dimensional free surface flows and moving boundary problems via elliptic grid methods based on variational principles abstract a new boundary fitted technique to describe free surface and moving boundary problems is presented we have extended the 2d elliptic grid generator developed by dimakopoulos and tsamopoulos 2003 19 and further advanced by chatzidai et al 2009 18 to 3d geometries the set of equations arises from the fulfillment of the variational principles established by brackbill and saltzman 1982 21 and refined by christodoulou and scriven 1992 22 these account for both smoothness and orthogonality of the grid lines of tessellated physical domains the elliptic grid equations are accompanied by new boundary constraints and conditions which are based either on the equidistribution of the nodes on boundary surfaces or on the existing 2d quasi elliptic grid methodologies the capabilities of the proposed algorithm are first demonstrated in tests with analytically described complex surfaces the sequence in which these tests are presented is chosen to help the reader build up experience on the best choice of the elliptic grid parameters subsequently the mesh equations are coupled with the navier stokes equations in order to reveal the full potential of the proposed methodology in free surface flows more specifically the problem of gas assisted injection in ducts of circular and square cross sections is examined where the fluid domain experiences extreme deformations finally the flow mesh solver is used to calculate the equilibrium shapes of static menisci in capillary tubes

the m m c queueing system in a random environment abstract an m m c queueing system operating in a markovian environment is studied this paper focuses on the stationary behavior and presents the theoretical framework for a special case analytical results are derived that are analogous to the classical solutions for the simple m m c queue the elaborate analysis of a specific case is given to illustrate the basic idea of the framework a technical proof with respect to the existence of d 1 roots is displayed to sustain the corresponding theory

on a class of birth death processes with time varying intensity functions abstract in this paper we investigate on a class of time inhomogeneous birth death chains obtained by applying the composition method to two time inhomogeneous double ended chains then we consider the corresponding restricted birth death process with zero reflecting boundary finally starting from the restricted process we construct a time inhomogeneous bd chain symmetric with respect to zero state we obtain closed form expressions for the transition probabilities and for the conditional moments furthermore the first passage time problem is also taken in consideration finally various numerical computations are performed for periodic intensity functions

a general topology godunov method we describe a numerical technique for solving 2 dimensional compressible multimaterial problems using a general topology mesh multimaterial problems are characterized by the presence of interfaces whose shapes may become arbitrarily complex in the course of dynamic evolution computational methods based on more conventional fixed connectivity quadrilateral meshes do not have adequate flexibility to follow convoluted interface shapes and frequently fail due to excessive mesh distortion the present method is based on a mesh of arbitrary polygonal cells because this mesh is dual to a triangulation its topology is unrestricted and it is able to accommodate arbitrary boundary shapes additionally this mesh is able to quickly and smoothly change local mesh resolution thus economizing on the number of mesh cells and it is able to improve mesh isotropy because in a region of uniform mesh the cells tend to become regular hexagons the underlying algorithms are based on those of the caveat code these consist of an explicit finite volume cell centered arbitrary lagrangian eulerian ale technique coupled with the godunov method which together are readily adaptable to a general topology mesh several special techniques have been developed for this extension to a more general mesh they include an interface propagation scheme based on huygens construction a near lagrangian mesh rezoning algorithm that minimizes advection while enhancing mesh regularity an efficient global remapping algorithm that is capable of conservatively transferring quantities from one general mesh to another and various mesh restructering algorithms such as mesh reconnection smoothing and point addition and deletion

asymptotic results for random walks in continuous time with alternating rates we investigate some large deviation problems for a random walk in continuous time n t t ge 0 with spatially inhomogeneous rates of alternating type we first deal with the large deviation principle for the convergence of n t t to a suitable constant then the case of moderate deviations is also discussed motivated by possible applications in chemical physics context we finally obtain an asymptotic lower bound for level crossing probabilities both in the case of finite and infinite horizon

