asymptotics in asep with step initial condition in previous work the authors considered the asymmetric simple exclusion process on the integer lattice in the case of step initial condition particles beginning at the positive integers there it was shown that the probability distribution for the position of an individual particle is given by an integral whose integrand involves a fredholm determinant here we use this formula to obtain three asymptotic results for the positions of these particles in one an apparently new distribution function arises and in another the distribution function f2 arises the latter extends a result of johansson on tasep to asep and hence proves kpz universality for asep with step initial condition

current fluctuations of the stationary asep and six vertex model our results in this article are twofold first we consider current fluctuations of the stationary asymmetric simple exclusion process asep run for some long time t and show that they are of order t1 3 along a characteristic line upon scaling by t1 3 we establish that these fluctuations converge to the long time height fluctuations of the stationary kardar parisi zhang kpz equation that is to the baik rains distribution this result has long been predicted under the context of kpz universality and in particular extends upon a number of results in the field including the work of ferrari and spohn from 2005 when they established the same result for the tasep and the work of balazs and seppalainen from 2010 when they established the t1 3 scaling for the general asep second we introduce a class of translation invariant gibbs measures that characterizes a one parameter family of slopes for an arbitrary ferroelectric symmetric six vertex model this family of slopes corresponds to what is known as the conical singularity or tricritical point in the free energy profile for the ferroelectric six vertex model we consider fluctuations of the height function of this model on a large grid of size t and show that they too are of order t1 3 along a certain characteristic line this confirms a prediction of bukman and shore from 1995 stating that the ferroelectric six vertex model should exhibit kpz growth at the conical singularity upon scaling the height fluctuations by t1 3 we again recover the baik rains distribution in the large t limit recasting this statement in terms of the asymmetric stochastic six vertex model confirms a prediction of gwa and spohn from 1992

a class of partition functions associated with e_ tau eta gl_3 by izergin korepin analysis recently a class of partition functions associated with higher rank rational and trigonometric integrable models were introduced by foda and manabe we use the dynamical r matrix of the elliptic quantum group e gl3 to introduce an elliptic analog of the partition functions associated with e gl3 we investigate the partition functions of foda manabe type by developing a nested version of the elliptic izergin korepin analysis and present the explicit forms as symmetrization of multivariable elliptic functions we show that special cases are essentially the elliptic weight functions introduced in the works by rimanyi tarasov and varchenko konno and felder rimanyi and varchenko

semi implicit characteristic based boundary treatment for acoustics in low mach number flows for low mach number flow calculation when acoustic waves have to be captured semi implicit methods allow to avoid the time step limitation that arises when explicit schemes are used a method is suggested to solve the boundary equations so that the semi implicitness of the algorithm is maintained as well as its pressure velocity coupling this method is studied theoretically and numerically in the low mach number regime partially non reflective characteristic based boundary conditions with the linear relaxation form suggested by rudy and strikwerda j comput phys 36 1980 55 70 are considered it is shown that their properties well known in the framework of explicit schemes are recovered with the proposed semi implicit treatment and an acoustic cfl number significantly larger than unity

periodic tasep with general initial conditions we consider the one dimensional totally asymmetric simple exclusion process with an arbitrary initial condition in a spatially periodic domain and obtain explicit formulas for the multi point distributions in the space time plane the formulas are given in terms of an integral involving a fredholm determinant we then evaluate the large time large period limit in the relaxation time scale which is the scale such that the system size starts to affect the height fluctuations the limit is obtained assuming certain conditions on the initial condition which we show that the step flat and step flat initial conditions satisfy hence we obtain the limit theorem for these three initial conditions in the periodic model extending the previous work on the step initial condition we also consider uniform random and uniform step random initial conditions

low mach number flows in time dependent domains we perform a multiple time scale single space scale analysis of a compressible fluid in a time dependent domain when the time variations of the boundary are small with respect to the acoustic velocity we introduce an average operator with respect to the fast time the averaged leading order variables satisfy modified incompressible equations which are coupled to linear acoustic equations with respect to the fast time we discuss possible initial boundary data for the asymptotic equations inherited from the initial boundary data for the compressible equations

