on the worst case complexity of potential reduction algorithms for linear programming there are several classes of interior point algorithms that solve linear programming problems in o nl iterations among them several potential reduction algorithms combine both theoretical o nl iterations and practical efficiency as they allow the flexibility of line searches in the potential function and thus can lead to practical implementations it is a significant open question whether interior point algorithms can lead to better complexity bounds in the present paper we give some negative answers to this question for the class of potential reduction algorithms we show that even if we allow line searches in the potential function and even for problems that have network structure the bound o nl is tight for several potential reduction algorithms i e there is a class of examples with network structure in which the algorithms need at least nl iterations to find an optimal solution

a gas kinetic scheme for the baer nunziato two phase flow model numerical methods for the baer nunziato bn two phase flow model have attracted much attention in recent years in this paper we present a new gas kinetic scheme for the bn two phase flow model containing non conservative terms in the framework of finite volume method in the view of microscopic aspect a generalized bhatnagar gross krook bgk model which matches with the bn model is constructed based on the integral solution of the generalized bgk model we construct the distribution functions at the cell interface then numerical fluxes can be obtained by taking moments of the distribution functions and non conservative terms are explicitly introduced into the construction of numerical fluxes in this method not only the complex iterative process of exact solutions is avoided but also the non conservative terms included in the equation can be handled well

the worst casr step in karmarkar s algorithm in this note we consider the worst case performance in a single step of karmarkar s projective algorithm for linear programming in the transformed problem which arises on each iteration we show that the critical ratio r r can be improved asymptotically by a factor of two we also show that in the original problem where performance is characterized by reduction in the potential function the worst case reduction can be improved to approximately 0 72 moreover we demonstrate that both of these bounds are tight so that no further improvement based on the analysis of a single step is possible

nonlinear resonance in systems of conservation laws the riemann problem for a general inhomogeneous system of conservation laws is solved in a neighborhood of a state at which one of the nonlinear waves in the problem takes on a zero speed the inhomogeneity is modeled by a linearly degenerate field the solution of the riemann problem determines the nature of wave interactions and thus the riemann problem serves as a canonical form for nonlinear systems of conservation laws generic conditions on the fluxes are stated and it is proved that under these conditions the solution of the riemann problem exists is unique and has a fixed structure this demonstrates that in the above sense resonant inhomogeneous systems generically have the same canonical form the wave curves for these systems are only lipschitz continuous in a neighborhood of the states where the wave speeds coincide and so in contrast to strictly hyperbolic systems the implicit function theorem cannot be applied directly to obtain existence and uniqueness here we show that existence

absorbing state phase transitions with quenched disorder quenched disorder in the sense of the harris criterion is generally a relevant perturbation at an absorbing state phase transition point here using a strong disorder renormalization group framework and effective numerical methods we study the properties of random fixed points for systems in the directed percolation universality class for strong enough disorder the critical behavior is found to be controlled by a strong disorder fixed point which is isomorph with the fixed point of random quantum ising systems in this fixed point dynamical correlations are logarithmically slow and the static critical exponents are conjecturedly exact for one dimensional systems the renormalization group scenario is confronted with numerical results on the random contact process in one and two dimensions and satisfactory agreement is found for weaker disorder the numerical results indicate static critical exponents which vary with the strength of disorder whereas the dynamical correlations are compatible with two possible scenarios either they follow a power law decay with a varying dynamical exponent like in random quantum systems or the dynamical correlations are logarithmically slow even for a weak disorder for models in the parity conserving universality class there is no strong disorder fixed point according to our renormalization group analysis

numerical investigation of a modified family of centered schemes applied to multiphase equations with nonconservative sources systems of hyperbolic partial differential equations are frequently used to model the flow of multiphase mixtures these equations often contain sources referred to as nozzling terms that cannot be posed in divergence form and have proven to be particularly challenging in the development of finite volume methods upwind schemes have recently shown promise in properly resolving the steady wave solution of the associated multiphase riemann problem however these methods require a full characteristic decomposition of the system eigenstructure which may be either unavailable or computationally expensive central schemes such as the kurganov tadmor kt family of methods require minimal characteristic information which makes them easily applicable to systems with an arbitrary number of phases however the proper implementation of nozzling terms in these schemes has been mathematically ambiguous the primary objectives of this work are twofold first an extension of the kt family of schemes is proposed that formally accounts for the nonconservative nozzling sources this modification results in a semidiscrete form that retains the simplicity of its predecessor and introduces little additional computational expense second this modified method is applied to multiple but equivalent forms of the multiphase equations to perform a numerical study by solving several one dimensional test problems both ideal and mie gruneisen equations of state are used with the results compared to an analytical solution this study demonstrates that the magnitudes of the resulting numerical errors are sensitive to the form of the equations considered and suggests an optimal form to minimize these errors finally a separate modification of the wave propagation speeds used in the kt family is also suggested that can reduce the extent of numerical diffusion in multiphase flows

