noncanonical quantization of gravity i foundations of affine quantum gravity the nature of the classical canonical phase space variables for gravity suggests that the associated quantum field operators should obey affine commutation relations rather than canonical commutation relations prior to the introduction of constraints a primary kinematical representation is derived in the form of a reproducing kernel and its associated reproducing kernel hilbert space constraints are introduced following the projection operator method which involves no gauge fixing no complicated moduli space nor any auxiliary fields the result which is only qualitatively sketched in the present paper involves another reproducing kernel with which inner products are defined for the physical hilbert space and which is obtained through a reduction of the original reproducing kernel several of the steps involved in this general analysis are illustrated by means of analogous steps applied to one dimensional quantum mechanical models these toy models help in motivating and understanding the analysis in the case of gravity

grid overlapping for implicit parallel computation of compressible flows the suitability of applying the overlapping grid method to parallel computation of steady and unsteady compressible inviscid flows with three point block tridiagonal implicit schemes is addressed in this paper an easily usable interface treatment is constructed and analyzed for both steady and unsteady problems the performance of the method such as convergence rate and time accuracy can be controlled through the overlapping width the method needs no iteration at each time step or modification of the thomas algorithm for the solution of the implicit parts in both steady and unsteady cases a very good absolute parallel efficiency is demonstrated for bidimensional subsonic and transonic flow computations

a scheme for conservative interpolation on overlapping grids this paper describes how to interpolate in a conservative manner when solving systems of conservative laws on overlapping grids overlapping grids are a flexible and efficient way to create grids for complicated regions before now however no general method had been developed for conservative interpolation the basic idea consists of assuming that the interpolation coefficients are free parameters and then deriving constraints to ensure that the interpolation is conservative a system of equations is then solved to determine the coefficients a two dimensional viscous burger s equation is solved to demonstrate the conservative nature of the scheme

on conservation at grid interfaces this paper considers the solution of hyperbolic systems of conservation laws on discontinuous grids in particular we consider what happens to conservation at grid interfaces a procedure is presented to derive conservative difference approximations at the grid interfaces for two dimensional grids which overlap in an arbitrary configuration the same procedures are applied to compute interface formulas for grids which are refined in space and or time and for continuous grids where a switch in the scheme causes the discontinuity

feynman formulae and phase space feynman path integrals for tau quantization of some levy khintchine type hamilton functions evolution semigroups generated by pseudo differential operators are considered these operators are obtained by different parameterized by a number procedures of quantization from a certain class of functions or symbols defined on the phase space this class contains hamilton functions of particles with variable mass in magnetic and potential fields and more general symbols given by the levy khintchine formula the considered semigroups are represented as limits of n fold iterated integrals when n tends to infinity such representations are called feynman formulae some of these representations are constructed with the help of another pseudo differential operator obtained by the same procedure of quantization such representations are called hamiltonian feynman formulae some representations are based on integral operators with elementary kernels these are called lagrangian feynman formulae langrangian feynman formulae provide approximations of evolution semigroups suitable for direct computatio

asymptotic analysis of the gunn effect with realistic boundary conditions a general asymptotic analysis of the gunn effect in n type gaas under general boundary conditions for metal semiconductor contacts is presented depending on the parameter values in the boundary condition of the injecting contact different types of waves mediate the gunn effect the periodic current oscillation typical of the gunn effect may be caused by moving charge monopole accumulation or depletion layers or by low or high field charge dipole solitary waves a new instability caused by multiple shedding of low field dipole waves is found in all cases the shape of the current oscillation is described in detail we show the direct relationship between its major features maxima minima plateaus etc and several critical currents which depend on the values of the contact parameters our results open the possibility of measuring contact parameters from the analysis of the shape of the current oscillation s1063 651x 97 04708 9

slowly modulated two pulse solutions in the gray scott model i asymptotic construction and stability two pulse solutions play a central role in the phenomena of self replicating pulses in the one dimensional 1 d gray scott model in the present work part i of two parts we carry out an existence study for solutions consisting of two symmetric pulses moving apart from each other with slowly varying velocities this corresponds to a mildly strong pulse interaction problem in which the inhibitor concentration varies on long spatial length scales critical maximum wave speeds are identified and odes are derived for the wave speed and for the separation distance between the pulses in addition the formal linear stability of these two pulse solutions is determined good agreement is found between these theoretical predictions and the results from numerical simulations the main methods used in this paper are analytical singular perturbation theory for the existence demonstration and the nonlocal eigenvalue problem nlep method developed in our earlier work for the stability analysis the analysis of

