a borcherds kac moody superalgebra with conway symmetry we construct a borcherds kac moody bkm superalgebra on which the conway group hbox co 0 acts faithfully we show that the bkm algebra is generated by the physical states brst cohomology classes in a chiral superstring theory we use this construction to produce denominator identities for the chiral partition functions of the conway module v s natural a supersymmetric c 12 chiral conformal field theory whose twisted partition functions enjoy moonshine properties and which has automorphism group isomorphic to hbox co 0 in particular these functions satisfy a genus zero property analogous to that of monstrous moonshine finally we suggest how one may promote the denominators to spacetime bps indices in type ii string theory which might thus furnish a physical explanation of the genus zero property of conway moonshine

twisting the fake monster superalgebra abstract we calculate the twisted denominator identities of the fake monster superalgebra corresponding to elements of 2 aut e 8 of odd order they give many new infinite product identities and new examples of generalized kac moody superalgebras we also obtain generalizations of jacobi s identity on theta functions

aeroelastic dynamic analysis of a full f 16 configuration for various flight conditions an overview is given of recent advances in a three field methodology for modeling and solving nonlinear fluid structure interaction problems and its application to the prediction of the aeroelastic frequencies and damping coefficients of a full f 16 configuration in various subsonic transonic and supersonic airstreams is reported in this three field methodology the flow is described by the arbitrary lagrangian eulerian form of the euler equations the structure is represented by a detailed finite element model and the fluid mesh is unstructured dynamic and updated by a robust torsional spring analogy method simulation results are presented for stabilized accelerated low g and high g flight conditions and correlated with flight test data consequently the practical feasibility and potential of the described computational fluid dynamics based computational method for the flutter analysis of high performance aircraft particularly in the transonic regime are discussed

generalized kac moody algebras automorphic forms and conway s group i abstract the moonshine properties imply that the twisted denominator identities coming from the action of the monster group on the monster algebra define modular forms in this paper we motivate the conjecture that the action of an extension of conway s simple group co 1 on the fake monster algebra gives rise to automorphic forms of singular weight on grassmannians we prove the conjecture for elements with square free level and nontrivial fixpoint lattice

a family of fourth order methods for solving non linear equations in this paper we present a family of new methods with the order of convergence four per iteration these methods require two evaluations of the function and one evaluation of its first derivative and therefore this family of methods has the efficiency index equal to 1 587 these methods can be of practical interest as we show in some examples

discontinuous galerkin spectral element approximations on moving meshes we derive and evaluate high order space arbitrary lagrangian eulerian ale methods to compute conservation laws on moving meshes to the same time order as on a static mesh we use a discontinuous galerkin spectral element method dgsem in space and one of a family of explicit time integrators such as adams bashforth or low storage explicit runge kutta the approximations preserve the discrete metric identities and the discrete geometric conservation law dgcl by construction we present time step refinement studies with moving meshes to validate the approximations the test problems include propagation of an electromagnetic gaussian plane wave a cylindrical pressure wave propagating in a subsonic flow and a vortex convecting in a uniform inviscid subsonic flow each problem is computed on a time deforming mesh with three methods used to calculate the mesh velocities from exact differentiation from the integration of an acceleration equation and from numerical differentiation of the mesh position

a generalized kac moody algebra of rank 14 abstract we construct a vertex algebra of central charge 26 from a lattice orbifold vertex operator algebra of central charge 12 the brst cohomology group of this vertex algebra is a new generalized kac moody algebra of rank 14 we determine its root space multiplicities and a set of simple roots

second order time accurate and geometrically conservative implicit schemes for flow computations on unstructured dynamic meshes abstract we consider the solution of two and three dimensional flow problems with moving boundaries using the arbitrary lagrangian eulerian formulation or dynamic meshes we focus on the case where spatial discretization is performed by unstructured finite volumes and or finite elements we formulate the consequence of the geometric conservation law on the second order implicit temporal discretization of the semi discrete equations governing such problems and use it as a guideline to construct a new family of second order time accurate and geometrically conservative implicit numerical schemes for flow computations on moving grids we apply these new algorithms to the solution of three dimensional flow problems with moving and deforming boundaries demonstrate their superior accuracy and computational efficiency and highlight their impact on the simulation of fluid structure interaction problems

