computation of steady and unsteady vortex dominated flows with shock waves the unsteady euler equations have been derived in the conservation form for the flow relative motion with respect to a rotating frame of reference the resulting equations are solved by using a central difference finite volume scheme with four state runge kutta time stepping for steady flow applications local time stepping is used and for unsteady applications the minimum global time stepping is used a three dimensional fully vectorized computer program has been developed and applied to steady and unsteady maneuvering delta wings the capability of the three dimensional program has been demonstrated for a rigid sharp edged delta wing undergoing uniform rolling in a conical flow and rolling oscillations in a locally conical flow

vertex based finite volume solution of the two dimensional navier stokes equations in the work the efficiency of the runge kutta scheme and the benefit of convergence acceleration techniques have been utilized the results obtained for turbulent flow past a naca 0012 airfoil have been compared with available numerical and experimental results

a fast algorithm for the calculation of transonic flow over wing body combinations a method to calculate transonic flows over wing body combinations using the full potential equation is described a sequence of transformations is used to transform the flowfield to the inside of a circular cylinder and the flow equation is solved in this space by a finite difference technique a new approximate factorization algorithm has been developed to obtain rapid convergence several times faster than a conventional relaxation method used previously results are presented for a realistic configuration showing the relative convergence rates of the two methods and comparing computed with experimental results

computation of vortex dominated flow for a delta wing undergoing pitching oscillation the conservative unsteady euler equations for the flow relative to a moving frame of reference are used to solve for the three dimensional steady and unsteady flows around a sharp edged delta wing the resulting equations are solved by using an implicit approximately factored finite volume scheme implicit second order and explicit second and fourth order dissipations are added to the scheme the boundary conditions are explicitly satisfied the grid is generated by locally using a modified joukowski transformation in crossflow planes at the grid chord stations the computational applications cover a steady flow around a delta wing whose results serve as the initial conditions for the unsteady flow around a pitching delta wing at a large mean angle of attack the steady results are compared with the experimental data and the unsteady results are compared with results of a flux difference splitting scheme

a general explicit or semi explicit algorithm for compressible and incompressible flows this note presents a rational basis for a unified finite element algorithm capable of dealing with a wide range of fluid flow in both steady and transient cases it is hoped that empiricism inherent in many previous approaches can be avoided and a sound basis provided the algorithm permits the use of equal interpolation for all variables by avoiding the need for the babuska brezzi constraints in regions where the flow is nearly incompressible the success of the algorithm which here is written for the non conservative equation form is demonstrated on several examples ranging from nearly incompressible through transonic regions to supersonic flows up to mild shocks such as those occurring in the examples presented in this paper no artificial viscosity is added at any stage the algorithm extends some concepts introduced in an earlier paper

propagation of moments and regularity for the 3 dimensional vlasov poisson system we prove that if the initial data has moments inv higher than three then the solution of vlasov poisson has also moments inv higher than three we deduce from this different regularity results on the local density the force field or the solution itself also we give a new uniqueness result and new regularity results for solutions satisfying only the energy andl bounds our proofs are based on a new representation formula and logarithmic estimates for the force field

fundamental groups of character varieties surfaces and tori we compute the fundamental group of moduli spaces of lie group valued representations of surface and torus groups

the classical limit of the relativistic vlasov maxwell system solutions of the relativistic vlasov maxwell system of partial differential equations are considered in three space dimensions the speed of light c appears as a parameter in this system for smooth cauchy data classical solutions are shown to exist on a time interval that is independent ofc then using an integral representation for the electric and magnetic fields due to glassey and strauss 6 conditions are given under which solutions of the relativistic vlasov maxwell system converge in pointwise sense to solutions of the non relativistic vlasov poisson system at the asymptotic rate of 1 c asc tends to infinity

euler correction method for two and three dimensional transonic flows an euler correction method based on the clebsch formulation of the euler equations has been developed to improve shock calculations in full potential methods in the clebsch treatment of steady rotational flows the velocity is decomposed into potential and rotational components written in terms of scalar functions the potential part is computed from the continuity equation using a modified version of an existing finite volume full potential solver the rotational parts are determined analytically from the momentum equation based on small perturbation approximations the solutions obtained for airfoils and wing bodies are compared with those using the time marching euler methods the agreement between the results obtained using these two approaches is good

