generation and monitoring of discrete stable random processes using multiple immigration population models some properties of classical population processes that comprise births deaths and multiple immigrations are investigated the rates at which the immigrants arrive can be tailored to produce a population whose steady state fluctuations are described by a pre selected distribution attention is focused on the class of distributions with a discrete stable law which have power law tails and whose moments and autocorrelation function do not exist the separate problem of monitoring and characterizing the fluctuations is studied analysing the statistics of individuals that leave the population the fluctuations in the size of the population are transferred to the times between emigrants that form an intermittent time series of events the emigrants are counted with a detector of finite dynamic range and response time this is modelled through clipping the time series or saturating it at an arbitrary but finite level whereupon its moments and correlation properties become finite distributions for the time to the first counted event and for the time between events exhibit power law regimes that are characteristic of the fluctuations in population size the processes provide analytical models with which properties of complex discrete random phenomena can be explored and in addition provide generic means by which random time series encompassing a wide range of intermittent and other discrete random behaviour may be generated

discontinuous generalized solutions of nonlinear nonconservative hyperbolic equations abstract nonlinear nonstationary problems arising in elastodynamics have naturally a nonconservative form for these systems it is not possible to define a weak solution according to distribution theory in order to define the concept of discontinuous solutions for these systems one is confronted with multiplications of distributions this is unavoidable from a physical viewpoint since discontinuous solutions are needed to represent shock waves the theory of generalized functions of the second author in which one may multiply arbitrary distributions gives a concept of generalized solutions that may be discontinuous functions existence of such global solutions of the cauchy problem for a system of two equations is proved by a compactness argument from a convergent numerical scheme in the case under consideration the generalized solutions are bounded variation functions the results thus obtained agree with the results expected by the engineers and lead to the development of new numerical schemes

the evolution of a batch immigration death process subject to counts a bivariate batch immigration death process is developed to study the degree to which the fundamental structure of a hidden stochastic process can be inferred purely from counts of escaping individuals this question is of immense importance in fields such as quantum optics where externally based radiation elucidates the nature of the underlying electromagnetic radiation process batches of i immigrants enter the population at rate qi and each individual dies independently at rate general expressions are developed for the population size cumulants and probabilities together with those for the associated counting process the strong link between these two structures is highlighted through two specific examples involving k batch immigration for i k and schoenberg batch immigration over i 2m m 0 1 2 and shows that high quality inferences on the hidden population process can be inferred purely from externally counted observations

markov branching processes with instantaneous immigration markov branching processes with instantaneous immigration possess the property that immigration occurs immediately the number of particles reaches zero i e the conditional expectation of sojourn time at zero is zero in this paper we consider the existence and uniqueness of such a structure we prove that if the sum of the immigration rates is finite then no such structure can exist and we provide a necessary and sufficient condition for existence for the case in which this sum is infinite study of the uniqueness problem shows that for honest processes the solution is unique

statistics of binomial number fluctuations when birth terms in the rate equation for a simple birth death population process are proportional to the difference between the number of individuals present and a larger fixed number the equilibrium population obeys a binomial distribution in this paper the statistics of such a process are investigated properties of the related counting process including interval statistics are calculated and the results used to evaluate the autocorrelation function of a binomial telegraph wave

random walks with power law fluctuations in the number of steps in this paper we derive limiting distributions for the resultant of an anisotropic random walk where the individual steps comprising the walk are drawn from distributions of arbitrary but finite variance and where the number of steps fluctuate according to a discrete power law distribution the consideration of discrete distributions with power law tails is motivated by their recently discovered relevance to complex systems and networks when this random walk is unbiased a power law decay for large values of the amplitude of the resultant occurs for a small directional bias the power law tail persists only in the direction parallel to the bias exhibiting an exponential decay in all other directions we consider the relevance of the limiting distributions to non diffusive transport

