two equation turbulence closure model for wall bounded and free shear flows the model can be used for both wall bounded and free shear flows using one set of model constants

high resolution schemes for conservation laws with locally varying time steps we develop upwind methods which use limited high resolution corrections in the spatial discretization and local time stepping for forward euler and second order time discretizations l infty stability is proven for both time stepping schemes for problems in one space dimension these methods are restricted by a local cfl condition rather than the traditional global cfl condition allowing local time refinement to be coupled with local spatial refinement numerical evidence demonstrates the stability and accuracy of the methods for problems in both one and two space dimensions

an improved k ω φ α turbulence model applied to near wall separated and impinging jet flows and heat transfer abstract a turbulence model based on elliptic blending concept referred to as improved k model compared against the original k model developed previously is developed and verified this model consists of four governing equations among them the k and equations are based on the wilcox s k model with some modifications and improvements according to the original k model and the and equations are extracted from the original k model directly without any change the improved k model is applied to near wall separated and impinging jet flows and convective heat transfer i e the 2d fully developed channel flow the 2d backward facing step flow the 2d impinging jet flow and the convective heat transfer in the 2d fully developed channel flow and the 2d impinging jet flow the computational results are compared with available dns and experimental data and also to those computed using the original k model and the popular menter s sst k model it is shown that the improved k model has better numerical stability higher computational efficiency and more concise form than the original k model in addition compared with the original k model the improved k model can yield similar velocity profiles in the fully developed channel flow and step flow and friction and pressure coefficients in the step flow and very close temperature profiles in the fully developed channel flow moreover it shows significant improvements on the predictions for the fluid flow and heat transfer in the impinging jet flow as a whole the improved k model predicts better results than both of the original k model and the sst k model

an explicit two step method exact for the scalar test equation y λy an explicit two step method exact for the scalar test equation y y re 0 is presented in this paper it is exponentially fitted l stable thus a stable and of order 2 with a new set of vector computations we also extend directly the method to systems of ordinary differential equations the numerical experiments demonstrate that this explicit two step method is suitable for stiff systems

an a posteriori a priori analysis of multiscale operator splitting in this paper we analyze a multiscale operator splitting method for solving systems of ordinary differential equations such as those that result upon space discretization of a reaction diffusion equation our goal is to analyze and accurately estimate the error of the numerical solution including the effects of any instabilities that can result from multiscale operator splitting we present both an a priori error analysis and a new type of hybrid a priori a posteriori error analysis for an operator splitting discontinuous galerkin finite element method both analyses clearly distinguish between the effects of the operator splitting and the discretization of each component of the decomposed problem the hybrid analysis has the form of a computable a posteriori leading order expression and a provably higher order a priori expression the hybrid analysis takes into account the fact that the adjoint problems for the original problem and a multiscale operator splitting discretization differ in significant ways in particular this provides the means to monitor global instabilities that can arise from operator splitting

a posteriori analysis and adaptive error control for multiscale operator decomposition solution of elliptic systems i triangular systems this paper we perform an a posteriori error analysis of a multiscale operator decomposition finite element method for the solution of a system of coupled elliptic problems the goal is to compute accurate error estimates that account for the effects arising from multiscale discretization via operator decomposition our approach to error estimation is based on a well known a posteriori analysis involving variational analysis residuals and the generalized green s function our method utilizes adjoint problems to deal with several new features arising from the multiscale operator decomposition in part i of this paper we focus on the propagation of errors arising from the solution of one component to another and the transfer of information between different representations of solution components we also devise an adaptive discretization strategy based on the error estimates that specifically controls the effects arising from operator decomposition in part ii of this paper we address issues related to the iterative solution of a fully coupled nonlinear system

adaptive finite element solution of multiscale pde ode systems we consider adaptive finite element methods for a multiscale system consisting of a macroscale model comprising a system of reaction diffusion partial differential equations coupled to a microscale

from quantum cellular automata to quantum lattice gases a natural architecture for nanoscale quantum computation is that of a quantum cellular automaton motivated by this observation we begin an investigation of exactly unitary cellular automata after proving that there can be no nontrivial homogeneous local unitary scalar cellular automaton in one dimension we weaken the homogeneity condition and show that there are nontrivial exactly unitary partitioning cellular automata we find a one parameter family of evolution rules which are best interpreted as those for a one particle quantum automaton this model is naturally reformulated as a two component cellular automaton which we demonstrate to limit to the dirac equation we describe two generalizations of this automaton the second of which to multiple interacting particles is the correct definition of a quantum lattice gas

