tests of mode coupling theory in two dimensions we analyze the glassy dynamics of binary mixtures of hard disks in two dimensions predictions of the mode coupling theory mct are tested with extensive brownian dynamics simulations measuring the collective particle density correlation functions in the vicinity of the glass transition we verify four predicted mixing effects for instance for large size disparities adding a small amount of small particles at a fixed packing fraction leads to a speedup in the long time dynamics while for small size disparities it leads to a slowing down qualitative features of the nonergodicity parameters and the relaxation which both depend in a nontrivial way on the mixing ratio are found in the simulated correlators studying one system in detail we are able to determine its ideal mct glass transition point as c 0 7948 and test mct predictions quantitatively

mode coupling approach to the ideal glass transition of molecular liquids linear molecules the mode coupling theory mct for the ideal liquid glass transition which was worked out for simple liquids mainly by gotze sjogren and their co workers is extended to a molecular liquid of linear and rigid molecules by use of the projection formalism of zwanzig and mori an equation of motion is derived for the correlators s sub lm l sup prime m sup prime bold q t of the tensorial one particle density rho sub lm bold q t which contains the orientational degrees of freedom for l greater than 0 application of the mode coupling approximation to the memory kernel results into a closed set of equations for s sub lm l sup prime m sup prime bold q t which requires the static correlators s sub lm l sup prime m sup prime bold q as the only input quantities the corresponding mct equations for the nonergodicity parameters f sub l sup m q equivalent f sub lm lm q bold e sub 3 are solved for a system of dipolar hard spheres by restricting the values for l to 0 and 1 depending on the packing fraction cursive phi and on the temperature t three different phases exist a liquid phase where translational tdof s l 0 and orientational odof s l 1 degrees of freedom are ergodic a phase where the tdof are frozen into a nonergodic glassy state whereas the odof s remain ergodic and finally a glassy phase where both tdof s and odof s are nonergodic from the nonergodicity parameters f sub 0 sup 0 q and f sub 1 sup 1 q for q 0 we may conclude that the corresponding relaxation strength of the alpha peak of the compressibility can be much smaller than the corresponding strength of the dielectric function

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

models and methods for two layer shallow water flows abstract two layer shallow water models present at least two fundamental difficulties that are addressed in the present contribution the first one is related to the lack of hyperbolicity of most existing models by considering weak compressibility of the phases a strictly hyperbolic formulation with pressure relaxation is obtained it is shown to tend to the conventional two layer model in the stiff pressure relaxation limit the second issue is related to the non conservative terms in the momentum equations analyzing the riemann problem structure local constants appear precisely at locations where the non conservative products need definition thanks to these local constants a locally conservative formulation of the equations is obtained simplifying the riemann problem resolution through a hll type riemann solver the method is compared to literature data showing accurate and oscillation free solutions additional numerical experiments show robustness and accuracy of the method

the time line interpolation method for large time step godunov type schemes abstract this paper describes the use of the time line interpolation procedure for the design of large time step godunov type schemes for systems of hyperbolic conservation laws in one dimension these schemes are based on a specific procedure to characterize the left and right states of the riemann problems at the cell interfaces when the courant number associated with the waves exceeds unity to do so the time line interpolation technique is used constant and linear reconstruction techniques are presented sonic or critical points are seen to be a source of difficulty in the algorithm and an appropriate treatment is proposed the algorithms are applied to the linear advection equation to the inviscid burgers equation and to the set of hyperbolic conservation laws that describe shallow water flow in one dimension these simulations show the superiority of the linear time reconstruction over the use of a constant time reconstruction when the linear reconstruction technique is used the modulus of the amplification factor of the scheme is equal to unity for all wave numbers inducing oscillations in the computed profile owing to the phase error the introduction of a slope limiter allows these oscillations to be eliminated but yields numerical diffusion thus restricting the range of applications of the scheme

glass transition of hard spheres in high dimensions we have investigated analytically and numerically the liquid glass transition of hard spheres for dimensions d ensuremath rightarrow ensuremath infty in the framework of mode coupling theory the numerical results for the critical collective and self nonergodicity parameters f c k d and f c s k d exhibit non gaussian k dependence even up to d 800 f c s k d and f c k d differ for k ensuremath sim d 1 2 but become identical on a scale k ensuremath sim d which is proven analytically the critical packing fraction ensuremath varphi c d ensuremath sim d 2 2 ensuremath d is above the corresponding kauzmann packing fraction ensuremath varphi k d derived by a small cage expansion its quadratic pre exponential factor is different from the linear one found earlier the numerical values for the exponent parameter and therefore the critical exponents a and b depend on d even for the largest values of d