why nonconservative schemes converge to wrong solutions error analysis this paper attempts to give a qualitative and quailtitative description of the numerical error introduced by using finite difference schemes in nonconservative form for scalar conservation laws we show that these schemes converge strongly in li norm to the solution of an inhomogeneous conservation law containing a borel measure source term moreover we analyze the properties of this borel measure and derive a sharp estimate for the l1 error between the limit function given by the scheme and the correct solution in general the measure source term is of the order of the entropy dissipation measure associated with the scheme in certain cases the error can be small for short times which makes it difficult to detect numerically but generically such an error will grow in time and this would lead to a large error for large time calculations finally we show that a local correction of any high order accurate scheme in nonconservative form is sufficient to ensure its convergence to the correct solution

accuracy analysis of measurements on a stable power law distributed series of events we investigate how finite measurement time limits the accuracy with which the parameters of a stably distributed random series of events can be determined the model process is generated by timing the emigration of individuals from a population that is subject to deaths and a particular choice of multiple immigration events this leads to a scale free discrete random process where customary measures such as mean value and variance do not exist however converting the number of events occurring in fixed time intervals to a 1 bit clipped process allows the construction of well behaved statistics that still retain vestiges of the original power law and fluctuation properties these statistics include the clipped mean and correlation function from measurements of which both the power law index of the distribution of events and the time constant of its fluctuations can be deduced we report here a theoretical analysis of the accuracy of measurements of the mean of the clipped process this indicates that for a fixed experiment time the error on measurements of the sample mean is minimized by an optimum choice of the number of samples it is shown furthermore that this choice is sensitive to the power law index and that the approach to poisson statistics is dominated by rare events or outliers our results are supported by numerical simulation

multiplications of distributions in elasticity and hydrodynamics it is shown how a mathematical theory of generalized functions in which the multiplications of distributions appearing in nonlinear equations of physics make sense gives new formulas and new numerical results the new methods shown here are quite general but since each particular problem requires its own study this paper is limited to elasticity and hydrodynamics in elasticity hooke s law gives systems in a nonconservative form the study of shock waves for these systems gives nonclassical multiplications of distributions of the form y y heaviside function dirac mass at the origin using this new mathematical tool new formulas are obtained more generally new numerical schemes in a first step ambiguous results are obtained then the ambiguity is removed in hydrodynamics a formulation is obtained that has a nonconservative form and is at the basis of efficient new numerical schemes strictly speaking the reader is not assumed to know anything either on distributions or on elasticity and hydrodynamics since the basic equations are recalled all computations done in this paper are rigorous from the mathematical viewpoint

intrinsic and measured statistics of discrete stochastic populations the notion that the nature of a measurement is critical to its outcome is usually associated with quantum phenomena in this paper we show that the observed statistical properties are also a function of the measurement technique in the case of simple classical populations in particular the measured and intrinsic statistics of a single population may be different while correlation and transfer of individuals between two populations may be hidden from the observer

fluctuations in a coupled population model we investigate a discrete markov process in which the immigration of individuals into one population is controlled by the fluctuations in another we examine the effect of coupling back the second population to the first through a similar mechanism and derive exact solutions for the generating functions of the population statistics we show that a stationary state exists over a certain parameter range and obtain expressions for moments and correlation functions in this regime when more than two populations are coupled cyclically transient oscillations and periodic behaviour of correlation functions are predicted we demonstrate that if the initial distribution of either population is stable or more generally has a power law tail that falls off like n 1 0 1 then for certain parameter values there exists a stationary state that is also power law but not stable this stationary state cannot be accessed from a single multiple immigrant population model but arises solely from the nonlinear interaction of the coupled system

continuous and discrete stable processes the one sided levy stable probability densities and the discrete stable distributions form a doubly stochastic poisson transform pair this relationship facilitates the formulation of a class of continuous stable stochastic processes

distinguishing population processes by external monitoring we investigate the statistical and correlation properties of two stochastic population models that give rise to identical first order probability densities we assume that the processes are monitored indirectly through measurement of the rate at which individuals emigrate from the population formulae characterizing the integrated statistics of these counting processes are derived and it is shown how they may be used to distinguish the population models

