global optimality conditions and optimization methods for constrained polynomial programming problems the general constrained polynomial programming problem gpp is considered in this paper problem gpp has a broad range of applications and is proved to be np hard necessary global optimality conditions for problem gpp are established then a new local optimization method for this problem is proposed by exploiting these necessary global optimality conditions a global optimization method is proposed for this problem by combining this local optimization method together with an auxiliary function some numerical examples are also given to illustrate that these approaches are very efficient

an implicit bidiagonal numerical method for solving the navier stokes equations in recent years much progress has been made in solving fluid dynamical problems using finite difference methods solving inviscid compressible problems in two and three dimensions has become almost routine with many suitable methods explicit or implicit available the problem of compressible viscous flows in complicated geometries remains however a major challenge here fine mesh spacing in the viscous flow regions makes the explicit methods with their simple boundary conditions extremely costly existing implicit methods can make use of large time steps but require inversions of large block tridiagonal matrices a method recently developed by maccormack eliminates this disadvantage by introducing a predictor corrector scheme requiring the inversion of only block bidiagonal matrices it is the aim of present work to extend this method to allow solution of viscous compressible problems in general coordinates for arbitrary two dimensional geometries

stationary distribution of a stochastic delayed sveir epidemic model with vaccination and saturation incidence abstract in this paper we develop and analyze a stochastic delayed sveir epidemic model with vaccination and saturation incidence by constructing a suitable stochastic lyapunov function we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model the existence of a stationary distribution implies stochastic weak stability numerical simulations are introduced to illustrate the analytical result

an extension of sums of squares relaxations to polynomial optimization problems over symmetric cones this paper is based on a recent work by kojima which extended sums of squares relaxations of polynomial optimization problems to polynomial semidefinite programs let varepsilon and varepsilon be a finite dimensional real vector space and a symmetric cone embedded in varepsilon examples of varepsilon and varepsilon include a pair of the n dimensional euclidean space and its nonnegative orthant a pair of the n dimensional euclidean space and n dimensional second order cones and a pair of the space of m m real symmetric or complex hermitian matrices and the cone of their positive semidefinite matrices sums of squares relaxations are further extended to a polynomial optimization problem over varepsilon i e a minimization of a real valued polynomial a x in the n dimensional real variable vector x over a compact feasible region bf x b bf x in varepsilon where b x denotes an varepsilon valued polynomial in x it is shown under a certain moderate assumption on the varepsilon valued polynomial b x that optimal values of a sequence of sums of squares relaxations of the problem which are converted into a sequence of semidefinite programs when they are numerically solved converge to the optimal value of the problem

nonlinear oscillations in epidemic models constant parameter epidemic models for a closed population described by integral and integrodifferential equations are analyzed to determine whether time delays can give rise to periodic oscillations delays can destabilize the steady state in one finite delay case and in one infinite delay case considered hopf bifurcation techniques are used to show the existence of locally asymptotically stable periodic solutions for certain parameter values inclusion of time delays in another related model does not alter the local asymptotic stability of the endemic steady state

semidefinite programming relaxations for semialgebraic problems a hierarchy of convex relaxations for semialgebraic problems is introduced for questions reducible to a finite number of polynomial equalities and inequalities it is shown how to construct a complete family of polynomially sized semidefinite programming conditions that prove infeasibility the main tools employed are a semidefinite programming formulation of the sum of squares decomposition for multivariate polynomials and some results from real algebraic geometry the techniques provide a constructive approach for finding bounded degree solutions to the positivstellensatz and are illustrated with examples from diverse application fields

a hepatitis b and c virus model with age since infection that exhibits backward bifurcation we propose a mathematical model describing the dynamics of hepatitis b or c virus infection the method of characteristics reduces the age structured model to a system of differential equations with distributed delay the model is rigorously analyzed and a detailed stability analysis is performed the model consisting of two mutually exclusive compartments representing the interaction of the virus in the liver and the blood has a locally asymptotically stable disease free equilibrium dfe whenever a certain epidemiological threshold known as the basic reproduction number r 0 is less than unity a sufficient condition for the global asymptotic stability of the trivial steady state is obtained further under biologically realistic hypotheses the model exhibits the phenomenon of backward bifurcation where the stable dfe coexists with a stable endemic equilibrium this means that reducing the basic reproduction number r 0 below 1 is not always sufficient to control hbv hcv infection when the viru

the use of domain splitting with an explicit hyperbolic solver abstract a method of splitting the solution domain in order to allow faster computation of practical first order hyperbolic problems is described results are presented which show the performance of the method in both one and two dimensions an indication is also given of the likely saving in computer time which can be achieved by using the method

upwind relaxation algorithms for the navier stokes equations analyse des erreurs de troncature de la differenciation spatiale et analyse de la stabilite de l algorithme de relaxation calcul pour une serie d ecoulements a l aide de la forme couche mince des equations calcul du decollement de couche limite induit par chocs

