connection between kinetic methods for fluid dynamic equations and macroscopic finite difference schemes the lattice boltzmann method lbm for the incompressible navier stokes ns equations and the gas kinetic scheme for the compressible ns equations are based on the kinetic theory of gases in the latter case however it is shown that the kinetic formulation is necessary only in the discontinuous reconstruction of fluid dynamic variables for shock capturing analogously we will discuss the reduction of a kinetic method for the incompressible case where the lbm scheme will be shown to shrink to an artificial compressibility type finite difference scheme we will prove first that a simple and compact lbm scheme cannot catch rarefied effects beyond navier stokes and hence that it is worth the effort to develop kinetic based fd alternatives finally we will propose two improvements to existing kinetic based fd schemes first of all a the proposed scheme is formulated purely in terms of macroscopic quantities on a compact stencil secondly b the semi implicit formulation is proposed in order to increase the stability we think that this work may be useful to others in realizing the actual possibilities of simple lbm schemes beyond navier stokes and in adopting the suggested improvements in their actual fd codes

strong approximation for zariski dense subgroups of semi simple algebraic groups 1 1 theorem let k be an algebraically closed field of characteristic different from 2 and 3 and g an almost simple connected and simply connected algebraic group defined over k let f be a finitely generated zariski dense subgroup of g k and a the subring of k generated by the traces tr ad y y e p then there exist b e a a subgroup f of finite index in f and a structure gab of a group scheme over ab on g such that f c ga ab and f is dense in gala b a

semi implicit linearized multiple relaxation time formulation of lattice boltzmann schemes for mixture modeling a lattice boltzmann model for mixture modeling is developed by applying the multiple relaxation time mrt approach to the hamel model which allows one to derive from a general framework different model equations independently proposed like the gross krook model and the sirovich model by imposing some physical constraints the mrt lattice boltzmann hamel model reduces to the generalized mrt lattice boltzmann gross krook model involving the local maxwellian centered on the barycentric velocity which allows one to tune independently the species diffusivity the mixture kinematic viscosity and the mixture bulk viscosity reducing the number of moving particles over the total is possible to deal effectively with mass particle ratios far from unity and for this reason to model the pressure driven diffusion a convenient numerical approach is proposed for solving the developed model which essentially widens the stability range of conventional schemes in terms of dimensionless relaxation frequencies by solving explicitly the advection operator together with the nonlinear terms of the collisional operator and solving implicitly the residual linear terms in this way the calculations are drastically reduced and the operative matrices can be computed once for all at the beginning of the calculation implying moderate additional computational demand following this approach a semi implicit linearized backward euler scheme ideal for parallel implementations is proposed in order to achieve the previous results the asymptotic analysis recently suggested for analyzing the macroscopic equations corresponding to lattice boltzmann schemes in the low mach number limit proves to be an effective tool some numerical tests are reported for proving the consistency of the proposed method with both the fick model and maxwell stefan model in the macroscopic limit

numerical stability of explicit off lattice boltzmann schemes the off lattice boltzmann olb method consists of numerical schemes which are used to solve the discrete boltzmann equation unlike the commonly used lattice boltzmann method the spatial and time steps are uncoupled in the olb method in the currently proposed schemes which can be broadly classified into runge kutta based and characteristics based the size of the time step is limited due to numerical stability constraints in this work we systematically compare the numerical stability of the proposed schemes in terms of the maximum stable time step in line with the overall lb method we investigate the available schemes where the advection approximation is explicit and the collision approximation is either explicit or implicit the comparison is done by implementing these schemes on benchmark incompressible flow problems such as taylor vortex flow poiseuille flow and lid driven cavity flow it is found that the characteristics based olb schemes are numerically more stable than the runge kutta based schemes additionally we have observed that with respect to time step size the scheme proposed by bardow et al 2006 1 is the most numerically stable and computationally efficient scheme compared to similar schemes for the flow problems tested here