generation of computational grids using optimization a method for generation of computational grids using principles of nonlinear programming optimization is described grids are generated so that certain discrete measures of grid smoothness and orthogonality are max imized using a fast iterative optimization procedure the method can also be used to improve an existing grid ir respective of the method used for its generation if the original grid contains regions of overlap nonpositive jacobian this method is capable of unraveling the grid and making it useful for computations the iterative op timization procedure is efficient due to the use of a conjugate direction method with exact line searching examples are given of the application of this technique to two and three dimensional computational grids the extension of the method to generate solution adaptive grids is discussed n the past few years there has been a great deal of interest in the development of computational grid generation techniques1 for discretizing complex regions for the numerical solution of partial differential equations the commonly used grid generation methods have achieved a high degree of sophistication and ease of use however for complex con figurations the existing methods do not always produce ac ceptable grids for computations grid quality deterioration is especially apparent in three dimensional grid generation methods and when two dimensional grids are combined to form a three dimensio nal grid 2 3 in addition to grid quality problems many methods suffer from computational ineffi ciency for these reasons the authors have perceived a need for a grid generatio n method that could be used to improve the quality of a given computational grid in addition the method should be capable of serving as a stand alone grid generation procedure independent of other techniques the basic concept behind this grid generation method is to assume from the outset that the grid to be generated or op timized consists of straight line segments joining the nodal grid points this is in contrast to methods that solve elliptic parabolic or hyperbolic partial differential equations or use conformal mapping these methods are based on con tinuous not discrete coordinate transformations and therefore suffer from discretization errors for any grid con sisting of a finite number of grid points the grid generation technique described herein formulates discrete measures of grid smoothness and orthogonality at each grid point and therefore does not suffer from truncation errors on coarse grids these measures of grid quality are then minimized us ing a conjugate direction procedure with exact line searching the resulting grids are optimal with respect to the particular smoothness and orthogonality measures chosen and there are many possible choices for their exact forms the next section describes the formulation of the method followed by some typical results of using this method to im prove existing grids or generate new grids finally exten sions of the method for generating solution adaptive grids are discussed and other areas of possible future research are pointed out analysis the formulation of the method will be illustrated for two dimensional grids the details of the method for the three dimensional case are given in the appendix we will discuss the grid generation method by first noting similarities with the saltzman brackbill4 variational grid generation method in the variational method two func tionals are introduced that provide measures of grid smoothness

coordinate system control adaptive meshes the discussion of the formulation and properties of the adaptive mesh algorithm is as complete as space permits as should be clear from the discussion adaptive gridding is most useful for singular perturbation problems where localized regions with large gradients develop spontaneously often choosing the correct weight function is not trivial and sometimes it is appropriate to cause the mesh to respond to structure in several dependent variables simultaneously

variational methods for generating meshes on surfaces in three dimensions variational methods for generating meshes are developed for arbitrary surfaces in three dimensions several variational principles are written down for surfaces the corresponding elliptic equations are listed and several simple examples are given in addition a short discussion of planar methods and relative scaling of integrals are included in this paper for completeness

linear distribution imaging of thin metallic cylinders under mutual scattering in this paper we address the problem of imaging thin metallic cylinders from the knowledge of the electric far field scattered under the incidence of plane waves a scattering model based on a multipole expansion accounting for the mutual scattering is introduced and then simplified under the single and second order scattering hypotheses the locations of the unknown cylinders for the inverse problem are described in terms of support of spl delta functions the performances of a truncated singular value decomposition based linear inversion algorithm in the presence of model errors due to mutual scattering is investigated by both analytical and numerical arguments in three different measurement configurations single frequency multiview multifrequency single view and multifrequency multiview the different effects of the angular and frequency diversities are pointed out

application of a single equation mg fas solver to elliptic grid generation equations subgrid and supergrid coefficient generation a single equation mg fas solver is applied to elliptic grid generation equations obtained from variational principle and to problems of fluid dynamics and electromagnetics on these grids the problem of automatic generation of subgrid coefficients given the user defined discretized problem on a defining grid is addressed in a novel and clear way which has some advantages the same idea is applied to supergrid generation of the elliptic grid generation equations which can result in substantial arithmetic savings for solution adaptive grid generation in 3d

adaptive grid generation from harmonic maps on reimannian manifolds abstract in this paper we describe a new method for generation of solution adaptive grids based on harmonic maps on riemannian manifolds the reliability of the method is assured by an existence and uniqueness theorem for one to one maps between multidimensional multiconnected domains we formulate an adaptive riemannian metric consistent with this theorem several examples demonstrating application of the developed procedure are provided

