multiple relaxation time lattice boltzmann model for incompressible miscible flow with large viscosity ratio and high peclet number a lattice boltzmann model with a multiple relaxation time mrt collision operator is proposed for incompressible miscible flow with a large viscosity ratio as well as a high peclet number in this paper the equilibria in the present model are motivated by the lattice kinetic scheme previously developed by inamuro et al philos trans r soc london ser a 360 477 2002 the fluid viscosity and diffusion coefficient depend on both the corresponding relaxation times and additional adjustable parameters in this model as a result the corresponding relaxation times can be adjusted in proper ranges to enhance the performance of the model numerical validations of the poiseuille flow and a diffusion reaction problem demonstrate that the proposed model has second order accuracy in space thereafter the model is used to simulate flow through a porous medium and the results show that the proposed model has the advantage to obtain a viscosity independent permeability which makes it a robust method for simulating flow in porous media finally a set of simulations are conducted on the viscous miscible displacement between two parallel plates the results reveal that the present model can be used to simulate to a high level of accuracy flows with large viscosity ratios and or high peclet numbers moreover the present model is shown to provide superior stability in the limit of high kinematic viscosity in summary the numerical results indicate that the present lattice boltzmann model is an ideal numerical tool for simulating flow with a large viscosity ratio and or a high peclet number

application of a fractional step method to incompressible navier stokes equations a numerical method for computing three dimensional time dependent incompressible flows is presented the method is based on a fractional step or time splitting scheme in conjunction with the approximate factorization technique it is shown that the use of velocity boundary conditions for the intermediate velocity field can lead to inconsistent numerical solutions appropriate boundary conditions for the intermediate velocity field are derived and tested numerical solutions for flows inside a driven cavity and over a backward facing step are presented and compared with experimental data and other numerical results

lattice boltzmann model for the incompressible navier stokes equation in this paper a lattice boltzmann lb model to simulate incompressible flow is developed the main idea is to explicitly eliminate the terms of o m2 where m is the mach number due to the density fluctuation in the existing lb models in the proposed incompressible lb model the pressure p instead of the mass density is the independent dynamic variable the incompressible navier stokes equations are derived from the incompressible lb model via chapman enskog procedure numerical results of simulations of the plane poiseuille flow driven either by pressure gradient or a fixed velocity profile at entrance as well as of the 2d womersley flow are presented the numerical results are found to be in excellent agreement with theory

ordinary and modular characters of su 3 p abstract this article deals with the relationship between ordinary and p modular characters of the group su 3 p parallel to the treatment of sl 3 p in j e humphreys ordinary and modular characters of sl 3 p j algebra 72 1981 8 16 here we denote by su 3 q the special unitary subgroup of sl 3 q2 where q is a power of the prime p the notation su 3 q2 is perhaps more standard but we want to emphasize the comparison with sl 3 q our main conclusion is that the decomposition behavior is essentially the same for both groups in a sense to be made more precise below

chip firing on dynkin diagrams and mckay quivers this paper establishes new connections between the representation theory of finite groups and sandpile dynamics two classes of avalanche finite matrices and their critical groups integer cokernels are studied from the viewpoint of chip firing sandpile dynamics namely the cartan matrices of finite root systems and the mckay cartan matrices for finite subgroups g of general linear groups in the root system case the recurrent and superstable configurations are identified explicitly and are related to minuscule dominant weights in the mckay cartan case for finite subgroups of the special linear group the cokernel is related to the abelianization of the subgroup g in the special case of the classical mckay correspondence the critical group and the abelianization are shown to be isomorphic

riemann roch and abel jacobi theory on a finite graph abstract it is well known that a finite graph can be viewed in many respects as a discrete analogue of a riemann surface in this paper we pursue this analogy further in the context of linear equivalence of divisors in particular we formulate and prove a graph theoretic analogue of the classical riemann roch theorem we also prove several results analogous to classical facts about riemann surfaces concerning the abel jacobi map from a graph to its jacobian as an application of our results we characterize the existence or non existence of a winning strategy for a certain chip firing game played on the vertices of a graph

walks on graphs and their connections with tensor invariants and centralizer algebras abstract the number of walks of k steps from the node 0 to the node on the mckay quiver determined by a finite group g and a g module v is the multiplicity of the irreducible g module g in the tensor power v k and it is also the dimension of the irreducible module labeled by for the centralizer algebra z k g end g v k this paper explores ways to effectively calculate that number using the character theory of g we determine the corresponding poincare series the special case 0 gives the poincare series for the tensor invariants t v g k 0 v k g and a tensor analog of molien s formula for polynomial invariants when g is abelian we show that the exponential generating function for the number of walks is a product of generalized hyperbolic functions many graphs such as circulant graphs can be viewed as mckay quivers and the methods presented here provide efficient ways to compute the number of walks on them

comparison techniques for random walk on finite groups we develop techniques for bounding the rate of convergence of a symmetric random walk on a finite group to the uniform distribution the techniques gives bounds on the second largest and other eigenvalues in terms of the eigenvalues of a comparison chain with known eigenvalues the techniques yield sharp rates for a host of previously intractable problems on the symmetric group

the spectrum of a coxeter transformation affine coxeter transformations and the defect map abstract the spectrum of the coxeter transformation r in a reflection group defined by a matrix a without odd cycles is determined in terms of spec a for affine a r determines the defect map which is given a simple formulation in terms of null roots the affine exponents determined by spec r are related to the coefficients of the fundamental co weight corresponding to the fork node of the coxeter dynkin diagram

note on the applicability of the james stein estimator in regional hydrologic studies the applicability of the james stein estimator in regional hydrologic studies which entail the estimation of an n dimensional location parameter is discussed regional studies are frequently characterized by relatively short generally correlated samples drawn from nonsymmetric and bounded i e nonnormal populations by means of computer simulation studies the james stein estimator subject to the lindley modification and adoption of the positive part rule suggested by efron and morris and conditioned on the assumption of independence was shown to be robust in the case of the hydrologically plausible distribution considered here namely weibull distributions with coefficient of skewness ranging from 0 to 10 however in contrast to traditional methods of regionalization the effect of cross correlation is a diminishment of the relative risk advantage of the james stein estimator even in the best case of normal variables this is discussed and illustrated