a staggered space time discontinuous galerkin method for the three dimensional incompressible navier stokes equations on unstructured tetrahedral meshes in this paper we propose a novel arbitrary high order accurate semi implicit space time discontinuous galerkin method for the solution of the three dimensional incompressible navier stokes equations on staggered unstructured curved tetrahedral meshes as is typical for space time dg schemes the discrete solution is represented in terms of space time basis functions this allows to achieve very high order of accuracy also in time which is not easy to obtain for the incompressible navier stokes equations similarly to staggered finite difference schemes in our approach the discrete pressure is defined on the primary tetrahedral grid while the discrete velocity is defined on a face based staggered dual grid while staggered meshes are state of the art in classical finite difference schemes for the incompressible navier stokes equations their use in high order dg schemes is still quite rare a very simple and efficient picard iteration is used in order to derive a space time pressure correction algorithm that achieves also high order of accuracy in time and that avoids the direct solution of global nonlinear systems formal substitution of the discrete momentum equation on the dual grid into the discrete continuity equation on the primary grid yields a very sparse five point block system for the scalar pressure which is conveniently solved with a matrix free gmres algorithm from numerical experiments we find that the linear system seems to be reasonably well conditioned since all simulations shown in this paper could be run without the use of any preconditioner even up to very high polynomial degrees for a piecewise constant polynomial approximation in time and if pressure boundary conditions are specified at least in one point the resulting system is in addition symmetric and positive definite this allows us to use even faster iterative solvers like the conjugate gradient method the flexibility and accuracy of high order space time dg methods on curved unstructured meshes allows to discretize even complex physical domains with very coarse grids in both space and time the proposed method is verified for approximation polynomials of degree up to four in space and time by solving a series of typical 3d test problems and by comparing the obtained numerical results with available exact analytical solutions or with other numerical or experimental reference data to the knowledge of the authors this is the first time that a space time discontinuous galerkin finite element method is presented for the three dimensional incompressible navier stokes equations on staggered unstructured tetrahedral grids high order staggered space time dg scheme for the 3d incompressible navier stokes equations primal grid based on curved tetrahedra dual grid based on non standard five point hexahedra new discretization of the viscous terms on the main grid using lifting operators on the dual grid very simple space time pressure correction algorithm providing also high order in time all linear systems have maximum sparsity and use the smallest possible optimal five point stencil

stochastic higher spin six vertex model and q taseps abstract we present two new connections between the inhomogeneous stochastic higher spin six vertex model in a quadrant and integrable stochastic systems from the macdonald processes hierarchy first we show how macdonald q difference operators with t 0 an algebraic tool crucial for studying the corresponding macdonald processes can be utilized to get q moments of the height function h in the higher spin six vertex model first computed in 21 using bethe ansatz this result in particular implies that for the vertex model with the step bernoulli boundary condition the value of h at an arbitrary point n 1 t z 2 z 1 has the same distribution as the last component n of a random partition under a specific t 0 macdonald measure on the other hand it is known that x n n n can be identified with the location of the nth particle in a certain discrete time q tasep started from the step initial configuration the second construction we present is a coupling of this q tasep and the higher spin six vertex model with the step bernoulli boundary condition along time like paths providing an independent probabilistic explanation of the equality of h n 1 t and x n n in distribution as an illustration of our main results we obtain gue tracy widom asymptotics of a certain discrete time q tasep with the step initial configuration and special jump parameters by means of schur measures which are t q macdonald measures this analysis combines our results with the identification of averages of observables between the stochastic higher spin six vertex model and schur measures obtained recently in 8

semi implicit extension of a godunov type scheme based on low mach number asymptotics i one dimensional flow a single scale multiple space scale asymptotic analysis provides detailed insight into the low mach number limit behavior of solutions of the compressible euler equations we use the asymptotics as a guideline for developing a low mach number extension of an explicit higher order shock capturing scheme this semi implicit scheme involves multiple pressure variables large scale differencing and averaging procedures that are discretized versions of standard operations in multiple scales asymptotic analysis advection and acoustic wave propagation are discretized explicitly and upwind and only one scalar elliptic equation is to be solved implicitly at each time step this equation is a pressure correction equation for incompressible flows when the mach number is zero in the low mach number limit the time step is restricted by a courant number based essentially on the maximum flow velocity for moderate and large mach numbers the scheme reduces to the underlying explicit higher order shock capturing algorithm

a deformation of affine hecke algebra and integrable stochastic particle system we introduce a deformation of the affine hecke algebra of type which describes the commutation relations of the divided difference operators found by lascoux and schutzenberger and the multiplication operators making use of its representation we construct an integrable stochastic particle system it is a generalization of the q boson system due to sasamoto and wadati we also construct eigenfunctions of its generator using the propagation operator as a result we get the same eigenfunctions for the boson process obtained by povolotsky