multi adaptive galerkin methods for odes ii implementation and applications continuing the discussion of the multi adaptive galerkin methods mathrm mcg q and mathrm mdg q presented in a logg siam j sci comput 24 2003 pp 1879 1902 we present adaptive algorithms for global error control iterative solution methods for the discrete equations features of the implementation tanganyika and computational results for a variety of odes examples include the lorenz system the solar system and a number of time dependent pdes

discontinuous polynomial approximations in the theory of one step hybrid and multistep methods for nonlinear ordinary differential equations this paper studies the approximation of the solution of nonlinear ordinary differen tial equations by discontinuous piecewise polynomials of degree k and traces at the nodes of discretization a mesh dependent variational framework underlying this discontinuous ap proximation is derived several families of one step hybrid and multistep schemes are obtained it is shown that the convergence rate in the l2 norm is k 1 the nodal conver gence rate can go up to 2 k 2 depending on the particular scheme under consideration the mesh dependent variational framework introduced here is of special interest in the approxi mation of the solution of optimal control problems governed by differential equations 1 introduction the object of this paper is the study of discontinuous piecewise polynomial approximations to the solution of systems of nonlinear ordinary dif

stability restrictions on time stepsize for numerical integration of first order partial differential equations mathematical models described by partial differential equations appear often when different phenomena related to atmospheric transport for example advection and diffusion processes are studied truncated fourier series can be used in the discretization of the space derivatives resulting in a pseudospectral method in this way the partial differential equation is transformed into a system of ordinary differential equations this system is normally solved by so called step by step integration methods the stability properties of these methods are studied some bounds for the time stepsize are derived several formulae and predictor corrector schemes with large stability intervals on the imaginary axis are constructed numerical experiments with eight time integration algorithms are carried out some recommendations concerning the choice of the time integration algorithms in three different situations are given it is emphasized that in a package for the solution of partial differential equations describing transport processes in the atmospheric environment one should have several time integration algorithms each of which can be chosen optionally finally the possibility of using variable stepsize variable formula time integration algorithms is briefly discussed

time point relaxation runge kutta methods for ordinary differential equations bellen a z jackiewicz and m zennaro time point relaxation runge kutta methods for ordinary differential equations journal of computational and applied mathematics 45 1993 121 137 we investigate convergence order and stability properties of time point relaxation runge kutta methods for systems of ordinary differential equations these methods can be implemented in gauss jacobi or gaussseidel modes denoted by trgjrk k or trgsrk k respectively where k stands for the number of picard lindelof iterations as k f 0 these modes tend to the same one step method for ordinary differential equations called diagonal split runge kutta dsrk method it is proved that these methods are convergent with order min k p where p is the order of the underlying runge kutta method recurrence relations resulting from application of trgjrk k trgsrk k and dsrk methods to the two dimensional test system u au pu u pu au t 3 0 where a and p are real parameters are derived and stability regions in the h p plane are plotted for some methods using a variant of the boundary locus method in most cases stability regions increase as the number of picard lindeldf iterations k becomes larger

discontinuous galerkin methods for ordinary differential equations a class of galerkin methods derived from discontinuous piecewise polynomial spaces is analyzed for polynomials of degree k these methods lead to a family of one step schemes generating approximations up to order 2k 2 for the solution of an ordinary differential equation

conditional strategies in iterated quantum games abstract iterated bipartite quantum games are implemented in terms of the discrete time quantum walk on the line our proposal allows for conditional strategies as two rational agents make a choice from a restricted set of two qubit unitary operations we discuss how several classical strategies are related to families of quantum strategies a quantum version of the well known prisoner s dilemma bipartite game in which both players use mixed strategies is presented as a specific example

efficient tests for equivalence of hidden markov processes and quantum random walks while two hidden markov process hmp resp quantum random walk qrw parametrizations can differ from one another the stochastic processes arising from them can be equivalent here a polynomial time algorithm is presented which can determine equivalence of two hmp parametrizations m1 m2 resp two qrw parametrizations q1 q2 in time o max n1 n2 4 where n1 n2 are the number of hidden states in m1 m2 resp the dimension of the state spaces associated with q1 q2 and is the set of output symbols previously avail able algorithms for testing equivalence of hmps were exponential in the number of hidden states in case of qrws algorithms for testing equivalence had not yet been presented the core subrou tines of this algorithm can also be used to efficiently test hidden markov processes and quantum random walks for ergodicity