noncanonical quantization of gravity ii constraints and the physical hilbert space the program of quantizing the gravitational field with the help of affine field variables is continued for completeness a review of the selection criteria that singles out the affine fields the alternative treatment of constraints and the choice of the initial before imposition of the constraints ultralocal representation of the field operators is initially presented as analogous examples demonstrate the introduction and enforcement of the gravitational constraints will cause sufficient changes in the operator representations so that all vestiges of the initial ultralocal field operator representation disappear to achieve this introduction and enforcement of the constraints a well characterized phase space functional integral representation for the reproducing kernel of a suitably regularized physical hilbert space is developed and extensively analyzed

absorbing boundary conditions for difference approximations to the multi dimensional wave equation construction des conditions aux limites absorbantes pour l equation des ondes multidimensionnelle a l aide d approximations aux differences formulation sous forme canonique des conditions aux limites absorbantes analytiques

classification and unfoldings of degenerate hopf bifurcations abstract this paper initiates the classification up to symmetry covariant contact equivalence of perturbations of local hopf bifurcation problems which do not satisfy the classical non degeneracy conditions the only remaining hypothesis is that i should be simple eigenvalues of the linearized right hand side at criticality then the lyapunov schmidt method allows a reduction to a scalar equation g x 0 where g x g x a definition is given of the codimension of g and a complete classification is obtained for all problems with codimension 3 together with the corresponding universal unfoldings the perturbed bifurcation diagrams are given for the cases with codimension 2 and for one case with codimension 3 for this last case one of the unfolding parameters is a modal parameter such that the topological codimension equals in fact 2 formulas are given for the calculation of the taylor coefficients needed for the application of the results and finally the results are applied to two simple problems a model of glycolytic oscillations and the fitzhugh nerve equations

solitary waves in semiconductors with finite geometry and the gunn effect an asymptotic analysis of the gunn effect oscillations of the current through a semiconductor under constant voltage bias is given the electric field inside the one dimensional semiconductor is described by a parabolic equation with small diffusivity plus zero field boundary conditions and a constant voltage integral constraint nonuniform stationary solutions are constructed and their stability analyzed under both current and voltage bias the oscillations are known to be produced by repeated generation at one boundary of a solitary wave that moves towards and is annihilated at the other boundary far from the boundaries the solitary wave is constructed and its stability analyzed the effect of the boundaries is qualitatively discussed and several open problems pointed out

a rigorous path integral for quantum spin using flat space wiener regularization adapting ideas of daubechies and klauder j math phys 26 2239 1985 we derive a rigorous continuum path integral formula for the semigroup generated by a spin hamiltonian more precisely we use spin coherent vectors parametrized by complex numbers to relate the coherent representation of this semigroup to a suitable schrodinger semigroup on the hilbert space l2 r2 of lebesgue square integrable functions on the euclidean plane r2 the path integral formula emerges from the standard feynman kac ito formula for the schrodinger semigroup in the ultradiffusive limit of the underlying brownian bridge on r2 in a similar vein a path integral formula can be constructed for the coherent representation of the unitary time evolution generated by the spin hamiltonian

local error estimates for discontinuous solutions of nonlinear hyperbolic equations let u x t be the possibly discontinuous entropy solution of a nonlinear scalar conservation law with smooth initial data suppose u varepsilon x t is the solution of an approximate viscosity regularization where varepsilon 0 is the small viscosity amplitude it is shown that by post processing the small viscosity approximation u varepsilon pointwise values of u and its derivatives with an error as close to e as desired can be recovered the analysis relies on the adjoint problem of the forward error equation which in this case amounts to a backward linear transport equation with discontinuous coefficients the novelty of our approach is to use a generalized e condition of the forward problem in order to deduce a w 1 infty energy estimate for the discontinuous backward transport equation this in turn leads to e uniform estimate on moments of the error u varepsilon u the approach presented does not follow the characteristics and therefore applies mutatis mutandis to o

constructing measures for spin variable path integrals by exploiting the overcompleteness of the spin coherent states we derive expressions for spin kinematics path integrals specifically for spin 1 2 and spin 1 in terms of genuine wiener measures on continuous paths lying on the unit sphere and for certain dynamical systems which when projected onto the subspace spanned by the proper spin coherent state matrix elements yield the appropriate quantum mechanical propagator

