accurate projection methods for the incompressible navier stokes equations abstract this paper considers the accuracy of projection method approximations to the initial boundary value problem for the incompressible navier stokes equations the issue of how to correctly specify numerical boundary conditions for these methods has been outstanding since the birth of the second order methodology a decade and a half ago it has been observed that while the velocity can be reliably computed to second order accuracy in time and space the pressure is typically only first order accurate in the l norm this paper identifies the source of this problem in the interplay of the global pressure update formula with the numerical boundary conditions and presents an improved projection algorithm which is fully second order accurate as demonstrated by a normal mode analysis and numerical experiments in addition a numerical method based on a gauge variable formulation of the incompressible navier stokes equations which provides another option for obtaining fully second order convergence in both velocity and pressure is discussed the connection between the boundary conditions for projection methods and the gauge method is explained in detail

effects of the computational time step on numerical solutions of turbulent flow effects of large computational time steps on the computed turbulence were investigated using a fully implicit method in turbulent channel flow computations the largest computational time step in wall units which led to accurate prediction of turbulence statistics was determined turbulence fluctuations could not be sustained if the computational time step was near or larger than the kolmogorov time scale

application of a fractional step method to incompressible navier stokes equations a numerical method for computing three dimensional time dependent incompressible flows is presented the method is based on a fractional step or time splitting scheme in conjunction with the approximate factorization technique it is shown that the use of velocity boundary conditions for the intermediate velocity field can lead to inconsistent numerical solutions appropriate boundary conditions for the intermediate velocity field are derived and tested numerical solutions for flows inside a driven cavity and over a backward facing step are presented and compared with experimental data and other numerical results

local existence of the borel transform in euclidean φ 4 4 we bound rigorously the large order behaviour of 44 euclidean perturbative quantum field theory as the simplest example of renormalizable but non super renormalizable theory the needed methods are developed to take into account the structure of renormalization which plays a crucial role in the estimates as a main thorem it is shown that the schwinger functions at ordern are bounded byknn which implies a finite radius of convergence for the borel transform of the perturbation series

splitting in large dimension and infrared estimates ii moment inequalities this is the continuation of notes written for the nato asi conference in il ciocco september 96 consisting of the analysis of the links between estimating the splitting between the two first eigenvalues for the schrodinger operator h and the proof of infrared estimates for quantities attached to gaussian type measures these notes were mainly reporting on the old contributions of dyson frohlich glimm jaffe lieb simon and spencer in the 1970s in connection with more recent contributions of pastur khoruzhenko barbulyak and kondrat ev which treat in general more sophisticated models here we concentrate on the simplest model related to field theory and extend the results of barbulyak and kondrat ev by mixing ideas coming from pastur and khozurenko related to the use of bogolyubov s inequality with classical inequalities due to ginibre lebowitz sokal and others or in the case when the temperature t is zero by applying rather elementary estimates on schrodinger operators in order to find

recursive construction of operator product expansion coefficients we derive a novel formula for the derivative of operator product expansion ope coefficients with respect to a coupling constant the formula involves just the ope coefficients themselves but no further input and is in this sense self consistent furthermore unlike other formal identities of this general nature in quantum field theory such as the formal expression for the lagrangian perturbation of a correlation function our formula requires no further uv renormalization i e it is completely well defined from the start this feature is a result of a cancelation of uv and ir divergences between various terms in our identity our proof and an analysis of the features of the identity is given for the example of massive euclidean varphi 4 theory in 4 dimensional euclidean space it relies on the renormalization group flow equation method and is valid to arbitrary but finite orders in perturbation theory the final formula however makes neither explicit reference to the renormalization group flow nor to perturbation theory and we conjecture that it also holds non perturbatively our identity can be applied constructively because it gives a novel recursive algorithm for the computation of ope coefficients to arbitrary finite perturbation order in terms of the zeroth order coefficients corresponding to the underlying free field theory which in turn are trivial to obtain we briefly illustrate the relation of this method to more standard methods for computing the ope in some simple examples

semiclassical asymptotics of eigenvalues for schrodinger operators with magnetic fields abstract we consider schrodinger operators with magnetic fields on a two dimensional compact manifold or on r 2 the purpose is to study the semiclassical asymptotics of the eigenvalues by two different methods we obtain some facts on the harmonic oscillators under uniform magnetic fields and we also discuss them

the operator product expansion converges in perturbative field theory we show within the framework of the massive euclidean varphi 4 quantum field theory in four dimensions that the wilson operator product expansion ope is not only an asymptotic expansion at short distances as previously believed but even converges at arbitrary finite distances our proof rests on a detailed estimation of the remainder term in the ope of an arbitrary product of composite fields inserted as usual into a correlation function with further spectator fields the estimates are obtained using a suitably adapted version of the method of renormalization group flow equations convergence follows because the remainder is seen to become arbitrarily small as the ope is carried out to sufficiently high order i e to operators of sufficiently high dimension our results hold for arbitrary but finite loop orders as an interesting side result of our estimates we can also prove that the gradient expansion of the effective action is convergent

on the local borel transform of perturbation theory we prove existence of the local borel transform for the perturbative series of massive varphi 4 4 theory as compared to previous proofs in the literature the present bounds are much sharper as regards the dependence on external momenta they are explicit in the number of external legs and they are obtained quite simply through a judiciously chosen induction hypothesis applied to the wegner wilson polchinski flow equations we pay attention not to generate an astronomically large numerical constant for the inverse radius of convergence of the borel transform