multicomponent flow calculations by a consistent primitive algorithm the dynamics of inviscid multicomponent fluids may be modelled by the euler equations augmented by one or more additional species equation s attempts to compute solutions for extended euler models in conservation form show strong oscillations and other computational inaccuracies near material interfaces these are due to erroneous pressure fluctuations generated by the conservative wave model this problem does not occur in single component computations and arises only in the presence of several species a nonconservative primitive euler formulation is proposed which results in complete elimination of the oscillations the numerical algorithm uses small viscous perturbations to remove leading order conservation errors and is conservative to the order of numerical approximation numerical experiments show clean monotonic solution profiles with acceptably small conservation error for shocks of weak to moderate strengths

proof of the macdonald conjecture a plane partition of n is an array a i not necessarily square of positive integers which has non increasing rows and columns such that the sum of its elements is n with such an array we associate the set d which is the set of all integer points i j k in the first octant such that aij is defined and 1 k aij a plane partition is cyclically symmetric if d is invariant under the mapping i j k o k i let m m n be the number of such cyclically symmetric partitions of n such that none of i j aij exceed m macdonald has conjectured that the generating function

binomial determinants paths and hook length formulae abstract we give a combinatorial interpretation for any minor or binomial determinant of the matrix of binomial coefficients this interpretation involves configurations of nonintersecting paths and is related to young tableaux and hook length formulae

microscopic profiles of shock waves and ambiguities in multiplications of distributions a rigorous mathematical method is introduced for studying discontinuous solutions for systems in nonconservative form the evidence of the agreement between the theoretical and numerical results is shown on simplified models of physics

generation and monitoring of a discrete stable random process a discrete stochastic process with stationary power law distribution is obtained from a death multiple immigration population model emigrations from the population form a random series of events which are monitored by a counting process with finite dynamic range and response time it is shown that the power law behaviour of the population is manifested in the intermittent behaviour of the series of events

laguerre population processes we analyse a number of stochastic processes that give rise to first order number statistics governed by laguerre distributions with properties that lie between poisson and geometric random variables these distributions have hitherto been used to characterize the photon statistics of a coherent mixture of thermal and laser light here we explore a number of discrete population processes that can lead to the same first order statistics and correlation functions and highlight the distinguishing features that may be used to identify the relevant model from data

fluctuations in quantum and classical populations characterization and measurement of fluctuations in quantum and classical populations are compared a simple method for estimating the population fluctuation time is outlined and approximate quantum and classical expressions for the two time correlation function are derived the utility of the method is demonstrated through analysis of the scully lamb laser model 1967 where it is shown to give correlation times in good agreement with numerical calculations for lasers operated below at and above threshold discrepancies in the predictions of a previous similar method are shown to originate from inconsistent separation of its quantum and classical versions

on the joint statistics of stable random processes a utilitarian continuous bi variate random process whose first order probability density function is a stable random variable is constructed results paralleling some of those familiar from the theory of gaussian noise are derived in addition to the joint probability density for the process these include fractional moments and structure functions although the correlation functions for stable processes other than gaussian do not exist we show that there is coherence between values adopted by the process at different times which identifies a characteristic evolution with time the distribution of the derivative of the process and the joint density function of the value of the process and its derivative measured at the same time are evaluated these enable properties to be calculated analytically such as level crossing statistics and those related to the random telegraph wave when the stable process is fractal the proportion of time it spends at zero is finite and some properties of this quantity are evaluated an optical interpretation for which is provided

connectivity patterns in loop percolation i the rationality phenomenon and constant term identities loop percolation also known as the dense o 1 loop model is a variant of critical bond percolation in the square lattice mathbb z 2 whose graph structure consists of a disjoint union of cycles we study its connectivity pattern which is a random noncrossing matching associated with a loop percolation configuration these connectivity patterns exhibit a striking rationality property whereby probabilities of naturally occurring events are dyadic rational numbers or rational functions of a size parameter n but the reasons for this are not completely understood we prove the rationality phenomenon in a few cases and prove an explicit formula expressing the probabilities in the cylindrical geometry as coefficients in certain multivariate polynomials this reduces the rationality problem in the general case to that of proving a family of conjectural constant term identities generalizing an identity due to di francesco and zinn justin our results make use of and extend algebraic techniques related to the quantum knizhnik zamolodchikov equation