the onset and end of the gunn effect in extrinsic semiconductors a hopf bifurcation analysis of the spontaneous current oscillation in direct current dc voltage biased extrinsic semiconductors is given for the classical model of the gunn effect in n gaas for semiconductor lengths l larger than a certain minimal value the steady state is linearly unstable for voltages in an interval phi alpha phi omega as l increases the branch of time periodic solutions bifurcating at simple eigenvalues when phi phi alpha turns from subcritical to supercritical and then back to subcritical again for very long semiconductors a quasi continuum of oscillatory modes bifurcates from the steady state at the onset of the instability the bifurcating branch is then described by a scalar reaction diffusion equation with cubic nonlinearity subject to antiperiodic boundary conditions on a subinterval of 0 l for the electron velocity curve we have considered the bifurcation is subcritical which may agree with experimental observations in n gaas an extension o

a new domain decomposition method with overlapping patches for ultrascale simulations application to biological flows we address the failure in scalability of large scale parallel simulations that are based on semi implicit time stepping and hence on the solution of linear systems on thousands of processors we develop a general algorithmic framework based on domain decomposition that removes the scalability limitations and leads to optimal allocation of available computational resources it is a non intrusive approach as it does not require modification of existing codes specifically we present here a two stage domain decomposition method for the navier stokes equations that combines features of discontinuous and continuous galerkin formulations at the first stage the domain is subdivided into overlapping patches and within each patch a c 0 spectral element discretization second stage is employed solution within each patch is obtained separately by applying an efficient parallel solver proper inter patch boundary conditions are developed to provide solution continuity while a multilevel communicating interface mci is developed to provide efficient communication between the non overlapping groups of processors of each patch the overall strong scaling of the method depends on the number of patches and on the scalability of the standard solver within each patch this dual path to scalability provides great flexibility in balancing accuracy with parallel efficiency the accuracy of the method has been evaluated in solutions of steady and unsteady 3d flow problems including blood flow in the human intracranial arterial tree benchmarks on bluegene p cray xt5 and sun constellation linux cluster have demonstrated good performance on up to 96 000 cores solving up to 8 21b degrees of freedom in unsteady flow problem the proposed method is general and can be potentially used with other discretization methods or in other applications

bifurcation behavior of a superlattice model we present a complete description of the stationary and dynamical behavior of semiconductor superlattices in the framework of a discrete drift model by means of numerical continuation singular perturbation analysis and bifurcation techniques the control parameters are the applied dc voltage phi and the doping nu in nondimensional units we show that the organizing centers for the long time dynamics are takens bogdanov bifurcation points in a broad range of parameters and we cast our results in a phi nu phase diagram for small values of the doping the system has only one uniform solution where all the variables are almost equal for high doping we find multistability corresponding to domain solutions and the stationary solutions may exhibit chaotic spatial behavior in the intermediate regime of nu the solution can be time periodic depending on the bias the oscillatory regions are related to the appearance and disappearance of hopf bifurcation tongues which can be sub or supercri

instability of difference models for hyperbolic initial boundary value problems a th00 eory of instability is presented for finite difference models of linear hyperbolic partial differential equations in one space dimension with a boundary according to this theory instability is caused by spurious radiation of wave energy from the boundary at a numerical group velocity c 0 to make this point of view precise we first develop a rigorous description of group velocity for difference schemes and of reflection of waves at boundaries from these results we then obtain lower bounds for growth rates of unstable finite difference solution operators in l2 norms which extend earlier results due to osher and to gustafsson kreiss and sundstrom in particular we investigate l2 instability with respect to both initial and boundary data and show how they are affected by a finite versus infinite reflection coefficients and b wave radiation with c 0 versus c 0

comment on semiclassical dynamics of a spin in an arbitrary magnetic field in a recent paper alscher and grabert claim to prove that a dominant tree level stationary phase approximation to the wiener regularized continuum su 2 coherent state path integral for the quantum propagator zf t exp i 0 h ds zi becomes exact provided h is a linear combination of the su 2 generators with arbitrary time dependent coefficients i find the derivation of this in fact obvious result unduly complicated and somewhat obscure the authors start from a classical spin action inconsistent with necessary boundary conditions and therefore are forced to invoke a nontrivial regularization of the action to render the latter meaningful alternatively when a su 2 symplectic potential consistent with the boundary conditions is employed no regularization is required to obtain the leading quasiclassical asymptotics

recent results regarding affine quantum gravity recent progress in the quantization of nonrenormalizable scalar fields has found that a suitable non classical modification of the ground state wave function leads to a result that eliminates term by term divergences that arise in a conventional perturbation analysis after a brief review of both the scalar field story and the affine quantum gravity program examination of the procedures used in the latter surprisingly shows an analogous formulation which already implies that affine quantum gravity is not plagued by divergences that arise in a standard perturbation study additionally guided by the projection operator method to deal with quantum constraints trial reproducing kernels are introduced that satisfy the diffeomorphism constraints furthermore it is argued that the trial reproducing kernels for the diffeomorphism constraints may also satisfy the hamiltonian constraint as well