generation of boundary conforming grids around wing body configurations using transfinite interpolation a computational procedure for generating three dimensional nonorthogonal surface fitted mesh systems around wing fuselage configurations is presented the method is based on the concept of transfinite interpolation which has been extended to handle very general mapping function specifications at the boundaries thereby making it possible to generate single block mappings with geometry data specified only at the outer boundaries of the computational domain since it is a direct algebraic mapping technique the method is very inexpensive in terms of computer cost different types of possible mappings are compared with respect to resolution and economy of nodal points a procedure for a novel type of mapping designated type o o is described and several plots of generated grids demonstrate the capabilities of the method the singular lines inherent in every three dimensional mesh for this type of surface geometry are also discussed

classical solutions and the glassey strauss theorem for the 3d vlasov maxwell system r glassey and w strauss have proved in arch rational mech anal 92 1986 59 90 that c1 solutions to the relativistic vlasov maxwell system in three space dimensions do not develop singularities as long as the support of the distribution function in the momentum variable remains bounded the present paper simplifies their proof

the classification of real projective structures on compact surfaces choi gratefully acknowledges partial support from garc kosef goldman gratefully acknowledges partial support from the national science foundation the alfred p sloan foundation and the institute for advanced computer studies at the university of maryland

influence of numerical dissipation on computational euler equations for vortex dominated flows etude d ecoulements supersoniques tourbillonnaires pour des ailes delta a aretes vives ou arrondies on developpe un schema de volumes finis

exact integrations of polynomials and symmetric quadrature formulas over arbitrary polyhedral grids this paper is concerned with two important elements in the high order accurate spatial discretization of finite volume equations over arbitrary grids one element is the integration of basis functions over arbitrary domains which is used in expressing various spatial integrals in terms of discrete unknowns the other consists of quadrature approximations to those integrals only polynomial basis functions applied to polyhedral and polygonal grids are treated here nontriangular polygonal faces are subdivided into a union of planar triangular facets and the resulting triangulated polyhedron is subdivided into a union of tetrahedra the straight line segment triangle and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices results are given both in terms of tensor products and products of cartesian coordinates the exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains using a coordinate free formulation simple and rational procedures are developed to derive virtually all quadrature formulas including some previously unpublished four symmetry groups of quadrature points are introduced to derive gauss formulas while their limiting forms are used to derive lobatto formulas representative gauss and lobatto formulas are tabulated the relative efficiency of their application to polyhedral and polygonal grids is detailed the extension to higher degrees of precision is discussed

global weak solutions of the vlasov maxwell system with boundary conditions boundaries occur naturally in physucal systems which satisfy the vlasov maxwell system assume perfect conductor boundary conditions for maxwell and either specular reflection or partial absorption for vlasov then weak solutions with finite energy exist for all time

an analysis of finite difference and finite volume formulations of conservation laws abstract finite difference and finite volume formulations are analyzed in order to clear up the confusion concerning their application to the numerical solution of conservation laws a new coordinate free formulation of systems of conservation laws is developed which clearly distinguishes the role of physical vectors from that of algebraic vectors which characterize the system the analysis considers general types of equations potential euler and navier stokes three dimensional unsteady flows with time varying grids are described using a single consistent nomenclature for both formulations grid motion due to a non inertial reference frame as well as flow adaptation is covered in comparing the two formulations it is found useful to distinguish between differences in numerical methods and differences in grid definition the former plays a role for non cartesian grids and results in only cosmetic differences in the manner in which geometric terms are handled the differences in grid definition for the two formulations is found to be more important since it affects the manner in which boundary conditions zonal procedures and grid singularities are handled at computational boundaries the proper interpretation of strong and weak conservation law forms for quasi one dimensional and axisymmetric flows is brought out