general bounce back scheme for concentration boundary condition in the lattice boltzmann method in this paper a general bounce back scheme is proposed to implement concentration or thermal boundary conditions of convection diffusion equation with the lattice boltzmann method lbm using this scheme the general concentration boundary conditions i e b 1 frac ensuremath partial c w ensuremath partial n b 2 c w b 3 can be easily implemented at boundaries with complex geometry structure like that in porous media the numerical results obtained using the present scheme are in excellent agreement with the analytical solutions of flows with both stationary and moving interfaces furthermore to better understand the halfway bounce back scheme an analytical study of the concentration jump is presented the studies of theoretical analysis and numerical experiments demonstrate that the proposed scheme has second order accuracy

a lattice boltzmann scheme of the navier stokes equation on a three dimensional cuboid lattice abstract the standard lattice boltzmann method lbm for fluid flow simulation is based on a square in 2d or a cubic in 3d lattice grids recently two new lattice boltzmann schemes have been developed on a 2d rectangular grid using the mrt multiple relaxation time collision model either by adding a free parameter in the definition of moments or by extending the equilibrium moments these models satisfy all isotropy conditions and are fully consistent to the navier stokes equations here we developed a lattice boltzmann model on a 3d cuboid lattice namely a lattice grid with different grid lengths in different spatial directions we designed the moment equations derived from our mrt lbm model through the chapman enskog analysis to be fully consistent with the navier stokes equations a second order term is added to the equilibrium moments in order to not only satisfy all isotropy conditions but also to better accommodate different values of shear and bulk viscosities the form of the second order term and the coefficients of the extended equilibrium moments are determined through an inverse design process an additional benefit of the model is that the shear viscosity can be adjusted independent of the stress moment relaxation parameter thus potentially improving the numerical stability of the model the resulting cuboid mrt lbm model is then validated through benchmark simulations using the laminar channel flow the turbulent channel flow and the 3d time dependent energy cascading taylor green vortex flow the second order accuracy of the proposed model is also demonstrated the aspect ratios for numerical stability appear to be constrained at high flow reynolds numbers especially for turbulent flow simulations an aspect requiring further investigation

an inverse design analysis of mesoscopic implementation of non uniform forcing in mrt lattice boltzmann models abstract in this paper the mesoscopic representation of non uniform forcing is investigated by an inverse design approach for several mrt multiple relaxation time lattice boltzmann models first the mesoscopic forcing representation of a standard lbm mrt model on a square lattice is re visited by the multiscale chapman enskog expansion we derive the most general form of the representation by taking advantage of the mrt formulation in particular we show that there are three free components in the mesoscopic representation of forcing second by the same methodology the forcing scheme of two new rectangular mrt lattice boltzmann models are derived based on the requirements of the navier stokes equations these theoretical results are then validated by numerical simulations of a forced taylor green vortex flow with several different forms of non uniform forcing to alter the kinetic energy evolution of the system the numerical results are in excellent agreement with the corresponding time dependent analytical solution of flow

trees parking functions syzygies and deformations of monomial ideals for a graph g we construct two algebras whose dimensions are both equal to the number of spanning trees of g one of these algebras is the quotient of the polynomial ring modulo certain monomial ideal while the other is the quotient of the polynomial ring modulo certain powers of linear forms we describe the set of monomials that forms a linear basis in each of these two algebras the basis elements correspond to g parking functions that naturally came up in the abelian sandpile model these ideals are instances of the general class of monotone monomial ideals and their deformations we show that the hilbert series of a monotone monomial ideal is always bounded by the hilbert series of its deformation then we define an even more general class of monomial ideals associated with posets and construct free resolutions for these ideals in some cases these resolutions coincide with scarf resolutions we prove several formulas for hilbert series of monotone monomial ideals and investigate when they are equal to hilbert series of deformations in the appendix we discuss the abelian sandpile model

a lattice bgk model for the navier stokes equations based on a rectangular grid abstract in this paper starting from the standard lattice bgk lbgk equation with an extended equilibrium distribution and applying the multiscale chapman enskog ce analysis we show theoretically that the correct navier stokes n s equations can be reproduced on a non standard rectangular grid using only the bgk collision model the parameters in the extended equilibrium distribution are determined through an inverse design process this new lbgk model is then validated using two benchmark cases i e the 2d decaying taylor green vortex flow and the lid driven cavity flow the accuracy and stability of the new model are discussed the new model clearly extends the standard lbgk model as it was previously thought to be impossible to construct an lbgk model for the n s equations on a rectangular grid

boundary conditions of the lattice boltzmann method for convection diffusion equations in this paper we employ an asymptotic analysis technique and construct two boundary schemes accompanying the lattice boltzmann method for convection diffusion equations with general robin boundary conditions one scheme is for straight boundaries with the boundary points locating at any distance from the lattice nodes and has second order accuracy the other is for curved boundaries has only first order accuracy and is much simpler than the existing schemes unlike those in the literature our schemes involve only the current lattice node such a single node boundary schemes are highly desirable for problems with complex geometries the two schemes are validated numerically with a number of examples the numerical results show the utility of the constructed schemes and very well support our theoretical predications

the partition algebra and the kronecker coefficients we propose a new approach to study the kronecker coefficients by using the schur weyl duality between the symmetric group and the partition algebra we explain the limiting behaviour and associated bounds in the context of the partition algebra our analysis leads to a uniform description of the reduced kronecker coefficients when one of the indexing partitions is a hook or a two part partition

on finite subgroups of su 2 simple lie algebras and the mckay correspondence the question is considered of how the restriction n where n is irreducible for all n and is a finite subgroup of su 2 decomposes into irreducibles for any arbitrary n unk it is announced that using the mckay correspondence the problem has an elegant solution in terms of the coxeter element for the associated lie algebra and that the numbers involved come in a beautiful way from the root structure

enumerating linear systems on graphs the divisor theory of graphs views a finite connected graph g as a discrete version of a riemann surface divisors on g are formal integral combinations of the vertices of g and linear equivalence of divisors is determined by the discrete laplacian operator for g as in the case of riemann surfaces we are interested in the complete linear system d of a divisor d the collection of nonnegative divisors linearly equivalent to d unlike the case of riemann surfaces the complete linear system of a divisor on a graph is always finite we compute generating functions encoding the sizes of all complete linear systems on g and interpret our results in terms of polyhedra associated with divisors and in terms of the invariant theory of the dual of the jacobian group of g if g is a cycle graph our results lead to a bijection between complete linear systems and binary necklaces our results also apply to a model in which the laplacian is replaced by an invertible integral m matrix

