on b function spectrum and rational singularity by duality 18 because r tr ccy 0 for i 0 by 6 31 this follows also from 13 21 23 where rc is assumed projective here coy denotes the dualizing sheaf i e the dualizing complex 18 shifted by the dimension to the right the trace morphism 0 2 is injective and its image is independent of the choice of resolution because 0 2 is an isomorphism if y is smooth we will denote by csy the image of 0 2 see 2 4 8 below now assume y is a reduced divisor d on a complex manifold x of dimension n let f be a reduced defining equation of d on a neighborhood of a c d the b function i e bernstein polynomial of f is a monic polynomial bf s in s with rational coefficients and is a generator of the ideal whose element b s satisfies the relation

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

jumping coefficients and spectrum of a hyperplane arrangement in an earlier version of this paper written by the second named author we showed that the jumping coefficients of a hyperplane arrangement depend only on the combinatorial data of the arrangement as conjectured by musta for this we proved a similar assertion on the spectrum after this first proof was written the first named author found a more conceptual proof using the hirzebruch riemann roch theorem where the assertion on the jumping numbers was proved without reducing to that for the spectrum in this paper we improve these methods and show that the jumping numbers and the spectrum are calculable in low dimensions without using a computer in the reduced case we show that these depend only on fewer combinatorial data and give completely explicit combinatorial formulas for the jumping coefficients and part of the spectrum in the case the ambient dimension is 3 or 4 we also give an analogue of musta s formula for the spectrum

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

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

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

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

feynman integrals and motives of configuration spaces we formulate the problem of renormalization of feynman integrals and its relation to periods of motives in configuration space instead of momentum space the algebro geometric setting is provided by the wonderful compactifications overline conf gamma x of arrangements of subvarieties associated to the subgraphs of a feynman graph with x a quasi projective variety the motive and the class in the grothendieck ring are computed explicitly for these wonderful compactifications in terms of the motive of x and the combinatorics of the feynman graph using recent results of li li the pullback to the wonderful compactification of the form defined by the unrenormalized feynman amplitude has singularities along a hypersurface whose real locus is contained in the exceptional divisors of the iterated blowup that gives the wonderful compactification a regularization of the feynman integrals can be obtained by modifying the cycle of integration by replacing the divergent locus with a leray coboundary the ambiguities are then defined by poincare residues while these residues give periods associated to the cohomology of the exceptional divisors and their intersections the regularized integrals give rise to periods of the hypersurface complement in the wonderful compactification

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

globally nilpotent differential operators and the square ising model we recall various multiple integrals with one parameter related to the isotropic square ising model and corresponding respectively to the n particle contributions of the magnetic susceptibility to the lattice form factors to the two point correlation functions and to their extensions the univariate analytic functions defined by these integrals are holonomic and even g functions they satisfy fuchsian linear differential equations with polynomial coefficients and have some arithmetic properties we recall the explicit forms found in previous work of these fuchsian equations as well as their russian doll and direct sum structures these differential operators are selected fuchsian linear differential operators and their remarkable properties have a deep geometrical origin they are all globally nilpotent or sometimes even have zero p curvature we also display miscellaneous examples of globally nilpotent operators emerging from enumerative combinatorics problems for which no integral representation is yet known focusing on the factorized parts of all these operators we find out that the global nilpotence of the factors resp p curvature nullity corresponds to a set of selected structures of algebraic geometry elliptic curves modular curves curves of genus five six and even a remarkable weight 1 modular form emerging in the three particle contribution 3 of the magnetic susceptibility of the square ising model noticeably this associated weight 1 modular form is also seen in the factors of the differential operator for another n fold integral of the ising class 3 h for the staircase polygons counting and in ap ry s study of 3 g functions naturally occur as solutions of globally nilpotent operators in the case where we do not have g functions but hamburger functions one irregular singularity at 0 or that correspond to the confluence of singularities in the scaling limit the p curvature is also found to verify new structures associated with simple deformations of the nilpotent property

on the mixed hodge structure on the cohomology of the milnor fibre in 18 the second author introduced a mixed hodge structure on the cohomology of the milnor fibre of an isolated hypersurface singularity for the definition of a mixed hodge structure el 17 sect 3 4 the weight filtration is essentially the monodromy weight filtration 18 sect 4 and thus simplifies the jordan normal form of the unipotent part of the monodromy the significance of the hodge filtration however is not so dear and its description seems difficult to use this paper gives another description of the hodge filtration which we hope is easier to understand and apply its definition does not use resolution of singularities instead it relies on the theory of holonomic modules in one variable with regular singularities this paper arose from conversations at the 1980 arbeitstagung in bonn where varchenko s conjectured hodge filtration 22 had been discussed in brieskorn s seminar we have since learned that varchenko obtained similar results to those in this paper in the summer and autumn of 1980 23 25 in sect 1 the milnor fibration is embedded in a family of smooth projective hypersurfaces the hodge theory of a smooth projective hypersurface is explained in the fashion of brylinski 2 in sect 2 in sect 3 we recall the description of the gauss manin system from 8 our new formula for the hodge filtration is explained in sects 4 5 in sect 6 we prove that it gives the same result as 18 we prove a thom sebastiani formula for the hodge filtration in sect 7 which leads to a proof of conjecture 5 4 of 18 in sect 8 we show how to prove varchenko s result about the jordan normal forms of multiplication by f in the jacobian ring of f and the logarithm of the unipotent monodormy of f with our method in the last chapter the mixed hodge structure is calculated for two examples

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

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

reduction to real infinitesimal character in affine hecke algebras the main result of this paper is to show that the problem of the determination of the unramified unitary dual of a split p adic group is equivalent to the problem of determining the unitary dual of the corresponding graded hecke algebra in bm the authors established this equivalence in the case of iwahori spherical representations under a certain restriction namely it was essential for the infinitesimal character to be real in the terminology of bmj in terms of the langlands deligne lusztig parameters s u p kul the restriction is that s e lg be a purely hyperbolic element the technique used in bm was to combine the notion of the signature of a k character in v with some facts which follow from kl namely that the 2w characters of tempered representations are linearly independent this is essentially true precisely when the infinitesimal character is real for if not s has an elliptic part se such that

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

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

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

intersection homology and torus actions in the bialynicki birula decomposition of x see 15 6 10 13 the same formula holds for appropriate integers my when c is replaced by a torus t c r in 9 it is shown that the formula 0 1 is valid even when x is singular provided that the bialynicki birula decomposition is good the aim of this paper is to generalize 0 1 to the case when x is singular in a different way which involves replacing ordinary homology by intersection homology with respect to the middle perversity however only rational coefficients are considered when x is nonsingular its intersection homology and ordinary homology coincide but when x is singular its intersection homology behaves better in many respects than its ordinary cohomology it is shown that when x is singular just as when x is nonsingular the rational intersection homology of x is determined by the action of t on an arbitrarily small neighborhood of the fixed point set xt as might be expected the formula 0 1 does not carry over directly when intersection homology replaces ordinary homology the terms hi 2m f z appearing in the right hand side are replaced by hypercohomology groups of certain complexes of sheaves over the f which depend upon how the f meet the singularities of x see they y orem 2 3 1 of this paper contains a review of a proof of 0 1 for rational coefficients which uses equivariant morse theory in 2 it is shown how this proof can be extended to apply to singular varieties when intersection homology is used the

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

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

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

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