first and second order methods for semidefinite programming in this paper we survey the most recent methods that have been developed for the solution of semidefinite programs we first concentrate on the methods that have been primarily motivated by the interior point ip algorithms for linear programming putting special emphasis in the class of primal dual path following algorithms we also survey methods that have been developed for solving large scale sdp problems these include first order nonlinear programming nlp methods and more specialized path following ip methods which use the preconditioned conjugate gradient or residual scheme to compute the newton direction and the notion of matrix completion to exploit data sparsity

application of the implicit maccormack scheme to the parabolized navier stokes equations application de la methode de differences finies implicite de maccormack a la resolution des equations bidimensionnelles parabolisees de navier stokes discussion des avantages et inconvenients de la methode comparaison avec le schema de beam warming en ce qui concerne la precision la stabilite le temps de calcul la place en memoire et la facilite d implementation application a un ecoulement laminaire hypersonique sur un coin de compression

convergent sdp relaxations in polynomial optimization with sparsity we consider a polynomial programming problem p on a compact basic semialgebraic set k subset r n described by m polynomial inequalities g j x geq0 and with criterion f in r x we propose a hierarchy of semidefinite relaxations in the spirit of those of waki e siam j optim 17 2006 pp 218 242 in particular the sdp relaxation of order r has the following two features a the number of variables is o kappa 2r where kappa max kappa 1 kappa 2 with kappa 1 resp kappa 2 being the maximum number of variables appearing in the monomials of f resp appearing in a single constraint g j x geq0 b the largest size of the linear matrix inequalities lmis is o kappa r this is to compare with the respective number of variables o n 2r and lmi size o n r in the original sdp relaxations defined in j b lasserre siam j optim 11 2001 pp 796 817 therefore great computational savings are expected in case of sparsity in the data g j f i e when k is small a frequent case in practical applications of interest the novelty with respect to h waki s kim m kojima and m maramatsu siam j optim 17 2006 pp 218 242 is that we prove convergence to the global optimum of p when the sparsity pattern satisfies a condition often encountered in large size problems of practical applications and known as the running intersection property in graph theory in such cases and as a by product we also obtain a new representation result for polynomials positive on a compact basic semialgebraic set a sparse version of putinar s positivstellensatz m putinar indiana univ math j 42 1993 pp 969 984

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

generalized lagrangian duals and sums of squares relaxations of sparse polynomial optimization problems sequences of generalized lagrangian duals and their sums of squares sos of polynomials relaxations for a polynomial optimization problem pop are introduced the sparsity of polynomials in the pop is used to reduce the sizes of the lagrangian duals and their sos relaxations it is proved that the optimal values of the lagrangian duals in the sequence converge to the optimal value of the pop using a method from the penalty function approach the sequence of sos relaxations is transformed into a sequence of semidefinite programing sdp relaxations of the pop which correspond to duals of modification and generalization of sdp relaxations given by lasserre for the pop

variable fidelity aerodynamic optimization for turbulent flows using a discrete adjoint formulation an aerodynamic shape optimization methodology based on a discrete adjoint solver for navier stokes flows is described the flow solver at the heart of this optimization process is a reynolds averaged navier stokes code for multiblock structured grids it uses osher s approximate riemann solver and the algebraic turbulence model of baldwin lomax a corresponding discrete navier stokes adjoint solver is derived analytically it has to calculate accurately the jacobian including the effect of the turbulence modeling the shape deformations

canonical primal dual algorithm for solving fourth order polynomial minimization problems this paper focuses on implementation of a general canonical primal dual algorithm for solving a class of fourth order polynomial minimization problems a critical issue in the canonical duality theory has been addressed i e in the case that the canonical dual problem has no interior critical point in its feasible space s a a quadratic perturbation method is introduced to recover the global solution through a primal dual iterative approach and a gradient based method is further used to refine the solution a series of test problems including the benchmark polynomials and several instances of the sensor network localization problems have been used to testify the effectiveness of the proposed algorithm

lyapunov functions and global stability for age structured hiv infection model we study the basic age structured population model describing the hiv infection process which is defined by pdes the model allows the production rate of viral particles and the death rate of productively infected cells to vary and depend on the infection age by using the direct lyapunov method and constructing suitable lyapunov functions dynamical properties of the age structured model without or with drug treatment are established the results show that the global asymptotic stability of the infection free steady state and the infected steady state depends only on the basic reproductive number determined by the burst size further we establish mathematically that the typical ode and dde delay differential equation models of hiv infection are equivalent to two special cases of the above pde models