a conservative approximation to compressible two phase flow models in the stiff mechanical relaxation limit in this article we present and analyze a conservative approximation to reduced one pressure one velocity models for compressible two phase flows that contain non conservative products this approximation is valid when certain material properties of the two phases are considerably different from each other although it cannot be applied to arbitrary mixtures it is applicable to many heterogeneous mixtures of technological interest herein we derive the rankine hugoniot relations and riemann invariants for the homogeneous part of the proposed model and develop an exact riemann solver for it further we investigate the structure of the steady two phase detonation waves with inert or reactive solid particles admitted by the proposed model comparisons with the corresponding gaseous detonations are also made moreover we derive a lower limit for the propagation speed of steady two phase detonations in the case of reactive particles at the limiting case of very dilute mixtures this minimum speed tends to the chapman jouguet velocity of gaseous detonations finally we report on numerical simulations of the transmission of a purely gaseous detonation to heterogeneous mixtures containing inert or reactive solid particles the effect of the solid particles on the structure of the resulting two phase detonation is discussed in detail

a godunov type method for the shallow water equations with discontinuous topography in the resonant regime abstract we investigate the riemann problem for the shallow water equations with variable and possibly discontinuous topography and provide a complete description of the properties of its solutions existence uniqueness in the non resonant regime multiple solutions in the resonant regime this analysis leads us to a numerical algorithm that provides one with a riemann solver next we introduce a godunov type scheme based on this riemann solver which is well balanced and of quasi conservative form finally we present numerical experiments which demonstrate the convergence of the proposed scheme even in the resonance regime except in the limiting situation when riemann data precisely belong to the resonance hypersurface

a positive and entropy satisfying finite volume scheme for the baer nunziato model we present a relaxation scheme for approximating the entropy dissipating weak solutions of the baer nunziato two phase flow model this relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in 16 for the isentropic baer nunziato model and consequently inherits its main properties to our knowledge this is the only existing scheme for which the approximated phase fractions phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable cfl condition for ideal gas and stiffened gas equations of state real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme it is also the only scheme for which a discrete entropy inequality is proven under a cfl condition derived from the natural sub characteristic condition associated with the relaxation approximation this last property which ensures the non linear stability of the numerical method is satisfied for any admissible equation of state we provide a numerical study for the convergence of the approximate solutions towards some exact riemann solutions the numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the baer nunziato model namely schwendeman wahle kapila s godunov type scheme 39 and tokareva toro s hllc scheme 44 the relaxation scheme also shows a higher precision and a lower computational cost for comparable accuracy than a standard numerical scheme used in the nuclear industry namely rusanov s scheme finally we assess the good behavior of the scheme when approximating vanishing phase solutions

hllc type riemann solver for the baer nunziato equations of compressible two phase flow we first construct an approximate riemann solver of the hllc type for the baer nunziato equations of compressible two phase flow for the subsonic wave configuration the solver is fully nonlinear it is also complete that is it contains all the characteristic fields present in the exact solution of the riemann problem in particular stationary contact waves are resolved exactly we then implement and test a new upwind variant of the path conservative approach such schemes are suitable for solving numerically nonconservative systems finally we use locally the new hllc solver for the baer nunziato equations in the framework of finite volume discontinuous galerkin finite element and path conservative schemes we systematically assess the solver on a series of carefully chosen test problems

real space renormalization group approach to driven diffusive systems we introduce a real space renormalization group procedure for driven diffusive systems which predicts both steady state and dynamic properties we apply the method to the boundary driven asymmetric simple exclusion process and recover exact results for the steady state phase diagram as well as the crossovers in the relaxation dynamics for each phase

stability of a resonant system of conservation laws modeling polymer flow with gravitation abstract we prove l 1 uniqueness and stability for a resonant 2 2 system of conservation laws that arise as a model for two phase polymer flow in porous media the analysis uses the equivalence of the eulerian and lagrangian formulation of this system and the results are first established for an auxiliary scalar equation our methods are based on front tracking approximations for the auxiliary equation and the kru kov entropy condition for scalar conservation laws