discrete scale free distributions and associated limit theorems consideration is given to the convergence properties of sums of identical independently distributed random variables drawn from a class of discrete distributions with power law tails which are relevant to scale free networks different limiting distributions and rates of convergence to these limits are identified and depend on the index of the tail for indices 2 the topology evolves to a random poisson network but the rate of convergence can be extraordinarily slow and unlikely to be yet evident for the current size of the www for example it is shown that treating discrete scale free behaviour with continuum or mean field approximations can lead to incorrect results

a split godunov scheme for solving one dimensional hyperbolic systems in a nonconservative form in this paper we developed a theoretical study for nonconservative sytems in one dimension in order to construct numerical schemes for solving the riemann problem the nonconservative form of our model system required the use of a well adapted theory in order to give us a sense of our problem we chose a framework of generalized functions for solving a scalar hyperbolic equation with a discontinuous coefficient sigma t u sigma x approx 0 where u is the velocity solution of a burgers s equation after an explicit solution of the riemann problem we derived godunov split schemes for computing an approximate solution of the cauchy problem we applied our study to a system modeling elasticity and a system modeling gas dynamics some stability properties of a scheme and its convergence to a generalized solution are proved for the first model numerical experiments confirmed this convergence result for the second model calculations of flows containing weak to moderate shocks showed that conservation errors are reduced when the mesh is refined but were not entirely eliminated

high order wave propagation algorithms for hyperbolic systems we present a finite volume method that is applicable to hyperbolic pdes including spatially varying and semilinear nonconservative systems the spatial discretization like that of the well known clawpack software is based on solving riemann problems and calculating fluctuations not fluxes the implementation employs weighted essentially nonoscillatory reconstruction in space and strong stability preserving runge kutta integration in time the method can be extended to arbitrarily high order of accuracy and allows a well balanced implementation for capturing solutions of balance laws near steady state this well balancing is achieved through the f wave riemann solver and a novel wave slope weno reconstruction procedure the wide applicability and advantageous properties of the method are demonstrated through numerical examples including problems in nonconservative form problems with spatially varying fluxes and problems involving near equilibrium solutions of balance laws

on spiking models for synaptic activity and impulsive differential equations we illustrate the problems that can arise in writing differential equations that include dirac delta functions to model equations with state dependent impulsive forcing specifically difficulties arise in the interpretation of the products of distributions with discontinuous functions we suggest several methods to resolve these ambiguities such as using limiting sequences and asymptotic analysis with applications of the results given for discrete maps these suggestions are applied to a popular model describing synaptic connections in the brain

nonclassical shocks and kinetic relations finite difference schemes we consider hyperbolic systems of conservation laws that are not genuinely nonlinear the solutions generated by diffusive dispersive regularizations may include nonclassical n c shock waves that do not satisfy the classical liu entropy criterion we investigate the numerical approximation of n c shocks via conservative difference schemes constrained only by a single entropy inequality the schemes are designed by comparing their equivalent equations with the continuous model and include discretizations of the diffusive and dispersive terms limits of these schemes are characterized via the kinetic relation introduced earlier by the authors we determine the kinetic function numerically for several examples of systems and schemes this study demonstrates that the kinetic relation is a suitable tool for the selection of unique n c solutions and for the study of their sensitive dependence on the critical parameters the ratios of diffusion dispersion and diffusion mesh size the shock strength and the order of discretization of the flux

symmetry classes of alternating sign matrices under one roof in a previous article math co 9712207 we derived the alternating sign matrix asm theorem from the izergin korepin determinant for a partition function for square ice with domain wall boundary here we show that the same argument enumerates three other symmetry classes of alternating sign matrices vsasms vertically symmetric asms even htsasms half turn symmetric asms and even qtsasms quarter turn symmetric asms the vsasm enumeration was conjectured by mills the others by robbins math co 0008045 we introduce several new types of asms uasms asms with a u turn side uuasms two u turn sides osasms off diagonally symmetric asms oosasms off diagonally off antidiagonally symmetric and uosasms off diagonally symmetric with u turn sides uasms generalize vsasms while uuasms generalize vhsasms vertically and horizontally symmetric asms and another new class vhpasms vertically and horizontally perverse osasms oosasms and uosasms are related to the remaining symmetry classes of asms namely dsasms diagonally symmetric dasasms diagonally anti diagonally symmetric and tsasms totally symmetric asms we enumerate several of these new classes and we provide several 2 enumerations and 3 enumerations our main technical tool is a set of multi parameter determinant and pfaffian formulas generalizing the izergin korepin determinant for asms and the tsuchiya determinant for uasms solv int 9804010 we evaluate specializations of the determinants and pfaffians using the factor exhaustion method