monstrous moonshine and monstrous lie superalgebras we prove conway and norton s moonshine conjectures for the infinite dimensional representation of the monster simple group constructed by frenkel lepowsky and meurman to do this we use the no ghost theorem from string theory to construct a family of generalized kac moody superalgebras of rank 2 which are closely related to the monster and several of the other sporadic simple groups the denominator formulas of these superalgebras imply relations between the thompson functions of elements of the monster i e the traces of elements of the monster on frenkel lepowsky and meurman s representation which are the replication formulas conjectured by conway and norton these replication formulas are strong enough to verify that the thompson functions have most of the moonshine properties conjectured by conway and norton and in particular they are modular functions of genus 0 we also construct a second family of kac moody superalgebras related to elements of conway s sporadic simple group col these superalgebras have even rank between 2 and 26 for example two of the lie algebras we get have ranks 26 and 18 and one of the superalgebras has rank 10 the denominator formulas of these algebras give some new infinite product identities in the same way that the denominator formulas of the a n n e kac moody algebras give the macdonald identities

new classes of iterative methods for nonlinear equations abstract in this paper we suggest and analyze some new iterative methods for solving nonlinear equations f x 0 by using the variational iteration technique these new methods includes the householder and its variant forms as special cases we also give several examples to illustrate the efficiency of these methods comparison with other similar methods is also given these new methods can be considered as an alternative to the newton method this technique can be used to suggest a wide class of new iterative methods for solving system of nonlinear equations

on the conservative and accurate cfd approximations for moving meshes and moving boundaries we are concerned with the conservative approximations of compressible flows in the context of moving mesh or interface tracking this paper makes a review of some numerical approaches based on the geometrical conservation law gcl property for computation with moving mesh or moving boundary those methods are reformulated and some comparisons are made we also propose a methodology to approximate accurately the mesh point trajectories and obtain accurate geometrical parameters in 2d and 3d satisfying the gcl property for time accurate schemes higher order geometrical parameters also act as a stabilization of the approximation the numerical effects of the higher order trajectories are illustrated for a 2d moving airfoil the efficiency of a mesh relaxation based on the modified linear elasticity equations is demonstrated for 3d computations of flow behavior in the combustion chamber of a four valves piston engine

an arbitrary lagrangian eulerian formulation for the numerical simulation of flow patterns generated by the hydromedusa aequorea victoria a new geometrically conservative arbitrary lagrangian eulerian ale formulation is presented for the moving boundary problems in the swirl free cylindrical coordinates the governing equations are multiplied with the radial distance and integrated over arbitrary moving lagrangian eulerian quadrilateral elements therefore the continuity and the geometric conservation equations take very simple form similar to those of the cartesian coordinates the continuity equation is satisfied exactly within each element and a special attention is given to satisfy the geometric conservation law gcl at the discrete level the equation of motion of a deforming body is solved in addition to the navier stokes equations in a fully coupled form the mesh deformation is achieved by solving the linear elasticity equation at each time level while avoiding remeshing in order to enhance numerical robustness the resulting algebraic linear systems are solved using an ilu k preconditioned gmres method provided by the petsc library the present ale method is validated for the steady and oscillatory flow around a sphere in a cylindrical tube and applied to the investigation of the flow patterns around a free swimming hydromedusa aequorea victoria crystal jellyfish the calculations for the hydromedusa indicate the shed of the opposite signed vortex rings very close to each other and the formation of large induced velocities along the line of interaction while the ring vortices moving away from the hydromedusa in addition the propulsion efficiency of the free swimming hydromedusa is computed and its value is compared with values from the literature for several other species

on the computation of the baer nunziato model using ale formulation with hll and hllc type solvers towards fluid structure interactions computation of compressible two phase flows with the unsteady compressible baer nunziato model in conjunction with the moving grid approach is discussed in this paper both hll and hllc type finite volume methods are presented and implemented in the context of arbitrary lagrangian eulerian formulation in a multidimensional framework the construction of suitable numerical methods is linked to proper approximations of the non conservative terms on moving grids the hll discretization follows global conservation properties such as free stream preservation and uniform pressure and velocity profiles preservation on moving grids the hllc solver initially proposed by tokareva and toro 1 for the baer nunziato model is based on an approximate solution of local riemann problems containing all the characteristic fields present in the exact solution both subsonic and supersonic configurations are considered in the construction of the present hllc solver in addition an adaptive 6 wave hllc scheme is also proposed for computational efficiency the methods are first assessed on a variety of 1 d riemann problems including both fixed and moving grids applications the methods are finally tested on 2 d and 3 d applications 2 d riemann problems a 2 d shock bubble interaction and finally a 3 d fluid structure interaction problem with a good agreement with the experiments