the method of space time conservation element and solution element a new approach for solving the navier stokes and euler equations a new numerical framework for solving conservation laws is being developed this new framework differs substantially in both concept and methodology from the well established methods i e finite difference finite volume finite element and spectral methods it is conceptually simple and designed to overcome several key limitations of the above traditional methods a two level scheme for solving the convection diffusion equation u t a u x 2u x2 0 0 is constructed and used to illuminate major differences between the present method and those mentioned above this explicit scheme referred to as the a scheme has two independent marching variables unj and ux nj which are the numerical analogues of u and u x at j n respectively the a scheme has the unusual property that its stability is limited only by the cfl condition i e it is independent of also it can be shown that the amplification factors of the a scheme are identical to those of the leapfrog scheme if o and to those of the dufort frankel scheme if a o these coincidences are unexpected because the a scheme and the above classical schemes are derived from completely different perspectives and the a scheme does not reduce to the above classical schemes in the limiting cases the a scheme is extended to solve the 1d time dependent navier stokes equations of a perfect gas stability of this explicit solver also is limited only by the cfl condition in spite of the fact that it does not use i any techniques related to the high resolution upwind methods and ii any ad hoc parameter the current navier stokes solver is capable of generating highly accurate shock tube solutions particularly for high reynolds number flows shock discontinuities can be resolved within one mesh interval the inviscid 0 a scheme is reversible in time it also is neutrally stable i e free from numerical dissipation such a scheme generally cannot be extended to solve the euler equations thus the inviscid version is modified stability of this modified scheme referred to as the a scheme is limited by the cfl condition and 0 1 where is a special parameter that controls numerical dissipation moreover if 0 the amplification factors of the a scheme are identical to those of the leapfrog scheme which has no numerical dissipation on the other hand if 1 the two amplification factors of the a scheme become the same function of the courant number and the phase angle unexpectedly this function also is the amplification factor of the highly diffusive lax scheme note that because the lax scheme is very diffusive and it uses a mesh that is staggered in time a two level scheme using such a mesh is often associated with a highly diffusive scheme the a scheme which also uses a mesh staggering in time demonstrates that it can also be a scheme with no numerical dissipation the euler extension of the a scheme has stability conditions similar to those of the a epsiv scheme itself it has the unusual property that numerical dissipation at all mesh points can be controlled by a set of local parameters moreover it is capable of generating accurate shock tube solutions with the cfl number ranging from close to 1 to 0 022

maximizing expected terminal utility of an insurer with high gain tax by investment and reinsurance abstract this paper investigates optimal investment and proportional reinsurance policies for an insurer who subjects to pay high gain tax the surplus process of the insurer and the return process of the financial market are both modulated by the external macroeconomic environment the dynamic of the external macroeconomic environment is specified by a markov chain with finite states once the insurer s accumulated profits attain a new maximum they have to pay high gain tax the objective of the insurer is to maximize the expected terminal utility by investment and reinsurance the controlled wealth process of the insurer turned out to be a controlled jump diffusion process with reflections and markov regime switching by the weak dynamic programming principle wdpp we prove that the value function is the unique viscosity solution to the coupled hamilton jacob bellman hjb equations with first derivative boundary constraints by the markov chain approximating method for the hjb equations we construct a numerical scheme for approximating the viscosity solution to the coupled hjb equations two numerical examples are presented to illustrate the impact of both high gain tax and regime switching on the optimal policies

finite volume treatment of dispersion relation preserving and optimized prefactored compact schemes for wave propagation in developing suitable numerical techniques for computational aero acoustics the dispersion relation preserving drp scheme by tam and co workers and the optimized prefactored compact opc scheme by ashcroft and zhang have shown desirable properties of reducing both dissipative and dispersive errors these schemes originally based on the finite difference attempt to optimize the coefficients for better resolution of short waves with respect to the computational grid while maintaining pre determined formal orders of accuracy in the present study finite volume formulations of both schemes are presented to better handle the nonlinearity and complex geometry encountered in many engineering applications linear and nonlinear wave equations with and without viscous dissipation have been adopted as the test problems highlighting the principal characteristics of the schemes and utilizing linear and nonlinear wave equations with different wavelengths as the test cases the performance of these approaches is documented for the linear wave equation there is no major difference between the drp and opc schemes for the nonlinear wave equations the finite volume version of both drp and opc schemes offers substantially better solutions in regions of high gradient or discontinuity

risk sensitive control of finite state machines on an infinite horizon i in this paper we consider robust and risk sensitive control of discrete time finite state systems on an infinite horizon the solution of the state feedback robust control problem is characterized in terms of the value of an average cost dynamic game the risk sensitive stochastic optimal control problem is solved using the policy iteration algorithm and the optimal rate is expressed in terms of the value of a stochastic dynamic game with average cost per unit time criterion by taking a small noise limit a deterministic dynamic game which is closely related to the robust control problem is obtained

finite volume approximation of two phase fluid flows based on an approximate roe type riemann solver abstract we introduce an approximate roe type riemann solver for the numerical simulation of two phase fluid flows composed of liquid droplets suspended in gas we compute a roe linearization of some well conditioned approximate rankine hugoniot relations in non conservation form the computed solutions are found to be in good agreement with the exact solution in one dimension slab geometry we extend this solver to two dimensional geometries using a finite volume formulation