compact subgroups of linear algebraic groups abstract the general problem underlying this article is to give a qualitative classification of all compact subgroups gl n f where f is a local field and n is arbitrary it is natural to ask whether is an open compact subgroup of h e where h is a linear algebraic group over a closed subfield e f we show that indeed has this form up to finite index and a finite number of abelian subquotients when is zariski dense in a connected semisimple group we give a precise openness result for the closure of the commutator group of in the case char f 0 the answers have long been known by results of chevalley and weyl the motivation for this work comes from the positive characteristic case where such results are needed to study galois representations associated to function fields we also derive openness results over a finite number of local fields

rationality of conformally invariant local correlation functions on compactified minkowski space rationality of the wightman functions is proven to follow from energy positivity locality and a natural condition of global conformal invariance gci in any number d of space time dimensions the gci condition allows to treat correlation functions as generalized sections of a vector bundle over the compactification of minkowski space m and yields a strong form of locality valid for all non isotropic intervals if assumed true for space like separations

the structure of the ladder insertion elimination lie algebra we continue our investigation into the insertion elimination lie algebra open image in new window of feynman graphs in the ladder case emphasizing the structure of this lie algebra relevant for future applications in the study of dyson schwinger equations we work out the relation to the classical infinite dimensional lie algebra open image in new window and we determine the cohomology of open image in new window

semi lagrangian implicit bhatnagar gross krook collision model for the finite volume discrete boltzmann method in order to increase the accuracy of temporal solutions reduce the computational cost of time marching and improve the stability associated with collisions for the finite volume discrete boltzmann method an advanced implicit bhatnagar gross krook bgk collision model using a semi lagrangian approach is proposed in this paper unlike existing models in which the implicit bgk collision is resolved either by a temporal extrapolation or by a variable transformation the proposed model removes the implicitness by tracing the particle distribution functions pdfs back in time along their characteristic paths during the collision process an interpolation scheme is needed to evaluate the pdfs at the traced back locations by using the first order interpolation the resulting model allows for the straightforward replacement of f eq n 1 by f eq n no matter where it appears after comparing the proposed model with the existing models under different numerical conditions e g different flux schemes and time marching schemes and using the proposed model to successfully modify the variable transformation technique three conclusions can be drawn first the proposed model can improve the accuracy by almost an order of magnitude second it can slightly reduce the computational cost therefore the proposed scheme improves accuracy without extra cost finally the proposed model can significantly improve the t limit compared to the temporal interpolation model while having the same t limit as the variable transformation approach the proposed scheme with a second order interpolation is also developed and tested however that technique displays no advantage over the simple first order interpolation approach both numerical and theoretical analyses are also provided to explain why the developed implicit scheme with simple first order interpolation can outperform the same scheme with second order interpolation as well as the existing temporal extrapolation and variable transformation schemes

unitary positive energy representations of scalar bilocal quantum fields the superselection sectors of two classes of scalar bilocal quantum fields in d 4 dimensions are explicitly determined by working out the constraints imposed by unitarity the resulting classification in terms of the dual of the respective gauge groups u n and o n confirms the expectations based on general results obtained in the framework of local nets in algebraic quantum field theory but the approach using standard lie algebra methods rather than abstract duality theory is complementary the result indicates that one does not lose interesting models if one postulates the absence of scalar fields of dimension d 2 in models with global conformal invariance another remarkable outcome is the observation that with an appropriate choice of the hamiltonian a lie algebra embedded into the associative algebra of observables completely fixes the representation theory