a linearized method for the frequency analysis of three dimensional fluid structure interaction problems in all flow regimes abstract we present a computational fluid dynamics cfd based linearized method for the frequency analysis of three dimensional fluid structure interaction problems this method is valid in the subsonic transonic and supersonic flow regimes and is insensitive to the frequency or damping level of the sought after coupled eigenmodes it is based on the solution by an orthogonal iteration procedure of a complex eigenvalue problem derived from the linearization of a three field fluid structure moving mesh formulation the key computational features of the proposed method include the reuse of existing unsteady flow solvers a second order approximation of the flux jacobian matrix and a parallel domain decomposition based iterative solver for the solution of large scale systems of discretized fluid structure equations while the frequency analysis method proposed here is primarily targeted at the extraction of the eigenpairs of a wet structure we validate it with the flutter analysis of the agard wing 445 6 for which experimental data is available

higher order subiteration free staggered algorithm for nonlinear transient aeroelastic problems the objective of this note is to present a new subiteration free implicit implicit staggered algorithm that has the same computational complexity as the css procedure and yet delivers a superior time accuracy that is similar to that of a monolithic implicit scheme or a strongly coupled full subiterations partitioned method hence this algorithm retains the computational efficiency and implementation advantages of partitioned mthods while offering the higher time accuracy of fully coupled implicit schemes

multidimensional modelling for the carotid artery blood flow abstract in this work a multidimensional 3d 1d fem model of the whole arterial tree is implemented it comprises a 3d compliant model of the carotid bifurcation coupled with a 1d model for the remaining part of the arterial tree with this approach difficulties arising from the treatment of boundary conditions for the 3d model are naturally handled the navier stokes equations are used as the governing equations for the blood flow while an elastic compliant model is implemented for the arterial wall also the a l e formulation is considered within the 3d blood regions taking into account the domain deformations produced by the moving artery wall this 3d model is complemented with a 1d model of the entire arterial tree in order to appropriately set inflow and outflow boundary conditions for the former the reduced 1d model solves the momentum and continuity equations in compliant tubes so as to reproduce the propagation of the pressure pulse in the arterial network also a volumetric flow rate is imposed at the inlet to model the systolic work of the heart the peripheral arteriole beds are simulated with the well known lumped windkessel model a standard geometry of the carotid bifurcation is discretized with p1 bubble p1 tetrahedral elements the obtained results properly reproduce the general flow patterns reported in the literature very good agreement between the outcomes of a pure 1d model and those of the combined multidimensional model was obtained it is worth noting that this kind of model may provide useful information to gain understanding in the genesis and development of arterial diseases

a note on new classes of iterative methods for nonlinear equations and some iterative methods free from second derivatives for nonlinear equations abstract in m a noor new classes of iterative methods for nonlinear equations appl math comput in press m a noor some iterative methods free from second derivatives for nonlinear equations appl math comput in press noor introduced a generalized one parameter halley s method x n 1 x n f x n f 2 x n f 3 x n f x n f x n for solving the nonlinear equation f x 0 noor further showed that for 1 2 f x n the above method reduces to the halley s method e halley a new exact and easy method for finding the roots of equations generally and without any previous reduction philos roy soc london 18 1964 136 147 it is interesting to note that for f 3 x n f x n f x n the above method fails in this note we point out some major bugs in the results of noor in press

implicit linearity preservation type schemes for moving meshes abstract we are concerned with the accurate implicit approximation of compressible flows in a fixed and moving mesh context such as piston engine flows geometries are commonly complex and flows compressible therefore it is convenient to develop the numerical approach in the context of a space time finite volume formulation for unstructured meshes the hyperbolic flux is obtained by a generalized riemann solver taking into account the mesh motion using the linearity preservation property we propose a new class of stable implicit schemes developing low numerical viscosity these schemes can be viewed as a correction of the usual muscl flux induced by the time derivative and mesh motion accurate numerical results are obtained for transonic shock tube as well as low mach number flows diesel engine it is numerically proved that for large time steps those approximations can be as accurate as some explicit schemes the proposed schemes due the compactness of the stencils are well adapted for parallelization strategy