choice of measure source terms in interface coupling for a model problem in gas dynamics this paper is devoted to the mathematical and numerical analysis of a coupling procedure for one dimensional euler systems the two systems have different closure laws and are coupled through a thin fixed interface following the work of 5 we propose to couple these systems by a bounded vector valued dirac measure concentrated at the coupling interface which in the applications may have a physical meaning we show that the proposed framework allows to control the coupling conditions and we propose an approximate riemann solver based on a relaxation approach preserving equilibrium solutions of the coupled problem numerical experiments in constrained optimization problems are then presented to assess the performances of the present method 1 introduction the study of large scale and complex problems exhibiting a wide range of physical space and time scales see for instance 62 35 14 usually requires separate solvers adapted to the resolution of specific scales this is the case of many industrial flows let us quote for example the numerical simulation of two phase flows applied to the burning liquid oxygen hydrogen gas in rocket engines 58 this kind of flow contains both separated and dispersed two phase flows due to atomization and evaporation phenomena this requires appropriate models and solvers for separated and dispersed phases that have to be appropriately coupled another example concerns turbomachine flows which can be modeled by the euler equations of gas dynamics with different closure laws between the stages of the turbine where the conditions of temperature and pressure are strongly heterogeneous the coupling of these different systems is thus necessary to give a complete description of the flow inside the whole turbine the method of interface coupling allows to represent the evolution of such flows where different models are separated by fixed interfaces first coupling conditions are specified at the interface to exchange information between the systems the definition of transmission conditions generally results from physical consideration e g the conservation or the continuity of given variables then the transmission conditions are represented at the discrete level the study of interface coupling for nonlinear hyperbolic systems has received attention for several years in 43 the authors study the scalar case from both mathematical and numerical points of view

on the solution to the riemann problem for the compressible duct flow the quasi one dimensional euler equations in a duct of variable cross section form probably one of the simplest nonconservative systems we consider the riemann problem for it and discuss its properties in particular for some initial conditions the solution to the riemann problem appears to be nonunique in order to rule out the nonphysical solutions we provide two dimensional computations of the euler equations in a duct of corresponding geometry and compare them with the one dimensional 1d results then the physically relevant 1d solutions satisfy a kind of entropy rate admissibility criterion

the riemann problem for the baer nunziato two phase flow model we consider the riemann problem for the two phase flow model proposed by baer and nunziato int j multiphase flows 12 1986 861 it describes the flame spread and the deflagration to detonation transition ddt in gaspermeable reactive granular materials the model is given by a non strictly hyperbolic non conservative system of partial differential equations we investigate the structure of the riemann problem and construct the exact solution for it we establish that the solution across one wave is not unique and propose to use the evolutionarity criterion to single out the admissible solution due to special structure of the riemann problem for the baer nunziato model we are able to introduce a notion of a weak solution for it finally we propose a number of test cases based on the exact solution to the riemann problem for the baer nunziato model

numerical simulation of a compressible two layer model a first attempt with an implicit explicit splitting scheme this work is devoted to the numerical simulation of the compressible two layer model developed in 16 the latter is an hyperbolic two fluid two pressure model dedicated to gas liquid flows in pipes especially stratified air water flows using explicit schemes one obtains a cfl condition based on the celerity of fast acoustic waves which typically brings large numerical diffusivity for the slow material waves and small time steps in order to overcome these drawbacks the proposed scheme involves an operator splitting and an implicit explicit time discretization thus the full system is split into two hyperbolic subsystems the first one deals with the transport equation on the liquid height using an explicit scheme and upwind fluxes the second one deals with the averaged mass and momentum conservation equations of both phases using an implicit scheme which handles the propagation of acoustic waves at last the positivity of heights and densities is ensured under a cfl condition which involves material velocities numerical experiments are performed using acoustic as well as material time steps adding the rusanov scheme for comparison the best accuracy is obtained with the proposed scheme used with acoustic time steps when used with material time steps efficiency on the slow waves and stability are obtained regarding analytical solutions of the convective part