characterization of structural reorganization in rice piles diagnostics applied to a rice pile cellular automaton reveal different mechanisms producing power law behaviors of statistical attributes of grains which are germane to self organised critical phenomena the probability distributions for these quantities can be derived from two distinct random walk models that account for correlated clustered behavior through incorporating fluctuations in the number of steps in the walk the first model describes the distribution for a spatial quantity the resultant flight length of grains this has a power law tail caused by grains moving through a discrete power law distributed number of random steps of finite length developing this model into a random walk obtains distributions for the resultant flight length with characteristics similar to l evy distributions the second random walk model is devised to explain a temporal quantity the distribution of trapping or residence times of grains at single locations in the pile diagnostics reveal that the trapping time can be constructed as a sum of subtrapping times which are described by a l evy distribution where the number of terms in the sum is a discrete random variable accurately described by a negative binomial distribution the infinitely divisible two parameter limit distribution for the resultant of such a random walk is discussed and describes a dual scale power law behavior if the number fluctuations are strongly clustered the form for the distribution of transit times of grains results as a corollary

the elastoplastic shock problem as an example of the resolution of ambiguities in the multiplication of distributions one dimensional collisions between two isotropic solids in which the equations of physics lead to multiplications of distributions are considered based on this example a general physicomathematical method to be adapted to each particular case is proposed to resolve the ambiguity inherent in such products this can be achieved with the aid of a new mathematical theory of generalized functions which permits dealing with mathematical phenomena of a microscopic nature that govern products of distributions having singularities at the same point this tool has recently been applied in various situations in continuum mechanics in which the equations of physics lead to heuristic products of distributions one obtains new algebraic formulas in the simplest cases and new numerical schemes in more general cases the key to the resolution of ambiguities lies in more precise statements of the laws of physics than are permitted within distribution theory and have no analog in classical analysis so that in general a resolution cannot be obtained from formal calculations

viscous shock profiles and primitive formulations weak solutions of hyperbolic systems in primitive nonconservative form for which a consistent conservation form exists are considered it is shown that for primitive formulations shock relations are not uniquely defined by the states to either side of the shock but also depend on the viscous path connecting the two consistent viscous shock profiles are enforced by adding scheme dependent small viscous perturbations that account for leading order conservation errors the resulting primitive algorithm is conservative to the order of the approximation one dimensional euler calculations of flows containing weak to moderate shocks show that conservation errors in primitive calculations are substantially reduced by including the viscous perturbation terms while not eliminating conservation errors entirely it is found that for a wide range of problems both conservative and primitive flow calculations are of comparable quality

population statistics and the counting process the authors investigate the outcome of different monitoring schemes applied to small classical populations explicit calculation for a solvable model establishes the relationship between the statistical properties of the population and those of the counting processes parallels are drawn with operator ordering in the second quantised formulation of photodetection

on nonconservative algorithms for grid interfaces in computations of fluid flows by domain decomposition methods the necessity of conservation at grid interfaces is now widely claimed in this paper we consider nonconservative algorithms for the interfaces our investigation begins with discussions about typical nonconservative interface treatments for one dimensional calculations the analysis shows that the conservation error of a numerical solution caused by a nonconservative interface matching has an upper bound when the solution itself is bounded furthermore if the numerical solution converges as the mesh size goes to zero it converges to a weak solution of the problem under certain conditions that may be detected numerically also we acquire similar results for two dimensional calculations on grids intersecting with each other in an arbitrary way in order to illustrate the theoretical results we present numerical examples and demonstrate that under those conditions conservation error reduces and accuracy for jumps as well as locations of discontinuities improves as the mesh size decreases