comparison of coordinate invariant and coordinate aligned upwinding for the euler equations a floating shock fitting method for the euler equations has been developed that uses one sided spatial differences along and across streamlines the coordinate invariant formulation of the spatial differences permits automatic capture of shears results are presented for unsteady shocked flow in a duct with a ramp for supercritical flow over a circular cylinder and for subsonic transonic and supersonic 0 3 m 1 5 flow over airfoils in flows with strong shears the coordinate invariant differencing concept appears to yield some gains in accuracy over euler methods that rely on coordinate aligned differencing concepts in applications to transonic airfoils fitted shocks have a tendency to be predicted upstream of captured shocks regardless of whether coordinate invariant or coordinate aligned differencing is used

dynamical aspects of an age structured sir endemic model the main idea of this work is to present and study the dynamical behavior of an age dependent sir endemic model first the age dependent sir endemic model is formulated from existing sir epidemic models by adding age dependent recruitment rate the behavior of the model is analyzed by using the basic reproductive number r 0 the stability theory is used for the analysis of disease free and endemic equilibrium finally finite difference method of characteristics is used to present numerical results for the suggested age structured endemic model

a lift and project cutting plane algorithm for mixed 0 1 programs we propose a cutting plane algorithm for mixed 0 1 programs based on a family of polyhedra which strengthen the usual lp relaxation we show how to generate a facet of a polyhedron in this family which is most violated by the current fractional point this cut is found through the solution of a linear program that has about twice the size of the usual lp relaxation a lifting step is used to reduce the size of the lp s needed to generate the cuts an additional strengthening step suggested by balas and jeroslow is then applied we report our computational experience with a preliminary version of the algorithm this approach is related to the work of balas on disjunctive programming the matrix cone relaxations of lovasz and schrijver and the hierarchy of relaxations of sherali and adams

computing of separated flow using the space marching conservative supra characteristics method steady hypersonic viscous flows over compression corners with streamwise separation have been computed using the space marching conservative supra characteristics method of lombard this method permits stable space marching of the parabolized navier stokes equations through large separated flow regions the present method has been used to compute surface pressure heat transfer and skin friction coefficients for two compression corner cases studied experimentally by holden and moselle the computed results compare favorably with previous navier stokes results and experimental data the present method has also been compared with the conventional beam warming scheme for solving the parabolized navier stokes equations comparisons are made for accuracy computer time and computer storage

numerical experiments with the osher upwind scheme for the euler equations the osher algorithm for solving the euler equations is an upwind finite difference procedure that is derived by combining the salient features of the theory of conservation laws and the mathematical theory of characteristi cs for hyperbolic systems of equations a first order accurate version of the numerical method was derived by osher circa 1980 for the one dimensional non isentropic euler equations in cartesian coordinates in this paper the extension of the scheme to arbitrary two dimensional geometries is explained results are then presented for several example problems in one and two dimensions future work will include extension of the method to second order accuracy and the development of implicit time differencing for the osher algorithm

cones of matrices and set functions and 0 1 optimization it has been recognized recently that to represent a polyhedron as the projection of a higher dimensional but simpler polyhedron is a powerful tool in polyhedral combinatorics a general method is developed to construct higher dimensional polyhedra or in some cases convex sets whose projection approximates the convex hull of 0 1 valued solutions of a system of linear inequalities an important feature of these approximations is that one can optimize any linear objective function over them in polynomial time in the special case of the vertex packing polytope a sequence of systems of inequalities is obtained such that the first system already includes clique odd hole odd antihole wheel and orthogonality constraints in particular for perfect and many other graphs this first system gives the vertex packing polytope for various classes of graphs including t perfect graphs it follows that the stable set polytope is the projection of a polytope with a polynomial number of facets an extension o

sparse sos relaxations for minimizing functions that are summations of small polynomials this paper discusses how to find the global minimum of functions that are summations of small polynomials small means involving a small number of variables some sparse sum of squares sos techniques are proposed we compare their computational complexity and lower bounds with prior sos relaxations under certain conditions we also discuss how to extract the global minimizers from these sparse relaxations the proposed methods are especially useful in solving sparse polynomial system and nonlinear least squares problems numerical experiments are presented which show that the proposed methods significantly improve the computational performance of prior methods for solving these problems lastly we present applications of this sparsity technique in solving polynomial systems derived from nonlinear differential equations and sensor network localization

improvements to a dual time stepping method for computing unsteady flows the nonlinear problem to be solved within an implicit time marching method has several differences from a typical steady state problem the initial guess is usually quite good and the degree of convergence required is quite small perhaps a few orders of magnitude reduction in residual therefore algorithms developed for steady problems may not be optimal for use in a dual time context we present some modifications to the diagonal approximately factored algorithm that lead to savings in a dual time stepping context