lattice boltzmann method and gas kinetic bgk scheme in the low mach number viscous flow simulations both lattice boltzmann method lbm and the gas kinetic bgk scheme are based on the numerical discretization of the boltzmann equation with collisional models such as the bhatnagar gross krook bgk model lbm tracks limited number of particles and the viscous flow behavior emerges automatically from the intrinsic particle stream and collisions process on the other hand the gas kinetic bgk scheme is a finite volume scheme where the time dependent gas distribution function with continuous particle velocity space is constructed and used in the evaluation of the numerical fluxes across cell interfaces currently lbm is mainly used for low mach number nearly incompressible flow simulation for the gas kinetic scheme the application is focusing on the high speed compressible flows in this paper we are going to compare both schemes in the isothermal low mach number flow simulations the methodology for developing both schemes will be clarified through the introduction of operator splitting boltzmann model and operator averaging boltzmann model from the operator splitting boltzmann model the error rooted in many kinetic schemes which are based on the decoupling of particle transport and collision can be easily understood as to the test case we choose to use the 2d cavity flow since it is one of the most extensively studied cases detailed simulation results with different reynolds numbers as well as the benchmark solutions are presented

weakly and strongly consistent formulations of irreversible processes if time evolution equations are formulated in terms of thermodynamic building blocks two possibilities arise to judge the consistency of models by the properties of the building blocks strong or structural consistency or solely by the implied evolution equations weak or dynamic consistency we propose a straightforward procedure to check for strong consistency by means of the eigenvalues and eigenmodes of the linearized equations which is related to establishing a fluctuation dissipation theorem by applying the general ideas to hydrodynamics we clarify the role of the controversial diffusion terms in hydrodynamic equations

multiple relaxation time lattice boltzmann scheme for homogeneous mixture flows with external force a lattice boltzmann scheme is developed for homogeneous mixture modeling based on the multiple relaxation time mrt formulation which fully recovers the maxwell stefan diffusion model in the continuum limit with a external force and b tunable schmidt number the theoretical basis of the proposed mrt formulation is a recently proposed bhatnagar gross krook type kinetic model for gas mixtures andries et al j stat phys 106 993 2002 and it substantially extends the applicability of a scheme already proposed by the same author which used only one relaxation parameter the recovered equations at the macroscopic level are derived by an innovative expansion technique based on the grad moment system some numerical simulations are reported for the solvent test case with external force aiming to find the numerical ranges for the transport coefficients that ensure acceptable accuracies the numerical results reduce the theoretical expectations which are based on a strong separation among the characteristic scales

infinite dimensional lie algebras in 4d conformal quantum field theory the concept of global conformal invariance gci opens the way of applying algebraic techniques developed in the context of two dimensional chiral conformal field theory to a higher even dimensional spacetime in particular a system of gci scalar fields of conformal dimension two gives rise to a lie algebra of harmonic bilocal fields vm x y where the m span a finite dimensional real matrix algebra closed under transposition the associative algebra is irreducible iff its commutant coincides with one of the three real division rings the lie algebra of the modes of the bilocal fields is in each case an infinite dimensional lie algebra a central extension of corresponding to the field of reals of u associated with the field of complex numbers and of so 4 related to the algebra of quaternions they give rise to quantum field theory models with superselection sectors governed by the global gauge groups o n u n and respectively

three ways to lattice boltzmann a unified time marching picture it is shown that the lattice boltzmann equation lbe corresponds to an explicit verlet time marching scheme for a continuum generalized boltzmann equation with a memory delay equal to a half time step this proves second order accuracy of lbe with respect to this generalized equation with no need of resorting to any implicit time marching procedure crank nicholson and associated nonlinear variable transformations it is also shown and numerically demonstrated that this equivalence is not only formal but it also translates into a complete equivalence of the corresponding computational schemes with respect to the hydrodynamic equations second order accuracy with respect to the continuum kinetic equation is also numerically demonstrated for the case of the taylor green vortex it is pointed out that the equivalence is however broken for the case in which mass and or momentum are not conserved such as for chemically reactive flows and mixtures for such flows the time centered implicit formulation may indeed offer a better numerical accuracy