mathematical and numerical modeling of two phase compressible flows with micro inertia a new model with full coupling between micro and macroscale motion is developed for compressible multiphase mixtures the equations of motion and the coupling microstructural equation an analogue of the rayleigh lamb equation are obtained by using the hamilton principle of stationary action in the particular case of bubbly fluids the resulting model contains eight partial differential equations one dimensional case and is unconditionally hyperbolic the equations are solved numerically by an adapted godunov method the model and methods are validated for two very different test problems the first one consists of a wave propagating in a liquid containing a small quantity of gas bubbles computed oscillating shock waves fit perfectly the experimental data then the one dimensional multiphase model is used as a reduction tool for the multidimensional interaction of a shock wave with a large bubble good agreement is again obtained

discrete equations for physical and numerical compressible multiphase mixtures we have recently proposed in 21 a compressible two phase unconditionally hyperbolic model able to deal with a wide range of applications interfaces between compressible materials shock waves in condensed multiphase mixtures homogeneous two phase flows bubbly and droplet flows and cavitation in liquids one of the difficulties of the model as always in this type of physical problems was the occurrence of non conservative products in 21 we have proposed a discretisation technique that was without any ambiguity only in the case of material interfaces not in the case of shock waves this model was extended to several space dimensions in 24 in this paper thanks to a deeper analysis of the model we propose a class of schemes that are able to converge to the correct solution even when shock waves interact with volume fraction discontinuities this analysis provides a more accurate estimate of closure terms but also an accurate resolution method for the conservative fluxes as well as non conservative terms even for situations involving discontinuous solutions the accuracy of the model and method is clearly demonstrated on a sequence of difficult test problems

two stage coarsening mechanism in a kinetically constrained model of an attractive colloid we study an attractive version of the east model using the real space renormalization group rg introduced by stella et al the former is a kinetically constrained model with an ising like interaction between excitations and shows striking agreement with the phenomonology of attractive colloidal systems we find that the rg predicts two nonuniversal dynamic exponents which suggests that in the out of equilibrium regime the model coarsens via a two stage mechanism we explain this mechanism physically and verify this prediction numerically in addition we predict that the characteristic relaxation time of the model is a nonmonotonic function of attraction strength again in agreement with numerical results

numerical resolution for a compressible two phase flow model based on the theory of thermodynamically compatible systems this paper is concerned with the numerical solution of the equations governing two phase gas solid mixture in the framework of thermodynamically compatible systems theory the equations constitute a non homogeneous system of nonlinear hyperbolic conservation laws a total variation diminishing tvd slope limiter centre slic numerical scheme based on the splitting approach is presented and applied for the solution of the initial boundary value problem for the equations the model equations and the numerical methods are systematically assessed through a series of numerical test cases strong numerical evidence shows that the model and the methods are accurate robust and conservative the model correctly describes the formations of shocks and rarefactions in two phase gas solid flow

asymptotic behaviour of karmarkar s method for linear programming the asymptotic behaviour of karmarkar s method is studied and an estimate of the rate of the objective function value decrease is given two possible sources of numerical instability are discussed and a stabilizing procedure is proposed

a robust and accurate riemann solver for a compressible two phase flow model in this paper we analyze the riemann problem for the widely used drift flux two phase flow model this analysis introduces the complete information that is attained in the representation of solutions to the riemann problem it turns out that the riemann waves have rarefactions a contact discontinuity and shocks within this respect an exact riemann solver is developed to accurately resolve and represent the complete wave structure of the gas liquid two phase flows to verify the solver a series of test problems selected from the literature are presented including validation against independent numerical simulations where the solution of the riemann problem is fully numerical in this framework the governing equations are discretized by finite volume techniques facilitating the application godunov methods of centred type it is shown that both analytical and numerical results demonstrate the broad applicability and robustness of the new exact riemann solver

variational principles and two fluid hydrodynamics of bubbly liquid gas mixtures abstract in a recent paper the two phase flow equations for a bubbly liquid gas mixture were derived by variational methods starting point was an euler form of hamilton s extended principle of least action the effect of the virtual mass of the gas bubbles was included it is demonstrated now that a variational principle in the langrange form yields the same two fluid equations in addition it is shown how the lagrange form is trandformed in the euler form by means of a canonical transformation with regard to a recent discussion in the literature the material frame indifference or objectivity of the virtual mass terms is investigated the mutual force between the two phases which is associated with the virtual mass of the gas bubbles turns out to be objective in the limit of low bubble concentrations the results of the one bubble theory are recovered a corrected value is derived for the lift coefficient of a gas bubble in a rotational flow it is indicated how a scheme of iterative solutions yields higher order approximations in which the mutual interaction of the gas bubbles is taken into account