airfoil computation at high angles of attack inviscid and viscous phenomena he existence of flow separation and recirculation is usually associated with viscous flows the physical basis is fairly well understood and has been extensively studied there are a number of physical phenomena that cause flow separation and recirculation in all cases in which recirculation is present vorticity must also be present and thus there must exist some mechanism that generates vorticity in a viscous wall bounded flow the boundary layer generates a velocity gradient vorticity and momentum losses in the presence of an adverse pressure gradient separation can occur with the subsequent development of a recirculating reverse flow region and possible reattachment a shock impinging on a boundary layer can cause flow separation the governing equations for these types of flows are the navierstokes equations or some subset of them recently there has been considerable interest in the numerical solution of the inviscid flow equations the euler equations for most of the work reported in the literature the accuracy of the results is quite good and the solutions obtained are representative of the physical flow of interest for instance when viscous effects are negligible such as for thin boundary layers the inviscid solutions are a good approximation to the solution of the full navier stokes equations in this situation certain quantities such as the pressure along the body can be predicted well by the euler equations in contrast numerical solutions to the euler equations have been reported that do not have a straightforward physical interpretation in particular flow separation and recirculation for solutions to the euler equations have been reported by a number of researchers e g salas1 the question naturally arises as to the physical interpretation of these flows in the absence of physical viscosity in trying to attach any physical meaning to these flows we must first examine the possible mechanisms that could generate vorticity actual fluid flow is never truly inviscid although in some cases the viscous effects are negligible in computations however we can solve numerical approximations to the euler equations the solution of the euler equations is

total pressure loss in vortical solutions of the conical euler equations a technique for the solution of the conically self similar form of the euler equations is described solutions for the flow past a flat plate delta wing at angle of attack are presented these solutions show strong leading edge vortices with large total pressure losses in the cores a study of the effects of various computational parameters on the total pressure loss is made an explanation for the cause of the total pressure loss is presented it is shown to be consistent with the results for both a quasi one dimensional model problem and the conically self similar flow past the flat plate delta wing

fresh look at floating shock fitting a fast implicit upwind procedure for the two dimensional euler equations is described that allows accurate computations of shocked flows on nonadapted meshes away from shocks the second order accurate upwinding is based on the split coefficient matrix scm method in the presence of shocks the difference stencils are modified using a floating shock fitting technique rapid convergence to steady state solutions is attained with a diagonalized approximate factorization af algorithm results are presented for riemann s problem for a regular shock reflection at an inviscid wall for supersonic flow past a cylinder and for a transonic airfoil all computed shocks are ideally sharp and in excellent agreement with other numerical results or exact solutions most importantly this has been accomplished on unusually crude meshes without any attempt to align grid lines with shock fronts or to cluster grid lines around shocks

euler and navier stokes solutions for flow over a conical delta wing the simulation of vortical flow about a conical delta wing 14 1 elliptic cone by the euler equations is studied navier stokes solutions are generated for comparison with the inviscid results at the flight condition considered the viscous solutions reveal a large primary leading edge separation vortex and a smaller secondary vortex the viscous solutions are shown to be grid resolved on a coarse grid the euler solutions result in a primary separation vortex but no secondary vortex a comparison of pressure coefficient with the viscous solution shows surprising agreement the agreement is unfortunately fortuitous when the euler equations are solved on the fine viscous grid the large separation vortex is eliminated instead a cross flow shock appears shock curvature introduces sufficient vorticity to produce a small vortex downstream of the shock this inviscid result fundamentally different from the viscous case is a valid solution to the euler equations the coarse grid euler solution is characterized by the production of spurious vorticity and entropy due to numerical error at the leading edge it is neither a valid solution to the euler equations nor a reliable approximation to the real viscous flow the use of a kutta condition is investigated for both the fineand coarse grid euler solutions it is shown that the kutta condition fails to produce a grid independent simulation of the actual viscous flow