analysis of random walks with an absorbing barrier and chemical rule recently tarabia and el baz a m k tarabia a h el baz transient solution of a random walk with chemical rule physica a 382 2007 430 438 have obtained the transient distribution for an infinite random walk moving on the integers 0 in random walk terminology the busy period concerns the first passage time to zero this relation of these walks to queuing problems is pointed out and the distributions of the queue length in the system and the first passage time busy period are derived as special cases of our result the conolly et al b w conolly p r parthasarathy s dharmaraja a chemical queue math sci 22 1997 83 91 solution and the probability density function pdf of the busy period for the m m 1 queue are easily obtained finally numerical values are given to illustrate the efficiency and effectiveness of the proposed approach

analysis of the m g 1 queue in multi phase random environment with disasters this paper studies an m g 1 queue in a multi phase random environment when in operative phase i i 1 2 n the system is subject to disastrous interruptions causing all present customers waiting and served to leave the system at an exponential failure instant the server abandons the service and the system goes directly to repair phase after an exponential repair time the system moves to operative phase i with probability qi i 1 2 n using the supplementary variable technique we obtain the distribution for the stationary queue at an arbitrary epoch we also derive results of the cycle analysis the sojourn time distribution and the length of the server s working time in a service cycle in addition some special cases and numerical examples are presented

a state dependent queueing system with asymptotic logarithmic distribution abstract a markovian single server queueing model with poisson arrivals and state dependent service rates characterized by a logarithmic steady state distribution is considered the laplace transforms of the transition probabilities and of the densities of the first passage time to zero are explicitly evaluated the performance measures are compared with those ones of the well known m m 1 queueing system finally the effect of catastrophes is introduced in the model and the steady state distribution the asymptotic moments and the first visit time density to zero state are determined

simple adaptive grids for 1 d initial value problems abstract in solving 1 d initial value problems by implicit finite difference methods it is advantageous to use an adaptive grid to provide local regions of high resolution and allow larger time steps to be taken a simple method of constructing such grids is presented and the benefits are demonstrated by calculations of sod s shock tube problem g a sod j comput phys 27 1 1978 and of a supernova explosion

the iterative time reversal process analysis of the convergence the efficiency of a time reversal acoustic mirror to focus on a reflective target through an inhomogeneous media has been demonstrated in a multitarget media the ability of such a mirror to work in an iterative mode in order to focus selectively on the strongest target was shown c prada f wu and m fink j acoust soc am 90 1119 1991 the theory of how the iterative time reversal process is built is based on a matrix formalism and treats the array of l transducers in a given medium as a linear system of l inputs l outputs the system is characterized at each frequency by its transfer matrix k and the time reversal iterative process is then described by a time reversal operator k k because of the reciprocity principle this operator is hermitian the following result is shown if the scattering medium is a set of well resolved targets of different reflectivities then each eigenvector of the operator k k with nonzero eigenvalue corresponds to one of the targets in the set and provides the opt

of dogs and fleas the dynamics of n uncoupled two state systems the historical ehrenfest model dating back to 1907 describes the process of equilibration together with fluctuations around the thermal equilibrium this approach represents a special case in the dynamics of n uncoupled two state systems in this article we present a generalization of the original model by introducing an additional parameter p which denotes the probability of a single state change analytical solutions for the probability distribution of the system s state as well as the fluctuation distribution are derived interestingly close inspection of the fluctuation distribution reveals an intrinsic time scale sampling the system s state at much slower rates yields the familiar macroscopic exponential distribution for equilibrium processes for faster measurements a power law extends roughly over log10 n orders of magnitude followed by an exponential tail at some point further increases of the sampling rate merely result in a shift of the fluctuation distribution towards higher values leaving plateau at small fluctuation sizes behind since the generic solution is rather unwieldy we derive and discuss simple and intuitive analytical solutions in the limit of small p and large n furthermore we relax the quantization of time by considering a complementary approach in continuous time finally we demonstrate that the fluctuation distributions resulting from the two different approaches bear identical characteristic features

exact results for the diffusion in a class of asymmetric bistable potentials we solve the fokker planck equations with drifts deriving from a class of asymmetric nonharmonic potentials which include bistable cases an analytical expression for the probability current over the potential barrier is obtained finally we compare our exact results with those obtained by kramers approximation