semiclassical limit of the lowest eigenvalue of a schrodinger operator on a wiener space abstract we study a semiclassical limit of the lowest eigenvalue of a schrodinger operator on a wiener space key results are semiboundedness theorem of the schrodinger operator laplace type asymptotic formula and ims localization formula we also make a remark on the semiclassical problem of a schrodinger operator on a path space over a riemannian manifold

on the spectrum of semi classical witten laplacians and schrodinger operators in large dimension we investigate the low lying spectrum of witten laplacians on forms of arbitrary degree in the semi classical limit and uniformly in the space dimension we show that under suitable assumptions implying that the phase function has a unique local minimum one obtains a number of clusters of discrete eigenvalues at the bottom of the spectrum moreover we are able to count the number of eigenvalues in each cluster we apply our results to certain sequences of schrodinger operators having strictly convex potentials and show that some well known results of semi classical analysis hold also uniformly in the dimension

on the convergence of planar diagram expansions renormalizable quantum field theories whose perturbation expansions are described by planar feynman diagrams only such as su gauge theory are considered in 4 dimensional euclidean space for studying asymptotic properties of the perturbation series one might wish to isolate first all those planar diagrams that do not contain any ultraviolet divergent subgraphs in this paper it is proved that this infinite set of diagrams when summed converges within a finite radius of convergence for the coupling constant

stability and bifurcation in a reaction diffusion model with nonlocal delay effect in this paper the existence stability and multiplicity of spatially nonhomogeneous steady state solution and periodic solutions for a reaction diffusion model with nonlocal delay effect and dirichlet boundary condition are investigated by using lyapunov schmidt reduction moreover we illustrate our general results by applications to models with a single delay and one dimensional spatial domain

stability and bifurcation in a diffusive lotka volterra system with delay in this paper we investigate the dynamics of a class of diffusive lotka volterra equation with time delay subject to the homogeneous dirichlet boundary condition in a bounded domain the existence of spatially nonhomogeneous steady state solution is investigated by applying lyapunov schmidt reduction the stability and nonexistence of hopf bifurcation at the spatially nonhomogeneous steady state solution with the changes of a specific parameter are obtained by analyzing the distribution of the eigenvalues moreover we illustrate our general results by applications to models with a single delay and one dimensional spatial domain

rigorous construction of planar diagram field theories in four dimensional euclidean space asymptotically free quantum field theories with planar feynman diagrams such as su gauge theory are considered in 4 dimensional euclidean space it is shown that if all particles involved have non vanishing masses and if the coupling constant s org2 are small enough crit then an absolutely convergent procedure exists to obtain green functions that uniquely solve the dyson schwinger equations

on the borel summability of planar perturbation series transition to minkowski space in recent years t hooft and rivasseau proved the borel summability of planar asymptotically free massive theories in euclidean space the corresponding borel sums in minkowski space are shown to exist as linear functionals if the euclidean counterparts are bounded polynomially in momentum space and fulfill certain analyticity conditions both can be verified in massive planar wrong sign 44 using rivasseau s approach the functionals alternatively are densely defined and unbounded on anlp space or bounded on the whole of a banach space with a more restrictive norm

hopf bifurcation in a diffusive lotka volterra type system with nonlocal delay effect abstract the dynamics of a diffusive lotka volterra type model for two species with nonlocal delay effect and dirichlet boundary conditions is investigated in this paper the existence and multiplicity of spatially nonhomogeneous steady state solutions are obtained by means of lyapunov schmidt reduction the stability of spatially nonhomogeneous steady state solutions and the existence of hopf bifurcation with the changes of the time delay are obtained by analyzing the distribution of eigenvalues of the infinitesimal generator associated with the linearized system by the normal form theory and the center manifold reduction the stability and bifurcation direction of hopf bifurcating periodic orbits are derived finally our theoretical results are illustrated by a model with homogeneous kernels and one dimensional spatial domain

on the large order behavior of φ44 we continue the rigorous study of the large order behavior of the perturbation series for the 4 model in 4 dimensions started in 1 in this paper we prove a result announced in 1 we show that the exact radius of convergence of the borel transform of the renormalized perturbation series for 44 is greater than or equal to the expected value given by the position of the first renormalon 2 this result holds for any vector 2 2 model withn components and makes use of the lipatov bound of 1 this result is based on a partial resummation of counterterms similar to the one of 3 but in a phase space analysis of the renormalized series

trace formulas a golden thompson inequality and classical limit in boson fock space trace formulas for the heat semi groups of second quantization operators and their perturbations in the abstract boson fock space are given in terms of path functional integral representations as applications an inequality of golden thompson type and a classical limit are derived for the trace of the heat semi group of a perturbed second quantization operator the abstract results are applied to a model ofp type in quantum field theory

generalized logarithmic borel summability the recently introduced logarithmic borel summation method is able to sum strongly divergent series of a particular type a satisfactory extension to the applicability of this method obtained by using the classical borel le roy transform is presented as examples we consider a class of nonpolynomial anharmonic oscillator models in the t hooft simplified form

isosystolic inequalities and the topological expansion for random surface and matrix models using the isosystolic inequalities on riemann surfaces we prove that for many random surface or matrix models the radius of convergence of the perturbative series at fixed genus is independent of the genus this result applies for instance to the dynamically triangulated random surface model in any dimension or to many matrix models with regular propagators in the superrenormalizable domain for instance 3 in dimensiond 6 lambda phi 4 sqrt lambda phi 3 in dimensiond 4 and various otherp 2 models in particular all those containing an odd power of we hope that this result is a first step towards a more rigorous understanding of the genus dependence of surface models or of quantum gravity coupled with matter fields