efficient real gas upwinded navier stokes computations of high speed flows an efficient method to account for the chemically frozen thermodynamic and transport properties of air in three dimensional navier stokes calculations has been demonstrated this approach uses an explicitly specified equation of state eos so that the fluid pressure temperature and transport properties are directly related to the flow variables the method is efficient since no subiterations are required to deduce the pressure and temperature from the flux variables and is modular by allowing different equations of state to be easily supplied to the code the flexibility of the eos approach is shown by its implementation into a high order total variation diminishing upwinding scheme as well as a standard central differencing scheme the eos approach is then demonstrated by computing the hypersonic flow through the corner region of two mutually perpendicular flat plates using both the upwind and central differencing schemes he capability to efficiently compute chemically frozen single stream flows using an explicitly specified equation of state eos has been added to a three dimensional navier stokes solver this flow solver is based upon the parc codes whose origin can be traced to the air2d 3d solvers by pul liam and steger 1 which used the block alternating direction implicit adi algorithm presented by beam and warming 2 to increase the computational efficiency and to reduce storage requirements pulliam3 diagonalized the block implicit opera tors of the original beam warming adi algorithm resulting in the arc2d 3d codes cooper4 further modified the arc codes to be used in a production environment for solving the propulsion oriented applications at the arnold engineering development center resulting in the parc codes coirier5 replaced the implicit operator with the lu sgs lower upper symmetric gauss seidel algorithm and demonstrated this scheme for hypersonic corner and gap seal problems this scheme is based on an lu decomposition method proposed by jameson and turkel6 and demonstrated by jameson and yoon7 for the euler equations in addition shuen and yoon8 and yu et al 9 with the rplus series of codes have shown the efficiency and robustness of this algorithm for solving the navier stokes equations fully coupled to the chemical trans port equations for computing finite rate chemically reacting flowfields for flows where the dissociation and recombination rates are much slower than the fluid residence time i e in the limit as the damkohler number approaches zero the fluid can be modeled as a mixture of inert chemically frozen gases when the converse is true i e the damkohler number approaches infinity the fluid can be modeled as if it were in chemical equilibrium if either of these limitations holds for the flow field to be considered great simplifications can be made and the resulting computational work reduced the present re search demonstrates the capability to efficiently model gen eral nonmixing chemically frozen flows using a method based on a generalized equation of state an eos for chemi cally frozen air is generated and its ease in implementation is shown for both a high order total variation diminishing tvd upwinding scheme based upon flux differencing10 and van leer s flux vector splitting11 as well as a standard central differencing scheme with added first and third difference dissi pation the upwinding scheme is then compared favorably to experimental data for the hypersonic flow through the corner region of two mutually perpendicular flat plates corner flow to demonstrate the eos a similar corner flowfield is com puted at a higher freestream stagnation enthalpy and detailed comparisons between the central difference and upwinding schemes are made for both 7 const and the chemically frozen air eos

role of artificial viscosity in euler and navier stokes solvers a method is proposed to determine directly the amount of artificial viscosity needed for stability using an eigenvalue analysis for a finite difference representation of the navier stokes equations the stability and growth of small perturbations about a steady flow over airfoils are analyzed for various amounts of artificial viscosity the eigenvalues were determined for a small time dependent perturbation about a steady inviscid flow over a naca 0012 airfoil at a mach number of 0 8 and angle of attack of 0 deg the method has been applied to inviscid flows here but as discussed is also applicable to viscous flows the movement of the eigenvalue constellation with respect to the amount of artificial viscosity is studied the stability boundaries as a function of the amount of artificial viscosity from both the eigenvalue analysis and the time marching scheme are also presented the eigenvalue procedure not only allows for determining the effect of varying amounts of artificial viscosity but also for the effects of different forms of artificial viscosity nomenclature a speed of sound e total energy per unit volume 7 identity matrix jacobian of transformation m mach number p pressure re reynolds number p v c fi t nondimensional physical time u v cartesian velocity components x y physical cartesian coordinates a angle of attack 6 finite difference operator eef e coefficients of artificial viscosity x eigenvalues ijl viscosity coefficient r transformed coordinates p density t transformed time