two low accuracy methods for stiff systems two low accuracy explicit one step methods for stiff ordinary differential equations are extended directly to solve systems of equations some defects of the component form of these methods are avoided to perform these a new set of vector computations are introduced some numerical experiments are presented to show the superiority of the new methods

improving the predictive capability of turbulence models using evidence theory when turbulence models are used in the simulation of a flow for which experimental results do not exist there is as yet no reliable procedure for choosing a model or for quantifying the uncertainty of the results the present study develops an approach based on evidence theory for the resolution of these issues the results of turbulence model validations and of predictions of those models are fused to determine the intervals in which a flow quantity is likely to fall and a measure of confidence for each interval the approach is tested in a subsonic flow around the rae 2822 airfoil nomenclature ij ij ij ab c matrix elements c airfoil chord k turbulent kinetic energy m basic probability assignment m mach number p proposition probability s proposition support u mean velocity e u experimental mean velocity or error boundaries if an experimental error range is available m

the relation between flux vector splitting and parabolized schemes abstract the relationship between pns and thin layer navier stokes algorithms is used to develop traditional as well as new pns procedures the use of characteristics based flux vector splitting gives rise to a parabolized system that is based on the predominant physics of the flow while pressure gradient based flux vector splitting is shown to give the traditional parabolized scheme of vigneron comparisons with tlns results show the characteristics based pns system gives results that are at least as accurate as the more traditional pressure gradient split pns system the use of a safety factor in the pressure gradient splitting is shown to cause inaccuracies and should be avoided the interpretation of pns procedures as the first sweep of a tlns adi procedure also suggests an obvious global pressure iteration method that is mathematically well posed and hence leads to an efficient rapidly converging global iteration procedure

computation of compression ramp flow with a cross diffusion modified k epsilon model we propose a new k e model with a cross diffusion term that can be used to analyze turbulent nonequilibrium flows

construction of a multirate rodas method for stiff odes multirate time stepping is a numerical technique for efficiently solving large scale ordinary differential equations odes with widely different time scales localized over the components this technique enables one to use large time steps for slowly varying components and small steps for rapidly varying ones multirate methods found in the literature are normally of low order one or two focusing on stiff odes in this paper we discuss the construction of a multirate method based on the fourth order rodas method special attention is paid to the treatment of the refinement interfaces with regard to the choice of the interpolant and the occurrence of order reduction for stiff linear systems containing a stiff source term we propose modifications for the treatment of the source term which overcome order reduction originating from such terms and which we can implement in our multirate method

approximate counting uniform generation and rapidly mixing markov chains the paper studies effective approximate solutions to combinatorial counting and uniform generation problems using a technique based on the simulation of ergodic markov chains it is shown that for self reducible structures almost uniform generation is possible in polynomial time provided only that randomised approximate counting to within some arbitrary polynomial factor is possible in polynomial time it follows that for self reducible structures polynomial time randomised algorithms for counting to within factors of the form 1 n are available either for all fl e r or for no fi e r a substantial part of the paper is devoted to investigating the rate of convergence of finite ergodic markov chains and a simple but powerful characterisation of rapid convergence for a broad class of chains based on a structural property of the underlying graph is established finally the general techniques of the paper are used to derive an almost uniform generation procedure for labelled graphs with a given degree sequence which is valid over a much wider range of degrees than previous methods this in turn leads to randomised approximate counting algorithms for these graphs with very good

comparison of the asymptotic stability properties for two multirate strategies this paper contains a comparison of the asymptotic stability properties for two multirate strategies for each strategy the asymptotic stability regions are presented for a 2x2 test problem and the differences between the results are discussed the considered multirate schemes use rosenbrock type methods as the main time integration method and have one level of temporal local refinement some remarks on the relevance of the results for 2x2 test problems are presented

a posteriori analysis of a multirate numerical method for ordinary differential equations in this paper we analyze a multirate time integration method for systems of ordinary differential equations that present significantly different scales within the components of the model the main purpose of this paper is to present a hybrid a priori a posteriori error analysis that accounts for the effects of projections between the coarse and fine scale discretizations the use of only a finite number of iterations in the iterative solution of the discrete equations the numerical error arising in the solution of each component and the effects on stability arising from the multirate solution the hybrid estimate has the form of a computable a posteriori leading order expression and a provably higher order a priori expression we support this estimate by an a priori convergence analysis we present several examples illustrating the accuracy of multirate integration schemes and the accuracy of the a posteriori estimate