numerical methods for tracking interfaces an overview is given of special numerical methods for tracking discontinuous fronts and interfaces these methods include surface tracking methods based on connected marker points along the interface volume tracking methods that track the volume occupied by the solution regions bounded by the interfaces and moving mesh methods where the underlying mesh is aligned and moved with the interface the pros and cons of the current methods are discussed and a new method is proposed that overcomes some of the difficulties encountered in approximating equations with multiple interacting interfaces

time dependent queues a single server queue is considered having exponentially distributed inter arrival and service times with slowly changing time dependent rates lambda varepsilon t and mu varepsilon t the parameter varepsilon is the ratio of an average inter arrival time to the time over which the rates change appreciably so it is small therefore an asymptotic solution valid for varepsilon small is constructed for the time dependent queue length probability distribution it consists of five typical parts corresponding to five typical time periods they are the initial period the period of light traffic when lambda mu 1 the saturation transition period when lambda mu increases through unity the oversaturation period when lambda mu starts out greater than unity and then decreases below unity and the transition period at the end of oversaturation when the queue returns to the light traffic condition by combining the solutions for these five intervals the solution fo

a moving mesh finite element method for the two dimensional stefan problems an r adaptive moving mesh method is developed for the numerical solution of an enthalpy formulation of two dimensional heat conduction problems with a phase change the grid is obtained from a global mapping of the physical to the computational domain which is designed to cluster mesh points around the interface between the two phases of the material the enthalpy equation is discretised using a semiimplicit galerkin finite element method using linear basis functions the moving finite element method is applied to problems where the phase front is cusp shaped and where the interface changes topology

an iterative grid redistribution method for singular problems in multiple dimensions we introduce an iterative grid redistribution method based on the variational approach the iterative procedure enables us to gain more precise control of the grid distribution near the regions of large solution variations the method is particularly effective for solving partial differential equations with singular solutions e g blowup solutions our method requires little prior information of the singular solutions and can handle multiple singularities the method is successfully applied to the nonlinear schrodinger equation and the keller segal equations where solutions with multiple blowup points can be solved up to times very close to the blowup time

optimal anisotropic meshes for minimizing interpolation errors in l p norm in this paper we present a new optimal interpolation error estimate in l p norm 1 p for finite element simplicial meshes in any spatial dimension a sufficient condition for a mesh to be nearly optimal is that it is quasi uniform under a new metric defined by a modified hessian matrix of the function to be interpolated we also give new functionals for the global moving mesh method and obtain optimal monitor functions from the viewpoint of minimizing interpolation error in the l p norm some numerical examples are also given to support the theoretical estimates

decomposition of the time reversal operator detection and selective focusing on two scatterers the decomposition of the time reversal operator dort method is a selective detection and focusing technique using an array of transmit receive transducers it relies on the theory of iterative time reversal mirrors which was presented by prada et al c prada j l thomas and m fink j acoust soc am 97 62 71 1995 the time reversal operator was defined as k k where is the frequency means complex conjugate and k is the transfer matrix of the array of l transducers insonifying a time invariant scattering medium it was shown that this time reversal operator can be diagonalized and that for ideally resolved scatterers of different reflectivities each of its eigenvectors of nonzero eigenvalue provides the phase law to be applied to the transducers in order to focus on one of the scatterers the dort method consists in determining these eigenvectors and using them for the selective focusing this paper presents a complete analysis of this method in the case of two scatterers the

a new formula for the transient behaviour of a non empty m m 1 queue this paper studies the most general model of the markovian queues namely m m 1 queue with any arbitrary number i of customers being present in the system initially for this model a new and simple series form is obtained for the transient state probabilities whence all particular cases concerning the system being empty and steady state situations can be derived straightaway the coefficients in this series satisfy iterative recurrence relations which would allow for the rapid and efficient numerical evaluations of the state probabilities moreover a simple algebraic proof to show the equivalence between different formulae of a non empty m m 1 and the new formula is established

a continuous time ehrenfest model with catastrophes and its jump diffusion approximation we consider a continuous time ehrenfest model defined over the integers from n to n and subject to catastrophes occurring at constant rate the effect of each catastrophe istantaneously resets the process to state 0 we investigate both the transient and steady state probabilities of the above model further the first passage time through state 0 is discussed we perform a jump diffusion approximation of the above model which leads to the ornstein uhlenbeck process with catastrophes the underlying jump diffusion process is finally studied with special attention to the symmetric case arising when the ehrenfest model has equal upward and downward transition rates