nonlinear stability of incoherence and collective synchronization in a population of coupled oscillators a mean field model of nonlinearly coupled oscillators with randomly distributed frequencies and subject to independent external white noises is analyzed in the thermodynamic limit when the frequency distribution isbimodal new results include subcritical spontaneous stationary synchronization of the oscillators supercritical time periodic synchronization bistability and hysteretic phenomena bifurcating synchronized states are asymptotically constructed near bifurcation values of the coupling strength and theirnonlinear stability properties ascertained

constructing measures for path integrals the overcompleteness of the coherent states for the heisenberg weyl group implies that many different integral kernels can be used to represent the same operator within such an equivalence class we construct an integral kernel to represent the quantum mechanical evolution operator for certain dynamical systems in the form of a path integral that involves genuine wiener measures on continuous phase space paths to achieve this goal it is necessary to employ an expression for the classical action different from the usual one

stability analysis of numerical boundary conditions and implicit difference approximations for hyperbolic equations abstract implicit noniterative finite difference schemes have recently been developed by several authors for multidimensional systems of nonlinear hyperbolic partial differential equations when applied to linear model equations with periodic boundary conditions those schemes are unconditionally stable a stable as applied in practice the algorithms often face a severe time step restriction a major source of the difficulty is the treatment of the numerical boundary conditions one conjecture has been that unconditional stability requires implicit numerical boundary conditions an apparent counterexample was the space time extrapolation considered by gustafsson kreiss and sundstrom in this paper we examine space implicit and space time explicit extrapolation using normal mode analysis for a finite and infinite number of spatial mesh intervals the results indicate that for unconditional stability with a finite number of spatial mesh intervals the numerical boundary conditions must be implicit

quantization of systems with a general phase space equipped with a riemannian metric quantization on phase spaces of general geometry devoid of any special symmetry properties is discussed on the basis of phase spaces endowed with a symplectic structure a riemannian geometry and a structure using techniques from differential geometry and especially exploiting the dirac operator we are able to offer a fully geometric quantization procedure for a wide class of symmetry free phase spaces our procedure leads to the conventional results in cases where the phase space is a symmetric space for which alternative quantization techniques suffice

semiclassical dynamics of a spin in an arbitrary magnetic field the spin coherent state path integral describing the dynamics of a spin system in a magnetic field of arbitrary time dependence is considered defining the path integral as the limit of a wiener regularized expression the semiclassical approximation leads to a continuous minimal action path with jumps at the endpoints the resulting semiclassical propagator is shown to coincide with the exact quantum mechanical propagator a nonlinear transformation of the angle variables allows for a determination of the semiclassical path and the jumps without solving a boundary value problem the semiclassical spin dynamics is thus readily amenable to numerical methods

existence of anti periodic mild solutions for semilinear evolution equations in this paper we study the existence of anti periodic mild solutions for a class of semilinear evolution equations in banach spaces and extend some related results in this direction an example is given to illustrate our results

weak coherent state path integrals weak coherent states share many properties of the usual coherent states but do not admit a resolution of unity expressed in terms of a local integral they arise e g in the case that a group acts on an inadmissible fiducial vector motivated by the recent affine quantum gravity program the present article studies the path integral representation of the affine weak coherent state matrix elements of the unitary time evolution operator since weak coherent states do not admit a resolution of unity it is clear that the standard way of constructing a path integral by time slicing is predestined to fail instead a well defined path integral with wiener measure based on a continuous time regularization is used to approach this problem the dynamics is rigorously established for linear hamiltonians and the difficulties presented by more general hamiltonians are addressed

quasiclassical path integral in coherent state manifolds quantization of classical dynamical systems with a poisson structure on homogeneous kahler manifolds is considered the quantization follows the method invented by berezin and represents the unitary transition operator as a quasiclassical path integral in the coherent state basis in case the coherent state manifold appears as a degenerate rank one co adjoint orbit of the symmetry group an explicit representation of the transition amplitude in terms of classical data can be derived for large values of the highest weight which corresponds to the quasiclassical approximation this representation is further shown to perfectly agree in contrast to some earlier approaches with the known exact results and may provide non trivial asymptotics of physical relevance