a weakly asymptotic preserving low mach number scheme for the euler equations of gas dynamics we propose a low mach number godunov type finite volume scheme for the numerical solution of the compressible euler equations of gas dynamics the scheme combines klein s non stiff stiff decomposition of the fluxes j comput phys 121 1995 pp 213 237 with an explicit implicit time discretization f cordier p degond and a kumbaro j comput phys 231 2012 pp 5685 5704 for the split fluxes this results in a scalar second order partial differential equation pde for the pressure which we solve by an iterative approximation due to our choice of a crucial reference pressure the stiff subsystem is hyperbolic and the second order pde for the pressure is elliptic the scheme is also uniformly asymptotically consistent numerical experiments show that the scheme needs to be stabilized for low mach numbers unfortunately this affects the asymptotic consistency which becomes nonuniform in the mach number and requires an unduly fine grid in the small mach number limit on the other han

the huygens subgridding for the numerical solution of the maxwell equations the huygens subgridding hsg is a subgridding technique developed for the numerical solution of the maxwell equations it relies on the theoretical equivalence of any physical volume with two or more fictitious volumes connected by equivalent currents the application of this concept to the finite difference time domain fdtd method has been previously published in the one dimensional and two dimensional cases in this paper the hsg is extended to the general three dimensional case the exchange of the electromagnetic energy between the two fdtd grids is investigated theoretically and some modifications to the hsg algorithm are presented with the objective of simplifying its implementation

analysis of artificial pressure equations in numerical simulations of a turbulent channel flow abstract recently several methods have been proposed to simulate incompressible fluid flows using an artificial pressure evolution equation avoiding the resolution of a poisson equation these methods can be seen as various levels of approximation of the compressible navier stokes equation in the low mach number limit we study the simulation of incompressible wall bounded flows using several artificial pressure equations in order to determine the most relevant approximations the simulations are stable using a finite difference method in a staggered grid system even without diffusive term and converge to the incompressible solution both in direct numerical simulations and for coarser meshes to be used in large eddy simulations a pressure equation with a convective and a diffusive term produces a more accurate solution than a compressible solver or methods involving more approximations this suggests that it is near to an optimal level of approximation the presence of a convective term in the pressure evolution equation is in particular crucial for the accuracy of the method the rate of convergence of the solution in terms of artificial mach number is studied numerically and validates the theoretical quadratic convergence rate we demonstrate that this property can be used to accelerate the rate of convergence using an extrapolation in terms of artificial mach number since the approach is based on an explicit and local system of equations the numerical procedure is massively parallelisable and has low memory requirements

numerical simulations of a transient injection flow at low mach number regime in this paper a transient injection flow at low mach number regime is investigated three different methods are used and analyzed two of them are based on asymptotic models of the navier stokes equations valid for small mach numbers whereas the other is based on the full compressible navier stokes equations with particular care given to the discretization at low mach numbers numerical solutions are computed both with or without the gravity force finally the performance of the solvers in terms of cpu time consumption is investigated and the sensitivity of the solution to some parameters which affect cpu time is also performed

spectral theory for interacting particle systems solvable by coordinate bethe ansatz we develop spectral theory for the q hahn stochastic particle system introduced recently by povolotsky that is we establish a plancherel type isomorphism result that implies completeness and biorthogonality statements for the bethe ansatz eigenfunctions of the system owing to a markov duality with the q hahn tasep a discrete time generalization of tasep with particles jump distribution being the orthogonality weight for the classical q hahn orthogonal polynomials we write down moment formulas that characterize the fixed time distribution of the q hahn tasep with general initial data the bethe ansatz eigenfunctions of the q hahn system degenerate into eigenfunctions of other not necessarily stochastic interacting particle systems solvable by the coordinate bethe ansatz this includes the asep the asymmetric six vertex model and the heisenberg xxz spin chain all models are on the infinite lattice in this way each of the latter systems possesses a spectral theory too in particular biorthogonality of the asep eigenfunctions which follows from the corresponding q hahn statement implies symmetrization identities of tracy and widom for asep with either step or step bernoulli initial configuration as corollaries another degeneration takes the q hahn system to the q boson particle system dual to q tasep studied in detail in our previous paper 2013 thus at the spectral theory level we unify two discrete space regularizations of the kardar parisi zhang equation stochastic heat equation namely q tasep and asep

