a current density conservative scheme for incompressible mhd flows at a low magnetic reynolds number part i on a rectangular collocated grid system a consistent conservative and accurate scheme has been designed to calculate the current density and the lorentz force by solving the electrical potential equation for magnetohydrodynamics mhd at low magnetic reynolds numbers and high hartmann numbers on a finite volume structured collocated grid in this collocated grid velocity u pressure p and electrical potential f are located in the grid center while current fluxes are located on the cell faces the calculation of current fluxes on the cell faces is conducted using a conservative scheme which is consistent with the discretization scheme for the solution of electrical potential poisson equation a conservative interpolation is used to get the current density at the cell center which is used to conduct the calculation of lorentz force at the cell center for momentum equations we will show that both conservative and consistent are important properties of the scheme to get an accurate result for high hartmann number mhd flows with a strongly non uniform mesh employed to resolve the hartmann layers and side layers of hunt s conductive walls and shercliff s insulated walls a general second order projection method has been developed for the incompressible navier stokes equations with the lorentz force included this projection method can accurately balance the pressure term and the lorentz force for a fully developed core flow this method can also simplify the pressure boundary conditions for mhd flows

arbitrary order exactly divergence free central discontinuous galerkin methods for ideal mhd equations ideal magnetohydrodynamic mhd equations consist of a set of nonlinear hyperbolic conservation laws with a divergence free constraint on the magnetic field neglecting this constraint in the design of computational methods may lead to numerical instability or nonphysical features in solutions in our recent work f li l xu s yakovlev central discontinuous galerkin methods for ideal mhd equations with the exactly divergence free magnetic field journal of computational physics 230 2011 4828 4847 second and third order exactly divergence free central discontinuous galerkin methods were proposed for ideal mhd equations in this paper we further develop such methods with higher order accuracy the novelty here is that the well established h div conforming finite element spaces are used in the constrained transport type framework and the magnetic induction equations are extensively explored in order to extract sufficient information to uniquely reconstruct an exactly divergence free magnetic field the overall algorithm is local and it can be of arbitrary order of accuracy numerical examples are presented to demonstrate the performance of the proposed methods especially when they are fourth order accurate

long term dissipativity of time stepping algorithms for an abstract evolution equation with applications to the incompressible mhd and navier stokes equations abstract this paper examines the long term dissipativity and unconditional non linear stability of time integration algorithms for the incompressible mhd equations the results apply as a particular case to the uncoupled incompressible navier stokes equations the analysis is performed in the setting defined by an abstract evolution equation possessing the same long term dissipative structure as the above physical systems a general class of time stepping schemes is analyzed in this context showing the non linear unconditional stability and long term dissipativity of particular members of this family of algorithms in particular algorithms showing these strong properties which additionally involve the solution of a linear problem at each time step are identified a particular linear algorithm is shown to exhibit optimal long term dissipative properties and to possess an algorithmic global attractor these abstract results apply rigorously to galerkin mixed finite element discretizations of the problem to this end it is shown that such galerkin type projection inherits the dissipative properties of the continuum problem computational aspects involved in the numerical implementation of these methods are addressed and illustrated in representative numerical simulations

an augmented lagrangian based approach to the oseen problem we describe an effective solver for the discrete oseen problem based on an augmented lagrangian formulation of the corresponding saddle point system the proposed method is a block triangular preconditioner used with a krylov subspace iteration like bicgstab the crucial ingredient is a novel multigrid approach for the 1 1 block which extends a technique introduced by schoberl for elasticity problems to nonsymmetric problems our analysis indicates that this approach results in fast convergence independent of the mesh size and largely insensitive to the viscosity we present experimental evidence for both isop2 p0 and isop2 p1 finite elements in support of our conclusions we also show results of a comparison with two state of the art preconditioners showing the competitiveness of our approach

grad div stablilization for stokes equations in this paper a stabilizing augmented lagrangian technique for the stokes equations is studied the method is consistent and hence does not change the continuous solution we show that this stabilization improves the well posedness of the continuous problem for small values of the viscosity coefficient we analyze the influence of this stabilization on the accuracy of the finite element solution and on the convergence properties of the inexact uzawa method