minimizing or maximizing the expected time to reach zero we treat the following control problems the process x 1 t with values in the interval infty 0 or 0 infty is given by the stochastic differential equation dx 1 t mu t dt sigma t dw t quad x 1 0 x 1 where the nonanticipative controls mu and sigma are to be chosen so that mu t sigma t remains in a given set mathcal s and the object is to minimize or maximize the expected time to reach the origin the minimization problem had been dicussed earlier by heath pestien and sudderth under various restrictions on the set mathcal s here an improved verification lemma is established which is used to solve the minimization and maximization problems for any mathcal s an application to a portfolio problem is discussed

exact and approximate riemann solvers for real gases a procedure is developed for solving the riemann problem rp for the flow of gases obeying an equation of state eos of the form p p a first method is introduced producing solutions of the exact rp the algorithm is validated by applying it to the classical test case of the shock tube for a perfect gas thereafter the method is applied to gases having eos of the van der waals or virial types with very good resulting accuracy however the procedure is somewhat demanding in computer time therefore some simplifying assumptions are introduced into the computation of simple waves leading to an approximate solution of the rp in most circumstances excellent results are obtained and the computer time is much more competitive however under certain extreme flow conditions it is recommended that a combination of the exact and approximate solvers for the rp be employed

stock trading an optimal selling rule trading in stock markets consists of three major steps select a stock purchase a number of shares and eventually sell them to make a profit the timing to buy and sell is extremely crucial a selling rule can be specified by two preselected levels a target price and a stop loss limit this paper is concerned with an optimal selling rule based on the model characterized by a number of geometric brownian motions coupled by a finite state markov chain such a policy can be obtained by solving a set of two point boundary value differential equations moreover the corresponding expected target period and probability of making money and that of losing money are derived analytic solutions are obtained in one and two dimensional cases finally a numerical example is considered to demonstrate the effectiveness of our method

regular article the space time conservation element and solution element method a new high resolution and genuinely multidimensional paradigm for solving conservation laws a new high resolution and genuinely multidimensional numerical method for solving conservation laws is being developed it was designed to avoid the limitations of the traditional methods and was built from ground zero with extensive physics considerations nevertheless its foundation is mathematically simple enough that one can build from it a coherent robust efficient and accurate numerical framework two basic beliefs that set the new method apart from the established methods are at the core of its development the first belief is that in order to capture physics more efficiently and realistically the modeling focus should be placed on the original integral form of the physical conservation laws rather than the differential form the latter form follows from the integral form under the additional assumption that the physical solution is smooth an assumption that is difficult to realize numerically in a region of rapid change such as a boundary layer or a shock the second belief is that with proper modeling of the integral and differential forms themselves the resulting numerical solution should automatically be consistent with the properties derived from the integral and differential forms e g the jump conditions across a shock and the properties of characteristics therefore a much simpler and more robust method can be developed by avoiding the explicit use of the above derived properties specifically to capture physics as fully as possible the method requires that i space and time be unified and treated as a single entity ii both local and global flux conservation in space and time be enforced and iii a multidimensional scheme be constructed without using the dimensional splitting approach such that multidimensional effects and source terms which are scalars can be modeled more realistically to simplify mathematics and broaden its applicability as much as possible the method attempts to use the simplest logical structures and approximation techniques specifically i it uses a staggered space time mesh such that flux at any interface separating two conservation elements can be evaluated internally in a simpler and more consistent manner without using a separate flux model ii it avoids the use of many well established techniques such as riemann solvers flux splittings and monotonicity constraints such that the complications and possibly even the limitations associated with them may be avoided and iii it avoids the use of special techniques that are not applicable to more general problems furthermore triangles in 2d space and tetrahedrons in 3d space are used as the basic building blocks of the spatial meshes such that the method i can be used to construct 2d and 3d nondissipative schemes in a natural manner and ii is compatible with the simplest unstructured meshes note that while numerical dissipation is required for shock capturing it may also result in annihilation of small disturbances such as sound waves and in the case of flow with a large reynolds number may overwhelm physical dissipation to overcome this difficulty two different and mutually complementary types of adjustable numerical dissipation are introduced in the present development

a local space time conservation scheme and its application in shock wave propagation abstract in this paper a local space time conservation scheme based on non staggered grids is introduced which is a variation of space time conservation element and solution element ce se scheme it inherits most features and advantages of ce se method including unified treatment of space and time and high accuracy resolution of hyperbolic conservation equations moreover riemann solvers are not needed to capture shocks and dimensional splitting methods are not needed in the multi dimensional schemes the stability of the present scheme is verified through von neumann analysis moreover several shock wave problems including one two and three dimensional cases are simulated by the present scheme by carefully comparing the present scheme s numerical results with exact solutions experimental results original ce se scheme s numerical results and third order eno scheme s numerical results it can be conclude that the present scheme is efficient and accurate

computational considerations for the simulation of shock induced sound the numerical study of aeroacoustic problems places stringent demands on the choice of a computational algorithm because it requires the ability to propagate disturbances of small amplitude and short wavelength the demands are particularly high when shock waves are involved because the chosen algorithm must also resolve discontinuities in the solution the extent to which a high order accurate shock capturing method can be relied upon for aeroacoustics applications that involve the interaction of shocks with other waves has not been previously quantified such a study is initiated in this work a fourth order accurate essentially nonoscillatory eno method is used to investigate the solutions of inviscid compressible flows with shocks the design order of accuracy is achieved in the smooth regions of a steady state quasi one dimensional test case however in an unsteady test case only first order results are obtained downstream of a sound shock interaction the difficulty in obtaining a globally high order accurate solution in such a case with a shock capturing method is demonstrated through the study of a simplified linear model problem some of the difficult issues and ramifications for aeroacoustic simulations of flows with shocks that are raised by these results are discussed