nonlinear generalized functions and jump conditions for a standard one pressure liquid gas model abstract the mixture of a liquid and a gas is classically represented by one pressure models these models are a system of pdes in nonconservative form and shock wave solutions do not make sense within the theory of distributions they give rise to products of distributions that are not defined within distribution theory but they make sense by applying a theory of nonlinear generalized functions to these equations in contrast to the familiar case of conservative systems the jump conditions cannot be calculated a priori jump conditions for these nonconservative systems can be obtained using the theory of nonlinear generalized functions by inserting some adequate physical information into the equations the physical information that we propose to insert for the one pressure models of a mixture of a liquid and a gas is a natural mathematical expression in the theory of nonlinear generalized functions of the fact that liquids are practically incompressible while gases are very compressible and so they do not satisfy equally well their respective state laws on the shock waves this modelization gives well defined explicit jump conditions the great numerical difficulty for solving numerically nonconservative systems is due to the fact that slightly different numerical schemes can give significantly different results the jump conditions obtained above permit to select the numerical schemes and validate those that give numerical solutions that satisfy these jump conditions which can be an important piece of information in the absence of other explicit discontinuous solutions and of precise observational results we expose with care the mathematical originality of the theory of nonlinear generalized functions an original abstract analysis issued by the leopoldo nachbin team on infinite dimensional holomorphy that permits to state mathematically physical facts that cannot be formulated within distribution theory and are the key for the removal of ambiguities that classically appear when one tries to calculate on multiplications of distributions that occur in the differential equations of physics

how to prevent pressure oscillations in multicomponent flow calculations a new numerical scheme for computing multicomponent flows is presented it is able to handle strong shocks is pressure oscillation free through the contact discontinuities and guarantees the posi tivity of mass fractions some numerical experiments on shock tubes indicate the convergence to the correct weak solution comparisons with classical finite volume schemes are also proposed

power law distributed level crossings define fractal behavior a relationship is established between the autocorrelation function of continuous gaussian and non gaussian stochastic processes and the discrete process that describes their zero or level crossings random fractals occur when the distribution for the number of crossings is described by a class of markov processes whose singlefold statistics are the discrete analog of the levy stable continuous probability densities

a constant term approach to enumerating alternating sign trapezoids abstract we show that there is the same number of n l alternating sign trapezoids as there is of column strict shifted plane partitions of class l 1 with at most n parts in the top row thereby proving a result that was conjectured independently by behrend and aigner the first objects generalize alternating sign triangles which have recently been introduced by ayyer behrend and the author who showed that they are counted by the same formula as alternating sign matrices column strict shifted plane partitions of a fixed class were introduced in a slightly different form by andrews and they essentially generalize descending plane partitions they also correspond to cyclically symmetric lozenge tilings of a hexagon with a triangular hole in the center in addition we also provide three statistics on each class of objects and show that their joint distribution is the same we prove our result by employing a constant term approach that is based on the author s operator formula for monotone triangles this paper complements a forthcoming paper of behrend and the author where the six vertex model approach is used to show equinumeracy as well as generalizations involving statistics that are different from those considered in the present paper

short note a comment on the computation of non conservative products we are interested in the solution of non conservative hyperbolic systems and consider in particular the so called path conservative schemes see e g 2 3 which rely on the theoretical work in 1 the example of the standard euler equations for a perfect gas is used to illuminate some computational issues and shortcomings of this approach

the evolution of a single paired immigration death process the general question of whether it is possible to determine the fundamental structure of a hidden stochastic process purely from counts of escaping individuals is of immense importance in fields such as quantum optics where externally based radiation elucidates the nature of the electromagnetic radiation process although the general probability structure has been derived in an earlier paper in terms of the joint probability generating function of the hidden population size and known counts its complex nature hides some particularly intriguing features of the underlying process our current objective is therefore to examine specific immigration regimes in order to highlight the underlying saw tooth behaviour of the underlying probability and moment structures the paper first explores paired and triple immigration schemes and then introduces birth in order to show that the technique is equally successful in exposing hidden multiplicative effects these analyses uncover novel and highly illuminating features and emphasize the potential of this population counting construct for expanding into more complex multi type situations