dynamical behavior of a general reaction diffusion advection model for two competing species it is well known that the studies of the evolution of biased movement along a resource gradient could create very interesting phenomena this paper deals with a general two species lotka volterra competition model for the same resources in an advective nonhomogeneous environment where the individuals are exposed to unidirectional flow advection but no individuals are lost through the boundary it is assumed that the two species have the same population dynamics but different diffusion and advection rates it is shown that at least five scenarios can occur i if one with a very strong biased movement relative to diffusion and the other with a more balanced approach the species with much larger advection dispersal rate is driven to extinction ii if one with a very strong biased movement and the other is smaller compare to its diffusion the two species can coexist since one species mainly pursues resources at places of locally most favorable environments while the other relies on resources from other parts of the habitat iii if both of the species random dispersal rates are sufficiently large respectively small two competing species coexist iv if one with a sufficiently large random dispersal rate and the other with a sufficiently small one two competing species still coexist v if one with a sufficiently small random dispersal rate and the other with a suitable diffusion which causes the extinction of the species with smaller random movement where iii iv and v show the global dynamics of 5 when both of the species dispersal rates are sufficiently large or sufficiently small these results provide a new mechanism for the coexistence of competing species and they also imply that selection is against excessive advection along environmental gradients respectively random dispersal rate and an intermediate biased movement rate respectively random dispersal rate may evolve finally we also apply a perturbation argument to illustrate the evolution of these rates

a high order immersed interface method for simulating unsteady incompressible flows on irregular domains immersed boundary methods and immersed interface methods are becoming increasingly popular for the computation of unsteady flows around complex geometries using a cartesian grid while good results both qualitative and quantitative have been obtained most of the methods rely on low order corrections to account for the immersed boundary the objective of the present work is to present as an alternative a high order modified immersed interface method for the 2d unsteady incompressible navier stokes equations in stream function vorticity formulation the method employs an explicit fourth order runge kutta time integration scheme fourth order compact finite differences for computation of spatial derivatives and a nine point fourth order compact discretization of the poisson equation for computation of the stream function corrections to the finite difference schemes are used to maintain high formal accuracy at the immersed boundary as confirmed by analytical tests to validate the method in its application to incompressible flows several physically relevant test cases are computed including uniform flow past a circular cylinder and tollmien schlichting waves in a boundary layer

renormalization in the complete mellin representation of feynman amplitudes the feynman amplitudes are renormalized in the formalism of the cm representation this mellin barnes type integral representation previously introduced for the study of asymptotic behaviours is shown to have the following interesting property in contrast with the usual subtraction procedures the renormalization leaves the cm integrand unchanged and only results into translations of the integration path the explicit cm representation of the renormalized amplitudes is given in addition the dimensional regularization and the extension to spinor amplitudes are sketched

the t hooft reparametrization respects borel summability in a renormalizable field theory with one coupling constant one may redefine the coupling in the sense of formal power series such that the function in the new coupling consists of the first two terms only it is shown that this change of coupling is borel summable if the original function was borel summable

bifurcation and spatiotemporal patterns in a homogeneous diffusive predator prey system abstract a diffusive predator prey system with holling type ii predator functional response subject to neumann boundary conditions is considered hopf and steady state bifurcation analysis are carried out in details in particular we show the existence of multiple spatially non homogeneous periodic orbits while the system parameters are all spatially homogeneous our results and global bifurcation theory also suggest the existence of loops of spatially non homogeneous periodic orbits and steady state solutions these results provide theoretical evidences to the complex spatiotemporal dynamics found by numerical simulation

computational design for long term numerical integration of the equations of fluid motion the integral constraints on quadratic quantities of physical importance such as conservation of mean kinetic energy and mean square vorticity will not be maintained in finite difference analogues of the equation of motion for two dimensional incompressible flow unless the finite difference jacobian expression for the advection term is restricted to a form which properly represents the interaction between grid points as derived in this paper it is shown that the derived form of the finite difference jacobian prevents nonlinear computational instability and thereby permits long term numerical integrations

a lipatov bound for φ 4 4 euclidean field theory we bound the large order behavior of these pieces of the renormalized perturbation expansion for 4 4 which do not contain renormalons 1 the bound we obtain has the form of the leading asymptotic behavior computed by the lipatov method with the exact value of the lipatov constant therefore this paper is a step towards the rigorous study of the large order behavior of 4 4 and towards a proof of existence of the first renormalon singularity which should prevent the theory from being borel summable using the results of this paper and the techniques of 15 one can for instance improve 17 the estimate 18 on the finiteness of the radius of convergence of the borel transform of renormalized 4 4 and obtain that this radius is at least the exact value conjectured in 1

analytic regularization of the ψiψi d2 model at finite temperature and density simultaneously using the dimensional and analytic regularization methods we reexamine the gross neveu model at finite temperature and density chemical potential in a d dimensional space time the regularized effective potential is presented at the 1 n large n approximation it is found that in d 3 the effective potential is finite

numerical investigation of the three dimensional development in boundary layer transition a numerical method for solving the complete navier stokes equations for incompressible flows is introduced that is applicable for investigating three dimensional transition phenomena in a spatially growing boundary layer results are discussed for a test case with small three dimensional disturbances for which detailed comparison to linear stability theory is possible the validity of our numerical model for investigating nonlinear transition phenomena is demonstrated by realistic spatial simulations of the experiments by kachanov and levchenko1 for a subharmonic resonance breakdown and of the experiments of klebanoff et al 2 for a fundamental resonance breakdown