a posteriori error bounds and global error control for approximation of ordinary differential equations the author analyzes a finite element method for the integration of initial value problems in ordinary differential equations general and contractive problems are treated and quasi optimal a priori and a posteriori error bounds obtained in each case in particular good results are obtained for a class of stiff dissipative problems these results are used to construct a rigorous and robust theory of global error control the author also derives an asymptotic error estimate that is used in a discussion of the behavior of the error in conclusion the properties of the error control are exhibited in a series of numerical experiments

numerical solution of ordinary differential equations is there anything left to do two decades ago many people thought that there was very little left to occupy the researcher in the numerical initial value problem for ordinary differential equations but there has since been an enormous increase in the effort devoted to this problem and related software is everything finally done so we can turn to more difficult areas this paper examines the development of numerical solution techniques from the identification of a problem to the never final preparation of automatic codes for the solution of classes of similar problems it discusses a number of ode problems that are only a part of the way along this path of development these problems include ones with highly oscillatory solutions ones with frequent discontinuities and ones in which very little accuracy is needed and which should be integrated at low cost there is a spectrum of problems from ones that can now be solved using very robust software to ones that we still do not know how to solve effectively the paper then surveys s

strengths and weaknesses of quantum computing recently a great deal of attention has been focused on quantum computation following a sequence of results bernstein and vazirani in proc 25th annual acm symposium theory comput 1993 pp 11 20 siam j comput 26 1997 pp 1277 1339 simon in proc 35th annual ieee symposium foundations comput sci 1994 pp 116 123 siam j comput 26 1997 pp 1340 1349 shor in proc 35th annual ieee symposium foundations comput sci 1994 pp 124 134 suggesting that quantum computers are more powerful than classical probabilistic computers following shor s result that factoring and the extraction of discrete logarithms are both solvable in quantum polynomial time it is natural to ask whether all of np can be efficiently solved in quantum polynomial time in this paper we address this question by proving that relative to an oracle chosen uniformly at random with probability 1 the class np cannot be solved on a quantum turing machine qtm in time o 2 n 2 we also show that relative to a permutation oracle chosen uniformly at random with probability 1 the class np cap conp cannot be solved on a qtm in time o 2 n 3 the former bound is tight since recent work of grover in it proc 28 th annual acm symposium theory comput 1996 shows how to accept the class np relative to any oracle on a quantum computer in time o 2 n 2

conservation errors and convergence characteristics of iterative space marching algorithms the new iterative space marching algorithms for numerical solution of the parabolized navier stokes equations are critically examined it is shown by analysis and numerical examples that employing parabolized flux difference splitting in the marching direction can lead to serious conservation errors even though a finite volume formulation is employed schemes employing parabolized flux vector splitting in the marching direction are shown to be conservative the structure of the iterative algorithm is examined to determine what factors play important roles in the convergence of the local iteration

stability of runge kutta methods used in modular integration a pair of runge kutta methods is applied to a system of ordinary differential equations in a modular fashion known as time point relaxation for a class of two by two linear systems with constant coefficients the concept of coupling stability is introduced this is one way of measuring the loss of stability due to the decoupling of the system into two scalar subsystems the strategy for handling the interactions between the two modules is controlled by a parameter where certain choices of the parameter correspond to the gauss jacobi and gauss seidel method results are obtained for the case when runge kutta methods in general are applied with only one iteration per time step the case with several iterations is investigated for the well known methods

discrete quantum walks hit exponentially faster this paper addresses the question what processes take polynomial time on a quantum computer that require exponential time classically we show that the hitting time of the discrete time quantum walk on the n bit hypercube from one corner to its opposite is polynomial in n this gives the first exponential quantum classical gap in the hitting time of discrete quantum walks we provide the basic framework for quantum hitting time and give two alternative definitions to set the ground for its study on general graphs we outline a possible application to sequential packet routing

quantum repeated games revisited we present a scheme for playing quantum repeated 2 2 games based on marinatto and weber s approach to quantum games as a potential application we study the twice repeated prisoner s dilemma game we show that results not available in the classical game can be obtained when the game is played in the quantum way before we present our idea we comment on the previous scheme of playing quantum repeated games proposed by iqbal and toor we point out the drawbacks that make their results unacceptable