a bayesian surrogate for regional skew in flood frequency analysis the problem of how to best utilize site and regional flood data to infer the shape parameter of a flood distribution is considered one approach to this problem is given in bulletin 17b of the u s water resources council 1981 for the log pearson distribution here a lesser known distribution is considered namely the power normal which fits flood data as well as the log pearson and has a shape parameter denoted by derived from a box cox power transformation the problem of regionalizing is considered from an empirical bayes perspective where site and regional flood data are used to infer the distortive effects of spatial correlation and heterogeneity of site sampling variance of are explicitly studied with spatial correlation being found to be of secondary importance the end product of this analysis is the posterior distribution of the power normal parameters expressing in probabilistic terms what is known about the parameters given site flood data and regional information on this distribution can be used to provide the designer with several types of information the posterior distribution of the t year flood is derived the effect of nonlinearity in on inference is illustrated because uncertainty in is explicitly allowed for the understatement in confidence limits due to fixing analogous to fixing log skew is avoided finally it is shown how to obtain the marginal flood distribution which can be used to select a design flood with specified exceedance probability

rectangular lattice boltzmann method a set of rectangular lattice boltzmann methods for fluid flows is developed it is shown that reformulating local equilibrium distribution functions can result in the rectangular lattice boltzmann models without the aid of an interpolation for shallow water equations navier stokes equations and axisymmetric flow equations in addition schemes for correct incorporation of force terms into the models are proposed for simulations of flows involving forces in practice the methods completely retain the innate kinetic features and the simple procedure of the standard lattice boltzmann method with an additional benefit of being suitable for rectangular lattices at little extra computational cost the methodology is illustrated and validated through its application to different flow problems demonstrating the potential power of the models

designing correct fluid hydrodynamics on a rectangular grid using mrt lattice boltzmann approach while the lattice boltzmann method lbm has become a powerful numerical approach for solving complex flows the standard lattice boltzmann method typically uses a square lattice grid in two spatial dimensions and cubic lattice grid in three dimensions for inhomogeneous and anisotropic flows it is desirable to have a lbm model that utilizes a rectangular grid there were two previous attempts to extend the multiple relaxation time mrt lbm to a rectangular lattice grid in 2d however the resulting hydrodynamic momentum equation was not fully consistent with the navier stokes equation due to anisotropy of the transport coefficients in the present work a new mrt model with an additional degree of freedom is developed in order to match precisely the navier stokes equation when a rectangular lattice grid is used we first revisit the previous attempts to understand the origin and nature of anisotropic transport coefficients by conducting an inverse design analysis within the chapman enskog procedure then an additional adjustable parameter that governs the relative orientation in the energy normal stress subspace is introduced it is shown that this adjustable parameter can be used to fully eliminate the anisotropy of transport coefficients thus the exact navier stokes equation can be derived on a rectangular grid our theoretical findings are confirmed by numerical solutions using three two dimension benchmark problems i e the channel flow the cavity flow and the decaying taylor green vortex flow the numerical results demonstrate that the proposed model shows remarkably good performance with appropriate choice of model parameters

self organized critical state of sandpile automaton models we study a general bak tang wiesenfeld type automaton model of self organized criticality in which the toppling conditions depend on local height but not on its gradient we characterize the critical state and determine its entropy for an arbitrary finite lattice in any dimension the two point correlation function is shown to satisfy a linear equation the spectrum of relaxation times describing the approach to the critical state is also determined exactly

regional flood quantile estimation for a weibull model estimation of annual flood quantiles at a given site based on a regional weibull model with independence in space and time is considered a common shape parameter over sites motivated by an index flood assumption was assumed an exact simple formula for the cramer rao lower bound for the variance of unbiased estimators of the quantile is obtained and the gain of regional flood frequency analysis over single site analysis can be quantified via this formula the estimation techniques of the method of moments the method of probability weighted moments and the method of maximum likelihood are compared

consistent second order boundary implementations for convection diffusion lattice boltzmann method in this study an alternative second order boundary scheme is proposed under the framework of the convection diffusion lattice boltzmann lb method for both straight and curved geometries with the proposed scheme boundary implementations are developed for the dirichlet neumann and linear robin conditions in a consistent way the chapman enskog analysis and the hermite polynomial expansion technique are first applied to derive the explicit expression for the general distribution function with second order accuracy then the macroscopic variables involved in the expression for the distribution function is determined by the prescribed macroscopic constraints and the known distribution functions after streaming see the paragraph after eq 29 for the discussions of the streaming step in lb method after that the unknown distribution functions are obtained from the derived macroscopic information at the boundary nodes for straight boundaries boundary nodes are directly placed at the physical boundary surface and the present scheme is applied directly when extending the present scheme to curved geometries a local curvilinear coordinate system and first order taylor expansion are introduced to relate the macroscopic variables at the boundary nodes to the physical constraints at the curved boundary surface in essence the unknown distribution functions at the boundary node are derived from the known distribution functions at the same node in accordance with the macroscopic boundary conditions at the surface therefore the advantages of the present boundary implementations are i the locality i e no information from neighboring fluid nodes is required ii the consistency i e the physical boundary constraints are directly applied when determining the macroscopic variables at the boundary nodes thus the three kinds of conditions are realized in a consistent way it should be noted that the present focus is on two dimensional cases and theoretical derivations as well as the numerical validations are performed in the framework of the two dimensional five velocity lattice model

static spherically symmetric solutions of the so 5 einstein yang mills equations globally regular ie asymptotically flat and regular interior spher ically symmetric and localised particle like solutions of the coupled ein stein yang mills eym equations with gauge group su 2 have been known for more than 20 years yet their properties are still not well understood spher ically symmetric yang mills fields are classified by a choice of isotropy genera tor and so 5 is distinguished as the simplest model with a non abelian resid ual little group su 2 u 1 and which admits globally regular particle like solutions we exhibit an algebraic gauge condition which normalises the resid ual gauge freedom to a finite number of discrete symmetries this generalises the well known reduction to the real magnetic potential w r t in the original su 2 ym model reformulating using gauge invariant polynomials dramat ically simplifies the system and makes numerical search techniques feasible we find three families of embedded su 2 eym equations within the so 5 system one of which was first detected only within the gauge invariant polyno mial reduced system numerical solutions representing mixtures of the three su 2 sub systems are found classified by a pair of positive integers