absorbing state phase transitions exact solutions of small systems i derive precise results for absorbing state phase transitions using exact numerically determined quasistationary qs probability distributions for small systems analysis of the contact process on rings of 23 or fewer sites yields critical properties control parameter order parameter ratios and critical exponents z and ensuremath beta ensuremath nu ensuremath perp with an accuracy of 0 06 or better precise results are also obtained for the pair contact process the qs distribution yields insights on the statistical entropy of these models preliminary application to a model in the stochastic sandpile class is also described

a phase decomposition approach and the riemann problem for a model of two phase flows abstract we present a phase decomposition approach to deal with the generalized rankine hugoniot relations and then the riemann problem for a model of two phase flows by investigating separately the jump relations for equations in conservative form in the solid phase we show that the volume fractions can change only across contact discontinuities then we prove that the generalized rankine hugoniot relations are reduced to the usual form it turns out that shock waves and rarefaction waves remain on one phase only and the contact waves serve as a bridge between the two phases by decomposing riemann solutions into each phase we show that riemann solutions can be constructed for large initial data furthermore the riemann problem admits a unique solution for an appropriate choice of initial data

on the improvement per iteration in karmarkar s algorithm for linear programming we investigate the decrease in potential at an iteration of karmarkar s projective method for linear programming for a fixed step length parameter so that we must have 0 1 the best possible guarantee n inn dimensional space is essentially ln 2 0 69 and to achieve this we must take about 1 indeed we show the precise result that n equals ln 1 ln 1 n 1 forn sufficiently large if we choose an optimal step length at each iteration then this guarantee increases only to about 0 72 we also shed some light on the remarkable empirical observation that the number of iterations required seems scarcely to grow with the size of the problem

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

two phase shock tube problems and numerical methods of solution the study involves the flow of compressible gas in a porous bed we are interested in exploring the solution to a shock tube problem that also includes a discontinuous jump in the porosity of the bed the averaging process that is used to derive the governing system of equations introduces terms that prevent the equations taking a standard conservation form the purpose of this work is to explore how the porosity jump effects the solution to the riemann problem and to assess whether standard conservative and nonconservative numerical methods can provide the correct solution to the riemann problem the study illustrates serious shortfalls in the numerical solution to these problems using standard techniques by exploring the exact solution the author suggests how the standard numerical methods can be modified to provide the correct solution to these systems

a multiphase godunov method for compressible multifluid and multiphase flows we propose a new model and a solution method for two phase compressible flows the model involves six equations obtained from conservation principles applied to each phase completed by a seventh equation for the evolution of the volume fraction this equation is necessary to close the overall system the model is valid for fluid mixtures as well as for pure fluids the system of partial differential equations is hyperbolic hyperbolicity is obtained because each phase is considered to be compressible two difficulties arise for the solution one of the equations is written in non conservative form non conservative terms exist in the momentum and energy equations we propose robust and accurate discretisation of these terms the method solves the same system at each mesh point with the same algorithm it allows the simulation of interface problems between pure fluids as well as multiphase mixtures several test cases where fluids have compressible behavior are shown as well as some other test problems where one of the phases is incompressible the method provides reliable results is able to compute strong shock waves and deals with complex equations of state

hllc type riemann solver with approximated two phase contact for the computation of the baer nunziato two fluid model abstract the computation of compressible two phase flows with the baer nunziato model is addressed only the convective part of the model that exhibits non conservative products is considered and the source terms of the model that represent the exchange between phases are neglected based on the solver proposed by tokareva toro 1 a new hllc type riemann solver is built the key idea of this new solver lies in an approximation of the two phase contact discontinuity of the model thus the riemann invariants of the wave are approximated in the subsonic case a major consequence of this approximation is that the resulting solver can deal with any equation of state it also allows to bypass the resolution of a non linear equation based on those riemann invariants we assess the solver and compare it with others on 1d riemann problems including grid convergence and efficiency studies the ability of the proposed solver to deal with complex equations of state is also investigated finally the different solvers have been compared on challenging 2d test cases due to the presence of both material interfaces and shock waves a shock bubble interaction and underwater explosions when compared with others the present solver appears to be accurate efficient and robust