implicit solution method for incompressible navier stokes equations including two layer k tau turbulence model the two dimensional incompressible navier stokes equations including a low reynolds number two layer k turbulence model are solved by an implicit time stepping routine using the method of artificial compressibility the two layer model uses a transport equation for the turbulent kinetic energy k and a new algebraic relationship for the turbulent time scale near the wall but reverts to the two equation k turbulence model in the bulk of the flow away from the wall the algebraic relationship for the turbulent time scale and the eddy viscosity damping function f are validated by direct numerical simulation data and asymptotic analysis of near wall turbulence a fifth order upwind biased differencing scheme is used to discretize the convective and pressure terms and second order central differences are employed for other spatial derivatives the nonlinear equations are solved using the preconditioned generalized minimal residual technique in conjunction with numerical linearization a ld 1 u factorization of the approximate jacobian matrix is used as preconditioning matrix

formulas for modular integration of systems of ode s abstract formulas are presented for modular integration of systems of first or second order ordinary differential equations which have been separated into subsystems using these formulas each subsystem or module may be integrated essentially independently using an appropriate processor or specialized integration technique included is a general mathematical procedure for devising formulas for modular integration depending on the order of accuracy required and other considerations

the accurate numerical solution of highly oscillatory ordinary differential equations we consider systems of ordinary differential equations with rapidly oscillating solutions conventional numerical methods require an excessively small time step t 0 eh where h is the step size necessary for the resolution of a smooth function of t and 1 e measures the size of the large eigenvalues of the system s jacobian for the linear problem with well separated large eigenvalues we introduce smooth transformations which lead to the separation of the time scales and computation with a large time step t 0 h for more general problems including systems with weak polynomial nonlinearities we develop an asymptotic theory which leads to expansions whose terms are suitable for numerical approximation resonances can be detected and resolved often with a large time step t 0 h passage through resonance in nonautonomous systems can be resolved by a moderate time step t 0 eh

unveiling and exemplifying the unitary equivalence of discrete time quantum walk models the two major discrete time formulations for quantum walks coined and scattering are unitarily equivalent for arbitrary position dependent transition amplitudes and any topology andrade et al 2009 phys rev a 80 052301 although the proof explicitly describes the mapping obtention its high technicality may hinder relevant physical aspects involved in the equivalence discussing concrete examples the most general constructions for the line square and honeycomb lattices here we unveil the similarities and differences of these two versions of quantum walks we moreover show how to derive the dynamics of one from the other by means of proper projections we perform calculations for different probability amplitudes such as hadamard grover discrete fourier transform and the uncommon in the area but interesting discrete hartley transform comparing the evolutions our study illustrates the models interplay an important issue for implementations and applications of such systems

a multirate time integrator for regularized stokeslets the method of regularized stokeslets is a numerical approach to approximating solutions of fluid structure interaction problems in the stokes regime regularized stokeslets are fundamental solutions to the stokes equations with a regularized point force term that are used to represent forces generated by a rigid or elastic object interacting with the fluid due to the linearity of the stokes equations the velocity at any point in the fluid can be computed by summing the contributions of regularized stokeslets and the time evolution of positions can be computed using standard methods for ordinary differential equations rigid or elastic objects in the flow are usually treated as immersed boundaries represented by a collection of regularized stokeslets coupled together by virtual springs which determine the forces exerted by the boundary in the fluid for problems with boundaries modeled by springs with large spring constants the resulting ordinary differential equations become stiff and hence the time step for explicit time integration methods is severely constrained unfortunately the use of standard implicit time integration methods for the method of regularized stokeslets requires the solution of dense nonlinear systems of equations for many relevant problems here an alternate strategy using an explicit multirate time integration scheme based on spectral deferred corrections is incorporated that in many cases can significantly decrease the computational cost of the method the multirate methods are higher order methods that treat different portions of the ode explicitly with different time steps depending on the stiffness of each component numerical examples on two nontrivial three dimensional problems demonstrate the increased efficiency of the multi explicit approach with no significant increase in numerical error

a posteriori error estimation and adaptive mesh refinement for a multiscale operator decomposition approach to fluid solid heat transfer we analyze a multiscale operator decomposition finite element method for a conjugate heat transfer problem consisting of a fluid and a solid coupled through a common boundary we derive accurate a posteriori error estimates that account for all sources of error and in particular the transfer of error between fluid and solid domains we use these estimates to guide adaptive mesh refinement in addition we provide compelling numerical evidence that the order of convergence of the operator decomposition method is limited by the accuracy of the transferred gradient information and adapt a so called boundary flux recovery method developed for elliptic problems in order to regain the optimal order of accuracy in an efficient manner in an appendix we provide an argument that explains the numerical results provided sufficient smoothness is assumed