on tensor categories of lie type en n 9 let v be the minuscule representation of the lie algebra g en n 6 7 we show that the centralizer of the action of the quantum group uqg en on v n is generated by the r matrices and one additional element appearing in the n 1 st tensor power a similar description can be given for the classical limit an analogous statement is true for a certain direct summand of v n for uqg en with n 5 n 9 here v is the module whose highest weight is the fundamental weight labeled by the vertex furthest from the triple point of the graph en moreover we obtain a 2 parameter family of braid representations generalizing a q version of the brauer centralizer algebras

momentum transfer correction for macroscopic gradient boundary conditions in lattice boltzmann methods the boundary conditions used to represent macroscopic gradient related effects in arbitrary geometries with the lattice boltzmann methods need a trade off between the complexity of the scheme due to the loss of localness and the difficulties for directly applying link based approaches and the accuracy obtained a generalization of the momentum transfer boundary condition is presented in which the arbitrary location of the boundary is addressed with link wise interpolation used for dirichlet conditions and the macroscopic gradient is taken into account with a finite difference scheme this leads to a stable approach for arbitrary geometries that can be used to impose neumann and robin boundary conditions the proposal is validated for stress boundary conditions at walls two dimensional steady and unsteady configurations are used as test case partial slip flow between two infinite plates and the slip flow past a circular cylinder

killing and the coxeter transformation of kac moody algebras on etudie le spectre de la transformation de coxeter associee a une algebre de kac moody arbitraire et plus particulierement a une algebre affine

boundary conditions for surface reactions in lattice boltzmann simulations a surface reaction boundary condition in multicomponent lattice boltzmann simulations is developed the method is applied to a test case with nonlinear reaction rates and nonlinear density profiles the results are compared to the corresponding analytical solution which shows that the error of the method scales with the square of the lattice spacing

high re solutions for incompressible flow using the navier stokes equations and a multigrid method the vorticity stream function formulation of the two dimensional incompressible navierstokes equations is used to study the effectiveness of the coupled strongly implicit multigrid csi mg method in the determination of high re fine mesh flow solutions the driven flow in a square cavity is used as the model problem solutions are obtained for configurations with reynolds number as high as 10 000 and meshes consisting of as many as 257 x 257 points for re 1000 the 129 x 129 grid solution required 1 5 minutes of cpu time on the amdahl 470 v 6 computer because of the appearance of one or more secondary vortices in the flow field uniform mesh refinement was preferred to the use of one dimensional gridclustering coordinate transformations the past decade has witnessed a great deal of progress in the area of computational fluid dynamics developments in computer technology hardware as well as in advanced numerical algorithms have enabled attempts to be made towards analysis and numerical solution of highly complex flow problems for some of these applications the use of simple iterative techniques to solve the navier stokes equations leads to a rather slow convergence rate for the solutions the solution convergence rate can be seriously affected if the coupling among the various governing differential equations is not properly honored either in the interior of the solution domain or at its boundaries the rate of convergence is also generally strongly dependent on such problem parameters as the reynolds number the mesh size and the total number of computational points this has led several researchers to examine carefully the recently emerging multigrid mg technique as a useful means for enhancing the convergence rate of iterative numerical methods for solving discretized equations at a number of computational grid points so large as to be considered impractical previously

invariant polynomials and molien functions the molien function associated with a finite dimensional representation of a compact lie group is a useful tool in representation theory because it acts as a generating function for counting the number of invariant polynomials on the representation space the main purpose of this paper is to introduce a more general and apparently new generating function which in the same sense counts not only the number of invariant real polynomials in a real representation or the number of invariant complex polynomials in a complex representation as a function of their degree but encodes the number of invariant real polynomials in a complex representation as a function of their bidegree the first and second component of this bidegree being the number of variables in which the polynomial is holomorphic and antiholomorphic respectively this is obviously an additional and non trivial piece of information for representations which are truly complex i e not self conjugate or are pseudo real but it provides ad

analytic solutions of simple flows and analysis of nonslip boundary conditions for the lattice boltzmann bgk model in this paper we analytically solve the velocity of the lattice boltzmann bgk equation lbgk for several simple flows the analysis provides a framework to theoretically analyze various boundary conditions in particular the analysis is used to derive the slip velocities generated by various schemes for the nonslip boundary condition we find that the slip velocity is zero as long as f e 0 at boundaries no matter what combination of distributions is chosen the schemes proposed by nobleet al and by inamuroet al yield the correct zeroslip velocity while some other schemes such as the bounce back scheme and the equilibrium distribution scheme would inevitably generate a nonzero slip velocity the bounce back scheme with the wall located halfway between a flow node and a bounce back node is also studied for the simple flows considered and is shown to produce results of second order accuracy the momentum exchange at boundaries seems to be highly related to the slip velocity at boundaries to be specific the slip velocity is zero only when the momentum dissipated by boundaries is equal to the stress provided by fluids

simulation bayes and bootstrap in statistical hydrology statistical simulation in hydrology is discussed from a bayesian perspective the inherent difficulties in both parametric simulation based on a parent distribution and classical nonparametric simulation based on the bootstrap are discussed as an alternative to these procedures a nonparametric bayesian simulation methodology polya resampling is introduced it consists of simulating from a nonparametric predictive distribution obtained from the analysis of a reference sample and it is asymptotically equivalent to the bootstrap the method is generalized to take into account a prior hypothesis on the parametric distribution of a variable a hybrid simulation model is then obtained that includes parametric and nonparametric simulation as particular cases an extensive application is presented in a related paper fortin et al 1997 where polya resampling is used to compare statistical models for flood frequency analysis in this paper an example is used to demonstrate how polya resampling can help assess the influence of a distribution hypothesis on simulation results

stein s method and random character ratios stein s method is used to prove limit theorems for random character ratios tools are developed for four types of structures finite groups gelfand pairs twisted gelfand pairs and association schemes as one example an error term is obtained for a central limit theorem of kerov on the spectrum of the cayley graph of the symmetric group generated by i cycles other main examples include an error term for a central limit theorem of ivanov on character ratios of random projective representations of the symmetric group and a new central limit theorem for the spectrum of certain random walks on perfect matchings the results are obtained with very little information a character formula for a single representation close to the trivial representation and estimates on two step transition probabilities of a random walk the limit theorems stated in this paper are for normal approximation but many of the tools developed are applicable for arbitrary distributional approximation

quantum random walk on the dual of su n we study a quantum random walk ona su n the von neumann algebra of su n obtained by tensoring the basic representation of su n two classical markov chains are derived from this quantum random walk by restriction to commutative subalgebras ofa su n and the main result of the paper states that these two markov chains are related by means of doob sh processes