calculation of supersonic flows with strong viscous inviscid interaction a procedure for the calculation of strong viscous inviscid interactions in two dimension al laminar super sonic flows with and without separation is described the equations solved are the so called parabolized navier stokes equations the streamwise pressure gradient term is written as a combination of a forward and a backward difference to provide a path for upstream propagation of information global iteration is utilized to repeatedly update the pressure field from an initial guess until convergence is achieved the numerical scheme employed is a new alternating direction explicit ade procedure which is used as an alternative to the more difficult to program multigrid strategy to accelerate convergence results are presented for flows past two flat plate related bodies he calculation of supersonic flows in which rapid changes in geometry or boundary condition occur often requires techniques other than classical prandtl boundary layer theory or other solution methods suitable for weakly interacting flows the reason for this is that at high reynolds number rapid changes in geometry or boundary condition induce large changes in the properties of the bound ary layer over a very short length scale when this occurs the phenomenon of upstream influence wherein information is propagated in the upstream direction becomes important this type of flow is referred to as a strongly interacting flow methods that treat such flows as initial value problems are not suitable because they are boundary value in nature in the predominant flow direction in this paper a procedure for two dimensional supersonic strongly interacting flows is developed which utilizes the parabolized or reduced navier stokes equations we will employ the former term here for simplicity it will be as sumed that x and y are nearly streamwise and stream normal directions respectively with special treatment of the pressure gradient term dp dx in the streamwise momentum equation one can develop a procedure which is well suited for calculating weakly interacting flows 1 4 in order to calculate strongly interacting flows a means for propagating information in the upstream direction is required this can be satisfied by utilizing a forward difference for the stream wise pressure gradient in subsonic flows where upstream influence is important even if the viscous inviscid interaction is weak a forward difference of px has been shown by rubin5 to allow the calculation of such flows lin and rubin6 later successfully applied forward differencing of px to a supersonic flow with weak interaction in that study forward differencing was utilized throughout the flowfield including the supersonic flow in the present technique for ward differencing of px is applied only in the subsonic por

a numerical method for solving the equations of compressible viscous flow although much progress has already been made in solving problems in aerodynamic design many new developments are still needed before the equations for unsteady compressible viscous flow can be solved routinely this paper describes one such development a new method for solving these equations has been devised that 1 is second order accurate in space and time 2 is unconditionally stable 3 preserves conservation form 4 requires no block or scalar tridiagonal inversions 5 is simple and straightforward to program estimated 10 modification for the update of many existing programs 6 is more efficient than present methods and 7 should easily adapt to current and future computer architectures computational results for laminar and turbulent flows at reynolds numbers from 3 x 10 exp 5 to 3 x 10 exp 7 and at cfl numbers as high as 10 exp 3 are compared with theory and experiment

global stability of an age structure epidemic model with imperfect vaccination and relapse abstract a new age structured epidemic model with imperfect vaccination and relapse is proposed the total population of our model is partitioned into five subclasses susceptible class s vaccinated class v exposed class e infectious class i and removed class r age structures are equipped with in exposed and recovered classes furthermore imperfect vaccination is also introduced in our model the basic reproduction number r 0 is defined and proved as a threshold parameter of the model asymptotic smoothness of solutions and uniform persistence of the system are showed via reformulating the system as a system of volterra integral equation furthermore by constructing proper volterra type lyapunov functional we get when r 0 1 the disease free equilibrium is globally asymptotically stable when r 0 1 the endemic equilibrium is globally stable our results show that to increase the efficiency of vaccination and reduce influence of relapse are vital essential for controlling epidemic

navier stokes analysis of wind tunnel interference on transonic airfoil flutter a time domain numerical method is used for the simulation and investigation of the transonic two degree offreedom bending torsion e utter characteristics of the national aerospace laboratory 7301 section measured in a wind tunnelexperiment animplicit time accurate two dimensional compressible thin layernavier stokeseow solver is coupled with a two degree of freedom structural model the wind tunnel walls are included to model the experimental e ow conditions more closely and to obtain accurate aerodynamic predictions in the computations a three block grid is used for the discretization of the domain including the airfoil and wind tunnel walls solid and porous wall boundary conditions are implemented and tested for the domain boundaries representing the tunnel walls computations of the steady transonic aerodynamic characteristics show good agreement with the experimental results when a 50 porosity wall boundary condition is assumed for the wind tunnel walls including the wall effectsimproved theagreementoftheaeroelasticcomputations which predicted limit cyclee utter amplitudes in closer agreement with the experiment compared to the unbounded e ow calculations

inviscid and viscous stationary waves of gas flow through contracting expanding nozzles abstract in this work we study steady states of one dimensional viscous isentropic compressible flows through a contracting expanding nozzle treating the viscosity coefficient as a singular parameter the steady state problem can be viewed as a singularly perturbed system for a contracting expanding nozzle a complete classification of steady states is given and the existence of viscous profiles is established via the geometric singular perturbation theory particularly interesting is the existence of a maximal sub to super transonic wave and its role in the formation of other complicated transonic waves consisting of a sub to super portion