application of the eisert wilkens lewenstein quantum game scheme to decision problems with imperfect recall we investigate implementations of the eisert wilkens lewenstein ewl scheme of playing quantum games beyond strategic games the scope of our research is decision problems i e one player extensive games the research is based on the examination of their features when the decision problems are carried out via the ewl protocol we prove that unitary operators can be adapted to play the role of strategies in decision problems with imperfect recall furthermore we prove that unitary operators provide the decision maker with possibilities that are inaccessible for classical strategies

a self adjusting multirate algorithm for robust time discretization of partial differential equations abstract we show the distinctive potential advantages of a self adjusting multirate method based on diagonally implicit solvers for the robust time discretization of partial differential equations the properties of the specific ode methods considered are reviewed with special focus on the tr bdf2 solver a general expression for the stability function of a generic one stage multirate method is derived which allows to study numerically the stability properties of the proposed algorithm in a number of examples relevant for applications several numerical experiments aimed at the time discretization of hyperbolic partial differential equations demonstrate the efficiency and accuracy of the resulting approach

a runge kutta method with stepsize control for separated systems of first order odes abstract this paper is concerned with a method developed earlier that may be used to solve a system of first order odes separated into two subsystems each system may be integrated essentially independently of the other one a runge kutta technique with automatic stepsize control is developed for the method taking both truncation and separation errors into account the paper also provides a proof of the existence of a solution to the separated problem

quantum dating market abstract we consider the dating market decision problem under the quantum mechanics point of view quantum states whose associated amplitudes are modified by men strategies are used to represent women the grover quantum search algorithm is used as a playing strategy success is more frequently obtained by playing quantum than playing classic

multi adaptive galerkin methods for odes i we present multi adaptive versions of the standard continuous and discontinuous galerkin methods for odes taking adaptivity one step further we allow for individual time steps order and quadrature so that in particular each individual component has its own time step sequence this paper contains a description of the methods an analysis of their basic properties and a posteriori error analysis in the accompanying paper a logg siam j sci comput submitted we present adaptive algorithms for time stepping and global error control based on the results of the current paper

implicit flux split schemes for the euler equations progress in the development of implicit algorithms for the euler equations using the flux vector splitting method is described comparisons of the relative efficiency of relaxation and spatially split approximately factored methods on a vector processor for transonic and supersonic twodimensional channel flows are made a hybrid threedimensional algorithm is developed that uses relaxation in one coordinate direction and approximate factorization in the crossflow plane the scheme is completely vectorizable and recovers conventional space marching schemes for fully supersonic flows the method is applied to a forebody shape in supersonic flow with an embedded pocket of subsonic flow

a random polynomial time algorithm for approximating the volume of convex bodies a randomized polynomial time algorithm for approximating the volume of a convex body k in n dimensional euclidean space is presented the proof of correctness of the algorithm relies on recent theory of rapidly mixing markov chains and isoperimetric inequalities to show that a certain random walk can be used to sample nearly uniformly from within k

a multirate w method for electrical networks in state space formulation subunits of coupled technical systems typically behave on differing time scales which are often separated by several orders of magnitude an ordinary integration scheme is limited by the fastest changing component whereas so called multirate methods employ an inherent step size for each subsystem to exploit these settings however the realization of the coupling terms is crucial for any convergence thus the approach to return to one step methods within the multirate concept is promising this paper introduces the multirate w method for ordinary differential equations and gives a theoretical discussion in the context of partitioned rosenbrock wanner methods finally the matlab implementation of an embedded scheme of order 3 2 is tested for a multirate version of prothero robinson s equation and the inverter chain benchmark

bounds for mixing time of quantum walks on finite graphs several inequalities are proved for the mixing time of discrete time quantum walks on finite graphs the mixing time is defined differently than in aharonov et al 2002 proc 33rd stoc 2001 new york acm pp 50 9 arxiv quant ph 0012090v2 and it is found that for particular examples of walks on a cycle a hypercube and a complete graph quantum walks provide no speedup in mixing over the classical counterparts in addition non unitary quantum walks i e walks with decoherence are considered and a criterion for their convergence to the unique stationary distribution is derived

computing general companion matrices and stability regions of multirate methods we obtain the necessary and sufficient conditions that guarantee the absolute stability of semi implicit multirate linear discretizations of 2 2 differential systems this result is based on the construction of a general companion matrix that characterizes the class of multirate discretizations built from linear and zero order interpolation these results are numerically verified for particular examples whose stability regions are graphically displayed copyright 2004 john wiley sons ltd