godunov type method on non structured meshes for three dimensional moving boundary problems abstract this paper presents a numerical method for the computation of compressible flows in domains whose boundaries move in a well defined predictable manner the method uses the space time formulation by godunov while the discretization is conducted on non structured tetrahedral meshes using roe s approximate riemann solver an implicit time stepping and a muscl type interpolation the computation of the geometrical parameters required to take into account the movement of the boundaries is described examples including the calculation of the flow in the cylinder of an internal combustion engine illustrates the possibilities of the method

variational iteration method some recent results and new interpretations this paper is an elementary introduction to the concepts of variational iteration method first the main concepts in variational iteration method such as general lagrange multiplier restricted variation correction functional are explained heuristically subsequently the solution procedure is systematically addressed in particular for nonlinear oscillators particular attention is paid throughout the paper to give an intuitive grasp for the method the main motivation is to put things together in a convenient form for later reference and systematic use

a scaled and minimum overlap restricted additive schwarz method with application to aerodynamics abstract a variant of the classical additive schwarz preconditioner as is presented and applied to the solution of a general class of two and three dimensional flow problems the scaled restricted additive schwarz ras with minimal overlap preconditioner is easy to parallelize since all the local communications among processors only involve information pertaining to the interface of the nonoverlapping subdomains the new method is superior to as and the jacobi algorithm in terms of both iteration counts and cpu time as well as the communication cost when implemented on distributed memory computers

simultaneous untangling and smoothing of moving grids in this work a technique for simultaneous untangling and smoothing of meshes is presented it is based on an extension of an earlier mesh smoothing strategy developed to solve the computational mesh dynamics stage in fluid structure interaction problems in moving grid problems mesh untangling is necessary when element inversion happens as a result of a moving domain boundary the smoothing strategy formerly published by the authors is defined in terms of the minimization of a functional associated with the mesh distortion by using a geometric indicator of the element quality this functional becomes discontinuous when an element has null volume making it impossible to obtain a valid mesh from an invalid one to circumvent this drawback the functional proposed is transformed in order to guarantee its continuity for the whole space of nodal coordinates thus achieving the untangling technique this regularization depends on one parameter making the recovery of the original functional possible as this parameter tends to 0 this feature is very important consequently it is necessary to regularize the functional in order to make the mesh valid then it is advisable to use the original functional to make the smoothing optimal finally the simultaneous untangling and smoothing technique is applied to several test cases including 2d and 3d meshes with simplicial elements as an additional example the application of this technique to a mesh generation case is presented copyright 2008 john wiley sons ltd

effect of randomness on multi frequency aeroelastic responses resolved by unsteady adaptive stochastic finite elements the unsteady adaptive stochastic finite elements uasfe method resolves the effect of randomness in numerical simulations of single mode aeroelastic responses with a constant accuracy in time for a constant number of samples in this paper the uasfe framework is extended to multi frequency responses and continuous structures by employing a wavelet decomposition pre processing step to decompose the sampled multi frequency signals into single frequency components the effect of the randomness on the multi frequency response is then obtained by summing the results of the uasfe interpolation at constant phase for the different frequency components results for multi frequency responses and continuous structures show a three orders of magnitude reduction of computational costs compared to crude monte carlo simulations in a harmonically forced oscillator a flutter panel problem and the three dimensional transonic agard 445 6 wing aeroelastic benchmark subject to random fields and random parameters with various probability distributions

computation of unsteady viscous flows around moving bodies using the k e turbulence model on unstructured dynamic grids abstract we consider the numerical solution on unstructured dynamic meshes of the averaged navier stokes equations equipped with the k e turbulence model and a wall function we discuss discretization issues pertaining to conservation laws moving grids and numerical dissipation we also present a robust spring analogy method for constructing dynamic meshes we validate our implementation of this two equation turbulence model and justify its usage for a class of vortex shedding problems by correlating our computational results with experimental data obtained for a flow past a square cylinder we also apply our solution methodology to the two dimensional aerodynamic stability analysis of the tacoma narrows bridge and report numerical results that are in good agreement with observed data

stability and geometric conservation laws for ale formulations the aim of this paper is to investigate a model ale scheme with respect to various possible choices of time discretizations for each time scheme we investigate the relationships between stability and the so called geometric conservation laws gcl we shall see that gcl condition proves neither necessary nor sufficient for stability in doing so we review some known theoretical results and we prove some new stability results for space time ale discretizations some new error estimates are also presented several numerical experiments confirm the theory