bifurcation of traveling waves in extrinsic semiconductors abstract we analyze the bifurcation of traveling waves in a standard model of electrical conduction in extrinsic semiconductors in scaled variables the corresponding traveling wave problem is a singularly perturbed nonlinear three dimensional o d e system the relevant bifurcation parameters are the wave speed s and the total current j by means of geometric singular perturbation theory it suffices to analyze a two dimensional reduced problem depending on the relative size of s and a dimensionless small parameter different types of traveling waves exist for 0 s the only waves are fronts corresponding to heteroclinic orbits for s similar fronts but with left and right states reversed exist the transition between these regimes occurs for s o in a complicated global bifurcation involving a hopf bifurcation bifurcation of multiple periodic orbits and heteroclinic and homoclinic bifurcations we present a consistent bifurcation diagram which is confirmed by numerical computations

the choice of numerical boundary conditions for hyperbolic systems abstract the aim of this paper is the discussion of two fundamental problems for mixed initial boundary value problems with applications in fluid mechanics first different stability properties are discussed which are of importance for long time integrations and steady state calculations second a new numerical technique for problems with an artificial boundary is introduced

a finite element method for approximating electromagnetic scattering from a conducting object we provide an error analysis of a fully discrete finite element fourier series method for approximating maxwell s equations the problem is to approximate the electromagnetic field scattered by a bounded inhomogeneous and anisotropic body the method is to truncate the domain of the calculation using a series solution of the field away from this domain we first prove a decomposition for the poincare steklov operator on this boundary into an isomorphism and a compact perturbation this is proved using a novel argument in which the scattering problem is viewed as a perturbation of the free space problem using this decomposition and edge elements to discretize the interior problem we prove an optimal error estimate for the overall problem

analysis of artificial boundary conditions for exterior boundary value problems in three dimensions simple boundary conditions on an artificial boundary are discussed then an exact boundary condition on the artificial boundary is obtained approximation to this boundary condition with high accuracy is given and the error estimates are obtained a numerical example is presented and the numerical results are compared with the exact solution

stability of interfaces with mesh refinement a study is conducted of the stability of mesh refinement in space and time for several different interface equations and finite difference approximations first a root condition which implies stability for the initial boundary value problem for this type of interface is derived from the root condition the stability of several interface equations is proved using the maximum principle in some cases the final verification steps can be done analytically in other cases a simple computer program has been written to check the condition for values of a parameter along the boundary of the unit circle using this method stability for lax wendroff with all the interface conditions considered and for leapfrog with interpolation interface conditions when the fine and coarse grids overlap is proved

uniqueness of steady state solutions for difference equations on overlapping grids the uniqueness of continuous and discontinuous steady state solutions is studied for difference approximations of hyperbolic problems on a strip with overlapping grids in the continuous case an easily verifiable uniqueness criterion is obtained from a normal mode analysis this criterion is applied to examine the uniqueness of commonly used interface treatments in the discontinuous case a shock is assumed to be contained in the overlap analysis for this case is developed on a linear model equation most of the results are further confirmed by computing smooth and shocked flows in a divergent duct the present theory can also be applied to analyze uniqueness for more general boundary value problems

quantum mechanical path integrals with wiener measure for all polynomial hamiltonians ii the coherent state representation of quantum mechanical propagators as well defined phase space path integrals involving wiener measure on continuous phase space paths in the limit that the diffusion constant diverges is formulated and proved this construction covers a wide class of self adjoint hamiltonians including all those which are polynomials in the heisenberg operators in fact this method also applies to maximal symmetric hamiltonians that do not possess a self adjoint extension this construction also leads to a natural covariance of the path integral under canonical transformations an entirely parallel discussion for spin variables leads to the representation of the propagator for an arbitrary spin operator hamiltonian as well defined path integrals involving wiener measure on the unit sphere again in the limit that the diffusion constant diverges

wiener measures for path integrals with affine kinematic variables the results obtained earlier have been generalized to show that the path integral for the affine coherent state matrix element of a unitary evolution operator exp ith can be written as a well defined wiener integral involving wiener measure on the lobachevsky half plane in the limit that the diffusion constant diverges this approach works for a wide class of hamiltonians including e g d2 dx2 v x on l2 r with v sufficiently singular at x 0

some response characteristics of finite element tidal models abstract small scale error can arise in finite element tidal models from different aspects of the spatial discretization one source is incompatibility in smoothness of interpolation of the pressure and velocity fields noise of this type can be eliminated completely by using stokes helmholtz potentials to represent the velocity and interpolating these potentials with the same smoothness as is given to the pressure another source is inhomogeneous triangulation in which the number of links is not the same at all nodes noise of this type can be suppressed by using a high resolution grid the resolution in question being that of the response rather than of the domain these points are illustrated by examining the response characteristics of idealized models it is found that in the models considered small scale noise can be ascribed to resonance anomalies associated with the method of spatial discretization in this analysis the time is continuous but some remarks are appended on the effect of time discretization and a formal proof is given of the time stepping stability of a general discretized form of laplace s tidal equations