semi classical limit of the bottom of spectrum of a schrodinger operator on a path space over a compact riemannian manifold abstract we determine the limit of the bottom of spectrum of schrodinger operators with variable coefficients on wiener spaces and path spaces over finite dimensional compact riemannian manifolds in the semi classical limit these are extensions of the results in s aida semiclassical limit of the lowest eigenvalue of a schrodinger operator on a wiener space j funct anal 203 2 2003 401 424 the problem on path spaces over riemannian manifolds is considered as a problem on wiener spaces by using ito s map however the coefficient operator is not a bounded linear operator and the dependence on the path is not continuous in the uniform convergence topology if the riemannian curvature tensor on the underling manifold is not equal to 0 the difficulties are solved by using unitary transformations of the schrodinger operators by approximate ground state functions and estimates in the rough path analysis

stability and hopf bifurcation in a diffusive logistic population model with nonlocal delay effect abstract a reaction diffusion model with logistic type growth nonlocal delay effect and dirichlet boundary condition is considered and combined effect of the time delay and nonlocal spatial dispersal provides a more realistic way of modeling the complex spatiotemporal behavior the stability of the positive spatially nonhomogeneous positive equilibrium and associated hopf bifurcation are investigated for the case of near equilibrium bifurcation point and the case of spatially homogeneous dispersal kernel

positive soliton solutions for generalized quasilinear schrodinger equations with critical growth this paper is concerned with the positive solutions for generalized quasilinear schrodinger equations in rn with critical growth which have appeared from plasma physics as well as high power ultrashort laser in matter by using a change of variables and variational argument we obtain the existence of positive solutions for the given problem

stability and bifurcation for a delayed predator prey model and the effect of diffusion abstract we consider a predator prey system with one or two delays and a unique positive equilibrium e its dynamics are studied in terms of the local stability of e and of the description of the hopf bifurcation that is proven to exist as one of the delays taken as a parameter crosses some critical values we also consider a reaction diffusion system with neumann conditions resulting from adding one spatial variable and diffusion terms in the previous model the spectral and bifurcation analysis in the neighborhood of e now as a stationary point of this latter system is addressed and the results obtained for the case without diffusion are applied

renormalization theory in four dimensional scalar fields i we present a renormalization group approach to the renormalization theory of 44 using techniques that have been introduced and used in previous papers and that lead to very simple methods to bound the coefficients of the effective potential and of the schwinger functions the main aim of this paper is to show how one can in this way obtain then bounds

a coarse grid projection method for accelerating incompressible flow computations we present a coarse grid projection cgp method for accelerating incompressible flow computations which is applicable to methods involving poisson equations as incompressibility constraints the cgp methodology is a modular approach that facilitates data transfer with simple interpolations and uses black box solvers for the poisson and advection diffusion equations in the flow solver after solving the poisson equation on a coarsened grid an interpolation scheme is used to obtain the fine data for subsequent time stepping on the full grid a particular version of the method is applied here to the vorticity stream function primitive variable and vorticity velocity formulations of incompressible navier stokes equations we compute several benchmark flow problems on two dimensional cartesian and non cartesian grids as well as a three dimensional flow problem the method is found to accelerate these computations while retaining a level of accuracy close to that of the fine resolution field which is significantly better than the accuracy obtained for a similar computation performed solely using a coarse grid a linear acceleration rate is obtained for all the cases we consider due to the linear cost elliptic poisson solver used with reduction factors in computational time between 2 and 42 the computational savings are larger when a suboptimal poisson solver is used we also find that the computational savings increase with increasing distortion ratio on non cartesian grids making the cgp method a useful tool for accelerating generalized curvilinear incompressible flow solvers

the accuracy of the fractional step method we analyze the accuracy of the fractional step method of kim and moin j comput phys 59 1985 pp 308 323 for the incompressible navier stokes equations we show that the boundary conditions cannot be exactly satisfied in the projection step and that this limits the accuracy of the method we also show that the pressure in any projection method can be at best first order accurate our analysis is simpler and more direct than the previous analyses of this method we also show that there is no numerical boundary layer for velocity or pressure but there is one for the auxiliary pressure variable

application of time iterative schemes to incompressible flow the computation of steady incompressible flows by an euler implicit algorithm is studied using both the incompressible equations and the low mach number compressible equations the incompressible equations are handled by adding an artificial time derivative to the continuity equation this allows both the pressure and velocity to be obtained implicitly in one dimensional problems both systems converge rapidly even at low mach numbers where the eigenvalues are very stiff in two dimensions where approximate factorization is required the presence of stiff eigenvalues is highly detrimental stiffness can be avoided in the incompressible equations by selecting an appropriate pseudo mach number this insures reliable convergence and results in an efficient incompressible flow algorithm in the case of compressible equations the mach number cannot be chosen arbitrarily and the contamination introduced by approximate factorization must be removed a matrix preconditioning factor that accomplishes this is developed and demonstrated with this modification the convergence rate is the same as in the incompressible case and is independent of mach number rapid convergence is observed at mach numbers as low as 6 05