convergence analysis of the defect correction iteration for hyperbolic problems this paper explains some of the convergence behaviour of iterative implicit and defect correction schemes for the solution of the discrete steady euler equations such equations are also commonly solved by pseudo time integration the steady solution being achieved as the limit for t to infty of the solution of a time dependent problem implicit schemes are then often chosen for their favourable stability properties permitting large timesteps for efficiency an important class of implicit schemes involving first and second order accurate upwind discretisations is considered in the limit of an infinite timestep these implicit schemes approach defect correction algorithms thus our analysis is informative for both types of construction simple scalar linear model problems are introduced for the one dimensional and two dimensional cases these model problems are analyzed in detail by both fourier and matrix analyses the convergence behaviour appears to be strongly dependent on a parameter beta

higher order time integration schemes for aeroelastic applications on unstructured meshes efficient techniques for computational aeroelasticity on unstructured meshes are investigated these include the formulation of a fourth order implicit runge kutta time integration scheme a third order backward difference time integration scheme and a second order backward difference time integration scheme for the coupled system of flow and structural equations strong coupling between the flow solution and structural equations is maintained by fully converging the fully coupled system at each time step or stage the time integration schemes are constructed such that discrete conservation is maintained in the flow solution in the presence of dynamically deforming meshes by verifying the discrete geometric conservation law efficient multigrid solution techniques are devised for solving both the governing flow equations and the mesh motion equations using the same agglomerated coarse levels for both problems the flutter boundary prediction of the agard 445 6 wing is used to demonstrate the accuracy and efficiency of these techniques as well as the sensitivity of flutter boundary prediction to time step size and temporal errors

discrete conservation and coupling strategies in nonlinear aeroelasticity abstract as a model problem of aeroelasticity the panel flutter problem is considered to study the discretization of nonlinear aeroelastic problems and the behaviour of the corresponding solution strategies a fluid structure discretization that mimics the energy budget of the continuous problem is derived the set of equations occurring in each time step are implicit in time over fluid and structure to solve these equations approximately we employ predictor strategies and fixed point iterations we compare the method with conventional fluid structure methods addressing applications from transonic aeroelasticity concerning in particular the numerical prediction of bifurcations

a positivity preserving finite element finite volume solver for the spalart allmaras turbulence model we propose a stable numerical method preserving the positivity of the turbulent viscosity in the spalart allmaras model focusing in particular on the stiffness of the source term the goal is to apply this model for turbulent flows using an effective numerical method based on a mixed fe fv method a mathematical analysis of stability and positivity of the continuous and numerical models is provided numerical tests on the 3d boundary layer over a flat plate show the convergence and robustness of the proposed method confirming the theoretical analysis 2006 elsevier b v all rights reserved

the fake monster superalgebra abstract we show that the physical states of a 10 dimensional superstring moving on a torus form a generalized kac moody superalgebra this gives the first explicit realizations of these algebras for a special torus the denominator function of this algebra is an automorphic form so that we can determine the simple roots we call this algebra the fake monster superalgebra

some iterative methods free from second derivatives for nonlinear equations in a recent paper noor m aslam noor new classes of iterative methods for nonlinear equations appl math comput 2007 doi 10 1016 j amc 2007 suggested and analyzed a generalized one parameter halley method for solving nonlinear equations using in this paper we modified this method which has fourth order convergence as special cases we obtain a family of third order iterative methods for appropriate and suitable choice of the parameter we have compared this modified noor method with some other iterative methods which shows that this new iterative method is robust and efficient one several examples are given to illustrate the efficiency and the performance of this new method

generalized moonshine ii borcherds products the goal of this paper is to construct infinite dimensional lie algebras by using infinite product identities and to use these lie algebras to reduce the generalized moonshine conjecture to a pair of hypotheses about group actions on vertex algebras and lie algebras we expect the lie algebras that we construct to manifest as algebras of physical states in an orbifold conformal field theory yet to be fully constructed with symmetries given by the monster simple group we introduce vector valued modular functions attached to families of modular functions of different levels and we prove infinite product identities for a distinguished class of automorphic functions on a product of two half planes we recast this result using the borcherds harvey moore singular theta lift and show that the vector valued functions attached to completely replicable modular functions with integer coefficients lift to automorphic functions with infinite product expansions at all cusps for each element of the monster simple group we construct an infinite dimensional lie algebra such that its denominator formula is an infinite product expansion of the automorphic function arising from that element s mckay thompson series these lie algebras have the unusual property that their simple roots and all root multiplicities are known we show that under certain hypotheses characters of groups acting on these lie algebras form functions on the upper half plane that are either constant or invariant under a genus zero congruence group