two dimensional computation of gas flow in a porous bed characterized by a porosity jump a finite volume method based on a vfroe solver to simulate the flow of compressible gas in a variable porous medium for two dimensional geometries is proposed the modeling is based on the euler system where a non conservative term is added to take the porosity variation into account a detailed presentation of the scheme is given the main point is the construction of non conservative fluxes to reproduce the non conservation aspect of the problem we compare the numerical method with an exact solution of the riemann problem and we check that the method preserves steady state situations even if we use a discontinuous jump for the porosity finally we present two simulations involving a two dimensional gas flow

stochastic discrete equation method sdem for two phase flows a new scheme for the numerical approximation of a five equation model taking into account uncertainty quantification uq is presented in particular the discrete equation method dem for the discretization of the five equation model is modified for including a formulation based on the adaptive semi intrusive asi scheme thus yielding a new intrusive scheme sdem for simulating stochastic two phase flows some reference test cases are performed in order to demonstrate the convergence properties and the efficiency of the overall scheme the propagation of initial conditions uncertainties is evaluated in terms of mean and variance of several thermodynamic properties of the two phases

a new fuzzy programming approach for multi period portfolio optimization with return demand and risk control abstract this paper considers a multi period portfolio selection problem imposed by return demand and risk control in a fuzzy investment environment in which the returns of assets are characterized by fuzzy numbers a fuzzy lower semi deviation is originally defined as the risk control of portfolio a proportion entropy constraint is added as the divergence measure of portfolio based on the theories of possibility and necessity measures a new multi period portfolio optimization model with return demand and risk control is proposed and then the proposed model is transformed into a crisp nonlinear programming problem by using fuzzy programming approach furthermore an improved differential evolution algorithm is designed for obtaining the optimal strategy finally a numerical example is given to illustrate the practicality and efficiency of the proposed model and the corresponding algorithm

a stochastic control approach to portfolio problems with stochastic interest rates we consider investment problems where an investor can invest in a savings account stocks and bonds and tries to maximize her utility from terminal wealth in contrast to the classical merton problem we assume a stochastic interest rate to solve the corresponding control problems it is necessary to prove a verification theorem without the usual lipschitz assumptions

a generalized multi period mean variance portfolio optimization with markov switching parameters in this paper we deal with a generalized multi period mean variance portfolio selection problem with market parameters subject to markov random regime switchings problems of this kind have been recently considered in the literature for control over bankruptcy for cases in which there are no jumps in market parameters see zhu s s li d wang s y 2004 risk control over bankruptcy in dynamic portfolio selection a generalized mean variance formulation ieee transactions on automatic control 49 447 457 we present necessary and sufficient conditions for obtaining an optimal control policy for this markovian generalized multi period mean variance problem based on a set of interconnected riccati difference equations and on a set of other recursive equations some closed formulas are also derived for two special cases extending some previous results in the literature we apply the results to a numerical example with real data for risk control over bankruptcy in a dynamic portfolio selection problem with markov jumps selection problem

mode coupling theory for the slow collective dynamics of fluids adsorbed in disordered porous media we derive a mode coupling theory for the slow dynamics of fluids confined in disordered porous media represented by spherical particles randomly placed in space its equations display the usual nonlinear structure met in this theoretical framework except for a linear contribution to the memory kernel which adds to the usual quadratic term the coupling coefficients involve structural quantities which are specific of fluids evolving in random environments and have expressions which are consistent with those found in related problems numerical solutions for two simple models with pure hard core interactions lead to the prediction of a variety of glass transition scenarios which are either continuous or discontinuous and include the possibility of higher order singularities and glass glass transitions the main features of the dynamics in the two most generic cases are reviewed and illustrated with detailed computations moreover a reentry phenomenon is predicted in the low fluid high matrix density regime and is interpreted as the signature of a de correlation mechanism by fluid fluid collisions competing with the localization effect of the solid matrix

dual control monte carlo method for tight bounds of value function in regime switching utility maximization abstract in this paper we study the dual control approach for the optimal asset allocation problem in a continuous time regime switching market we find the lower and upper bounds of the value function that is a solution to a system of fully coupled nonlinear partial differential equations these bounds can be tightened with additional controls to the dual process we suggest a monte carlo algorithm for computing the tight lower and upper bounds and show the method is effective with a variety of utility functions including power non hara and yaari utilities the latter two utilities are beyond the scope of any current methods available in finding the value function