a mathematical study of a model for childhood diseases with non permanent immunity protecting children from diseases that can be prevented by vaccination is a primary goal of health administrators since vaccination is considered to be the most effective strategy against childhood diseases the development of a framework that would predict the optimal vaccine coverage level needed to prevent the spread of these diseases is crucial this paper provides this framework via qualitative and quantitative analysis of a deterministic mathematical model for the transmission dynamics of a childhood disease in the presence of a preventive vaccine that may wane over time using global stability analysis of the model based on constructing a lyapunov function it is shown that the disease can be eradicated from the population if the vaccination coverage level exceeds a certain threshold value it is also shown that the disease will persist within the population if the coverage level is below this threshold these results are verified numerically by constructing and then simulating a robust semi explicit second order finite difference method

viscous standing asymptotic states of isentropic compressible flows through a nozzle in this work we consider a viscous regularization of a well known one dimensional model for isentropic viscous compressible flows through a nozzle for the existence and multiplicity of standing asymptotic states for a certain type of ducts a complete analysis in a framework of dynamical systems is provided as an application of the geometric singular perturbation theory we show that all standing asymptotic states admit viscous profiles

the use of domain decomposition in accelerating the convergence of quasihyperbolic systems this paper proposes an alternate form of the active domain method k nakahashi and e saitoh aiaa j 35 1280 1997 that is applicable to streamwise separated flows named the marching window the algorithm consists of performing pseudo time iterations on a minimal width subdomain composed of a sequence of cross stream planes of nodes the upstream boundary of the subdomain is positioned such that all nodes upstream exhibit a residual smaller than the user specified convergence threshold the advancement of the downstream boundary follows the advancement of the upstream boundary except in zones of significant streamwise ellipticity where a streamwise ellipticity sensor ensures its continuous progress compared to the standard pseudo time marching approach the marching window decreases the work required for convergence by up to 24 times for flows with little streamwise ellipticity and by up to eight times for flows with large streamwise separated regions storage is reduced by up to six times by not allocating memory to the nodes not included in the computational subdomain the marching window satisfies the same convergence criterion as the standard pseudo time stepping methods hence resulting in the same converged solution within the tolerance of the user specified convergence threshold the algorithm is not restricted to a discretization stencil and pseudo time stepping scheme in particular and is used here with the yee roe scheme and block implicit approximate factorization solving the favre averaged navier stokes fans equations closed by the wilcox k turbulence model the eigenstructure of the fans equations is also presented

optimal explicit strong stability preserving general linear methods this paper constructs strong stability preserving general linear time stepping methods that are well suited for hyperbolic pdes discretized by the method of lines these methods generalize both runge kutta rk and linear multistep schemes they have high stage orders and hence are less susceptible than rk methods to order reduction from source terms or nonhomogeneous boundary conditions a global optimization strategy is used to find the most efficient schemes that have low storage requirements numerical results illustrate the theoretical findings

a contribution to the numerical prediction of unsteady flows methods based on flux differe nce splitting are investigated with reference to the prediction of unsteady compressible flows they combine the feature of taking into account the wake like nature of these flows and the capability of correctly capturing shock waves two recently proposed approaches and a third one suggested here are compared for one dimensional flow with particular reference to the means of operating the splitting they are extended to the cases of variable area ducts and a general transformation of the independent variables firstand second order accurate schemes are presented and procedures for the computation at the boundaries are shown finally numerical experiments are reported and discussed

parabolized navier stokes algorithm for solving supersonic flows with upstream influences a new parabolized navier stokes pns algorithm has been developed to efe ciently compute supersonic e ows with embedded regions that produce upstream effects innovative techniques are used to automatically detect and measure the extent of the embedded regions within the embedded regions the pns equations are globally iterated to duplicate the results that would be obtained with the complete navier stokes ns equations once an embedded region is computed the algorithm returns to the standard space marching pns mode until the next embedded region is encountered this procedure has been successfully incorporated into nasa s upwind pns code and it has been validated by its application to several two dimensional test cases all of these test cases include embedded regions that produce signie cant upstream effects the present numerical results arein excellent agreement with previous ns computations and experimental data in addition these calculations demonstrate the signie cant reduction in computer time and storage that can be achieved by the use of this approach

space marching calculations about hypersonic configurations using a solution adaptive mesh algorithm a solution adaptive marching algorithm is developed and applied to a three dimensional parabolized navierstokes equation solver the resulting algorithm obtains accurate solutions by using a spatial marching adaptivegrid procedure the adaptation step redistributes grid points line by line in both crossflow directions with grid point motion controlled by forces analogous to tensional and torsional spring forces with the tensional force proportional to the error measure or weighting functions the solution adaptive marching procedure is applied to the hypersonic flow about two generic aircraft configurations the first of these is an all body type geometry with elliptical cross sections and is studied at angles of attack of 0 5 and 15 deg the second geometry is a generic blended vv ing body design results are presented that demonstrate the improvements in flow field resolution obtainable with the solution adaptive marching procedure over conventional fixed grid techniques computed pitot pressure profiles obtained using the solution adaptive algorithm show improved agreement with experimental data compared to predictions obtained using a fixed grid