some progress in lattice boltzmann method part i nonuniform mesh grids a new lattice boltzmann algorithm is proposed to simulate the navier stokes equation on arbitrary nonuniform mesh grids the new algorithm retains the advantages of the lattice boltzmann method parallel of algorithm ease of programming and ability to incorporate microscopic interactions a simulation of flow in a two dimensional symmetric channel with sudden expansion is carried out using the new algorithm on a nonuniform mesh the results of the simulation are in excellent agreement with previous experimental and numerical results

norm convergence of random walks on compact hypergroups where ig is the order of g and p is the nth convolut ion power of p they show that this is a natural tool for studying strong uniform times for r a n d o m walks on g and they show in theorem 7 of 1 stated as theorem 5 in 7 chap 4c that if i p ml o as n then s n o as n at a rate that depends on how fast l ip m converges to 0 but does not depend on the size of the group g in particular if j p m is small then s 2n is small

two component extreme value distribution for flood frequency analysis theoretical considerations supported by statistical analysis of 39 annual flood series afs of italian basins suggest that the two component extreme value tcev distribution can be assumed as a parent flood distribution i e one closely representative of the real flood experience this distribution belongs to the family of distributions of the annual maximum of a compound poisson process which is a solid theoretical basis for afs analysis however the two parameter distribution of this family obtained on the assumption of identically distributed floods does not account for the high variability of both observed skewness and largest order statistics so that a significant number of observed floods qualify as outliers under this distribution the more general tcev distribution assumes individual floods to arise from a mixture of two exponential components its four parameters can be estimated by the maximum likelihood method a regionalized tcev distribution with parameters representative of a set of 39 italian afs s was shown to closely reproduce the observed distribution of skewness and that of the largest order statistic

simulation of cavity flow by the lattice boltzmann method a detailed analysis is presented to demonstrate the capabilities of the lattice boltzmann method thorough comparisons with other numerical solutions for the two dimensional driven cavity flow show that the lattice boltzmann method gives accurate results over a wide range of reynolds numbers studies of errors and convergence rates are carried out compressibility effects are quantified for different maximum velocities and parameter ranges are found for stable simulations the paper s objective is to stimulate further work using this relatively new approach for applied engineering problems in transport phenomena utilizing parallel computers

invariants equivariants and characters in symmetric bifurcation theory in the analysis of stability in bifurcation problems it is often assumed that the appropriate reduced equations are in normal form in the presence of symmetry the truncated normal form is an equivariant polynomial map therefore the determination of invariants and equivariants of the group of symmetries of the problem is an important step in general these are hard problems of invariant theory and in most cases they are tractable only through symbolic computer programs nevertheless it is desirable to obtain some of the information about invariants and equivariants without actually computing them for example the number of linearly independent homogeneous invariants or equivariants of a certain degree generating functions for these dimensions are generally known as molien functions we obtain formulae for the number of linearly independent homogeneous invariants or equivariants for hopf bifurcation in terms of characters we also show how to construct molien functions for invariants and equivariants for hopf bifurcation our results are then applied to the computation of the number of invariants and equivariants for hopf bifurcation for several finite groups and the continuous group o 3

second order curved boundary treatments of the lattice boltzmann method for convection diffusion equations in this paper we present a kind of second order curved boundary treatments for the lattice boltzmann method solving two dimensional convection diffusion equations with general nonlinear robin boundary conditions the key idea is to derive approximate boundary values or normal derivatives on computational boundaries with second order accuracy by using the prescribed boundary condition once the approximate information is known the second order bounce back schemes can be perfectly adopted our boundary treatments are validated with a number of numerical examples the results show the utility of our boundary treatments and very well support our theoretical predications on the second order accuracy thereof the idea is quite universal it can be directly generalized to 3 dimensional problems multiple relaxation time models and the navier stokes equations

conditioned random walks from kac moody root systems random paths are time continuous interpolations of random walks by using littelmann path model we associate to each irreducible highest weight module of a kac moody algebra g a random path w under suitable hypotheses we make explicit the probability of the event e w never exits the weyl chamber of g we then give the law of the random walk defined by w conditioned by the event e and proves this law can be recovered by applying to w the generalized pitmann transform introduced by biane bougerol and o connell this generalizes the main results of 10 and 16 to kac moody root systems and arbitrary highest weight modules moreover we use here a completely new approach by exploiting the symmetry of our construction under the action of the weyl group of g rather than renewal theory and doob s theorem on martin kernels

multiple relaxation time lattice boltzmann model for the convection and anisotropic diffusion equation a lattice boltzmann model with a multiple relaxation time mrt collision operator for the convection diffusion equation is presented the model uses seven discrete velocities in three dimensions d3q7 model the off diagonal components of the relaxation time matrix which originate from the rotation of the principal axes enable us to take into account full anisotropy of diffusion an asymptotic analysis of the model equation with boundary rules for the dirichlet and neumann type specified flux conditions is carried out to show that the model is first and second order accurate in time and space respectively the results of the analysis are verified by several numerical examples it is also shown numerically that the error of the mrt model is less sensitive to the variation of the relaxation time coefficients than that of the classical bgk model in addition an alternative treatment for the neumann type boundary condition that improves the accuracy on a curved boundary is presented along with a numerical example of a spherical boundary

algebraic model for the evolution of the genetic code a search for symmetries based on the compact simple lie algebras is performed to verify to what extent the genetic code is a manifestation of some underlying symmetry an exact continuous symmetry group cannot be found to reproduce the present genetic code however a unique approximate symmetry group is compatible with codon assignment for the fundamental amino acids and the termination codon in order to obtain the actual genetic code the symmetry must be slightly broken

poincare series for tensor invariants and the mckay correspondence abstract for a finite group g and a finite dimensional g module v we prove a general result on the poincare series for the g invariants in the tensor algebra t v k 0 v k we apply this result to the finite subgroups g of the 2 2 special unitary matrices and their natural module v of 2 1 column vectors because these subgroups are in one to one correspondence with the simply laced affine dynkin diagrams by the mckay correspondence the poincare series obtained are the generating functions for the number of walks on the simply laced affine dynkin diagrams