steady and unsteady shock waves on overlapping grids the interaction between steady and unsteady shock waves and interfaces of overlapping grids is studied conditions permitting shock penetration through an interface and ensuring solution uniqueness are derived easily usable corrections ensuring shock interface penetration and convergence are devised

on numerical boundary treatment of hyperbolic systems for finite difference and finite element methods it is well known that the stability of the initial boundary value problem for a scalar equation does not necessarily imply stability for a vector equation with a similar boundary treatment in fact we show that for any boundary treatment one can construct systems for which the boundary treatment on the natural variables is not stable our main theorem is that one can introduce a treatment of the boundaries for which the stability of the system follows immediately from the stability for a scalar equation this is accomplished by operating on the characteristic variables for those quantities that are not specified on the boundary in a working code this can be accomplished by adding a correction term to the existing boundary algorithm the analysis and computational results are presented for both finite differences and semi discrete galerkin methods

the convergence rate for difference approximations to general mixed initial boundary value problems the convergence rate is investigated for the solutions to difference schemes approximating the mixed initial boundary value problem for general systems of differential equations it is shown that if an energy estimate holds then the extra boundary conditions can be of one order lower accuracy without destroying the convergence rate expected from the approximation at inner points if the maximal order of the derivatives occurring in the boundary conditions is low enough then even lower accuracy can be permitted for the extra boundary conditions

on nonconservative algorithms for grid interfaces in computations of fluid flows by domain decomposition methods the necessity of conservation at grid interfaces is now widely claimed in this paper we consider nonconservative algorithms for the interfaces our investigation begins with discussions about typical nonconservative interface treatments for one dimensional calculations the analysis shows that the conservation error of a numerical solution caused by a nonconservative interface matching has an upper bound when the solution itself is bounded furthermore if the numerical solution converges as the mesh size goes to zero it converges to a weak solution of the problem under certain conditions that may be detected numerically also we acquire similar results for two dimensional calculations on grids intersecting with each other in an arbitrary way in order to illustrate the theoretical results we present numerical examples and demonstrate that under those conditions conservation error reduces and accuracy for jumps as well as locations of discontinuities improves as the mesh size decreases

periodically generated propagating pulses certain equations with integral constraints have as solutions time periodic pulses of a fieldlike unknown while a currentlike unknown oscillates periodically with time a general asymptotic theory of this phenomenon the generalized gunn effect has been found recently here we extend this theory to the case of nonlinearities having only one stable zero which is the case for the usual gunn effect in n gaas our ideas are presented in the context of a simple scalar model where the waves can be constructed analytically and explicit expressions for asymptotic approximations can be found

stability of finite difference models containing two boundaries or interfaces it is known that the stability of finite difference models of hyperbolic initial boundary value problems is connected with the propagation and reflection of parasitic waves here the waves point of view is applied to models containing two boundaries or interfaces where repeated reflection of trapped packets is a potential new source of instability our analysis accounts for various known instability phenomena in a unified way and leads to several new results three of which are as follows 1 dissipativity does not ensure stability when three or more formulas are concatenated at a boundary or internal interface 2 algebraic gks instabilities can be converted by a second boundary to exponential instabilities only when an infinite numerical reflection coefficient is present 3 gks stability and p stability can be established in certain problems by showing that the numerical reflection coefficient matrices have norm less than one

absorbing boundary conditions for the discretization schemes of the one dimensional wave equation when computing a partial differential equation it is often necessary to introduce artificial boundaries here we explain a systematic method to obtain boundary conditions for the wave equation in one dimension fitting to the discretization scheme and stable moreover we give error estimates on the reflected part

implicit methods of second order accuracy for the euler equations this paper presents a study of noniterative implicit finite difference methods for hyperbolic systems new space centered methods involving two time levels are considered an analysis is made of various properties such as solvability stability dissipation dispersion and efficient solution of the algebraic systems the computation of shock waves with a cfl number larger than the unity is discussed unconditional stability results are proved for a case having several space variables accurate solutions of the euler equations are obtained that offer major reductions in computing costs over explicit methods

quantum mechanical path integrals with wiener measures for all polynomial hamiltonians we construct arbitrary matrix elements of the quantum evolution operator for a wide class of self adjoint canonical hamiltonians including those which are polynomial in the heisenberg operators as the limit of well defined path integrals involving wiener measure on phase space as the diffusion constant diverges a related construction achieves a similar result for an arbitrary spin hamiltonian