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

multicomponent flow calculations by a consistent primitive algorithm the dynamics of inviscid multicomponent fluids may be modelled by the euler equations augmented by one or more additional species equation s attempts to compute solutions for extended euler models in conservation form show strong oscillations and other computational inaccuracies near material interfaces these are due to erroneous pressure fluctuations generated by the conservative wave model this problem does not occur in single component computations and arises only in the presence of several species a nonconservative primitive euler formulation is proposed which results in complete elimination of the oscillations the numerical algorithm uses small viscous perturbations to remove leading order conservation errors and is conservative to the order of numerical approximation numerical experiments show clean monotonic solution profiles with acceptably small conservation error for shocks of weak to moderate strengths

an accurate low mach scheme for a compressible two fluid model applied to free surface flows classical approximate riemann solvers are known to be too much dissipative in the low mach number regime for this reason since the mach number in liquids is generally very small usual upwind schemes may provide inaccurate solutions when applied to the simulation of two phase flows in this paper to circumvent this difficulty while keeping a compressible model for the description of both gas and liquid an original accurate low mach scheme is introduced and theoretically studied extending some ideas already used for the gas dynamics system the proposed scheme is based on a centred formulation for the pressure gradient term in the momentum equation and on the introduction of a stabilising term proportional to the pressure difference between two neighbouring cells the scheme stability is ensured and theoretically proved under a convective cfl like condition by using a semi implicit time discretisation algorithm finally the correct asymptotic behaviour of the scheme in the limit of small mach numbers is assessed on several academic test cases

application of space time ce se method to shallow water magnetohydrodynamic equations in this article we apply a space time conservation element and solution element ce se method for the approximate solution of shallow water magnetohydrodynamic smhd equations in one and two space dimensions these equations model the dynamics of nearly incompressible conducting fluids for which the evolution is nearly two dimensional with magnetic equilibrium in the third direction in this article we are using a variant of the ce se method developed by zhang et al a space time conservation element and solution element method for solving the two dimensional unsteady euler equations using quadrilateral and hexahedral meshes j comput phys 175 2002 168 199 this method uses structured and unstructured quadrilateral and hexahedral meshes in two and three space dimensions respectively in this method a single conservation element at each grid point is employed for solving conservation laws no matter in one two and three space dimensions the present scheme use the conservation element to calculate flow variables only while the gradients of flow variables are calculated by central differencing reconstruction procedure we give both one and two dimensional test computations a qualitative comparison reveals an excellent agreement with previous published results of wave propagation method and evolution galerkin schemes the one and two dimensional computations reported in this paper demonstrate the remarkable versatility of the present ce se scheme

simulation of compressible two phase flows with topology change of fluid fluid interface by a robust cut cell method we develop a robust cut cell method for numerical simulation of compressible two phase flows with topology change of the fluid fluid interface in cut cell methods the flows can be solved in the finite volume framework and the jump conditions at the interface are resolved by solving a local riemann problem therefore cut cell methods can obtain interface evolution with high resolution and at the same time satisfactorily maintain the conservation of flow quantities however it remains a challenge for the cut cell methods to handle interfaces with topology change or very high curvature where the mesh is not sufficiently fine to resolve the interface inappropriate treatment could give rise to either distorted interface advection or unphysical oscillation of flow variables especially when the regularization process e g reinitialization in the level set methods is implemented a robust cut cell method is proposed here with the interface being tracked by a level set function the local unphysical oscillation of flow variables in the presence of topology change is shown to be greatly suppressed by using a delayed reinitialization the method can achieve second order accuracy with respect to the interface position in the absence of topology changes of interface while locally degrading to first order at the interface region where topology change occurs its performance is examined through a variety of numerical tests such as rayleigh collapse shock bubble interaction and shock induced bubble collapse in water numerical results are compared against either benchmark solutions or experimental observations and good agreement has been achieved qualitatively and or quantitatively finally we apply the method to investigating the collapse process of two tandem bubbles in water

computations of two fluid models based on a simple and robust hybrid primitive variable riemann solver with ausmd this paper is to continue our previous work in 2008 on solving a two fluid model for compressible liquid gas flows we proposed a pressure velocity based diffusion term original derived from ausmd scheme of wada and liou in 1997 to enhance its robustness the proposed ausmd schemes have been applied to gas and liquid fluids universally to capture fluid discontinuities such as the fluid interfaces and shock waves accurately for the ransom s faucet problem air water shock tube problems and 2d shock water liquid interaction problems however the proposed scheme failed at computing liquid gas interfaces in problems under large ratios of pressure density and volume of fraction the numerical instability has been remedied by chang and liou in 2007 using the exact riemann solver to enhance the accuracy and stability of numerical flux across the liquid gas interface here instead of the exact riemann solver we propose a simple ausmd type primitive variable riemann solver pvrs which can successfully solve 1d stiffened water air shock tube and 2d shock gas interaction problems under large ratios of pressure density and volume of fraction without the expensive cost of tedious computer time in addition the proposed approach is shown to deliver a good resolution of the shock front rarefaction and cavitation inside the evolution of high speed droplet impact on the wall