conservative space time mesh refinement methods for the fdtd solution of maxwell s equations a new variational space time mesh refinement method is proposed for the fdtd solution of maxwell s equations the main advantage of this method is to guarantee the conservation of a discrete energy that implies that the scheme remains l 2 stable under the usual cfl condition the only additional cost induced by the mesh refinement is the inversion at each time step of a sparse symmetric positive definite linear system restricted to the unknowns located on the interface between coarse and fine grid the method is presented in a rather general way and its stability is analyzed an implementation is proposed for the yee scheme in this case various numerical results in 3 d are presented in order to validate the approach and illustrate the practical interest of space time mesh refinement methods

transversal fluctuations of the asep stochastic six vertex model and hall littlewood gibbsian line ensembles we consider the asep and the stochastic six vertex model started with step initial data after a long time t it is known that the one point height function fluctuations for these systems are of order t1 3 we prove the kpz prediction of t2 3 scaling in space namely we prove tightness and brownian absolute continuity of all subsequential limits as t goes to infinity of the height function with spatial coordinate scaled by t2 3 and fluctuations scaled by t1 3 the starting point for proving these results is a connection discovered recently by borodin bufetov wheeler between the stochastic six vertex height function and the hall littlewood process a certain measure on plane partitions interpreting this process as a line ensemble with a gibbsian resampling invariance we show that the one point tightness of the top curve can be propagated to the tightness of the entire curve

k theoretic boson fermion correspondence and melting crystals we study non hermitian integrable fermion and boson systems from the perspectives of grothendieck polynomials the models considered in this article are the five vertex model as a fermion system and the non hermitian phase model as a boson system both models are characterized by different solutions satisfying the same yang baxter relation from our previous works on the identification between the wavefunctions of the five vertex model and grothendieck polynomials we introduce skew grothendieck polynomials and derive the addition theorem among them using these relations we derive the wavefunctions of the non hermitian phase model as a determinant form which can also be expressed as grothendieck polynomials namely we establish a k theoretic boson fermion correspondence at the level of wavefunctions as a by product the partition function of the statistical mechanical model of a three dimensional 3d melting crystal is exactly calculated by use of the scalar products of the wavefunctions of the phase model the resultant expression can be regarded as a k theoretic generalization of the macmahon function describing the generating function of the plane partitions which interpolates the generating functions of two dimensional 2d and 3d young diagrams

combinatorial properties of symmetric polynomials from integrable vertex models in finite lattice we introduce and study several combinatorial properties of a class of symmetric polynomials from the point of view of integrable vertex models in a finite lattice we introduce the l operator related to the uq sl2 r matrix and construct the wavefunctions and their duals we prove the exact correspondence between the wavefunctions and symmetric polynomials which is a quantum group deformation of the grothendieck polynomials this is proved by combining the matrix product method and an analysis on the domain wall boundary partition functions as applications of the correspondence between the wavefunctions and symmetric polynomials we derive several properties of the symmetric polynomials such as the determinant pairing formulas and the branching formulas by analyzing the domain wall boundary partition functions and the matrix elements of the b operators

on the integrability of zero range chipping models with factorized steady states the conditions of the integrability of general zero range chipping models with factorized steady states which were proposed in evans et al 2004 j phys a math gen 37 l275 are examined we find a three parametric family of hopping probabilities for the models solvable by the bethe ansatz which includes most of known integrable stochastic particle models as limiting cases the solution is based on the quantum binomial formula for two elements of an associative algebra obeying generic homogeneous quadratic relations which is proved as a byproduct we use the bethe ansatz to solve an eigenproblem for the transition matrix of the markov process on its basis we conjecture an integral formula for the green function of the evolution operator for the model on an infinite lattice and derive the bethe equations for the spectrum of the model on a ring

stationary stochastic higher spin six vertex model and q whittaker measure in this paper we consider the higher spin six vertex model on the lattice mathbb z ge 2 times mathbb z ge 1 we first identify a family of translation invariant measures and subsequently we study the one point distribution of the height function for the model with certain random boundary conditions exact formulas we obtain prove to be useful in order to establish the asymptotic of the height distribution in the long space time limit for the stationary higher spin six vertex model in particular along the characteristic line we recover baik rains fluctuations with size of characteristic exponent 1 3 we also consider some of the main degenerations of the higher spin six vertex model and we adapt our analysis to the relevant cases of the q hahn particle process and of the exponential jump model