une preuve simple des conjectures de langlands pour gl n sur un corps p adique let f be a finite extension of p for each integer n 1 we construct a bijection from the set f 0 n of isomorphism classes of irreducible degree n representations of the absolute weil group of f onto the set f 0 n of isomorphism classes of smooth irreducible supercuspidal representations of gl n f those bijections preserve epsilon factors for pairs and hence we obtain a proof of the langlands conjectures for gl n over f which is more direct than harris and taylor s our approach is global and analogous to the derivation of local class field theory from global class field theory we start with a result of kottwitz and clozel on the good reduction of some shimura varieties and we use a trick of harris who constructs non galois automorphic induction in certain cases

periodic heterogeneous structures new explicit solutions and effective characteristics of refraction of an imposed field complex variable methods are applied to study three double periodic two phase planar heterogeneous structures explicit expressions of functionals of energy dissipation and of effective resistivities conductivities are found on the basis of strict analytical solutions of a boundary value problem for an arbitrary direction of an imposed external field comparisons with the results of bakhvalov and panasenko homogenization of processes in periodic media nauka moscow 1984 dykhne zh eksp teor fiz 59 1970 pp 110 113 soviet phys jetp 32 1971 pp 63 65 emets zh eksp teor fiz 96 1989 pp 701 711 soviet phys jetp 96 1989 keller j appl phys 34 1963 pp 991 993 and mendelson j appl phys 46 1975 pp 4740 4741 are made in particular the dissipation in the general case is shown essentially to depend on the direction of the external field for a rectangular checkerboard dissipation within the two phases does not coincide it is rigorously pr

regular hexagonal three phase checkerboard abstract a two dimensional doubly periodic three phase hexagonal structure is considered the flow in the structure is generated by three sets of vortexes sinks sources which are the same in each phase and are located in the centers of the hexagons complex analysis methods are utilized to reduce the doubly periodic r linear conjugation problem to the simpler one riemann hilbert rh problem on a three sheeted riemann surface in turn the latter problem is reduced to a rh problem involving three joined sectors on the plane which was previously investigated in 3 the limiting cases with one non conducting phase and two phases of the same conductivities are investigated all solutions derived are verified both numerically and analytically examples of relevant flow networks streamlines and equipotentials are plotted in the whole structure and separately in each phase

a proof of langland s conjecture on plancherel measures complementary series of p adic groups analysis of p adic reductive groups our first result theorem 7 9 proves a conjecture of langlands on normalization of intertwining operators by means of local langlands root numbers and l functions at least when the group is quasi split and the inducing representation is generic assuming two natural conjectures in harmonic analysis of p adic groups we also prove the validity of the conjecture in general theorem 9 5 as our second result we obtain all the complementary series and special representations of quasi split p adic groups coming from rank one parabolic subgroups and generic supercuspidal represen

four phase checkerboard composites two dimensional periodic rectangular checkerboard media are considered in the situation where mean fluxes are prescribed across the structure the closed form solution is obtained in the general case where the checkerboard is constructed using four rectangular cells each having a different constant resistivity this four cell structure then repeats doubly periodically to cover the whole plane this general solution is then used to calculate the effective properties thus this four phase checkerboard encapsulates many limiting and special cases as a starting point we develop a concise closed form solution to a basic problem involving four joined quarter planes each of a different resistivity subsequent manipulations yield solutions to problems posed in increasingly convoluted domains while retaining the essentially simple structure found for joined quarter planes

exact solution of a boundary value problem for a rectangular checkerboard field a class of two phase composite materials with a biperiodic structure is investigated by the methods of complex analysis two interface conditions continuity of normal component of a desired vector w and tangential component of w at the contact boundary as well as the double periodicity condition are involved in rigorous form the exact analytic solution of the corresponding generalized riemann boundary value problem is obtained the explicit values of the effective parameters namely effective resistivity and dissipation of energy of an elementary cell and resistivities along the symmetry axes are calculated in closed analytic form the coincidence of our formulae with the well known effective resistivity conductivity formula of keller 1964 dykhne 1970 and mendelson 1975 and the dissipation formula of dykhne 1970 is shown in the case of square checkerboard field the keller 1963 identity is generalized for the heterogeneous structure studied