modification of the osher upwind scheme for use in three dimensions the pertinent formulas are given by eq 24 for the variation of c kleb with the modified clauser pressure gradient parameter by eq 14 for the variation of ccp with ckleb and by eq 26 for the variation of the clauser factor k with low reynolds number as presented here the relations for the baldwin lomax factors have an indirect experimental validity by being derived from the experimentally confirmed velocity similarity laws finally it should be apparent that for boundary layers in pressure gradients constant values for the baldwin lomax factors are unsatisfactory in satisfying the velocity similarity laws to approach the same accuracy as the parent cebeci smith method the baldwinlomax factors should be varied as indicated

an implicit form for the osher upwind scheme conservative upwind schemes for the euler equations such as the osher scheme accurately resolve flow discontinuities and correctly model the physics of the problem however these schemes require many more arithmetic operations per integration step than simple central difference schemes and hence result in large computing times an implicit version of the first order and second order accurate osher schemes in two spatial dimensions and generalized coordinates is developed in this study because implicit schemes permit the use of large integration steps in many cases they require fewer integration steps to reach steady state especially in calculations on grids with widely varying mesh cell sizes the implicit scheme developed in this study accelerated convergence speeds by almost an order of magnitude in the problems considered test cases include quasi one dimensional nozzle flow and supersonic flow past a cylinder

linear stability of the sub to super inviscid transonic stationary wave for gas flow in a nozzle of varying area abstract in this work we consider the linear stability of the sub to super inviscid transonic stationary wave of a one dimensional model of isentropic compressible flows through a nozzle of varying area this sub to super inviscid transonic stationary wave is newly founded by the authors using the geometric singular perturbation theory the main result of this work is to show that the sub to super inviscid transonic stationary wave is physically relevant in the sense that it is l linearly stable on any bounded space interval as long as its velocity is greater than 1 2 of the sound speed

upwind schemes and boundary conditions with applications to euler equations in general geometries abstract a unified treatment of several upwind shock capturing algorithms is presented each algorithm has a riemann initial value problem as its basis the treatment of boundaries involves solving the associated riemann initial boundary value problem the first author s algorithm applied to multidimensional euler equations in general geometries is then presented its worth is verified by various calculations which include mach 8 supersonic flow past a circular cylinder

grid adaptation for functional outputs application to two dimensional inviscid flows this paper presents an error estimation and grid adaptive strategy for estimating and reducing simulation errors in integral outputs functionals of partial differential equations adaptive criteria are derived using an adjoint based error correction technique that relates the local residual errors of both the primal and adjoint solutions to the global error in the prescribed functional this relationship allows local error contributions to be used as indicators in a grid adaptive strategy designed to produce specially tuned grids for accurately estimating the chosen functional in this paper attention is limited to two dimensional inviscid flows using a standard finite volume discretization although the procedure may be readily applied to other types of multidimensional problems and discretizations numerical examples demonstrate that the proposed adaptive procedure compares favorably in terms of accuracy efficiency and robustness relative to a commonly used gradient based adaptive method

global optimization with polynomials and the problem of moments we consider the problem of finding the unconstrained global minimum of a real valued polynomial p x mathbb r n to mathbb r as well as the global minimum of p x in a compact set k defined by polynomial inequalities it is shown that this problem reduces to solving an often finite sequence of convex linear matrix inequality lmi problems a notion of karush kuhn tucker polynomials is introduced in a global optimality condition some illustrative examples are provided

global results for an epidemic model with vaccination that exhibits backward bifurcation vaccination of both newborns and susceptibles is included in a transmission model for a disease that confers immunity the interplay of the vaccination strategy together with the vaccine efficacy and waning is studied in particular it is shown that a backward bifurcation leading to bistability can occur under mild parameter constraints compound matrices are used to show that each orbit limits to an equilibrium in the case of bistability this global result requires a novel approach since there is no compact absorbing set

analysis of complex hypersonic flows with strong viscous inviscid interaction etude de deux methodes utilisees pour ameliorer la prevision de l interaction visqueuse non visqueuse dans les ecoulements hypersoniques

one sided difference approximations for nonlinear conservation laws we analyze one sided or upwind finite difference approximations to hyperbolic partial differential equations and in particular nonlinear conservation laws second order schemes are designed for which we prove both nonlinear stability and that the entropy condition is satisfied for limit solutions we show that no such stable approximation of order higher than two is possible these one sided schemes have desirable properties for shock calculations we show that the proper switch used to change the direction in the upwind differencing across a shock is of great importance new and simple schemes are developed for which we prove qualitative properties such as sharp monotone shock profiles existence uniqueness and stability of discrete shocks numerical examples are given