flood frequency analysis with historical and paleoflood information an investigation is made of flood quantile estimators which can employ historical and paleoflood information in flood frequency analyses two categories of historical information are considered censored data where the magnitudes of historical flood peaks are known and binomial data where only threshold exceedance information is available a monte carlo study employing the two parameter lognormal distribution shows that maximum likelihood estimators mles can extract the equivalent of an additional 10 30 years of gage record from a 50 year period of historical observation the mle routines are shown to be substantially better than an adjusted moment estimator similar to the one recommended in bulletin 17b of the united states water resources council hydrology committee 1982 the mle methods performed well even when floods were drawn from other than the assumed lognormal distribution

stein s method and characters of compact lie groups stein s method is used to study the trace of a random element from a compact lie group or symmetric space central limit theorems are proved using very little information character values on a single element and the decomposition of the square of the trace into irreducible components this is illustrated for lie groups of classical type and dyson s circular ensembles the approach in this paper will be useful for the study of higher dimensional characters where normal approximations need not hold

robust flood frequency models the concept of a robust model is briefly explored in the context of flood frequency analysis two necessary properties of a robust model are advanced namely resistance and efficiency strategies for seeking more robust models are discussed because of its versatility the five parameter wakeby distribution can credibly be considered a parent flood distribution four regionalized wakeby parents are employed in simulation studies to search for robust models these parents were shown by houghton to be representative of u s flood experience in the sense that certain raw flood data characteristics could be reproduced a limited range of sampling experiments were undertaken the results suggest that of the site specific estimators considered the two parameter log normal maximum likelihood estimator is most resistant with gumbel estimators employing either maximum likelihood or probability weighted moments displaying comparable resistance several estimators which utilize regional flood information were compared included were empirical bayes estimators which are structurally similar to james stein rules and regionalized estimators based on the flood index method these estimators exhibited substantial improvements in aggregate risk performance over their site specific counterparts particularly for short record lengths regionalized estimators appear to be preferable for short record lengths while estimators which combine both site and regional flood information are preferable for longer record lengths when such estimation procedures are considered other distributional models such as log pearson type iii and wakeby become practical alternatives to the two parameter log normal model

tensor product markov chains abstract we analyze families of markov chains that arise from decomposing tensor products of irreducible representations this illuminates the burnside brauer theorem for building irreducible representations the mckay correspondence and pitman s 2 m x theorem the chains are explicitly diagonalizable and we use the eigenvalues eigenvectors to give sharp rates of convergence for the associated random walks for modular representations the chains are not reversible and the analytical details are surprisingly intricate in the quantum group case the chains fail to be diagonalizable but a novel analysis using generalized eigenvectors proves successful

kinetic boundary conditions in the lattice boltzmann method derivation of the lattice boltzmann method from the continuous kinetic theory x he and l s luo phys rev e 55 r6333 1997 x shan and x he phys rev lett 80 65 1998 is extended in order to obtain boundary conditions for the method for the model of a diffusively reflecting moving solid wall the boundary condition for the discrete set of velocities is derived and the error of the discretization is estimated numerical results are presented which demonstrate convergence to the hydrodynamic limit in particular the knudsen layer in the kramers problem is reproduced correctly for small knudsen numbers

asymmetric abeiian sandpile models in the abelian sandpile models introduced by dhar long time behavior is determined by an invariant measure supported uniformly on a set of implicitly defined recurrent configurations of the system dhar proposed a simple procedure theburning algorithm as a possible test of whether a configuration is recurrent and later with majumdar verified the correctness of this test when the toppling rules of the sandpile are symmetric we observe that the test is not valid in general and give a new algorithm which yields a test correct for all sandpiles we also obtain necessary and sufficient conditions for the validity of the original test the results are applied to a family of deterministic one dimensional sandpile models originally studied by lee liang and tzeng

simulation of flows around an impulsively started circular cylinder by taylor series expansion and least squares based lattice boltzmann method the two dimensional incompressible viscous flow past an impulsively started circular cylinder for a wide range of reynolds numbers re 20 9500 is studied computationally by using an explicit taylor series expansion and least squares based lattice boltzmann method the final equation for distribution function in our method is in an explicit form and essentially has no limitation on choice of mesh structure and lattice model it can be easily applied to simulation of flows with curved boundaries such as the problem considered in this work for the flow past an impulsively started circular cylinder numerical results obtained by present method agree very well with experimental data and computational results of navier stokes equations available in the literature

the partial order of dominant weights abstract the weight lattice of a crystallographic root system is partially ordered by the rule that if is a nonnegative integer linear combination of positive roots in this paper we study the subposet formed by the dominant weights in particular we prove that covers in this partial order only if belongs to a distinguished subset of the positive roots also if the root system is irreducible we prove that the mobius function of the partial order takes on only the values 0 1 2

critical groups of group representations abstract this paper investigates the critical group of a faithful representation of a finite group it computes the order of the critical group in terms of the character values and gives some restrictions on its subgroup structure it also computes the precise structure of the critical group both for the regular representation of any finite group and for the reflection representation of s n

lattice boltzmann equation on a two dimensional rectangular grid abstract we construct a multirelaxation lattice boltzmann model 1 on a two dimensional rectangular grid the model is partly inspired by a previous work of koelman 2 to construct a lattice bgk model on a two dimensional rectangular grid the linearized dispersion equation is analyzed to obtain the constraints on the isotropy of the transport coefficients and galilean invariance for various wave propagations in the model the linear stability of the model is also studied the model is numerically tested for three cases a a vortex moving with a constant velocity on a mesh with periodic boundary conditions b poiseuille flow with an arbitrary inclined angle with respect to the lattice orientation and c a cylinder asymmetrically placed in a channel the numerical results of these tests are compared with either analytic solutions or the results obtained by other methods satisfactory results are obtained for the numerical simulations

one point second order curved boundary condition for lattice boltzmann simulation of suspended particles abstract the lattice boltzmann method lbm has been widely considered as a distinctive and reliable approach for simulating the complex particulate flows as an intrinsic kinetic scheme it is quite convenient for lbm to apply the bounce back bb type methods to handle the moving boundaries with complicated geometry which is a tricky task for general interface resolved methods however the two major schemes in lbm i e the simple bb rule and the curved boundary condition cbc are presently encountered by the problems of low precision and loss of local computation respectively to overcome those two deficiencies in the boundary treatment simultaneously a one point second order cbc is proposed in this paper information of only a single node is required in the present scheme and the second order accuracy is validated in the channel flow and cylindrical couette flow applications to the particulate flows are further implemented to verify the present scheme numerical results are in good agreement with those in the literature