transient solution of a random walk with chemical rule abstract conolly et al math scientist 22 1997 83 91 have obtained the transient distribution for a random walk moving on the integers k of the real line their analysis is based on a generating function technique in this paper an alternative technique is used to derive elegant explicit expressions for the transient state distribution of an infinite random walk having chemical rule and starting initially at any arbitrary integer position say i as a special case of our result conolly et al s 1997 solution is easily obtained moreover the transient solution of the infinite symmetric continuous random walk is also presented finally numerical values testing the quality of our analytical results are illustrated

large deviations for markov processes with resetting markov processes restarted or reset at random times to a fixed state or region in space have been actively studied recently in connection with random searches foraging and population dynamics here we study the large deviations of time additive functions or observables of markov processes with resetting by deriving a renewal formula linking generating functions with and without resetting we are able to obtain the rate function of such observables characterizing the likelihood of their fluctuations in the long time limit we consider as an illustration the large deviations of the area of the ornstein uhlenbeck process with resetting other applications involving diffusions random walks and jump processes with resetting or catastrophes are discussed

a phase and space coherent direct imaging method a direct imaging algorithm for point and extended targets is presented the algorithm is based on a physical factorization of the response matrix of a transducer array the factorization is used to transform a passive target problem to an active source problem and to extract principal components tones in a phase consistent way the multitone imaging function can superpose multiple tones spatial diversity aperture of the array and frequencies bandwidth of the probing signal based on phase coherence the method is a direct imaging algorithm that is simple and efficient since no forward solver or iteration is needed robustness of the algorithm with respect to noise is demonstrated via numerical examples

exact transient solutions of nonempty markovian queues it has been shown by sharma and tarabia 1 that a power series technique can be successfully applied to derive the transient solution for an empty m m 1 n queueing system in this paper we further illustrate how this technique can be used to extend 1 solution to allow for an arbitrary number of initial customers in the system moreover from this other more commonly sought results such as the transient solution of a nonempty m m 1 queue can be computed easily the emphasis in this paper is theoretical but numerical assessment of operational consequences is also given

variational barrier method of adaptive grid generation in hyperbolic problems of gas dynamics application of the harmonic mapping using a variational approach to generate moving adaptive grids in the hyperbolic problems of gas dynamics is considered using the example of a three point model of adaptation the possibility to generate an unfolded mesh with strong grid lines condensing in the vicinity of discontinuities of the control monitor function is demonstrated the algorithm of redistributing the boundary nodes is suggested and consists of using constrained minimization of the discrete harmonic functional when constraints define the boundary of the domain in real computations due to mesh adaptation it is possible to reduce the errors caused by shock waves smearing over the cells by many factors of ten modeling of the two dimensional 2 d supersonic gas flow in the channel has shown that the same accuracy on the adaptive grid with the same structure as the quasi uniform mesh can be acheived while requiring less cpu memory by a factor of 25 and less running time by a factor of 50 to 60 computational tests of the steady transonic and supersonic flow over an airfoil demonstrate the ability of the method to control mesh sizes across shocks

m m 1 queue in two alternating environments and its heavy traffic approximation abstract we investigate an m m 1 queue operating in two switching environments where the switch is governed by a two state time homogeneous markov chain this model allows to describe a system that is subject to regular operating phases alternating with anomalous working phases or random repairing periods we first obtain the steady state distribution of the process in terms of a generalized mixture of two geometric distributions in the special case when only one kind of switch is allowed we analyze the transient distribution and investigate the busy period problem the analysis is also performed by means of a suitable heavy traffic approximation which leads to a continuous random process its distribution satisfies a partial differential equation with randomly alternating infinitesimal moments for the approximating process we determine the steady state distribution the transient distribution and a first passage time density