vectorized schemes for conical potential flow using the artificial density method a method is developed to determine solutions to the full potential equation for steady supersonic conical flow using the artificial density method various update schemes used generally for transonic potential solu tions are investigated the schemes are compared for speed and robustness all versions of the computer code have been vectorized and are currently running on the cyber 203 computer the update schemes are vec torized where possible either fully explicit schemes or partially implicit schemes since each version of the code differs only by the update scheme and elements other than the update scheme are completely vec torizable comparisons of computational effort and convergence rate among schemes are a measure of the specific scheme s performance results are presented for circular and elliptical cones at angle of attack for subcritical and supercritical crossflows he computational solution of steady supersonic conical potential flow has been approached from several dif ferent directions using either the conservative or non conservative approach the previous conservative methods generally fit the bow shock cross flow shocks are most often captured grossman1 and siclari2 have developed codes using the nonconservative formulation of the full potential equation for conical and three dimensional flows respectively grossman used successive line overrelaxation slor as the update scheme for the potential and siclari investigated the effectiveness of the approximate factorization af schemes for this problem siclari showed both af1 and af2 using the notation introduced in ref 2 to be generally faster than slor with af1 faster than af2 sritharan3 approached the problem using the conservative approach with a jameson type artificial viscosity formula tion4 to provide dissipation in supersonic regions the up date scheme was line relaxation with mesh refinement to speed convergence shankar5 also developed a conservative scheme for conical and three dimensional flows although shankar s code originally used the artificial density formula tion of hafez 6 his current code introduces artificial viscosity through the density term using a switching scheme based on characteristics theory shankar also used approximate fac torization for the update scheme a method is developed here to obtain solutions for super sonic conical flow using the three dimensional steady com pressible full potential equation in conservative nondimen sional form and the artificial density method all shocks are captured those schemes studied are successive line over relaxation slor checkerboard successive overrelaxation cksor approximate factorization 1 af1 and approx imate factorization 2 af2 the question is posed here as to whether or not the explicit schemes can become comparable to or better than the implicit schemes in overall computing times if both types of schemes are vectorized either com pletely or partially and processed on vector computers a slight advantage through vector processing noticeable in this quasi three dimensional conical flow problem could become a significant advantage for extension to general three dimensional flows a stability restriction for the in termediate body boundary condition in the af2 scheme as investigated by south and hafez7 has been applied to the conical flow problem and shown to be valid

a nonlinear hybrid vortex method for wings at large angle of attack a steady and unsteady nonlinear hybrid vortex nhv method is developed for low aspect ratio wings at large angles of attack the method uses vortex panels with linear vorticity distribution equivalent to a quadratic doublet distribution to calculate the induced velocity in the near field using closed form expressions in the far field the distributed vorticity is reduced to concentrated vortex lines and the simpler biot savart law is employed the method is applied to rectangular wings in steady and unsteady flows the numerical results show that the method accurately predicts the distributed aerodynamic loads and that it is of acceptable computational efficiency n recent years the development of numerical methods for predicting the steady and unsteady aerodynamic characteristics of lifting surfaces exhibiting leading and or side edge separations has received considerable attention for the steady flow problems several numerical techniques have been developed these include the nonlinear discrete vortex1 6 ndv methods higher order doublet panel methods 7 9 and nonlinear hybrid vortex nhv methods 10 11 for the unsteady flow problems the literature shows fewer numerical techniques which include the ndv methods12 15 and constant doublet panel methods 16 17 the literature lacks high order panel methods for the unsteady flow problems for this reason we are presenting in this paper an efficient and accurate method for the steady and unsteady flow problems of lifting surfaces at large angles of attack in this method vortex panels with linear vorticity distribution are used in the near field calculations in the farfield calculations the distributed vorticity over each far field panel is lumped into equivalent concentrated vortex lines in this way accuracy is satisfied in the near field while computational efficiency is maintained in the far field the coupling of a continuous vortex sheet representation and a concentrated vortex line representation for solving the nonlinear lifting surface problem is called the nonlinear hybrid vortex nhv method