composite overlapping meshes for the solution of partial differential equations abstract we discuss the generation of curvilinear composite overlapping grids and the numerical solution of partial differential equations on them a composite overlapping grid consists of a set of curvilinear component grids that cover a region and overlap where they meet continuity conditions interpolation are imposed at the overlapping boundaries the principal advantage of composite grids is in the generation of grids for regions with complicated geometries the grid construction program cmpgrd is used to create composite grids with any number of component grids we describe some techniques for the solution of elliptic and time dependent pdes on composite meshes applications to the solution of the compressible navier stokes equations are presented

feynman path integrals for polynomially growing potentials abstract a general class of infinite dimensional oscillatory integrals with polynomially growing phase functions is studied a representation formula of the parseval type is proved as well as a formula giving the integrals in terms of analytically continued absolutely convergent integrals these results are applied to provide a rigorous feynman path integral representation for the solution of the time dependent schrodinger equation with a quartic anharmonic potential the borel summability of the asymptotic expansion of the solution in power series of the coupling constant is also proved

an analysis of two step time discretizations in the solution of the linearized shallow water equations abstract a fourier analysis for evaluating the accuracy of finite element methods which solve the linearized shallow water equations is extended to include group velocity the technique is first applied to the selection of a spatial discretization and then assuming a specific finite element discretization to finding the most accurate two step time stepping method

wiener and poisson process regularization for coherent state path integrals by introducing a suitable continuous time regularization into a formal phase space path integral it follows that the propagator is given by the limit of well defined functional integrals involving standard stochastic processes and their associated probability measures such regularizations require pinning of both coordinate and momenta variables and automatically lead to coherent state representations it is found that each standard independent increment process involving a superposition of a wiener and a poisson process is associated with a specific generally non gaussian fiducial vector with which the coherent states are defined

efficient parallel algorithms for parabolic problems domain decomposition algorithms for parallel numerical solution of parabolic equations are studied for steady state or slow unsteady computation implicit schemes are used in order to march with large time steps parallelization is realized by approximating interface values using explicit computation various techniques are examined including a multistep second order explicit scheme and a one step high order scheme we show that the resulting schemes are of second order global accuracy in space and stable in the sense of osher or in l infty they are optimized with respect to the parallel efficiency

coherent state path integral calculation of the wigner function we consider a set of operators 1 n with diagonal representatives p n in the space of generalized coherent states n d n p n nn we regularize the coherent state path integral as a limit of a sequence of averages l over polygonal paths with l vertices n1 l the distribution of the path centroid 1 l l 1lp nl tends to the wigner function w x the joint distribution for the operators w x lim l n x l this result is proved in the case where the hamiltonian commutes with the wigner function is non positive if the dominant paths with path centroid in a certain region have berry phases close to odd multiples of for finite l the path centroid distribution is a wigner function convolved with a gaussian of variance inversely proportional to l the results are illustrated by numerical calculations of the spin wigner function from su 2 coherent states the relevance to the quantum monte carlo sign problem is also discussed

analytic representations in quantum mechanics various euclidean hyperbolic and elliptic analytic representations are introduced and relations among them are discussed the bargmann analytic representation in the complex plane is considered and its relation to other phase space methods for the harmonic oscillator is reviewed the general theory that relates the growth of analytic functions with the density of their zeros is applied to bargmann functions and it leads to theorems on the completeness of sequences of glauber coherent states two hyperbolic analytic representations in the unit disc based on su 1 1 coherent states and also on phase states are introduced a third analytic representation in the complex plane based on barut girardello states is also considered and transformations which relate it to the other ones are studied in the case of systems with finite dimensional hilbert space an elliptic analytic representation in the extended complex plane and also another analytic representation based on theta functions are introduced the berezin formalism in the euclidean hyperbolic and elliptic cases is discussed contour analytic representations in these three cases are also presented

steady shock tracking and newton s method applied to one dimensional duct flow abstract a new computational approach combining shock tracking and newton s method is applied to steady one dimensional flow through a variable area duct on a transformed computational grid where the shock is fixed the physical shock location appears explicitly as an unknown in a set of finite difference equations and is coupled to the other unknowns the space time characteristics for the associated time dependent problem are used in formulating the boundary conditions the resulting system is solved by newton s method the computed results agree very well with an exact solution and the newton iterates converge rapidly in comparison to some explicit shock capturing time asymptotic methods