boundary fitted coordinate systems for numerical solution of partial differential equations a review a comprehensive review of methods of numerically generating curvilinear coordinate systems with coordinate lines coincident with all boundary segments is given some general mathematical framework and error analysis common to such coordinate systems is also included the general categories of generating systems are those based on conformal mapping orthogonal systems nearly orthogonal systems systems produced as the solution of elliptic and hyperbolic partial differential equations and systems generated algebraically by interpolation among the boundaries also covered are the control of coordinate line spacing by functions embedded in the partial differential operators of the generating system and by subsequent stretching transformation dynamically adaptive coordinate systems coupled with the physical solution and time dependent systems that follow moving boundaries are treated references reporting experience using such coordinate systems are reviewed as well as those covering the system development

analysis of the time reversal operator for a small spherical scatterer in an electromagnetic field the time reversal operator tro for a planar array of crossed dipole elements illuminating a small conducting and or dielectric sphere is investigated in order to determine the general properties of an electromagnetic time reversing array system the behavior of such a system for a given frequency is analyzed by studying the eigenvalues and eigenvectors of the tro each eigenvector specifies a set of complex driving currents for the array elements that produce received voltages that are proportional to the conjugates of the drive currents the proportionality constant is equal to the square root of the associated eigenvalue and is the same for all elements the eigenvalues and eigenvectors can be determined by performing a singular value decomposition svd on the multistatic data matrix of the array the eigenvalues of the tro are the squares of the singular values and the eigenvectors are identical to the singular vectors we have shown that the maximum number of singular vectors associated with the sphere is equal to the number of orthogonal orientations of the dipole moments induced in the sphere when irradiated by the array so there is a maximum of six for a conducting sphere but only three are significant when the conductivity is small and the sphere may be considered being just a dielectric numerical results are presented for linear and circular arrays to show the general behavior of the system

a robust elliptic grid generator a variational principle is proposed that results in a robust elliptic grid generator having many of the strengths of original winslow or homogeneous thompson thames mastin method httm the new grid generator places grid lines more uniformly over the domain than does httm without loss of orthogonality numerically generated examples are given to demonstrate these effects grid quality measures are introduced to quantify differences between discrete grids both the httm and the new grid generator can generate folded grids on certain pathological regions but overall they are very robust grid weighting for solution adaptive calculations is briefly considered generalization of the new method to surface and volume grid generation is straightforward

an adaptive grid solution procedure for convection diffusion problems abstract a computationally efficient and stable adaptive grid solution procedure is developed for convection diffusion problems in this method grid refinement and adaptation is based on an equidistribution law but is only performed in regions with high error estimates that are flagged from a preliminary coarse grid solution the equidistribution law is implicit in the grid generation procedure which requires the solution of two poisson equations with control functions that are obtained directly from the error estimates or weighting functions at the grid points solution on the refined equidistributed mesh in the flagged region is obtained with boundary conditions interpolated from the coarse grid results accurate solutions in both the flagged region and the coarse grid regions of the domain are obtained with a multigrid approach that requires successive solutions on the refined equidistributed mesh in the flagged region and on the coarse mesh in the entire domain the adaptive grid method including the multigrid calculations can be extended to several levels of refinement the acronym lame is coined for this procedure in view of its local adaptation multigridding and equidistribution features the method is shown to be stable computationally efficient and accurate by applying it to three test problems and comparing with conventional calculations on a fixed curvilinear grid

generalized pollaczek khinchin formula for markov channels the wireless fading channels with finite input buffer poisson arrivals and two state markov modulated service processes mmsp are modeled as m mmsp 1 k queues in this paper the existing performance analyses of markov channels are almost all based on the matrix geometric method which provides little physical insights for system design by contrast we focus on deriving closed form analytic expressions with physical interpretations in terms of system parameters of interest our main contribution is to derive the generalized pollaczek khinchin p k formula of m mmsp 1 k queue from start service probability to explore the impact of state transitions on the queueing behavior of markov channels this generalized p k formula reveals that the performance of wireless channels with varying rates can be fully characterized by a newly defined system parameter called state transition factor which clearly explains the reason that the channel with slow state transition rate owns a larger delay for the same channel capacity in the extreme case when the state transition factor approaches 0 we show that the channel under consideration can be approximately modeled as an m g 1 queue we use the type i hybrid arq system with a fixed data rate as an example in this paper to illustrate our results