a fredholm determinant representation in asep in previous work tracy and widom in commun math phys 279 815 844 2008 the authors found integral formulas for probabilities in the asymmetric simple exclusion process asep on the integer lattice the dynamics are uniquely determined once the initial state is specified in this note we restrict our attention to the case of step initial condition with particles at the positive integers and consider the distribution function for the mth particle from the left in tracy and widom commun math phys 279 815 844 2008 an infinite series of multiple integrals was derived for the distribution in this note we show that the series can be summed to give a single integral whose integrand involves a fredholm determinant we use this determinant representation to derive non rigorously at this writing a scaling limit

on asep with step bernoulli initial condition this paper extends earlier work on asep to the case of step bernoulli initial condition the main results are a representation in terms of a fredholm determinant for the probability distribution of a fixed particle and asymptotic results which in particular establish kpz universality for this probability in one regime and as a corollary for the current fluctuations

analysis of a uwb hemispherical antenna array in fdtd with a time domain huygens method electromagnetic modeling is needed in a wide variety of large and complex situations existing numerical techniques such as finite difference time domain fdtd can in principle solve any problem no matter how large or complicated given a sufficiently powerful computer however in practice there remain problems which require more computer power than is available recently the time domain huygens tdh approach has been shown to be effective for enabling large problems such as propagation on body area networks bans to be modeled in fdtd in this paper it is shown that the much larger problem of the conformal antenna array which is used in the maria breast cancer tumor detection system is also very amenable to this technique with even greater savings in computer resources accurate results are obtained using less that a tenth of the resources needed to solve the same problem using existing advanced fdtd tools the details of how this method is applied and the choices which need to be made are discussed

total current fluctuations in the asymmetric simple exclusion process a limit theorem for the total current in the asymmetric simple exclusion process asep with step initial condition is proven this extends the result of johansson on tasep to asep

vertex models tasep and grothendieck polynomials we examine the wavefunctions and their scalar products of a one parameter family of integrable five vertex models at a special point of the parameter the model investigated is related to an irreversible interacting stochastic particle system the so called totally asymmetric simple exclusion process tasep by combining the quantum inverse scattering method with a matrix product representation of the wavefunctions the on off shell wavefunctions of the five vertex models are represented as a certain determinant form up to some normalization factors we find that the wavefunctions are given by grothendieck polynomials which are a one parameter deformation of schur polynomials introducing a dual version of the grothendieck polynomials and utilizing the determinant representation for the scalar products of the wavefunctions we derive a generalized cauchy identity satisfied by the grothendieck polynomials and their duals several representation theoretical formulae for the grothendieck polynomials are also presented as a byproduct the relaxation dynamics such as green functions for the periodic tasep are found to be described in terms of the grothendieck polynomials

singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids many interesting problems in classical physics involve the limiting behavior of quasilinear hyperbolic systems as certain coefficients become infinite using classical methods the authors develop a general theory of such problems this theory is broad enough to study a wide variety of interesting singular limits in compressible fluid flow and magneto fluid dynamics including new constructive local existence theorems for the time singular limit equations in particular the authors give an entirely self contained classical proof of the convergence of solutions of the compressible fluid equations to their incompressible limits as the mach number becomes small the theory depends upon a balance between certain inherently nonlinear structural conditions on the matrix coefficients of the system together with appropriate initialization procedures similar results are developed also for the compressible and incompressible navier stokes equations with periodic initial data independent of the viscosity coefficients as they tend to zero

godunov type schemes with an inertia term for unsteady full mach number range flow calculations an inertia term is introduced in the ausm up scheme the resulting scheme called ausm it it for inertia term is designed as an extension of the ausm up scheme allowing for full mach number range calculations of unsteady flows including acoustic features in line with the continuous asymptotic analysis the ausm it scheme satisfies the conservation of the discrete linear acoustic energy at first order in the low mach number limit its capability to properly handle low mach number unsteady flows that may include acoustic waves or discontinuities is numerically illustrated the approach for building the ausm it scheme from the ausm up scheme is applicable to any other godunov type scheme