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

sparsity in sums of squares of polynomials representation of a given nonnegative multivariate polynomial in terms of a sum of squares of polynomials has become an essential subject in recent developments of sums of squares optimization and semidefinite programming sdp relaxation of polynomial optimization problems we discuss effective methods to obtain a simpler representation of a sparse polynomial as a sum of squares of sparse polynomials by eliminating redundancy

global attractivity and permanence of a sveir epidemic model with pulse vaccination and time delay in this study we propose a new sveir epidemic disease model with time delay and analyze the dynamic behavior of the model under pulse vaccination pulse vaccination is an effective strategy for the elimination of infectious disease using the discrete dynamical system determined by the stroboscopic map we obtain an infection free periodic solution we also show that the infection free periodic solution is globally attractive when some parameters of the model under appropriate conditions the permanence of the model is investigated analytically our results indicate that a large vaccination rate or a short pulse of vaccination or a long latent period is a sufficient condition for the extinction of the disease

experimental analytical and computational methods applied to hypersonic compression ramp flows experimental data on fully laminar and transitional shock wave boundary layer interactions in two dimensional compression corners are provided and used for the validation of two full navier stokes solvers as well as for checking the capabilities and limitations of simple analytical prediction methods viscous pressure interaction free interaction and inviscid oblique shock theory are found to predict well the pressure levels on the flat plate upstream of the interaction within the separated region and downstream of the interaction respectively the reference temperature theory is found to perform well in attached flow regimes both upstream and downstream of the interaction region and to provide the basis for a universal peak heating correlation law full navier stokes computations are necessary however to predict the extent of the interaction region and the associated influence on the pressure distribution control effectiveness as well as the detailed heat transfer distribution to achieve this very fine gridding coupled with the use of strict convergence criteria based on the evolution of the location of the separation point rather than on standard density residuals is shown to be necessary it is finally shown that although sophisticated turbulence models need to be further developed before the detailed characteristics of fully turbulent shock wave boundary layer interactions may be predicted transitional interactions where transition typically occurs in the neighborhood of reattachment may be adequately handled by algebraic turbulence models switched on just downstream of reattachment

an epidemic model of a vector borne disease with direct transmission and time delay abstract this paper considers an epidemic model of a vector borne disease which has direct mode of transmission in addition to the vector mediated transmission the incidence term is assumed to be of the bilinear mass action form we include both a baseline ode version of the model and a differential delay model with a discrete time delay the ode model shows that the dynamics is completely determined by the basic reproduction number r 0 if r 0 1 the disease free equilibrium is globally stable and the disease dies out if r 0 1 a unique endemic equilibrium exists and is locally asymptotically stable in the interior of the feasible region the delay in the differential delay model accounts for the incubation time the vectors need to become infectious we study the effect of that delay on the stability of the equilibria we show that the introduction of a time delay in the host to vector transmission term can destabilize the system and periodic solutions can arise through hopf bifurcation

cones of matrices and successive convex relaxations of nonconvex sets let f be a compact subset of the n dimensional euclidean space rn represented by finitely or infinitely many quadratic inequalities we propose two methods one based on successive semidefinite programming sdp relaxations and the other on successive linear programming lp relaxations each of our methods generates a sequence of compact convex subsets ck k 1 2 of rn such that a the convex hull of f subseteq c k 1 subseteq c k monotonicity b cap k 1 infty c k text the convex hull of f asymptotic convergence our methods are extensions of the corresponding lovasz schrijver lift and project procedures with the use of sdp or lp relaxation applied to general quadratic optimization problems qops with infinitely many quadratic inequality constraints utilizing descriptions of sets based on cones of matrices and their duals we establish the exact equivalence of the sdp relaxation and the semi infinite convex qop relaxation proposed originally by fujie and kojima using this equivalence we investigate some fundamental features of the two methods including a and b above

grid independent upwind scheme for multidimensional flow recent advances in the development of a grid independent finite volume scheme for the euler equations of gas dynamics are described in the proposed method flowfield gradient data are reconstructed locally on a triangle using five elementary planar waves and an upwind numerical flux function for grid oblique waves is developed to model the effect of the passage of these waves on the data in a cell numerical examples for several two dimensional test problems are included

a new approach for building bounded skew upwind schemes abstract a new methodology for the construction of streamline bounded high resolution schemes is presented the route followed in the development is to combined existing streamline schemes with the normalized variable formulation nvf bounding approach the procedure is applied to the skew upwind differenting scheme suds to yield a new composite high resolution bounded convective scheme nvf suds the increase in computational cost with nvf suds is very small as compared to the unbounded suds the new scheme is tested and compared with the composite high resolution stoic scheme the upwind scheme and the unbounded suds by solving for three pure convection test problems results generated demonstrate the capability of the new upwind scheme in accurately resolving steep gradients as accurate as the ones obtained with the third order stoic scheme while retaining the solution bounded