wall normal free reynolds stress model for rotating flows applied to turbomachinery a recently developed near wall wall normal free reynolds stress model is extended and applied to the computation of transonic three dimensional e ows in turbomachinery rotors with tip clearance the reynolds stress model used is completely independent of the distance from the wall and of the normal to the wall direction this is achieved by using a pseudonormal direction dee ned by the gradients of turbulence length scale and anisotropy tensor invariants in the pressure strain echo terms the effects of rotation are included through theexact coriolis termsin the reynolds stress transport equations and through the isotropization of absolute e ow production model used for the rapid pressure strain terms the model is initially validated by comparison with measurements in rotating fully developed plane channel e ows computational results obtained with the proposed reynolds stress model are compared with measurements and with k computations for various operating points of the nasa 37 rotor using a 3 10 6 multiblock computational grid with 41 radial stations within the tip clearance gap the proposed model substantially improves the agreement with measurements compared to existing algebraic and two equation models

staggered finite volume scheme for solving cascade flow with a k omega turbulence model a k turbulence model by wilcox is applied to cascade flow calculations a staggered finite volume scheme is proposed to solve the compressible reynolds averaged navier stokes equations and the k equations are solved on staggered control volumes with k and defined at the cell vertices of the original grid by use of this combination of the cell centered and cell vertex schemes the method maintains a small stencil for all diffusion terms and closely couples the navier stokes and k equations

recurrence and polya number of quantum walks we analyze the recurrence probability polya number for d dimensional unbiased quantum walks a sufficient condition for a quantum walk to be recurrent is derived as a by product we find a simple criterion for localization of quantum walks in contrast with classical walks where the polya number is characteristic for the given dimension the recurrence probability of a quantum walk depends in general on the topology of the walk choice of the coin and the initial state this allows us to change the character of the quantum walk from recurrent to transient by altering the initial state

explicit multi time stepping methods for convection dominated flow problems abstract in this paper we introduce a multi time stepping method for convection dominated flow problems the idea behind this method and its applications will be explained and the stability and accuracy of the method will be studied by using a one dimensional model problem the convection diffusion equation here the method is applied to a uniform two block grid we will prove that local stability conditions in the blocks are sufficient for global stability of the multi time stepping scheme under certain conditions some numerical experiments are performed to investigate cases beyond the theory we will show that in case of rung kutta 3 time integration extremely large ratios between mesh widths and time steps may be used without affecting the stability of the multi time stepping method conditions for time accurate behaviour are also investigated by means of numerical experiments

a posteriori analysis and improved accuracy for an operator decomposition solution of a conjugate heat transfer problem we consider the accuracy of an operator decomposition finite element method for a conjugate heat transfer problem consisting of two materials coupled through a common boundary we derive accurate a posteriori error estimates that account for the transfer of error between components of the operator decomposition method as well as the differences between the adjoints of the full problem and the discrete iterative system we use these estimates to guide adaptive mesh refinement in addition we address a loss of order of convergence that results from the decomposition and show that the order of convergence is limited by the accuracy of the transferred gradient information we employ a boundary flux recovery method to regain the expected order of accuracy in an efficient manner

numerical approximations to nonlinear conservation laws with locally varying time and space grids an explicit time differencing technique is introduced to approximate nonlinear conservation laws this differencing technique links together an arbitrary number of space regimes containing fine and coarse time increments previous stability requirements i e the cfl condition placed a global bound on the size of the time increments for scalar monotone approximations in one space dimension using this variable step time differencing convergence to the correct physical solution is proven given only a local cfl condition

n person quantum russian roulette abstract we generalize the concept of quantum russian roulette introduced in schmidt and da silva 2013 our model coincides with the previous one in the case of the game with two players and gives the suitable quantum description for any finite number of players as an example we provide a detailed study of the three and four person case

disordered quantum walks in one lattice dimension we study a spin 12 particle moving on a one dimensional lattice subject to disorder induced by a random space dependent quantum coin the discrete time evolution is given by a family of random unitary quantum walk operators where the shift operation is assumed to be deterministic each coin is an independent identically distributed random variable with values in the group of two dimensional unitary matrices we derive sufficient conditions on the probability distribution of the coins such that the system exhibits dynamical localization put differently the tunneling probability between two lattice sites decays rapidly for almost all choices of random coins and after arbitrary many time steps with increasing distance our findings imply that this effect takes place if the coin is chosen at random from the haar measure or some measure continuous with respect to it but also for a class of discrete probability measures which support consists of two coins one of them being the hadamard coin