large order estimates for ground state energy perturbation series a general treatment is given using path integral methods of obtaining accurate estimates on the rate of growth at large order of the perturbation coefficients for the lowest eigenvalue ground state energy of a large class of anharmonic oscillators simple sufficient conditions are given on the potentialv x so that accurate upper and lower bounds on the perturbation coefficients may be derived several examples are given which generalize previous results examples from euclidean quantum field theory are also considered

semi classical limit of the lowest eigenvalue of a schrodinger operator on a wiener space ii p ϕ 2 model on a finite volume abstract we determine the semi classical limit of the lowest eigenvalue of a p 2 hamiltonian on a finite volume interval

numerical steady state and hopf bifurcation analysis on the diffusive nicholson s blowflies equation1research partially supported by natural sciences and engineering research council of canada 1 for the dirichlet boundary value problem of the diffusive nicholson s blowflies equation it was shown in ref 17 that in a certain range of the parameter space there is a unique positive steady state solution in this paper we propose a scheme to compute this steady state numerically in addition we describe an iterative procedure to locate the critical values of the delay where a hopf bifurcation of time periodic solutions takes place near the steady state some numerical simulations of both schemes are given

a cartesian grid method for modeling multiple moving objects in 2d incompressible viscous flow we present an efficient method for solving 2d incompressible viscous flows around multiple moving objects our method employs an underlying regular cartesian grid to solve the system using a streamfunction vorticity formulation and with discontinuities representing the embedded objects the no penentration condition for the moving geometry is satisfied by superposing a homogenous solution to the poisson s equation for the streamfunction the no slip condition is satisfied by generating vorticity on the surfaces of the objects both the initial poisson solution and the evaluation of the homogenous solution require embedding irregular discontinuities in a fast poisson solver computation time is dictated by the time required to do a fast poisson solution plus solve an integral form of laplace s equation there is no significant increase in computational cost if the geometry of the embedded objects is variable and moving relative to the underlying grid we test the method against the canonical example of flow past a cylinder and obtained new results on the flow and forces of two cylinders moving relative to each other

unsteady solution of incompressible navier stokes equations abstract a new time accurate finite difference numerical method for solving incompressible navier stokes equations is presented with primitive variables as the unknowns the numerical scheme is a crank nicolson implicit treatment of all terms of the equations with central differencing for space derivatives the pressure and the nonlinearities in convection terms are not lagged to obtain the incompressible solution at the advanced time level a continuous auxiliary system is introduced in pseudo time with artificial compressibility time accurate solutions are presented for two dimensional fluid flows in a square cavity with an impulsively starting lid and with an oscillating lid

thecpn 1 1 n action by inverse scattering transformation in angular momentum the effective action which generates 1 n expansion of thecpn 1 model in two dimensions is studied here by inverse problem methods the action contains a functional determinant in which auxiliary scalar and vector fields are assumed to have a spherical symmetry this leads to the introduction as an associated linear problem of a radial schrodinger equation with two potentialsv and and a potential dependent centrifugal term l r 2 r2 1 4r2 the full inverse scattering formalism is developed here for this diffusion problem it is formulated in terms of two component jost solutions and leads to a matricial gel fand levitan marchenko equation the scattering data associated to the potentials by this ist are then used to obtain a closed local form for the whole effective action this is indeed possible for thecpn 1 model owing to the classical integrability moreover it is found that no spherically symmetric instanton exists in this case however the absence of supplementary informations on the 1 n series due to the non integrability at quantum level does not allow safe quantitative conclusions on the general behaviour of the 1 n series at large orders

a second order projection method for the incompressible navier stokes equations in this paper we describe a second order projection method for the time dependent incom pressible navier stokes equations as in the original projection method developed by chorin we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields by introducing more coupling between the diffusion onvection step and the projection step we obtain a temporal discretiza tion that is second order accurate our treatment of the diffusion convection step uses a specialized higher order godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high reynolds number the godunov procedure is second order accurate for smooth flow and remains stable for discontinuous initial data even in the zero viscosity limit we approximate the projection directly using a galerkin procedure that uses a local basis for discretely divergence free vector fields numerical results are presented validating the convergence properties of the method we also apply the method to doubly periodic shear layers to assess the performance of the method on more difficult

construction and borel summability of planar 4 dimensional euclidean field theory we use the methods of 1 to show that the planar part of the renormalized perturbation theory for 4 4 euclidean field theory is borel summable on the asymptotically free side of the theory the borel sum can therefore be taken as a rigorous definition of then limit of a massiven n matrix model with a trg 4 interaction hence with wrong sign ofg our construction is relevant for a solution of the ultra violet problem for planar qcd we also propose a program for studying the structure of the renormalons singularities within the planar world

limiting structure of steady states to the lotka volterra competition model with large diffusion and advection abstract this paper is concerned with the neumann problem of a stationary lotka volterra competition model with diffusion and advection first we obtain some sufficient conditions of the existence of nonconstant solutions by the leray schauder degree theory next we derive a limiting system as diffusion and advection of one of the species tend to infinity the limiting system can be reduced to a semilinear elliptic equation with nonlocal constraint in the simplified 1d case the global bifurcation structure of nonconstant solutions of the limiting system can be classified depending on the coefficients for example this structure involves a global bifurcation curve which connects two different singularly perturbed states boundary layer solutions and internal layer solutions our proof employs a levelset analysis for the associate integral mapping

construction and borel summability of infrared φ 4 4 by a phase space expansion we construct the thermodynamic limit of the critical massless 4 model in 4 dimensions with an ultraviolet cutoff by means of a partly renormalized phase space expansion this expansion requires in a natural way the introduction of effective or running constants and the infrared asymptotic freedom of the model i e the decay of the running coupling constant plays a crucial role we prove also that the correlation functions of the model are the borel sums of their perturbation expansion