existence and uniqueness criteria for conservative uni instantaneous denumerable markov processes until now denumerable markov processes with instantaneous states have not been extensively considered and so in this paper we present a detailed examination of the conservative uni instantaneous cui case we determine criteria for the existence and uniqueness of a specific cui pregenerator and consider the general problem of constructing cui processes

generalized solutions to a cauchy problem for a nonconservative hyperbolic system in this paper we show the existence of generalized solutions in the sense of colombeau to a cauchy problem for a nonconservative system of hyperbolic equations which has applications in elastodynamics

a high resolution godunov method for compressible multi material flow on overlapping grids a numerical method is described for inviscid compressible multi material flow in two space dimensions the flow is governed by the multi material euler equations with a general mixture equation of state composite overlapping grids are used to handle complex flow geometry and block structured adaptive mesh refinement amr is used to locally increase grid resolution near shocks and material interfaces the discretization of the governing equations is based on a high resolution godunov method but includes an energy correction designed to suppress numerical errors that develop near a material interface for standard conservative shock capturing schemes the energy correction is constructed based on a uniform pressure velocity flow and is significant only near the captured interface a variety of two material flows are presented to verify the accuracy of the numerical approach and to illustrate its use these flows assume an equation of state for the mixture based on the jones wilkins lee jwl forms for the components this equation of state includes a mixture of ideal gases as a special case flow problems considered include unsteady one dimensional shock interface collision steady interaction of a planar interface and an oblique shock planar shock interaction with a collection of gas filled cylindrical inhomogeneities and the impulsive motion of the two component mixture in a rigid cylindrical vessel

scale free characteristics of random networks the topology of the world wide web the world wide web forms a large directed graph whose vertices are documents and edges are links pointing from one document to another here we demonstrate that despite its apparent random character the topology of this graph has a number of universal scale free characteristics we introduce a model that leads to a scale free network capturing in a minimal fashion the self organization processes governing the world wide web c 2000 elsevier science b v all rights reserved pacs 84 35 i 64 60 fr 87 23 ge

determinants and alternating sign matrices let m be an n by n matrix by a connected minor of m of size k we mean a minor formed from k consecutive rows and k consecutive columns we give formulas for det m in terms of connected minors one involving minors of two consecutive sizes and one involving minors of three consecutive sizes the formulas express det m as sums indexed by sets of alternating sign matrices these matrices are described here and by w h mills d p robbins and h rumsey jr invent math 66 1982 73 87 j combin theory ser a 34 1983 340 359 the former study has led to the solution of macdonald s conjecture on cyclically symmetric plane partitions g e andrews invent math 53 1979 193 225 i g macdonald symmetric functions and hall polynomials p 53 oxford univ press clarendon oxford 1979

fluctuations in the zeros of differentiable gaussian processes the stochastic point processes formed by the zero crossings or extremal points of differentiable stationary gaussian processes are studied as a function of their autocorrelation function the properties of these point processes are mapped to the space formed by the parameters appearing in the autocorrelation function their adopted form being sensitive to the structure of the autocorrelation function principally in the vicinity of the origin the distribution for the number of zeros occurring in an asymptotically large interval are approximately negative binomial or binomial depending upon whether the relative variance or fano factor is greater or less than unity the correlation properties of the zeros are such that they are repelled from each other or are antibunched if the autocorrelation function of the gaussian process is characterized by a single scale size but occur in clusters if more than one characteristic scale size is present the intervals between zeros can be interpreted in terms of the autocorrelation function of the zeros themselves when bunching occurs the interval density becomes bimodal indicating the interval sizes within and between the clusters the interevent periods are statistically dependent on one another with densities whose asymptotic behavior is governed by that of the autocorrelation function of the gaussian process at large delay times poisson distributed fluctuations of the zeros occur only exceptionally but never form a poisson process