the riemann problem and a high resolution godunov method for a model of compressible two phase flow this paper considers the riemann problem and an associated godunov method for a model of compressible two phase flow the model is a reduced form of the well known baer nunziato model that describes the behavior of granular explosives in the analysis presented here we omit source terms representing the exchange of mass momentum and energy between the phases due to compaction drag heat transfer and chemical reaction but retain the non conservative nozzling terms that appear naturally in the model for the riemann problem the effect of the nozzling terms is confined to the contact discontinuity of the solid phase treating the solid contact as a layer of vanishingly small thickness within which the solution is smooth yields jump conditions that connect the states across the contact as well as a prescription that allows the contribution of the nozzling terms to be computed unambiguously an iterative method of solution is described for the riemann problem that determines the wave structure and the intermediate states of the flow for given left and right states a godunov method based on the solution of the riemann problem is constructed it includes non conservative flux contributions derived from an integral of the nozzling terms over a grid cell the godunov method is extended to second order accuracy using a method of slope limiting and an adaptive riemann solver is described and used for computational efficiency numerical results are presented demonstrating the accuracy of the numerical method and in particular the accurate numerical description of the flow in the vicinity of a solid contact where phases couple and nozzling terms are important the numerical method is compared with other methods available in the literature and found to give more accurate results for the problems considered

convergence of the 2 2 godunov method for a general resonant nonlinear balance law we introduce a generalized solution of the riemann problem for a general resonant nonlinear balance law and we prove the convergence of the 2 x 2 godunov numerical method based on these solutions in particular we obtain generic conditions that guarantee a canonical structure for the elementary waves in the solution of the riemann problem and an interesting multiplicity of time asymptotic wave patterns is observed and characterized

modelling evaporation fronts with reactive riemann solvers this work deals with the modelling of permeable fronts and the building of a numerical method allowing the multi dimensional propagation of such fronts a particular attention is given to evaporation waves that appear in cavitating systems these ones are considered as discontinuities through which a non equilibrium liquid turns to a liquid vapor mixture at thermodynamic equilibrium such transformation occurs at finite rate in order to determine this kinetics the evaporation front is assumed to propagate at the maximum admissible speed corresponding to the chapman jouguet deflagration point j r simoes moreira j e shepherd evaporation waves in superheated dodecane j fluid mech 382 1999 63 86 using this particular kinetic relation rankine hugoniot relations are closed at such fronts then it is possible to solve the associated reactive riemann problem however another difficulty is present to solve the multi dimensional propagation of permeable fronts this kind of front is subsonic and a conventional averaging scheme such as godunov scheme is inappropriate to overcome this difficulty the reactive riemann problem solution is embedded into the discrete equations method dem r abgrall r saurel discrete equations for physical and numerical compressible multiphase mixtures j comp phys 186 2003 361 396 r saurel s gavrilyuk f renaud a multiphase model with internal degrees of freedom application to shock bubble interaction j fluid mech 495 2003 283 321 this numerical method necessitates deep extensions that are detailed herein numerical results are shown and validated over experimental data some examples show that the same method may be applied to the propagation of detonation fronts

a riemann problem in gas dynamics with bifurcation abstract we construct the solution of the riemann problem for 2 2 isothermal gas dynamics in a duct with discontinuous diameter besides shocks and rarefaction there are standing waves the solution exists globally it is obtained as an asymptotic solution for an appropriate cauchy problem with continuous data in certain cases bifurcation occurs and there are three solutions one of which is unstable this is an example of a riemann problem whose solution depends discontinuously on the initial data

how to prevent pressure oscillations in multicomponent flow calculations a new numerical scheme for computing multicomponent flows is presented it is able to handle strong shocks is pressure oscillation free through the contact discontinuities and guarantees the posi tivity of mass fractions some numerical experiments on shock tubes indicate the convergence to the correct weak solution comparisons with classical finite volume schemes are also proposed

a robust numerical method for approximating solutions of a model of two phase flows and its properties the objective of the present paper is to extend our earlier works on simpler systems of balance laws in nonconservative form such as the model of fluid flows in a nozzle with variable cross section to a more complicated system consisting of seven equations which has applications in the modeling of deflagration to detonation transition in granular materials first we transform the system into an equivalent one which can be regarded as a composition of three subsystems then depending on the characterization of each subsystem we propose a convenient numerical treatment of the subsystem separately precisely in the first subsystem of the governing equations in the gas phase stationary waves are used to absorb the nonconservative terms into an underlying numerical scheme in the second subsystem of conservation laws of the mixture we can take a suitable scheme for conservation laws for the third subsystem of the compaction dynamics equation the fact that the velocities remain constant across solid contacts suggests us to employ the technique of engquist osher s scheme then we prove that our method possesses some interesting properties it preserves the positivity of the volume fractions in both phases and in the gas phase our scheme is capable of capturing equilibrium states preserves the positivity of the density and satisfies the numerical minimum entropy principle numerical tests show that our scheme can provide reasonable approximations for data the supersonic regions but the results are not satisfactory in the subsonic region however the scheme is numerically stable and robust