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 phase flows second order schemes and boundary conditions a second order numerical method suitable to unstructured grids is developed for the solution of two phase flow equations a number of assumptions are introduced justified on physical grounds when the dispersed phase concentration is low their effect is to change the mathematical nature of the system of equations the new numerical method put forward builds on van leer s original ideas the solution of two riemann problems is involved one for the gas phase and a second for the dispersed phase the method is first tested on a one dimensional case with excellent results it is then generalized to two dimensions

strongly confined fluids diverging time scales and slowing down of equilibration the newtonian dynamics of strongly confined fluids exhibits a rich behavior its confined and unconfined degrees of freedom decouple for confinement length l 0 in that case and for a slit geometry the intermediate scattering functions s q t simplify resulting for 0 0 in a knudsen gas like behavior of the confined degrees of freedom and otherwise in s q t describing the structural relaxation of the unconfined ones taking the coupling into account we prove that the energy fluctuations relax exponentially for smooth potentials the relaxation times diverge as l 3 and l 4 respectively for the confined and unconfined degrees of freedom the strength of the l 3 divergence can be calculated analytically it depends on the pair potential and the two dimensional pair distribution function experimental setups are suggested to test these predictions

portfolio optimization with markov modulated stock prices and interest rates a financial market with one bond and one stock is considered where the risk free interest rate the appreciation rate of the stock and the volatility of the stock depend on an external finite state markov chain we investigate the problem of maximizing the expected utility from terminal wealth and solve it by stochastic control methods for different utility functions due to explicit solutions it is possible to compare the value function of the problem to one where we have constant average market data the case of benchmark optimization is also considered

bellman equations of risk sensitive control risk sensitive control problems are considered existence of a nonnegative solution to the bellman equation of risk sensitive control is shown the result is applied to prove that no breaking down occurs asymptotic behaviour of the nonnegative solution is studied in relation to ergodic control problems and the relationship between the asymptotics and the large deviation principle is noted

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

a space time conservation element and solution element method for solving the two and three dimensional unsteady euler equations using quadrilateral and hexahedral meshes in this paper we report a version of the space time conservation element and solution element ce se method in which the 2d and 3d unsteady euler equations are simulated using structured or unstructured quadrilateral and hexahedral meshes respectively in the present method mesh values of flow variables and their spatial derivatives are treated as independent unknowns to be solved for at each mesh point the value of a flow variable is obtained by imposing a flux conservation condition on the other hand the spatial derivatives are evaluated using a finite difference weighted average procedure note that the present extension retains many key advantages of the original ce se method which uses triangular and tetrahedral meshes respectively for its 2d and 3d applications these advantages include efficient parallel computing ease of implementing nonreflecting boundary conditions high fidelity resolution of shocks and waves and a genuinely multidimensional formulation without the need to use a dimensional splitting approach in particular because riemann solvers the cornerstones of the godunov type upwind schemes are not needed to capture shocks the computational logic of the present method is considerably simpler to demonstrate the capability of the present method numerical results are presented for several benchmark problems including oblique shock reflection supersonic flow over a wedge and a 3d detonation flow

transport of pollutant in shallow flows a space time ce se scheme abstract this paper focuses on implementation of space time ce se scheme for computing the transport of a passive pollutant by a flow the flow model comprises of the saint venant system of shallow water equations and the pollutant propagation is described by a transport equation the one dimensional and two dimensional flow equations are numerically investigated using the ce se scheme a number of test problems are presented to check the accuracy and efficiency of the proposed scheme the results of ce se scheme are compared with the central scheme both the schemes are found to be in close agreement however our proposed ce se scheme accurately captures shocks and discontinuous profiles

an asymptotic preserving scheme for the two fluid euler poisson model in the quasineutral limit this paper deals with the modeling of a plasma in the quasineutral limit using the two fluid euler poisson system in this limit explicit numerical schemes suffer from severe numerical constraints related to the small debye length and large plasma frequency here we propose an implicit scheme which reduces to a scheme for the quasineutral euler model in the quasineutral limit such a property is referred to as asymptotic preservation one of the distinctive features of this scheme is that it has a comparable numerical cost to that of an explicit scheme simply the poisson equation is replaced by a different but formally equivalent elliptic problem we present numerical simulations for two different one dimensional test cases they confirm the expected stability of the scheme in the quasineutral limit they also show that this scheme has some accuracy problems in the limit of small electron to ion mass ratio in reproducing the correct electron velocity but this problem is already present in the results of the classical algorithm numerical simulations are also performed for a two dimensional problem of a plasma expansion in vacuum between two electrodes

an acoustic convective splitting based approach for the kapila two phase flow model in this paper we propose a new acoustic convective splitting based numerical scheme for the kapila five equation two phase flow model the splitting operator decouples the acoustic waves and convective waves the resulting two submodels are alternately numerically solved to approximate the solution of the entire model the lagrangian form of the acoustic submodel is numerically solved using an hllc type riemann solver whereas the convective part is approximated with an upwind scheme the result is a simple method which allows for a general equation of state numerical computations are performed for standard two phase shock tube problems a comparison is made with a non splitting approach the results are in good agreement with reference results and exact solutions

risk sensitive control on an infinite time horizon stochastic control problems on an infinite time horizon with exponential cost criteria are considered the donsker varadhan large deviation rate is used as a criterion to be optimized the optimum rate is characterized as the value of an associated stochastic differential game with an ergodic expected average cost per unit time cost criterion if we take a small noise limit a deterministic differential game with average cost per unit time cost criterion is obtained this differential game is related to robust control of nonlinear systems