a three phase tessellation solution and effective properties two dimensional doubly periodic three phase structures are considered in the situation where mean fluxes are applied across the structure the approach is to utilize complex variables and to use a mapping that reduces the doubly periodic problem to a m uch simpler one involving joined sectors this is a model composite structure in electrostatics and mathematically analogous areas such as porous media anti plane elasticit y heat conduction and we find various eectiv e parameters and investigate limiting cases the structure is also amenable to asymptotic methods in the case of highly varying composition and we provide these solutions partly as a check upon our analysis and partly as they are useful in their own right

on a certain metaplectic eisenstein series and the twisted symmetric square l function in our earlier paper based on a paper by bump and ginzburg we used an eisenstein series on the double cover of text gl r to obtain an integral representation of the twisted symmetric square l function of text gl r using that we showed that the incomplete twisted symmetric square l function of text gl r is holomorphic for text re s 1 in this paper we will determine the possible poles of this eisenstein series more precisely and show that the incomplete twisted symmetric square l function is entire except possible simple poles at s 0 and s 1

the twisted symmetric square l function of gl r in this paper we consider the partial symmetric square l function ls s sym2 of an irreducible cuspidal automorphic representation of glr a twisted by a hecke character in particular we will show that the l function ls s sym2 is holomorphic for the region re s 1 1 r with the exception that if r 2 1 a pole might occur at s 1 where is the central character of our method of proof is essentially a nontrivial modification of the one by bump and ginzburg in which they considered the case 1

grad div stabilization and subgrid pressure models for the incompressible navier stokes equations in this paper the grad div stabilization for the incompressible navier stokes finite element approximations is considered from two different viewpoints i as a variational multiscale approach for the pressure subgrid modeling and ii as a stabilization procedure of least square type some new error estimates for the linearized problem with the grad div stabilization are proved with the help of norms induced by the pressure schur complement operator we discuss the stabilization parameter choice arising in the frameworks of least square and multiscale methods and consider assumptions which allow to relate both approaches

on the existence uniqueness and finite element approximation of solutions of the equations of stationary incompressible magnetohydrodynamics the authors consider the equations of stationary incompressible magneto hydrodynamics posed in a bounded domain in three dimensions and treat the full coupled system of equations with inhomogeneous boundary conditions under certain conditions on the data they show that the existence and uniqueness of the solution of a weak formulation of the equations can be guaranteed they discuss a finite element discretization of the equations and prove an optimal estimate for the error of the approximate solution

stable finite element pair for stokes problem and discrete stokes complex on quadrilateral grids in this paper we construct a stable finite element pair for incompressible stokes problem and a discrete stokes complex associated with that pair on general quadrilateral grids the finite element spaces involved consist of piecewise polynomials only and the divergence free condition is imposed in a primal formulation these constructions can be generated onto grids that consist of both triangular and quadrilateral cells

a mixed finite element method with exactly divergence free velocities for incompressible magnetohydrodynamics abstract we introduce and analyze a mixed finite element method for the numerical discretization of a stationary incompressible magnetohydrodynamics problem in two and three dimensions the velocity field is discretized using divergence conforming brezzi douglas marini bdm elements and the magnetic field is approximated by curl conforming nedelec elements the h 1 continuity of the velocity field is enforced by a dg approach a central feature of the method is that it produces exactly divergence free velocity approximations and captures the strongest magnetic singularities we prove that the energy norm error is convergent in the mesh size in general lipschitz polyhedra under minimal regularity assumptions and derive nearly optimal a priori error estimates for the two dimensional case we present a comprehensive set of numerical experiments which indicate optimal convergence of the proposed method for two dimensional as well as three dimensional problems