explicit finite difference lattice boltzmann method for curvilinear coordinates in this paper a finite difference based lattice boltzmann method for curvilinear coordinates is proposed in order to improve the computational efficiency and numerical stability of a recent method r mei and w shyy j comput phys 143 426 1998 in which the collision term of the boltzmann bhatnagar gross krook equation for discrete velocities is treated implicitly in the present method the implicitness of the numerical scheme is removed by introducing a distribution function different from that being used currently as a result an explicit finite difference lattice boltzmann method for curvilinear coordinates is obtained the scheme is applied to a two dimensional poiseuille flow an unsteady couette flow a lid driven cavity flow and a steady flow around a circular cylinder the numerical results are in good agreement with the results of previous studies extensions to other lattice boltzmann models based on nonuniform meshes are also discussed

diagonal actions in positive characteristic we prove positive characteristic analogues of certain measure rigidity theorems in characteristic 0 more specifically we give a classification result for positive entropy measures on quotients of sld and a classification of joinings for higher rank actions on simply connected absolutely almost simple groups

word maps and waring type problems waring s problem asks whether every natural number is a sum of g k fcth powers where g is a suitable function this was solved affirmatively by hubert in 1909 optimizing g k has been a central problem in additive number theory ever since see na for more detail and background recently there has been considerable interest in group theoretic analogues of this phenomenon where the aim is to present group elements as short products of certain special elements these special elements can be powers or commutators or values of a general word w or elements of a special conjugacy class in the group the motivation for this is sometimes topological let g be a topologically finitely generated pro p group using expressions of elements of the commutator subgroup g1 as bounded products of commutators serre showed that g is closed and deduced that every finite index subgroup of g is open a recent deep result of nikolov and segal nsi ns2 shows that this holds for every finitely generated profinite group again the core of the proof is presenting group elements as short products of values of certain words

four dimensional conformal field theory models with rational correlation functions recently established rationality of correlation functions in a globally conformal invariant quantum field theory satisfying wightman axioms is used to construct a family of soluble models in four dimensional minkowski spacetime we consider in detail a model of a neutral scalar field of dimension two it depends on a positive real parameter c an analogue of the virasoro central charge and admits for all finite c an infinite number of conserved symmetric tensor currents the operator product algebra of is shown to coincide with a simpler one generated by a bilocal scalar field v x1 x2 of dimension 1 1 the modes of v together with the unit operator span an infinite dimensional lie algebra v whose vacuum i e zero energy lowest weight representations only depend on the central charge c wightman positivity i e unitarity of the representations of v is proven to be equivalent to c

quasifinite highest weight modules over the lie algebra of differential operators on the circle we classify positive energy representations with finite degeneracies of the lie algebraw 1 and construct them in terms of representation theory of the lie algebra hat gl infty r m of infinites matrices with finite number of non zero diagonals over the algebrar m t t m 1 the unitary ones are classified as well similar results are obtained for the sin algebras

on some pro p groups from infinite dimensional lie theory we study some pro p groups arising from infinite dimensional lie theory the starting point is incomplete kac moody groups over finite fields there are various completion procedures always providing locally pro p groups we show topological finite generation for their pro p sylow subgroups in most cases whatever the algebraic geometric or representation theoretic completion this implies abstract simplicity for complete kac moody groups and provides identifications of the pro p groups obtained from the same incomplete group we also discuss the question of non linearity of these pro p groups

harmonic bilocal fields generated by globally conformal invariant scalar fields the twist two contribution in the operator product expansion of phi 1 rm x 1 phi 2 rm x 2 for a pair of globally conformal invariant scalar fields of equal scaling dimension d in four space time dimensions is a field v1 x1 x2 which is harmonic in both variables it is demonstrated that the huygens bilocality of v1 can be equivalently characterized by a single pole property concerning the pole structure of the rational correlation functions involving the product phi 1 rm x 1 phi 2 rm x 2 this property is established for the dimension d 2 of phi 1 phi 2 as an application we prove that any system of gci scalar fields of conformal dimension 2 in four space time dimensions can be presented as a possibly infinite superposition of products of free massless fields