operator product expansion algebra we establish conceptually important properties of the operator product expansion ope in the context of perturbative euclidean 4 quantum field theory first we demonstrate generalizing earlier results and techniques of hep th 1105 3375 that the 3 point ope oa1oa2oa3 cca1a2a3c oc usually interpreted only as an asymptotic short distance expansion actually converges at finite and even large distances we further show that the factorization identity ca1a2a3b cca1a2ccca3b is satisfied for suitable configurations of the spacetime arguments again the infinite sum is shown to be convergent our proofs rely on explicit bounds on the remainders of these expansions obtained using refined versions mostly due to kopper et al of the renormalization group flow equation method these bounds also establish that each ope coefficient is a real analytic function in the spacetime arguments for non coinciding points our results hold for arbitrary but finite loop orders they lend support to proposals for

the double well splitting of the low energy levels for the schrodinger operator of discrete φ4 models on tori the formula is obtained for the asymptotics of the splitting of the first two eigenvalues of the schrodinger operator that stands for the discrete multidimensional 4 model on tori the behavior of the main term is investigated in the limit of the large number of particles

phase space analysis and particle structure in field theory progress in the last few years in constructive field theory has included 1 the construction of three dimensional non abelian gauge theories in a finite volume 2 the construction of models that are asymptotically free or have a nontrivial fixed point 3 a new presentation of perturbation theory yielding old and new large order estimates and 4 asymptotic completeness for renormalizable models in the two particle region the existence of multiparticle structure equations in the euclidean region provided that the coupling constant goes to zero as the energy increases these equations yield formally the asymptotic completeness in obtaining most of these results the phase space expansion pioneered by glimm and jaffe plays a crucial role the first part of this review is a description of the phase space expansion in the ecole polytechnique version the second part is devoted to the construction of models the third part treats perturbation theory and the last part deals with asymptotic completeness

geometric analysis of φ4 fields and ising models parts i and ii we provide here the details of the proof announced in 1 that ind 4 dimensions the even 4 euclidean field theory with a lattice cut off is inevitably free in the continuum limit in the single phase regime the analysis is nonperturbative and is based on a representation of the field variables or spins in ising systems as source sink creation operators in a system of random currents which may be viewed as the mediators of correlations in this dual representation the onset of long range order is attributed to percolation in an ensemble of sourceless currents and the physical interaction in the 4 field and other aspects of the critical behavior in ising models are directly related to the intersection properties of long current clusters an insight into the criticality of the dimensiond 4 is derived from an analogy foreseen by k symanzik with the intersection properties of paths of brownian motion other results include the proof that in certain respect the critical behavior in ising models is in exact agreement with the mean field approximation in high dimensionsd 4 but not in the low dimensiond 2 for which we establish the universality of hyperscaling

a new algorithm for calculating adomian polynomials for nonlinear operators in this paper a reliable technique for calculating adomian polynomials for nonlinear operators will be developed the new algorithm offers a promising approach for calculating adomian polynomials for all forms of nonlinearity the algorithm will be illustrated by studying suitable forms of nonlinearity a nonlinear evolution model will be investigated

exponential perturbations of the harmonic oscillator the operators h p2 x2 erx r r 0 in l 2 r are studied the spectrum is discrete for arg the eigenvalues admit an asymptotic expansion as 0 and they have no bender wu type singularities in the analytic continuation to any punctured sector of a logarithmic riemann surface for 0 h defines a symmetric operator with deficiency indices 1 1 and all its self adjoint extensions have discrete spectrum however any eigenvalue of h when continued to 0 can be interpreted as a resonance of the problem

renormalization proof for massive phi_4 4 theory on riemannian manifolds in this paper we present an inductive renormalizability proof for massive phi 4 4 theory on riemannian manifolds based on the wegner wilson flow equations of the wilson renormalization group adapted to perturbation theory the proof goes in hand with bounds on the perturbative schwinger functions which imply tree decay between their position arguments an essential prerequisite is precise bounds on the short and long distance behaviour of the heat kernel on the manifold with the aid of a regularity assumption often taken for granted we also show that for suitable renormalization conditions the bare action takes the minimal form that is to say there appear the same counterterms as in flat space apart from a logarithmically divergent one which is proportional to the scalar curvature

a renormalizable field theory the massive gross neveu model in two dimensions the euclidean massive gross neveu model in two dimensions is just renormalizable and asymptotically free thanks to the pauli principle bare perturbation theory with an ultra violet cut off and the correct ansatz for the bare mass is convergent in a disk whose radius corresponds by asymptotic freedom to a small finite renormalized coupling constant therefore the theory can be fully constructed in a perturbative way it satisfies the o s axioms and is the borel sum of the renormalized perturbation expansion of the model

fast and high accuracy multigrid solution of the three dimensional poisson equation we employ a fourth order compact finite difference scheme fos with the multigrid algorithm to solve the three dimensional poisson equation we test the influence of different orderings of the grid space and different grid transfer operators on the convergence and efficiency of our high accuracy algorithm fourier smoothing analysis is conducted to show that fos has a smaller smoothing factor than the traditional second order central difference scheme cds a new method of fourier smoothing analysis is proposed for the partially decoupled red black gauss seidel relaxation with fos numerical results are given to compare the computed accuracy and the computational efficiency of fos with multigrid against cds with multigrid