a current density conservative scheme for incompressible mhd flows at a low magnetic reynolds number part ii on an arbitrary collocated mesh a conservative formulation of the lorentz force is given here for magnetohydrodynamic mhd flows at a low magnetic reynolds number with the current density calculated based on ohm s law and the electrical potential formula this conservative formula shows that the total momentum contributed from the lorentz force is conservative when the applied magnetic field is constant for the case with a non constant applied magnetic field the lorentz force has been divided into two parts a strong globally conservative part and a weak locally conservative part the conservative formula has been employed to develop a conservative scheme for the calculation of the lorentz force on an unstructured collocated mesh only the current density fluxes on the cell faces which are calculated using a consistent scheme with good conservation are needed for the calculation of the lorentz force meanwhile a conservative interpolation technique is designed to get the current density at the cell center from the current density fluxes on the cell faces this conservative interpolation can keep the current density at the cell center conservative which can be used to calculate the lorentz force at the cell center with good accuracy the lorentz force calculated from the conservative current at the cell center is equivalent to the lorentz force from the conservative formula when the applied magnetic field is constant which can conserve the total momentum we will further prove that the simple interpolation scheme used in the part i m j ni r munipalli n b morley p y huang m abdou a current density conservative scheme for mhd flows at a low magnetic reynolds number part i on a rectangular collocated grid system journal of computational physics in press doi 10 1016 j jcp 2007 07 025 of this series of papers is conservative on a rectangular grid and can keep the total momentum conservative in a rectangular grid

twisted endoscopy and reducibility of induced representations for p adic groups 1 introduction this is the first in a series of papers in which we study the reducibility of representations induced from discrete series representations of the levi factors ofmaximal parabolic subgroups of p adic groups on the unitary axis the problem is equivalent to determining certain local langlands l functions which are of arithmetic significance by themselves one of the main aims of this paper is to interpret our results in the direction of the parametrization problem by means of the theory of twisted endoscopy for which our method seems to be very suitable when the representation is supercuspidal we also study the reducibility of the induced representations off the unitary axis let f be a p adic field of characteristic zero fix a positive integer n 1 and let g be either of the groups sp2n s02n or s02n l in all three cases there is a conjugacy class of maximal parabolic subgroups which has gl as its levi factor let p mn be the standard parabolic subgroup ofg in this conjugacy class then m gl let tr be a discrete series representation of m gln f and given s c let i s tr be the representation of g g f induced from tr r idet ls let i tr i 0 tr

block compatible metaplectic cocycles has cardinality r 1 let g be the f rational points of a simple chevalley group defined over f in his thesis matsumoto 5 gave a beautiful construction for the metaplectic cover g of g a central extension of g by r f whose existence is intimately connected with the deep properties of the r th order hilbert symbol f f f r f metaplectic groups figure prominently in the study of number theory representation theory and physics arising naturally in the theory of theta functions dual pair correspondences weil representations and spin geometry in this paper we study the class of central extensions of a simple chevalley group over an arbitrary infinite field of which the metaplectic groups form an important subclass metaplectic groups were constructed quite explicitly in weil s memoir 10 in the case that g is symplectic in 3 and 4 kubota gave the construction of the r fold metaplectic cover of gl2 f moreover he described an explicit 2 cocycle k on gl2 f that represents the second cohomology class of the extension cf 3 corollary 8 which makes it possible to deal quite rapidly with many concrete problems in this setting steinberg 9 and moore 7 considered the algebraic problem of determining the central extensions of a simple chevelley group over an arbitrary field they were also led to the metaplectic groups this line of investigation was completed by matsumoto 5 whose work forms the foundation of the present paper to summarize our results let f be an infinite field g the f rational points of a simple chevalley group defined over f a an abelian group and c f f a a steinberg symbol that is bilinear if g is not symplectic cf 1 in this paper we describe an explicit 2 cocycle g in z g a that represents the cohomology class in h g a of the central extension g of g by a constructed by matsumoto 5

a charge conservative finite element method for inductionless mhd equations part i convergence a charge conservative finite element method is proposed to solve the inductionless and incompressible magnetohydrodynamic mhd equations in three dimensions the method yields an exactly divergenc