error estimates and adaptive time step control for a class of one step methods for stiff ordinary differential equations we prove new optimal a priori error estimates for a class of implicit one step methods for stiff ordinary differential equations obtained by using the discontinuous galerkin method with piecewise polynomials of degree zero and one starting from these estimates we propose a new algorithm for automatic time step control and we discuss the relation between this algorithm and earlier algorithms implemented in packages for the numerical solution of stiff ordinary differential equations

stability of a multi rate method for numerical integration of ode s abstract this paper derives sufficient conditions for the absolute stability of a certain multi rate method of numerical integration of systems of first order ode s which have been separated into two subsystems the second system being made up of the faster response equation it is assumed that the subsystems are integrated with fourth order and third order runge kutta methods respectively it is shown that there will be regions of stability provided the original system is sufficiently diagonally dominant if the subsystems are weakly coupled the regions of stability are nearly as large as the classical regions

advance in the theory of variable stepsize variable formula methods for ordinary differential equations the theory of the constant stepsize constant formula methods cscfm s for solving initial value problems for ordinary differential equations ode s is well developed however the integration methods are often used as variable stepsize variable formula methods vsvfm s in the codes for automatic solution of ode s this fact explains why it is necessary to develop a rigorous theory for the vsvfm s also results obtained until now in the efforts to develop a theory for the vsvfm s are presented in a systematic way and compared with the well known results for cscfm s the comparison is used to outline the directions in which further efforts in the attempt to improve the theoretical results and to obtain new results are most needed the integration methods can be separated into two large groups implicit methods and explicit methods including here the predictor corrector schemes it is discussed what kind of results are needed for each of these two groups assume that a set f of cscfm s is given from a practical point of view it is highly desirable that the cscfm s belonging to set f have the following property if every cscfm from set f is consistent zero stable and convergent then any vsvfm induced by the cscfm s of set f is also consistent zero stable and convergent for a sufficiently large class of grids a theorem concerning a class of cscfm s with this property is presented the application of this theorem in the selection of methods for solving large systems of ode s arising after the space discretization of air pollution models is discussed it is explained why the vsvfm s based on this class provide a very efficient computational process in the treatment of air pollution models

multiadaptive galerkin methods for odes iii a priori error estimates the multiadaptive continuous discontinuous galerkin methods mcgq and mdgq for the numerical solution of initial value problems for ordinary differential equations are based on piecewise polynomial approximation of degree q on partitions in time with time steps which may vary for different components of the computed solution in this paper we prove general order a priori error estimates for the mcgq and mdgq methods to prove the error estimates we represent the error in terms of a discrete dual solution and the residual of an interpolant of the exact solution the estimates then follow from interpolation estimates together with stability estimates for the discrete dual solution

critical evaluation of two equation models for near wall turbulence abstract a variety of two equation turbulence models including several versions of the k epsilon model as well as the k omega model are analyzed critically for near wall turbulent flows from a theoretical and computational standpoint it is shown that the k epsilon model has two major problems associated with it the lack of natural boundary conditions for the dissipation rate and the appearance of higher order correlations in the balance of terms for the dissipation rate at the wall in so far as the former problem is concerned either physically inconsistent boundary conditions have been used or the boundary conditions for the dissipation rate have been tied to higher order derivatives of the turbulent kinetic energy which leads to numerical stiffness the k omega model can alleviate these problems since the asymptotic behavior of w is known in more detail and since its near wall balance involves only exact viscous terms however the modeled form of the omega equation that is used in the literature is incomplete an exact viscous term is missing which causes the model to behave in an asymptotically inconsistent manner by including this viscous term and by introducing new wall damping functions with improved asymptotic behavior a new k tau model where tau 1 omega is turbulent time scale is developed it is demonstrated that this new model is computationally robust and yields improved predictions for turbulent boundary layers jhd

a posteriori analysis of an iterative multi discretization method for reaction diffusion systems abstract this paper is concerned with the accurate computational error estimation of numerical solutions of multi scale multi physics systems of reaction diffusion equations such systems can present significantly different temporal and spatial scales within the components of the model indicating the use of independent discretizations for different components however multi discretization can have significant effects on accuracy and stability we perform an adjoint based analysis to derive asymptotically accurate a posteriori error estimates for a user defined quantity of interest these estimates account for leading order contributions to the error arising from numerical solution of each component an error due to incomplete iteration an error due to linearization and for errors arising due to the projection of solution components between different spatial meshes several numerical examples with various settings are given to demonstrate the performance of the error estimators