sums of squares and semidefinite program relaxations for polynomial optimization problems with structured sparsity unconstrained and inequality constrained sparse polynomial optimization problems pops are considered a correlative sparsity pattern graph is defined to find a certain sparse structure in the objective and constraint polynomials of a pop based on this graph sets of the supports for sums of squares sos polynomials that lead to efficient sos and semidefinite program sdp relaxations are obtained numerical results from various test problems are included to show the improved performance of the sos and sdp relaxations

epidemiological models for mutating pathogens we formulate epidemiological models for the transmission of a pathogen that can mutate in the host to create a second infectious mutant strain the models account for mutation rates that depend on how long the host has been infected we derive explicit formulas for the reproductive number of the epidemic based on the local stability of the infection free equilibrium we analyze the existence and stability of the boundary equilibrium whose infection components are zero and positive respectively and the endemic equilibrium whose components are all positive we establish the conditions for global stability of the infection free and boundary equilibria and local stability of the endemic equilibrium for the case where there is no age structure for the pathogen in the infected population we show that under certain circumstances there is a hopf bifurcation where the endemic equilibrium loses its stability and periodic solutions appear we provide examples and numerical simulations to illustrate the hopf b

solution adaptive grid procedure for high speed parabolic flow solvers a solution adaptive grid procedure based bn an error equidistribution scheme is developed and applied to a parabolized navier stokes solver an improved method of selecting weighting functions is introduced that involves normalizing a combination of flowfield gradients and curvature of a number of dependent variables and then selecting the largest at each point the scheme redistributes grid points line by line with grid point motion controlled by forces analogous to tensional and torsional spring forces with the spring constants set equal to the weighting functions torsional terms are functions of the grid point positions along neighboring grid lines and provide grid smoothness and stability a grid fitting scheme is introduced for external flows in which the number of grid points in the freestream are reduced to a minimum results for several problems are presented to demonstrate the improvements obtainable with the solution adaptive grid procedure

global stability of an sveir epidemic model with ages of vaccination and latency the vaccination period i e the time period retaining acquired immunity following vaccination and the latent period are two important factors affecting disease dynamics classical compartmental disease models unrealistically assume that these periods are exponentially distributed in this paper these two ages are assumed to have arbitrary distributions that are represented by age specific rates leaving the vaccinated and the exposed classes resulting in an sveir model with population dynamics we investigate the global behavior of this model and derive its basic reproduction number the basic reproduction number completely determines the global dynamics of the model i e the disease free equilibrium is globally asymptotically stable and the disease always dies out when the basic reproduction number is less than unity whereas when the basic reproduction number is larger than unity there exists a unique endemic equilibrium which is globally asymptotically stable and the disease persists at this endemic equilibrium if it initially exists the contributions of the vaccine wane rate to the basic reproduction number and the level of the endemic equilibrium are displayed

discretization and localization in successive convex relaxation methods for nonconvex quadratic optimization based on the authors previous work which established theoretical foundations of two conceptual successive convex relaxation methods i e the ssdp successive semidefinite programming relaxation method and the ssilp successive semi infinite linear programming relaxation method this paper proposes their implementable variants for general quadratic optimization problems these problems have a linear objective function c t x to be maximized over a nonconvex compact feasible region f described by a finite number of quadratic inequalities we introduce two new techniques discretization and localization into the ssdp and ssilp relaxation methods the discretization technique makes it possible to approximate an infinite number of semi infinite sdps or semi infinite lps which appeared at each iteration of the original methods by a finite number of standard sdps or standard lps with a finite number of linear inequality constraints we establish given any open convex set u containing f there is an implementable discretization of the ssdp or ssilp relaxation method which generates a compact convex set c such that f c u in a finite number of iterations the localization technique is for the cases where we are only interested in upper bounds on the optimal objective value for a fixed objective function vector c but not in a global approximation of the convex hull of f this technique allows us to generate a convex relaxation of f that is accurate only in certain directions in a neighborhood of the objective direction c this cuts off redundant work to make the convex relaxation accurate in unnecessary directions we establish given any positive number e there is an implementable localization discretization of the ssdp or ssilp relaxation method which generates an upper bound of the objective value within e of its maximum in a finite number of iterations

recognizing underlying sparsity in optimization exploiting sparsity is essential to improve the efficiency of solving large optimization problems we present a method for recognizing the underlying sparsity structure of a nonlinear partially separable problem and show how the sparsity of the hessian matrices of the problem s functions can be improved by performing a nonsingular linear transformation in the space corresponding to the vector of variables a combinatorial optimization problem is then formulated to increase the number of zeros of the hessian matrices in the resulting transformed space and a heuristic greedy algorithm is applied to this formulation the resulting method can thus be viewed as a preprocessor for converting a problem with hidden sparsity into one in which sparsity is explicit when it is combined with the sparse semidefinite programming relaxation by waki et al for polynomial optimization problems the proposed method is shown to extend the performance and applicability of this relaxation technique preliminary numerical results are presented to illustrate this claim