the performance of the two component extreme value distribution in regional flood frequency analysis the performance of the regional two component extreme value tcev estimation procedure in estimating both dimensionless regional frequency curves showing the t year flood as a multiple of the mean annual flood and site curves incorporating local and regional information was assessed using computer simulation experiments it was found that the tcev procedure produces estimates of both dimensionless regional curves and scaled site quantiles that are relatively unbiased but very variable when data are drawn from tcev or wakeby parents although estimates are very biased when data follow a gev distribution the tcev procedure is robust in the sense that its worst efforts are less bad than those of the alternatives considered but performance declines significantly as sample sizes reduce

application of multi block approach in the immersed boundary lattice boltzmann method for viscous fluid flows the immersed boundary lattice boltzmann method was presented recently to simulate the rigid particle motion it combines the desirable features of the lattice boltzmann and immersed boundary methods it uses a regular eulerian grid for the flow domain and a lagrangian grid for the boundary for the lattice boltzmann method as compared with the single relaxation time collision scheme the multi relaxation time collision scheme has better computational stability due to separation of the relaxations of various kinetic models especially near the geometric singularity so the multi relaxation time collision scheme is used to replace the single relaxation time collision scheme in the original immersed boundary lattice boltzmann method in order to obtain an accurate result very fine lattice grid is needed near the solid boundary to reduce the computational effort local grid refinement is adopted to offer high resolution near a solid body and to place the outer boundary far away from the body so the multi block scheme with the multi relaxation time collision model is used in the immersed boundary lattice boltzmann method in each block uniform lattice spacing can still be used in order to validate the multi block approach for the immersed boundary lattice boltzmann method with multi relaxation time collision scheme the numerical simulations of steady and unsteady flows past a circular cylinder and airfoil are carried out and good results are obtained

robust flood frequency analysis performance of ema with multiple grubbs beck outlier tests flood frequency analysis generally involves the use of simple parametric probability distributions to smooth and extrapolate the information provided by short flood records to estimate extreme flood flow quantiles parametric probability distributions can have difficulty simultaneously fitting both the largest and smallest floods a danger is that the smallest observations in a record can distort the exceedance probabilities assigned to the large floods of interest the identification and treatment of such potentially influential low floods pilfs frees a fitting algorithm to describe the distribution of the larger observations this can allow parametric flood frequency analysis to be both efficient and also robust to deviations from the proposed probability model s lower tail historically pilf identification involved subjective judgement we propose a new multiple grubbs beck outlier test mgbt for objective pilf identification mgbt pilf identification rates akin to type i errors are reported for the lognormal ln distribution and the log pearson type iii lp3 distribution with a variety of skew coefficients mgbt pilf identification generally matched subjective identification from a recent california flood frequency study monte carlo results show that censoring of pilfs identified by the mgbt algorithm improves the extreme quantile estimator efficiency of the expected moments algorithm ema for negatively skewed lp3 distributions and has little effect for zero or positive skews simultaneously it protects against deviations from the lp3 in the lower tail as illustrated by distorted ln examples thus mgbt generally makes flood frequency analysis based on the lp3 distribution with ema both more accurate and more robust

mckay centralizer algebras for a finite subgroup g of the special unitary group su2 we study the centralizer algebra zk g endg v k of g acting on the k fold tensor product of its defining representation v c2 the mckay corre spondence relates the representation theory of these groups to an associated affine dynkin diagram and we use this connection to study the structure and representation theory of zk g via the combinatorics of the dynkin diagram when g equals the binary tetrahedral octahedral or icosahedral group we exhibit remarkable connections between zk g and the martin jones set partition algebras

boundary conditions for thermal lattice boltzmann equation method we propose a thermal boundary condition treatment based on the bounce back idea and interpolation of the distribution functions for both the dirichlet and neumann normal derivative conditions in the thermal lattice boltzmann equation tlbe method the coefficients for the distribution functions involved are determined to satisfy the dirichlet or neumann condition with second order accuracy for the dirichlet condition there is an adjustable parameter in the treatment and three particular schemes are selected for demonstration while for the neumann condition the second order accurate scheme is unique when applied to inclined or curved boundaries the dirichlet condition treatment can be directly used while the neumann condition given in the normal direction of the boundary should be converted into derivative conditions in the discrete velocity directions of the tlbe model a spatially coupled formula relating the boundary temperature boundary normal heat flux and the distribution functions near the boundary is thus derived for the neumann problems on curved boundaries the applicability and accuracy of the present boundary treatments are examined with several numerical tests for which analytical solutions are available including the 2 dimensional 2 d steady state channel flow the 1 d transient heat conduction in an inclined semi infinite solid the 2 d steady state and transient heat conduction inside a circle and the 3 d steady state circular pipe flow while the dirichlet condition treatment leads to second order accuracy for the temperature field it only gives a first order accurate boundary heat flux because of the irregularity of the cuts by the curved boundary with the lattices with the neumann condition on the curved boundary the accuracy for the temperature field obtained is first order when the tangential temperature gradient on the boundary is decoupled second order convergence of the temperature field can be obtained with neumann conditions

comparisons of two moments based estimators that utilize historical and paleoflood data for the log pearson type iii distribution 1 the expected moments algorithm ema cohn et al 1997 and the bulletin 17b interagency committee on water data 1982 historical weighting procedure b17h for the log pearson type iii distribution are compared by monte carlo computer simulation for cases in which historical and or paleoflood data are available the relative performance of the estimators was explored for three cases fixed threshold exceedances a fixed number of large floods and floods generated from a different parent distribution ema can effectively incorporate four types of historical and paleoflood data floods where the discharge is explicitly known unknown discharges below a single threshold floods with unknown discharge that exceed some level and floods with discharges described in a range the b17h estimator can utilize only the first two types of historical information including historical paleoflood data in the simulation experiments significantly improved the quantile estimates in terms of mean square error and bias relative to using gage data alone ema performed significantly better than b17h in nearly all cases considered b17h performed as well as ema for estimating x100 in some limited fixed threshold exceedance cases ema performed comparatively much better in other fixed threshold situations for the single large flood case and in cases when estimating extreme floods equal to or greater than x500 b17h did not fully utilize historical information when the historical period exceeded 200 years robustness studies using gev simulated data confirmed that ema performed better than b17h overall ema is preferred to b17h when historical and paleoflood data are available for flood frequency analysis

comment on rectangular lattice boltzmann method it is shown both analytically and numerically that the suggested lattice boltzmann model on rectangular grids j g zhou phys rev e 81 026705 2010 leads to anisotropic dissipation of fluid momentum and thus does not recover the navier stokes equations hence it cannot be used for the simulation of hydrodynamics