an hllc type riemann solver and high resolution godunov method for a two phase model of reactive flow with general equations of state abstract a high resolution godunov method is developed for a two phase model of reactive flow the model considers general equations of state of mie gruneisen form and different choices for the reaction rate both relevant for simulations of the dynamical behavior of detonations in pbx type granular explosives the numerical approach employs a riemann solver and various options ranging from an exact solver to an approximate solver of hllc type are described a principal aim of the paper is an assessment of the approximate riemann solvers in terms of the accuracy and efficiency of numerical solutions of the two phase model in particular this study considers the state sensitive behavior in different regimes of the solutions in a reverse impact configuration including compaction run to detonation and the evolution to compaction led and reaction led steady detonations for these regimes the convergence properties of the numerical approach are examined for the different choices of the riemann solver as is the error in the solutions at lower grid resolution finally the computational performance of the time stepping scheme is assessed for the different solvers

a risk sensitive control dual approach to a large deviations control problem we consider a control problem of an ergodic process where the objective is to maximize over long term the probability to overperform a given level this is formulated as a large deviations control problem for which the standard dynamic programming methods may not be applied directly we solve this problem by adopting a duality approach leading to a risk sensitive ergodic control problem in a continuous time diffusion setting we state a verification theorem in terms of partial differential equations for this dual problem we then turn back to the primal problem by means of large deviations techniques we derive the optimal rate function and nearly optimal controls for the large deviations optimization problem finally explicit solutions are provided in a linear quadratic case

completely monotone solutions of the mode coupling theory for mixtures we establish that a mode coupling approximation for the dynamics of multi component systems obeying smoluchowski dynamics preserves a subtle yet fundamental property the partial density correlation functions are considered as matrices completely monotone i e they can exactly be written as superpositions of decaying exponentials only this statement holds no matter what further approximations are needed to calculate the theory s coupling parameters the long time limit of these functions fulfills a maximum property and an iteration scheme for its numerical determination is given we also show the existence of a unique solution to the equations of motion for which power series both for short times and small frequencies exist the latter except at special points where ergodic to nonergodic transitions occur these transitions are bifurcations that are proven to be of the cuspoid family

a well balanced scheme for the numerical processing of source terms in hyperbolic equations in a variety of physical problems one encounters source terms that are balanced by internal forces and this balance supports multiple steady state solutions that are stable typical of these are gravity driven flows such as those described by the shallow water equations over a nonuniform ocean bottom 1 10 qquad h t hu x 0 text and hu t left hu 2 frac gh 2 2 right x ga x x h 0 many classic numerical schemes cannot maintain these steady solutions or achieve them in the long time limit with an acceptable level of accuracy because they do not preserve the proper balance between the source terms and internal forces we propose here a numerical scheme adapted to a scalar conservation law that preserves this balance and that can it is hoped be extended to more general hyperbolic systems the proof of convergence of this scheme toward the entropy solution is given and some numerical tests are reported

optimal control of favorable games with a time limit this paper shows how to optimally control a stochastic process if one seeks to reach a certain value before a fixed time without first hitting zero the process has a drift in the favorable direction discrete time random walks as well as continuous time diffusion processes are considered the controls available are such that zero variance means zero drift and more variance means more drift to be more precise in the continuous time case it holds that dx t sigma x t t mu t dt db t where sigma is the control variable as corollaries of the results some interesting inequalities for stochastic processes are obtained

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

portfolio selection in the enlarged markovian regime switching market we study a portfolio selection problem in a continuous time markovian regime switching model the market in this model is in general incomplete we adopt a method to complete the market based on an enlargement of the market using a set of geometric markovian jump securities we solve the portfolio selection problem in the enlarged market for a power utility and a logarithmic utility closed form solutions for the optimal portfolio strategies and the value functions are obtained in both cases we also establish the relationship between the optimal portfolio problems in the enlarged market and the original market

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

testing mode coupling theory for a supercooled binary lennard jones mixture i the van hove correlation function we report the results of a large scale computer simulation of a binary supercooled lennard jones liquid we find that at low temperatures the curves for the mean squared displacement of a tagged particle for different temperatures fall onto a master curve when they are plotted versus rescaled time td t where d t is the diffusion constant the time range for which these curves follow the master curve is identified with the ensuremath alpha relaxation regime of mode coupling theory mct this master curve is fitted well by a functional form suggested by mct in accordance with idealized mct d t shows a power law behavior at low temperatures the critical temperature of this power law is the same for both types of particles and also the critical exponents are very similar however contrary to a prediction of mct these exponents are not equal to the ones determined previously for the divergence of the relaxation times of the intermediate scattering function phys rev lett 73 1376 1994 at low temperatures the van hove correlation function self as well as distinct part shows almost no sign of relaxation in a time interval that extends over about three decades in time this time interval can be interpreted as the ensuremath beta relaxation regime of mct from the investigation of these correlation functions we conclude the hopping processes are not important on the time scale of the ensuremath beta relaxation for this system and for the temperature range investigated we test whether the factorization property predicted by mct holds and find that this is indeed the case for all correlation functions investigated the distance dependences of the critical amplitudes are in qualitative agreement with the ones predicted by mct for some other mixtures the non gaussian parameter for the self part of the van hove correlation function for different temperatures follows a master curve when plotted against time t