a finite element method for three dimensional unstructured grid smoothing the finite element method is applied to grid smoothing in three dimensional geometry generalizing earlier results obtained for planar geometry the underlying set of equations for the cartesian components of grid coordinates based on the notion of harmonic coordinates has a natural variational formulation to estimate the target metric tensor that drives the elliptic grid equations the metric tensor components are computed on a coarse grained grid numerical examples illustrating the proposed approach are presented together with results from the smoothness functional which is used to measure the quality of the resulting grid

properties of additive functionals of brownian motion with resetting we study the distribution of additive functionals of reset brownian motion a variation of normal brownian motion in which the path is interrupted at a given rate and placed back to a given reset position our goal is two fold 1 for general functionals we derive a large deviation principle in the presence of resetting and identify the large deviation rate function in terms of a variational formula involving large deviation rate functions without resetting 2 for three examples of functionals positive occupation time area and absolute area we investigate the effect of resetting by computing distributions and moments using a formula that links the generating function with resetting to the generating function without resetting

a birth and death process related to the rogers ramanujan continued fraction abstract time dependent system size probabilities of a birth and death process related to the rogers ramanujan continued fraction are obtained the range for the parameter in this continued fraction is obtained to ensure the positivity of the recursively defined birth and death rates the general behavior of the birth and death rates is described and the asymptotic behavior of the transition probabilities and the quasi stationary distribution is determined for the transient case the birth and death process can be seen as a model in queuing theory where the length of the queue encourages customers to join the queue the more the merrier

iterative schemes and algorithms for adaptive grid generation in one dimension some iterative adaptive grid generators developed by the author are numerically explored in detail to assess their relative merits against conventional grid generators based on a direct method of integration and interpolation we find that some of these iterative adaptive grid generators are preferable to a direct method of integration and interpolation in contrast with a direct method appropriate use of these iterative adaptive grid generators produces adaptive grids with a smooth variation of the grid spacing ratio and resolution all adaptive grid generators are a subclass of a more general iterative map general features of this iterated map which are related to the function to be resolved are briefly discussed the results obtained here supplements recent investigations on these adaptive grid generators by the author

the fokker planck equation for a bistable potential univ estadual paulista unesp inst biociencia letras ciencias exatas dept fis br 15054000 sao jose do rio preto sp brazil

parameter estimation in variational grid generation two approaches to numerical variational grid generation use a linear combination of three variational problems to control the properties of the grid previously the parameters in the linear combination were determined by experimentation good estimates for these parameters can be obtained from simple model problems

spectral properties of birth death polynomials we consider sequences of polynomials that are defined by a three terms recurrence relation and orthogonal with respect to a positive measure on the nonnegative axis by a famous result of karlin and mcgregor such sequences are instrumental in the analysis of birth death processes inspired by problems and results in this stochastic setting we present necessary and sufficient conditions in terms of the parameters in the recurrence relation for the smallest or second smallest point in the support of the orthogonalizing measure to be larger than zero and for the support to be discrete with no finite limit point

discretization of free surface flows and other moving boundary problems a system of elliptic partial differential equations and boundary conditions has been developed for generating boundary fitted element discretizations of two dimensional free and moving boundary problems terms in the differential equations are scaled for dimensional homogeneity and adjustable weighting of orthogonality smoothness and concentration of the coordinate mesh they govern grid points become finite element nodes mapped isoparametrically or subparametrically from a simple or patched computational domain concentration terms contain control functions and parameters that influence node spacing along each coordinate independently overall control is by patchwise parameters and functions successful selection of these to follow deforming flow regions is straightforward and is illustrated by analysis of steady and transient slide coating flows

multistatic response matrix of a 3 d inclusion in half space and music imaging recent work on the retrieval of 3 d bounded dielectric and or magnetic inclusions in free space is extended to burial in a half space though emphasis is on the case of a single inclusion enabling the derivation of closed form mathematical results in illuminating fashion the approach extends to the case of an unknown number of well separated inclusions within an asymptotic field formulation derived from exact contrast source vector integral formulations satisfied by the time harmonic fields and using proper reciprocity relationships of the dyadic green s functions the multistatic response matrix of the inclusion is constructed from the leading order term of the fields its singular value structure is analyzed in detail for a dielectric or a magnetic contrast or both contrasts this is performed in the case of a unique electric dipole array operated in the transmit receive mode at a single frequency a multiple signal classification type algorithm follows from the decomposition yielding a cost functional the magnitude of which peaks at the inclusion center numerical results illustrate the above as a function of the geometric and electromagnetic parameters of the configuration imaging of a spherical inclusion is in particular investigated from severely noisy synthetic data as well as of two inclusions embedded within a non conductive or conductive half space