the mathematical theory of resonances whose widths are exponentially small ii abstract it is shown how the rigorous justification of resonance widths in paper i 5 can be simplified by exploiting langer s trick of expanding the independent variable rather than the dependent variable 9

implicit solutions of incompressible navier stokes equations using the pressure gradient method a modified pressure gradient method is developed for solving the incompressible twoand three dimensional navier stokes equations in primitive variables velocity and pressure gradient vectors rather than the velocity and pressure are considered as dependent variables this choice of the dependent variables is consistent with the flow physics as the velocity field of incompressible flows is not dependent on the pressure but rather the pressure gradient this introduces one and two additional dependent variables for two and three dimensions respectively to close the system of equations additional equations are obtained from the identity that the curl of the pressure gradient is zero this choice of dependent variables also leads to dirichlet boundary conditions for the pressure gradient which improves numerical stability and convergence rates the modified pressure gradient method includes a pressure gradient averaging term in the momentum equations to stabilize the solution this term is extended here to general curvilinear coordinates the system of equations is discritized using a conservative finite volume formulation time integration is achieved with a fully implicit scheme including implicit boundary conditions the implicit scheme guarantees that continuity is satisfied to machine zero numerical results compare well with solutions available in the literature for the cavity flow problem and flow about a circular cylinder at reynolds number 40

dirichlet problem for the diffusive nicholson s blowflies equation abstract the object of this paper is to consider the asymptotic behavior of solutions of the diffusive nicholson s blowflies equation under dirichlet boundary condition a new approach is developed to study the global attractivity of the positive steady state for a reaction diffusion equation with time delay when monotone or quasi monotone conditions fail to apply this approach should be applicable to other dirichlet problems as well even though our analysis is tailored to the diffusive nicholson s blowflies equation

construction of a non trivial planar field theory with ultraviolet stable fixed point we study a 4 4 planar euclidean quantum field theory with propagator 1 p 2 2 0 with the help of the tree expansion of gallavotti and nicolo 1 this non renormalizable theory is shown to have a non trivial ultraviolet stable fixed point at negative coupling constant the vicinity of the fixed point is discussed

hopf bifurcations in a reaction diffusion population model with delay effect abstract a reaction diffusion population model with a general time delayed growth rate per capita is considered the growth rate per capita can be logistic or weak allee effect type from a careful analysis of the characteristic equation the stability of the positive steady state solution and the existence of forward hopf bifurcation from the positive steady state solution are obtained via the implicit function theorem where the time delay is used as the bifurcation parameter the general results are applied to a food limited population model with diffusion and delay effects as well as a weak allee effect population model

comparison of second and fourth order discretizations for multigrid poisson solvers we combine a compact high order difference approximation with multigrid v cycle algorithm to solve the two dimensional poisson equation with dirichlet boundary conditions this scheme along with several different orderings of grid space and projection operators is compared with the five point formula to show the dramatic improvement in computed accuracy on serial and vector machines

instantons of two dimensional fermionic effective actions by inverse scattering transformation effective actions containing the logarithm of a functional dirac determinant appear in 1 n expansions of fermionic theories n being the number of flavours we introduce a method to find symmetric solutions of the corresponding non linear and non local saddle point equations this method consists in using the scattering data of the rotationally symmetric dirac equation in two dimensions with the angular mometum as a spectral parameter we apply the method to fermionic theories with scalar and pseudoscalar quartic couplings the effective action that generates the 1 n expansion admits a closed form in terms of the scattering data only in the particular case when the model is integrable gross neveu and chiral gross neveu model no instanton solutions are present in these two particular cases this fact together with the exact results for thes matrix and form factors suggests that the 1 n expansion could be convergent in the general case the quantum model has an additional dimensionless parametergr gr gives the chiral gross neveu model whengr 0 tachyons appear forgr 0 andgr generically complex action instantons exists indicating a possibly borel summable 1 n expansion

the lipatov argument for φ 3 4 perturbation theory we extend to 3 4 the work of s breen on the leading behavior at large order of 2 4 perturbation theory using a phase space expansion to obtain new estimates on the high energy behavior of 3 4 feynman graphs and a rigorous semiclassical expansion we prove that the radius of convergence of the borel transform of the pertubative series for 3 4 euclidean field theory is the one computed by the lipatov method

tunneling for spatially cut off p phi _2 hamiltonians we study the asymptotic behavior of low lying eigenvalues of spatially cut off p 2 hamiltonian in the semi classical limit we determine the semi classical limit of the lowest eigenvalue of the hamiltonian in terms of the hessian of the potential function of the corresponding classical equation moreover we prove that the gap of the lowest two eigenvalues goes to 0 exponentially fast in the semi classical limit when the potential function is double well type in fact we prove that the exponential decay rate is greater than or equal to the agmon distance between two zero points of the symmetric double well potential function also we study basic properties of the agmon distance and instanton

steady states of a leslie gower model with diffusion and advection abstract this paper focuses on a stationary leslie gower model with diffusion and advection firstly some existence conditions of nonconstant positive solutions are obtained by means of the leray schauder degree theory as diffusion and advection of one of the species both tend to infinity we obtain a limiting system which is a semi linear elliptic equation with nonlocal constraint in the simplified 1d case the global bifurcation structure of nonconstant solutions of the limiting system is classified

bounds on renormalized feynman graphs we prove two bounds on the value of renormalized euclidean feynman graphs one is a relatively crude but widely applicable bound the other a finer bound applicable to 4 4 like models