corrections to the coherent state path integral comments upon a speculation of l s schulman intuitively the feynman path integral corresponds to a weighted sum over classical paths an interpretation that fails for the phase space path integral to address the question of whether there exists a path integral expression conforming to a sum over paths in phase space an examination of the discrete coherent state path integral cspi is undertaken via an alternative formulation of the cspi it is shown that the coherent state action for a broad class hamiltonians can be transformed from the variables q p to q q for these hamiltonians such a transformation along with the inclusion of all terms o e zi zi 1 yields an expression which for finite e can be interpreted as a sum over classical paths with gaussian weight the numerical evaluation of this expression through importance sampling monte carlo is demonstrated

an accuracy analysis of boundary conditions for the forced shallow water equations the accuracy of numerical boundary conditions for the linearized one dimensional shallow water equations is determined by extending the dispersion fourier analysis originally presented by c k chu and a sereny j comput phys 15 476 1974 accuracy is measured by calculating steady state amplitudes of incoming and outgoing numerical waves at a boundary as functions of a forcing frequency radiating closed and forced radiating boundary conditions are studied in combination with two numerical schemes the richardson sielecki explicit finite difference scheme and the galerkin finite element method with piecewise linear basis functions and crank nicolson time stepping contamination of the finite element solution with short waves is seen to vary with the choice of extraneous boundary conditions an example of l n trefethen s j comput phys 49 199 1983 interpretation of the b gustafsson h kreiss and a sundstrom math comput 26 649 1972 instability is also given for the finite element method

the gunn effect instability of the steady state and stability of the solitary wave in long extrinsic semiconductors a linear stability analysis of the stationary solution of a one dimensional drift diffusion model used to describe the gunn effect in gaas is performed it is shown that for long semiconductor samples under do voltage bias conditions and small diffusivity the steady state may lose stability via a hopf bifurcation in the limit of infinitely long samples there is a quasicontinuum of oscillatory modes of the equation linearized about the steady state that a acquire positive real part for voltages larger than a certain critical value the linear stability of the solitary wave characteristic of the gunn effect is proved for an idealized electron velocity curve in the zero diffusion limit

artificial boundary conditions for computation of oscillating external flows in this paper we propose a new technique for the numerical treatment of external flow problems with oscillatory behavior of the solution in time specifically we consider the case of unbounded compressible viscous plane flow past a finite body airfoil oscillations of the flow in time may be caused for example by the time periodic injection of fluid into the boundary layer which in accordance with experimental data may essentially increase the performance of the airfoil to conduct the actual computations we have to somehow restrict the original unbounded domain that is to introduce an artificial external boundary and to further consider only a finite computational domain consequently we will need to formulate some artificial boundary conditions abcs at the introduced external boundary the abcs we are aiming to obtain must meet the following fundamental requirement one should be able to uniquely complement the solution calculated inside the finite computational domain to its infinite exterior so that the original problem is solved within the desired accuracy our construction of such abcs for oscillating flows is based on an essential assumption the navier stokes equations can be linearized in the far field against the free stream background to actually compute the abcs we represent the far field solution as a fourier series in time and then apply the difference potentials method dpm of v s ryaben kii this paper contains a general theoretical description of the algorithm for setting the dpm based abcs for time periodic external flows based on our experience in implementing analogous abcs for steady state problems a simpler case we expect that these boundary conditions will become an effective tool for constructing robust numerical methods to calculate oscillatory flows

the klauder daubechies construction of the phase space path integral and the harmonic oscillator the canonical operator quantisation formulation corresponding to the klauder daubechies construction of the phase space path integral is considered this formulation is explicitly applied and solved in the case of the harmonic oscillator thereby illustrating in a manner complementary to klauder and daubechies original work some of the promising features offered by their construction of a quantum dynamics the klauder daubechies functional integral involves a regularisation parameter eventually taken to vanish which defines a new physical time scale when extrapolated to the field theory context besides providing a new regularisation of short distance divergences keeping a finite value for that time scale offers some tantalising prospects when it comes to strong gravitational quantum systems comment 18 pages

efficient parallel method for implicit upwind schemes approximating the euler equations in gas dynamics a grid overlapping parallel method for some three point implicit schemes has been proposed by wu and zou j comput phys 157 2000 2 in this paper we conduct a theoretical analysis of the convergence speed to steady state for this parallel method when multipoint one sided upwind schemes are used the theoretical parallel efficiency is found to be near 100 for the totally time lagging interface treatment numerical experiments for compressible flows are conducted to confirm the linear theory moreover numerical experiments will also be demonstrated for schemes which are not completely upwind