the self duality equations on a riemann surface in this paper we shall study a special class of solutions of the self dual yang mills equations the original self duality equations which arose in mathematical physics were defined on euclidean 4 space the physically relevant solutions were the ones with finite action the so called instantons the same equations may be dimensionally reduced to euclidean 3 space by imposing invariance under translation in one direction these equations also have physical relevance the solutions which have finite action in three dimensions are the magnetic monopoles if we take the reduction process one step further and consider solutions which are invariant under two translations we obtain a set of equations in the plane here however there is no clear physical meaning and indeed attempts to find finite action solutions have failed nevertheless these are the equations we shall consider despite the lack of interesting solutions in r2 the equations have the important property conformal invariance which allows them to be defined on manifolds modelled on r2 by conformal maps namely riemann surfaces we shall consider here solutions of the self duality equations defined on a compact riemann surface there are in fact solutions as we shall show and the moduli space of all solutions turns out to be a manifold with an extremely rich geometric structure which will be the focus of our study it brings together in a harmonious way the subjects of riemannian geometry topology algebraic geometry and symplectic geometry illuminating all these facets of the same object accounts for the length of this paper the self duality equations are equations from gauge theory geometrically they are defined in terms of connections on principal bundles while the group of the principal bundle may be chosen arbitrarily for the equations to make sense we restrict attention here to the simplest case of su 2 or so 3 there are two reasons for this the first and most obvious is that it simplifies calculations and avoids the use of inductive processes which are inherent in the consideration of a general lie group of higher rank the second reason is that solutions for su 2 have an intimate relationship with the internal structure of the riemann surface as a consequence of results we shall prove about solutions to the self duality equations we learn something about the moduli space of complex structures on the surface itself namely teichmuller space

the topology of moduli spaces of free group representations for any complex affine reductive group g and a fixed choice of maximal compact subgroup k we show that the g character variety of a free group strongly deformation retracts to the corresponding k character space which is a real semi algebraic set combining this with constructive invariant theory and classical topological methods we show that the rm slm 3 mathbb c character variety of a rank 2 free group is homotopic to an 8 sphere and the rm slm 2 mathbb c character variety of a rank 3 free group is homotopic to a 6 sphere

damped euler equation method to compute transonic flow around wing body combinations inviscid transonic flows containing either strong shock waves or complex vortex structure call for the euler equations as a realistic model presented here is a computational procedure for solving the euler equations for transonic flow around a wing and fuselage upon an o o mesh generated by transfinite interpolation an explicit time marching finite volume procedure solves the flow equations and features a nonreflecting far field boundary condition an internal mechanism for temporal damping and use of the local time step all of which improve the convergence of the computation converged after several hundred iterations results computed on the cyber 203 vector processor are compared with experimental data and potential flow computations the euler equation model is found to predict the existence of a tip vortex created by inviscid flow separation in the downstream region of the tip of the m6 wing where the radius of curvature approaches zero ast year a workshop 1 was held in order to assess the currently used computational procedures one against the other in several carefully specified two dimensional transonic flow problems while reasonable agreement among the results given by the various full potential and euler equation methods was obtained in the subcritical cases a disparity between the results of these two models was found to grow with cases of increasing shock strength for the naca 0012 airfoil and conditions m 0 80 and a 1 25 deg for example the lift coefficients cl given by all the euler methods ranged between 0 30 and 0 38 whereas the range of cl for the potential method was 0 28 1 1 this discrepancy has led to a reconsideration of the validity of the potential model when strong shocks are present in the flow not only locally in terms of the isentropic shock jumps but also and perhaps even more importantly with regard to the correct modeling of vortex phenomena throughout the entire flowfield in the potential representation the vorticity that is bound to the airfoil is accounted for by a jump in the potential across a line originating at the trailing edge and lying a priori along some chosen coordinate direction downstream the so called kutta condition the euler equations in contrast admit vorticity in the solution and the equivalent to the kutta condition evidently does not need to be enforced explicitly this situation is currently under study by researchers using a variety of numerical methods in three dimensions the flow past a finite wing is even more complex and less is known vortices for example are shed continuously from the wing tips and the entire trailing edge whether a kutta condition or its equivalent is necessary in this case has not been in vestigated but because vorticity is so crucial to the realism achieved by inviscid flow models interest has been aroused in questions like this and in numerical methods that solve the euler equations a number of methods 2 4 exist to solve the euler equations for three dimensional flow but they have been developed exclusively for and applied only to internal flows apparently the solution of the euler equations for