a non staggered grid fractional step method for time dependent incompressible navier stokes equations in curvilinear coordinates a numerical method for solving three dimensional time dependent incompressible navier stokes equations in curvilinear coordinates is presented the non staggered grid method originally developed by c m rhie and w l chow aiaaj 21 1525 1983 for steady state problems is extended to compute unsteady flows in the computational space the cartesian velocity components and the pressure are defined at the center of a control volume while the volume fluxes are defined at the mid point on their corresponding cell faces the momentum equations are integrated semi implicitly by the approximate factorization technique the intermediate velocities are interpolated onto the faces of the control volume to form the source terms of the pressure poisson equation which is solved iteratively with a multigrid method the compatibility condition of the pressure poisson equation is satisfied in the same manner as in a staggered grid method mass conservation can be satisfied to machine accuracy the pressure boundary condition is derived from the momentum equations solutions of both steady and unsteady problems including the large eddy simulation of a rotating and stratified upwelling flow in an irregular container established the favorable accuracy and efficiency of the present method

a novel dynamic framework for subgrid scale parametrization of mesoscale eddies in quasigeostrophic turbulent flows abstract this paper puts forth a modular dynamic subgrid scale modeling framework for large eddy simulation of quasigeostrophic turbulence based on minimizing the errors between structural and functional subgrid scale models the approximate deconvolution ad procedure is used to estimate the free modeling parameters for the eddy viscosity coefficient parameterized in space and time using the smagorinsky and leith models the novel idea here is to estimate the modeling parameters using the ad method rather than the traditionally used test filtering approach first a priori and a posteriori analyses are presented for solving a canonical homogeneous isotropic decaying turbulence problem the proposed model is then applied to a wind driven quasigeostrophic four gyre ocean circulation problem which is a standard prototype of more realistic ocean dynamics results show that the proposed model captures the quasi stationary ocean dynamics and provides the time averaged four gyre circulation patterns taking locally resolved flow characteristics into account the model dynamically provides higher eddy viscosity values for lower resolutions

leading large order asymptotics for φ4 2 perturbation theory we develop a rigorous semiclassical expansion to compute the radius of convergence of the borel transform for the pressure in 4 2 field theory this result gives a partial justification for the lipatov method of finding large order perturbation theory asymptotics in quantum field theory

local existence of the borel transform in euclidean massless φ 4 4 we extend the methods of 1 to prove large order estimates on the renormalized feynman amplitudes of massless 4 4 euclidean field theory at non exceptional momenta the borel transform of the perturbative series is analytic in a disk centered at the origin of the complex plane this result is a step towards the rigorous investigation of the infra red singularities in the borel plane for theories containing massless particles like the gauge theories

an overview of projection methods for incompressible flows a series of numerical issues related to the analysis and implementation of fractional step methods for incompressible flows are addressed in this paper these methods are often referred to in the literature as projection methods and can be classified into three classes namely the pressure correction methods the velocity correction methods and the consistent splitting methods for each class of schemes theoretical and numerical convergence results available in the literature are reviewed and open questions are discussed the essential results are summarized in a table which could serve as a useful reference to numerical analysts and practitioners published by elsevier b v msc 65n35 65n22 65f05 35j05

bounds on completely convergent euclidean feynman graphs letg be a euclidean feynman graph containingl g lines we prove that ifg has massive propagators and does not contain any divergent subgraphs its value is bounded bykl g we also prove the infrared analogue of this bound

a time integration method using artificial compressibility for unsteady viscous flows abstract a time accurate integration method for the study of unsteady incompressible viscous flows is presented based on a three point backward implicit discretization of the navier stokes equations in real time and a pseudo time relaxation with artificial compressibility to advance the solution between consecutive real time levels the spatial discretization uses central differencing based on a stretched staggered grid a factored adi scheme with lagged non linearities is used to reduce the problem to the solution of scalar tridiagonal systems this method displays very good computing efficiency and accuracy when applied for validation to several typical steady and unsteady flow problems

dynamics of the diffusive nicholson s blowflies equation with distributed delay in this paper we study the diffusive nicholson s blowflies equation generalizing previous works we model the generation delay by using an integral convolution over all past times and results are obtained for general delay kernels as far as possible the linearized stability of the non zero uniform steady state is studied in detail mainly by using the principle of the argument global stability both of this state and of the zero state are studied by using energy methods and by employing a comparison principle for delay equations finally we consider what bifurcations are possible from the non zero uniform state in the case when it is unstable

the inverse scattering transformation in the angular momentum plane the inverse scattering transformation ist with the angular momentum as a spectral variable turned out to be a useful method to deal with rotationally invariant problems in field theory at higher spatial dimensions refs 1 and 2 we derive the direct and inverse scattering problems for thev dimensional radial schrodinger equation for variable and fixed energy negative or positive we determine the scattering data sd in one to one correspondence with the potential and derive the corresponding gelfand levitan equation a family of exactly solvable potentials for any and fixed energy is obtained the trace identities associated to this ist are derived for both signs of the energy they relate integrals of local polynomials in the potential and its derivatives timesr2n 1 n 1 with the sd the presence of this power ofr makes these relations useful in higher dimensions

local borel summability of euclidean 311 1311 1311 1a simple proof via differential flow equations it is shown how the differential flow equation or equivalently the continous renormalization group method can be employed to give an astonishingly easy proof of the local borel summability of the renormalized perturbative euclidean massive 44