characters of algebras containing a jones basic construction the temperley lieb okada brauer and birman wenzl algebras abstract we begin by determining in a general form the characters of irreducible representations of a jones basic construction and use this result to compute the characters of the temperley lieb algebras and the okada algebras in the case of the birman wenzl algebra some of the characters are determined by the general theorem and the others are computed by using the duality between the birman wenzl algebras and the drinfeld jimbo quantum groups of types b and c the computations involve certain characters of the quantum group these are polynomials invariant under the weyl group of type b we are able to decompose these weyl group symmetric functions and obtain a combinatorial rule for computing the irreducible characters of the birman wenzl algebras the combinatorial rules for computing the irreducible characters of the iwahori hecke algebras and the combinatorial rule for computing the irreducible characters of the brauer algebras are both special cases of our rule for the birman wenzl algebras

a hydrodynamically consistent mrt lattice boltzmann model on a 2d rectangular grid a multiple relaxation time mrt lattice boltzmann lb model on a d2q9 rectangular grid is designed theoretically and validated numerically in the present work by introducing stress components into the equilibrium moments this mrt lb model restores the isotropy of diffusive momentum transport at the macroscopic level or in the continuum limit leading to moment equations that are fully consistent with the navierstokes equations the model is derived by an inverse design process which is described in detail except one moment associated with the energy square all other eight equilibrium moments can be theoretically and uniquely determined the model is then carefully validated using both the two dimensional decaying taylorgreen vortex flow and lid driven cavity flow with different grid aspect ratios the corresponding results from an earlier model bouzidi et al 2001 28 are also presented for comparison the results of bouzidi et al s model show problems associated with anisotropy of viscosity coefficients while the present model exhibits full isotropy and is accurate and stable

multi block lattice boltzmann method extension to 3d and validation in turbulence abstract in this paper a multi block method is applied to 3d problems in this application interpolation schemes are carefully addressed to avoid the inconsistency when information is transferred from coarse to fine blocks two test cases are employed to assess information transfer scheme and accuracy improvement with respect to grid refinement

differential invariants for symplectic lie algebras realized by boson operators the study of algebraic symplectic models in high energy physics and even in molecular genetics has received much attention in the past decades in this paper we first survey one known bosonic realization with n types of bosons operators in a 2j 1 dimensional space with j being the semi integer then using the general theory of differential invariants we determine two sets of sp 2j 1 differential invariants in one set when n 2j 1 all independent invariants of any order are obtained in a simple closed form when n 2j 1 we could present only particular matrix forms in the latter case the differential invariants up to the second order are explicitly presented for the symplectic algebras sp 2 sp 4 and sp 6 realized by up to three types of bosons as applications we present the simplest sp 2 invariant lagrangians null lagrangians new solutions to the helmholtz inverse problem and evolution equations which will be of fundamental importance in the construction of dynamical systems invariant under the symplectic group

boundary scheme for linear heterogeneous surface reactions in the lattice boltzmann method a boundary scheme is proposed to treat the linear heterogeneous surface reaction i e general robin boundary condition for the lattice boltzmann method lbm in this study the basic idea of the present scheme is to compute the scalar variable gradient in the boundary condition with the moment of the nonequilibrium distribution functions the unknown distribution functions on the boundary can then be obtained on the basis of the given boundary condition for a straight wall where the lattice nodes are located on the boundaries both the scalar variable and its gradient can be expressed in terms of the distribution functions at the boundary node and the scheme is purely local the scheme is also extended to problems with a curved wall in which a linear extrapolation is employed to realize the exact boundary position a common feature of the two schemes lies in the easy treatment of the heterogenous reactions in comparison with existing methods a number of simulations are performed to test the accuracy of the schemes the results show that for flat walls the scheme can achieve second order accuracy while for curved walls the order of the accuracy is between 1 0 and 1 5

poincare series exponents of affine lie algebras and mckay slodowy correspondence abstract let n be a normal subgroup of a finite group g and v a fixed finite dimensional g module the poincare series for the multiplicities of induced modules and restriction modules in the tensor algebra t v k 0 v k are studied in connection with the mckay slodowy correspondence in particular it is shown that the closed formulas for the poincare series associated with the distinguished pairs of subgroups of su 2 give rise to the exponents of all untwisted and twisted affine lie algebras except a 2 n 1

numerics of the lattice boltzmann method effects of collision models on the lattice boltzmann simulations we conduct a comparative study to evaluate several lattice boltzmann lb models for solving the near incompressible navier stokes equations including the lattice boltzmann equation with the multiple relaxation time mrt the two relaxation time trt the single relaxation time srt collision models and the entropic lattice boltzmann equation elbe the lid driven square cavity flow in two dimensions is used as a benchmark test our results demonstrate that the elbe does not improve the numerical stability of the srt or the lattice bhatnagar gross krook lbgk model our results also show that the mrt and trt lb models are superior to the elbe and lbgk models in terms of accuracy stability and computational efficiency and that the elbe scheme is the most inferior among the lb models tested in this study thus is unfit for carrying out numerical simulations in practice our study suggests that to optimize the accuracy stability and efficiency in the mrt model it requires at least three independently adjustable relaxation rates one for the shear viscosity ensuremath nu or the reynolds number text re one for the bulk viscosity ensuremath zeta and one to satisfy the criterion imposed by the dirichlet boundary conditions which are realized by the bounce back type boundary conditions

root system chip firing i interval firing jim propp recently introduced a variant of chip firing on a line where the chips are given distinct integer labels hopkins mcconville and propp showed that this process is confluent from some but not all initial configurations of chips we recast their set up in terms of root systems labeled chip firing can be seen as a root firing process which allows the moves for alpha in phi whenever langle lambda alpha vee rangle 0 where phi is the set of positive roots of a root system of type a and lambda is a weight of this root system we are thus motivated to study the exact same root firing process for an arbitrary root system actually this central root firing process is the subject of a sequel to this paper in the present paper we instead study the interval root firing processes determined by for alpha in phi whenever langle lambda alpha vee rangle in k 1 k 1 or langle lambda alpha vee rangle in k k 1 for any k ge 0 we prove that these interval firing processes are always confluent from any initial weight we also show that there is a natural way to consistently label the stable points of these interval firing processes across all values of k so that the number of weights with given stabilization is a polynomial in k we conjecture that these ehrhart like polynomials have nonnegative integer coefficients