analysis of the time reversal operator for scatterers of finite size recently it was shown that the time reversal operator for a single small spherical scatterer could have up to four distinguishable eigenstates chambers and gautesen j acoust soc am 109 2616 2624 2001 in this paper that analysis is generalized for scatterers of arbitrary shape and larger size it is shown that the time reversal operator may have an indefinitely large number of distinguishable eigenstates with the exact number depending on the nature of the scatterer and the geometry of the time reversal mirror in addition the case of a multiple number of well separated scatterers is investigated with the result that the total spectrum is the direct combination of the eigenstates associated with each scatterer as an example the singular value spectrum of the time reversal operator for a linear array is calculated explicitly for bubbles and hard rubber spheres of finite size both resonance peaks and apparent crossing points can be observed in the spectrum as the size of the scatterer increases

exact solution for the diffusion in bistable potentials we solve analytically the fokker planck equation for a one parameter family of symmetric attractive nonharmonic potentials which include double well situations the exact knowledge of the eigenfunctions and eigenvalues allows us to fully discuss the transient behavior of the probability density in particular for the bistable potentials we can give analytical expressions for the probability current over the working barrier and for the onset time which characterizes the transition from uni to bimodal probability densities

diffusion with optimal resetting we consider the mean time to absorption by an absorbing target of a diffusive particle with the addition of a process whereby the particle is reset to its initial position with rate r we consider several generalisations of the model of m r evans and s n majumdar 2011 diffusion with stochastic resetting phys rev lett 106 160601 i a space dependent resetting rate r x ii resetting to a random position z drawn from a resetting distribution p z iii a spatial distribution for the absorbing target pt x as an example of i we show that the introduction of a non resetting window around the initial position can reduce the mean time to absorption provided that the intial position is sufficiently far from the target we address the problem of optimal resetting that is minimising the mean time to absorption for a given target distribution for an exponentially decaying target distribution centred at the origin we show that a transition in the optimal resetting distribution occurs as the target distribution narrows

ehrenfest model with large jumps in finance changes returns in stock index prices and exchange rates for currencies are argued based on empirical data to obey a stable distribution with characteristic exponent 2 for short sampling intervals and a gaussian distribution for long sampling intervals in order to explain this phenomenon an ehrenfest model with large jumps elj is introduced to explain the empirical density function of price changes for both short and long sampling intervals

a fast algorithm for the first passage times of gauss markov processes with holder continuous boundaries even for simple diffusion processes treating first passage problems analytically proves intractable for generic barriers and existing numerical methods are inaccurate and computationally costly here we present a novel numerical method that is faster and has more tightly controlled accuracy our algorithm is a probabilistic variant of dichotomic search for the computation of first passage times through non negative homogeneously holder continuous boundaries by gauss markov processes these include the ornstein uhlenbeck process underlying the ubiquitous leaky integrate and fire model of neuronal excitation our method evaluates discrete points in a sample path exactly and refines this representation recursively only in regions where a passage is rigorously estimated to be probable e g when close to the boundary

a birth death process suggested by a chain sequence we consider a birth death process whose birth and death rates are suggested by a chain sequence we use an elegant transformation to find the transition probabilities in a simple closed form we also find an explicit expression for time dependent mean we find parallel results in discrete time finally we show that the processes under investigation are transient and hence the stationary distribution does not exist

efficient computation of dendritic growth with r adaptive finite element methods this paper deals with the application of a moving grid method to the solution of a phase field model for dendritic growth in two and three dimensions a mesh is found as the solution of an optimization problem that automatically includes the boundary conditions and is solved using a multi grid approach the governing equations are discretized in space by linear finite elements and a split time level scheme is used to numerically integrate in time one novel aspect of the method is the choice of a regularized monitor function the moving grid method enables us to obtain accurate numerical solutions with much less degree of freedoms it is demonstrated numerically that the tip velocity obtained by our method is in good agreement with the previously published results