transonic vortex flows past delta wings integral equation approach the steady full potential equation is written in the form of poisson s equation and the solution of the velocity field is expressed in terms of an integral equation the solution consists of a surface integral of vorticity distribution on the wing and its free vortex sheets and a volume integral of source distribution within a volume around the wing and its free vortex sheets the solution is obtained through successive iteration cycles the density gradient in the source distribution is computed by using a type differencing scheme the method is applied to delta wings and the numerical examples show that a curved shock is captured on the suction side of the wing it is attached to the lower surface of the leading edge vortex but does not necessarily reach the wing surface the present solution does not suffer from the numerical diffusion problem usually encountered with the finite difference solutions of euler equations

asymptotic behavior of weak solutions for the relativistic vlasov maxwell equations with large light speed abstract we study here the behavior of time periodic weak solutions for the relativistic vlasov maxwell boundary value problem in a three dimensional bounded domain with strictly star shaped boundary when the light speed becomes infinite we prove the convergence toward a time periodic weak solution for the classical vlasov poisson equations

plane curves associated to character varieties of 3 manifolds consider a compact 3 manifold m with boundary consisting of a single torus the papers cs1 cs2 cgls discuss the variety of characters of sl2 c representations of zl m and some of the ways in which the topological structure of m is reflected in the algebraic geometry of the character variety we will describe in this paper a certain affine algebraic curve dm which is naturally associated to the character variety of m a basis b 9 1 for the peripheral subgroup of m determines an embedding p8 of dm into c x c with coordinates l and m the closure in c 2 of ps dm is a plane algebraic curve and therefore is defined by a polynomial am n0 m that after certain normalizations is uniquely determined up to multiplication by constants the polynomial am b is effectively computable and is an invariant of the manifold m together with the choice of basis b the results in this paper describe how geometric properties of the character variety and hence topological properties of m are reflected by the polynomial am b in the case that m is the complement of a knot k in a homology 3 sphere we may take the basis b to consist of the longitude and meridian of k with the usual orientation conventions this basis is well defined modulo the involution which inverts both the longitude and meridian it will follow from the construction of dm that if the basis b is obtained from b by inverting both generators then the regular maps pb and pb have the same image thus ar am s am b is an invariant of the knot the polynomial am b displays in a striking way information about the incompressible surfaces in m this involves the newton polygon of am b

global weak solutions to the nordstrom vlasov system abstract the nordstrom vlasov system is a lorentz invariant model for a self gravitating collisionless gas we establish suitable a priori bounds on the solutions of this system which together with energy estimates and the smoothing effect of momentum averaging yield the existence of global weak solutions to the corresponding initial value problem in the process we improve the continuation criterion for classical solutions which was derived recently the weak solutions are shown to preserve mass

finite difference solutions of the euler equations in the vicinity of sharp edges attempts have been made to explain why finite difference solutions of the euler equations can describe flows with large vortical structures around sharp edged bodies the present paper is concerned with the influence of a singular sharp edge on the truncation error for a set of discretized euler equations an analysis is conducted of the distribution of the truncation error of one finite difference approximation of the euler equations near a sharp edge of a thin plate the analysis leads to a determination of the size of the region of the neighborhood of such a singularity attention is given to the consistency of a discretization of the euler equations and numerical experiments

finite speed propagation of the solutions for the relativistic vlasov maxwell system in this paper we investigate the continuous dependence with respect to the initial data of the solutions for the 1d and 1 5d relativistic vlasov maxwell system more precisely we prove that these solutions propagate with finite speed we formulate our results in the framework of mild solutions i e the particle densities are solutions by characteristics and the electro magnetic fields are lipschitz continuous functions

unsteady navier stokes computations past oscillating delta wing at high incidence the unsteady compressible thin layer navier stokes equations written in the moving frame of reference for the flow relative motion are solved for the unsteady supersonic flow around a round edged delta wing for supersonic flow a local conical flow solution has been obtained from the three dimensional equations pseudotime stepping is used for the steady flow problem while time accurate stepping is used for the unsteady flow problem the computational scheme is an implicit approximately factored finite volume scheme which uses implicit and explicit dissipation terms the scheme is verified for the steady flow solution the scheme is then applied to a delta wing undergoing rolling oscillation at a reduced frequency of 1 337 with 15 deg maximum amplitude about a mean angle of attack of 10 deg for a mach number of 2 and a reynolds number of 0 5 x 10 6