distribution of dynamical quantities in the contact process random walks and quantum spin chains in random environments we study the distribution of dynamical quantities in various one dimensional disordered models the critical behavior of which is described by an infinite randomness fixed point in the disordered contact process the survival probability mathcal p t is found to show multiscaling in the critical point meaning that mathcal p t t ensuremath ensuremath delta where the environment and time dependent exponent ensuremath delta has a universal limit distribution when t ensuremath rightarrow ensuremath infty the limit distribution is determined by the strong disorder renormalization group method analytically in the end point of a semi infinite lattice where it is found to be exponential while in the infinite system conjectures on its limiting behaviors for small and large ensuremath delta which are based on numerical results are formulated by the same method the survival probability in the problem of random walks in random environments is also shown to exhibit multiscaling with an exponential limit distribution in addition to this the imaginary time spin spin autocorrelation function of the random transverse field ising chain is found to have a form similar to that of survival probability of the contact process at the level of the renormalization approach consequently a relationship between the corresponding limit distributions in the two problems can be established finally the distribution of the spontaneous magnetization in this model is also discussed

the riemann problem near a hyperbolic singularity the classification of solutions of quadratic riemann problems 1 the purpose of this paper is to classify the solutions of riemann problems near a hyperbolic singularity in a nonlinear system of conservation laws hyperbolic singularities play the role in the theory of riemann problems that rest points play in the theory of ordinary differential equations indeed generically only a finite number of structures can appear in a neighborhood of such a singularity in this the first of three papers the program of classification is discussed in general and the simplest structure that occurs is characterized

one dimensional contact process duality and renormalization we study the one dimensional contact process in its quantum version using a recently proposed real space renormalization technique for stochastic many particle systems exploiting the duality and other properties of the model we can apply the method for cells with up to 37 sites after suitable extrapolation we obtain exponent estimates that are comparable in accuracy with the best known in the literature

runge kutta discontinuous galerkin method for the approximation of baer and nunziato type multiphase models a high order numerical method is developed for the computation of compressible multiphase flows the model we use is based on the baer and nunziato type systems 4 among all the other available models in the literature these systems present the advantage to be able to simulate either interface or mixture problems nevertheless they still raise some issues mainly based on their non conservative feature the numerical method we propose is a discontinuous galerkin type in this work the interior side integrals are computed thanks to 2 robustness and high order of accuracy of the method are proved on classical interface problems but also on suitably derived analytical solutions

solid fluid diffuse interface model in cases of extreme deformations diffuse interface methods have been recently proposed and successfully used for accurate compressible multi fluid computations abgrall 1 kapila et al 20 saurel et al 30 these methods deal with extended systems of hyperbolic equations involving a non conservative volume fraction equation and relaxation terms following the same theoretical frame we derive here an eulerian diffuse interface model for elastic solid compressible fluid interactions in situations involving extreme deformations elastic effects are included following the eulerian conservative formulation proposed in godunov 16 miller and colella 23 godunov and romenskii 17 plohr and plohr 27 and gavrilyuk et al 14 we apply first the hamilton principle of stationary action to derive the conservative part of the model the relaxation terms are then added which are compatible with the entropy inequality in the limit of vanishing volume fractions the euler equations of compressible fluids and a conservative hyperelastic model are recovered it is solved by a unique hyperbolic solver valid at each mesh point pure fluid pure solid and mixture cell capabilities of the model and methods are illustrated on various tests of impacts of solids moving in an ambient compressible fluid

the resonant cases and the riemann problem for a model of two phase flows abstract the resonant cases in the riemann problem for a model of two phase flows with resonance are investigated which complete the construction of riemann solutions the model is given by a nonconservative hyperbolic system of balance laws the phase decomposition method is developed to construct solutions in each phase in a relatively separated way but still glued to each other via the contact discontinuities composite wave curves can be built and intersections of wave curves in each phase plane help to determine various configurations of riemann solutions in particular solutions containing multiple waves propagating with the same shock speed are constructed