symmetric functions and wavefunctions of xxz type six vertex models and elliptic felderhof models by izergin korepin analysis we present a method to analyze the wavefunctions of six vertex models by extending the izergin korepin analysis originally developed for domain wall boundary partition functions first we apply the method to the case of the basic wavefunctions of the xxz type six vertex model by giving the izergin korepin characterization of the wavefunctions we show that these wavefunctions can be expressed as multiparameter deformations of the quantum group deformed grothendieck polynomials as a second example we show that the izergin korepin analysis is effective for analysis of the wavefunctions for a triangular boundary and present the explicit forms of the symmetric functions representing these wavefunctions as a third example we apply the method to the elliptic felderhof model which is a face type version and an elliptic extension of the trigonometric felderhof model we show that the wavefunctions can be expressed as one parameter deformations of an elliptic analog of the vandermonde determinant and elliptic symmetric functions we present a method to analyze the wavefunctions of six vertex models by extending the izergin korepin analysis originally developed for domain wall boundary partition functions first we apply the method to the case of the basic wavefunctions of the xxz type six vertex model by giving the izergin korepin characterization of the wavefunctions we show that these wavefunctions can be expressed as multiparameter deformations of the quantum group deformed grothendieck polynomials as a second example we show that the izergin korepin analysis is effective for analysis of the wavefunctions for a triangular boundary and present the explicit forms of the symmetric functions representing these wavefunctions as a third example we apply the method to the elliptic felderhof model which is a face type version and an

integral formulas for the asymmetric simple exclusion process in this paper we obtain general integral formulas for probabilities in the asymmetric simple exclusion process asep on the integer lattice mathbb z with nearest neighbor hopping rates p to the right and q 1 p to the left for the most part we consider an n particle system but for certain of these formulas we can take the n to infty limit first we obtain for the n particle system a formula for the probability of a configuration at time t given the initial configuration for this we use bethe ansatz ideas to solve the master equation extending a result of schutz for the case n 2 the main results of the paper derived from this are integral formulas for the probability for given initial configuration that the mth left most particle is at x at time t in one of these formulas we can take the n to infty limit and it gives the probability for an infinite system where the initial configuration is bounded on one side for the special case of the totally asymmetric simple exclusion process tasep our formulas reduce to the known ones

asymptotic single and multiple scale expansions in the low mach number limit an asymptotic analysis of the euler equations in the limit of vanishing mach number is presented which can be employed to extend the validity of numerical methods from the compressible to the low mach number regime r klein j comput phys 121 1995 pp 213 237 l hoffmann and a meister in proceedings of the fourth eccomas computational fluid dynamics conference vol 1 c hirsch et al eds athens 1998 pp 567 572 the work is based on the analysis recently proposed by klein whereby the paper is devoted to a rigorous mathematical justification of this asymptotic investigation in order to give reliable statements concerning the assumptions under which the results hold in contrast to klein a single scale as well as multiple scale expansion is used depending on the spatial domain under consideration

a new stable hybrid three dimensional generalized finite difference time domain algorithm for analyzing complex structures in this paper we propose a new stable hybrid three dimensional 3 d generalized finite difference time domain algorithm formulated by using of the cell method cm a finite volumes type method designed to analyze objects with fine details without using very small time steps dictated by the courant condition the new algorithm is an extension to the 3 d cases of an analogous hybrid two dimensional algorithm also formulated by the cm and presented earlier by the authors in a previous publication we carry out a detailed analysis of the stability of the proposed algorithm paying special attention to the phenomenon of late time instabilities finally the results of some numerical tests are provided to show the absence of instabilities and the efficiency of the hybrid algorithm

rotated nonuniform subgrids in the fdtd method with application to a hemispherical antenna array the use of subgrids in the finite difference time domain method to facilitate the analysis of multiscale problems is now well established however many of the proposed algorithms are restricted to cases where the subgrid and the main grid share the same cartesian coordinate system and where the ratio of the cell sizes in the two grids has a constant integer ratio more recently it has been shown that subgrids based on cartesian grids which are rotated with respect to the main grid can be effectively used but the cell size ratio was still kept constant in this contribution the method is further generalized in order to allow nonuniform subgrids to be used this greatly increases the range of structures which can be efficiently analyzed the effectiveness of the method is demonstrated by application to a 31 element hemispherical array of broadband cavity backed slot antenna elements

on a family of symmetric rational functions abstract this paper is about a family of symmetric rational functions that form a one parameter generalization of the classical hall littlewood polynomials we introduce two sets of skew and non skew functions that are akin to the p and q hall littlewood polynomials we establish a a combinatorial formula that represents our functions as partition functions for certain path ensembles in the square grid b symmetrization formulas for non skew functions c identities of cauchy and pieri type d explicit formulas for principal specializations e two types of orthogonality relations for non skew functions our construction is closely related to the half infinite volume finite magnon sector limit of the higher spin six vertex or xxz model with both sets of functions representing higher spin six vertex partition functions and or transfer matrices for certain domains