on the fundamental group of rm hom mathbb z k g let g be a compact lie group consider the variety rm hom mathbb z k g of representations of mathbb z k into g we can see this as a based space by taking as base point the trivial representation open image in new window the goal of this paper is to prove that pi 1 rm hom mathbb z k g is naturally isomorphic to 1 g k

numerical investigation of supersonic wing tip vortices steady high reynolds number flowfields about a finite span rectangular wing mounted upright in a supersonic stream were generated numerically to investigate formation of the tip vortex solutions were obtained by integration of the time dependent three dimensional compressible euler and thin layer laminar and mass averaged turbulent navier stokes equations in the turbulent case a two equation k e closure model was employed which included low reynolds number terms and a compressibility correction details of the computations are summarized and a grid resolution study is provided to assess the accuracy of the numerical results comparisons are made between solutions of the various governing equations as well as with experimental data in terms of pressure and mach number component distributions in the vortex core

a time split finite volume algorithm for three dimensional flowfield simulation a general finite volume algorithm is developed for solving three dimensional time dependent compressible navier stokes equations for high reynolds number flows over an arbitrary geometry this algorithm adapts maccormack s 1982 explicit implicit scheme to a time split three dimensional finite volume concept in a general coordinate system it is shown that the thin layer approximation in all three spatial directions significantly reduces the evaluation of viscous terms and allows the algorithm to solve more complicated geometries with all boundaries in two or all three directions the calculated results using this method are found to be in good agreement with the experimental measurements of a blunt fin induced shock wave and boundary layer interaction problems observations of the existence of peak pressure primary horseshoe and secondary vortices and reversed supersonic zones show that computational fluid dynamics can effectively supplement the wind tunnel tests for aerodynamic design as well as for understanding basic fluid dynamics

energy of sections of the deligne hitchin twistor space we study a natural functional on the space of holomorphic sections of the deligne hitchin moduli space of a compact riemann surface generalizing the energy of equivariant harmonic maps corresponding to twistor lines we show that the energy is the residue of the pull back along the section of a natural meromorphic connection on the hyperholomorphic line bundle recently constructed by hitchin as a byproduct we show the existence of a hyper kahler potentials for new components of real holomorphic sections of twistor spaces of hyper kahler manifolds with rotating s 1 action additionally we prove that for a certain class of real holomorphic sections of the deligne hitchin moduli space the energy functional is basically given by the willmore energy of corresponding equivariant conformal map to the 3 sphere as an application we use the functional to distinguish new components of real holomorphic sections of the deligne hitchin moduli space from the space of twistor lines

global weak solutions of vlasov maxwell systems we study here the vlasov maxwell system in its classical and relativistic form we prove the stability of solutions in weak topologies and deduce from this stability result the global existence of a weak solution with large initial data the main tools consist of a new regularity result for velocity averages of solutions of some general linear transport equations and the method of renormalization introduced by the authors in previous work

mirror symmetry langlands duality and the hitchin system among the major mathematical approaches to mirror symmetry are those of batyrev borisov and strominger yau zaslow syz the first is explicit and amenable to computation but is not clearly related to the physical motivation the second is the opposite furthermore it is far from obvious that mirror partners in one sense will also be mirror partners in the other this paper concerns a class of examples that can be shown to satisfy the requirements of syz but whose hodge numbers are also equal this provides significant evidence in support of syz moreover the examples are of great interest in their own right they are spaces of flat slr connections on a smooth curve the mirror is the corresponding space for the langlands dual group pglr these examples therefore throw a bridge from mirror symmetry to the duality theory of lie groups and more broadly to the geometric langlands program

regularity of the moments of the solution of a transport equation let u u x v satisfy the transport equation u v xu f x rn v rnwhere f belongs to some space of type lp dx d v where is a positive bounded measure on rn we study the resulting regularity of the moment u x v d v in terms of fractional sobolev spaces for example counter examples are given in order to test the optimality of our results