convergence analysis of the projective scaling algorithm based on a long step homogeneous affine scaling algorithm in this paper we give a new convergence analysis of a projective scaling algorithm we consider a long step affine scaling algorithm applied to a homogeneous linear programming problem obtained from the original linear programming problem this algorithm takes a fixed fraction 2 3 of the way towards the boundary of the nonnegative orthant at each iteration the iteration sequence for the original problem is obtained by pulling back the homogeneous iterates onto the original feasible region with a conical projection which generates the same search direction as the original projective scaling algorithm at each iterate the recent convergence results for the long step affine scaling algorithm by the authors are applied to this algorithm to obtain some convergence results on the projective scaling algorithm specifically we will show i polynomiality of the algorithm with complexities of o nl and o n2l iterations for 2 3 and 2 3 respectively ii global covnergence of the algorithm when the optimal face is unbounded iii convergence of the primal iterates to a relative interior point of the optimal face iv convergence of the dual estimates to the analytic center of the dual optimal face and v convergence of the reduction rate of the objective function value to 1

long range epidemic spreading in a random environment modeling long range epidemic spreading in a random environment we consider a quenched disordered d dimensional contact process with infection rates decaying with distance as 1 r d ensuremath sigma we study the dynamical behavior of the model at and below the epidemic threshold by a variant of the strong disorder renormalization group method and by monte carlo simulations in one and two spatial dimensions starting from a single infected site the average survival probability is found to decay as p t ensuremath sim t ensuremath d z up to multiplicative logarithmic corrections below the epidemic threshold a griffiths phase emerges where the dynamical exponent z varies continuously with the control parameter and tends to z c d ensuremath sigma as the threshold is approached at the threshold the spatial extension of the infected cluster in surviving trials is found to grow as r t ensuremath sim t 1 z c with a multiplicative logarithmic correction and the average number of infected sites in surviving trials is found to increase as n s t ensuremath sim lnt ensuremath chi with ensuremath chi 2 in one dimension

the equilibrium limit of a constitutive model for two phase granular mixtures and its numerical approximation in this paper we analyze the equilibrium limit of the constitutive model for two phase granular mixtures introduced in papalexandris 2004 13 and develop an algorithm for its numerical approximation at equilibrium the constitutive model reduces to a strongly coupled overdetermined system of quasilinear elliptic partial differential equations with respect to the pressure and the volume fraction of the solid granular phase first we carry a perturbation analysis based on standard hydrostatic type scaling arguments which reduces the complexity of the coupling of the equations the perturbed system is then supplemented by an appropriate compatibility condition which arises from the properties of the gradient operator further based on the helmholtz decomposition and ladyzhenskaya s decomposition theorem we develop a projection type successive over relaxation numerical method this method is general enough and can be applied to a variety of continuum models of complex mixtures and mixtures with micro structure we also prove that this method is both stable and consistent hence under standard assumptions convergent the paper concludes with the presentation of representative numerical results

virtual mass in two phase bubbly flow abstract the two phase flow equations in their usual form are unstable it is known that the inclusion of the virtual mass of the gas bubbles greatly improves the stability of numerical computations since there is some confusion concerning the proper form of the virtual mass terms we first present a systematic derivation of the two fluid equations for a liquid gas mixture from a generalised form of hamilton s variational principle the two fluid theory of superfluid 4he has been derived in a similar way the resulting equations do not seem to have been presented before in the literature on two phase flow the derivation demonstrates how the pressure of the liquid gas mixture can be defined in a natural way two independent vorticities can be distinguished each having its own law of transportation kelvin theorem a subsequent stability analysis shows that at neutral stability the virtual mass coefficient m takes the form m 1 2 1 1 3 in the case of spherical gas bubbles with void fraction the corresponding local distribution of gas bubbles is anisotropic the vanishing of the virtual mass at 1 3 is interpreted as the breakdown of bubbly flow dissipative terms are introduced and analysed in an appendix

an exact riemann solver for compressible two phase flow models containing non conservative products in this article we present a new numerical procedure for solving exactly the riemann problem of compressible two phase flow models containing non conservative products these products appear in the expressions for the interactions between the two phases thus in the compressible limit the governing equations are hyperbolic but can not be written as conservation laws i e in divergence form in general the solution to the riemann problem of these models contains six distinct centered waves according to the relative position of these waves in the x t plane the possible solutions can be classified into four principal configurations the riemann solver we propose herein investigates sequentially each of these configurations until an admissible solution is calculated special configurations corresponding to coalescence of waves are also analyzed and included in the solver further we examine the accuracy and robustness of three known methods for the integration of the non conservative products via a series of numerical tests finally the issue of existence and uniqueness of solutions to the riemann problem is discussed