method for optimally controlling unsteady shock strength in one dimension this paper presents a new formulation and computational solution of an optimal control problem concerning unsteady shock wave attenuation the adjoint system of equations for the unsteady euler system in one dimension is derived and used in an adjoint based solution procedure for the optimal control a novel algorithm is used to satisfy all necessary first order optimality conditions while locally minimizing an appropriate cost functional distributed control solutions with certain physical constraints are calculated for attenuating blast waves similar to those generated by ignition overpressure from the shuttle s solid rocket booster during launch results are presented for attenuating shocks traveling at mach 1 5 and 3 5 down to 85 80 and 75 of the uncontrolled wave s driving pressure the control solutions give insight into the magnitude and location of energy dissipation necessary to decrease a given blast wave s overpressure to a set target level over a given spatial domain while using only as m

gpu accelerated cese method for 1d shock tube problems in the present study a gpu accelerated 1d space time cese method is developed and applied to shock tube problems with and without condensation we have demonstrated how to implement the cese algorithm to solve 1d shock tube problems using an older generation gpu the nvidia 9800 gt with relatively limited memory to optimize the code performance we used shared memory and solved the inter block boundary problem in two ways namely the branch scheme and the overlapping scheme the implementations of these schemes are discussed in detail and their performances are compared for the sod shock tube problems for the sod problem without condensation the speedup over an intel cpu e7300 is 23 for the branch scheme and 41 for the overlapping scheme respectively while for problems with condensation both schemes achieve higher acceleration ratios 53 and 71 respectively the higher speedup of the condensation case can be ascribed to the source term calculation which has a local dependence on the mesh point and the source kernel has a higher acceleration ratio

aeroacoustic computations using a high order shock capturing scheme for aeroacoustic computations in the supersonic regime it is necessary to use a numerical scheme that can represent shock waves without generating spurious numerical oscillations the centered schemes that are usually used with success in the subsonic case combined with a selective filtering will generally oscillate in the presence of discontinuities a new class of shock capturing schemes the one step monotonicity preserving schemes combine the high accuracy and the nonoscillating property it is thus a good candidate for supersonic aeroacoustic applications the good spectral properties of these schemes are illustrated in the scalar linear case results of aeroacoustic test problems for the euler and navier stokes equations are compared with a dispersion relation preserving scheme the application to a supersonic cavity flow which induces a complex pattern of moving shocks shows that the one step monotonicity preserving schemes capture the moving discontinuities without spurious oscillations and preserve a high accuracy at the same time

constrained optimization framework for interface aware sub scale dynamics closure model for multimaterial cells in lagrangian and arbitrary lagrangian eulerian hydrodynamics abstract a systematic description of the new interface aware sub scale dynamics ia ssd closure model for the lagrangian stage of multimaterial arbitrary lagrangian eulerian methods is presented the ia ssd closure model consists of two stages during the first bulk stage the well known equal compressibility model is used during the second stage sub scale interactions of the materials inside the multimaterial cell are taken into account at this stage information about the topology of the materials inside the multimaterial cell is utilized allowing the orientations of internal interfaces to be included in the model each material interacts in a pair wise fashion with the materials with which it has a common boundary the interactions are based on the solution of the acoustic riemann problem between each pair of materials and is limited using physically justified constraints positivity of volume positivity of internal energy and controlled rate of pressure relaxation to determine the values of the limiter coefficients a constrained optimization framework is employed using a quadratic objective function with linear constraints the algorithm guarantees the positivity of the material volume and internal energy as well as the smooth relaxation of the pressure this allows a significant increase in the robustness of the overall algorithm the results of comprehensive testing of the new model have been presented for one and two dimensional multimaterial lagrangian hydrodynamics along with representative results for 2d multimaterial arbitrary lagrangian eulerian ale calculations the numerical tests have shown that in most cases the new ia ssd closure model produces better results compared to the well known tipton s closure model

optimal investment for worst case crash scenarios a martingale approach we investigate the optimal portfolio problem under the threat of a financial market crash in a multidimensional jump diffusion framework we set up a nonprobabilistic crash model and consider an investor that seeks to maximize crra utility in the worst possible crash scenario we recast the problem as a stochastic differential game with the help of the fundamental notion of indifference strategies we completely solve the portfolio problem using martingale arguments

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

solving the mhd equations by the space time conservation element and solution element method we apply the space time conservation element and solution element cese method to solve the ideal mhd equations with special emphasis on satisfying the divergence free constraint of magnetic field i e b 0 in the setting of the cese method four approaches are employed i the original cese method without any additional treatment ii a simple corrector procedure to update the spatial derivatives of magnetic field b after each time marching step to enforce b 0 at all mesh nodes iii a constraint transport method by using a special staggered mesh to calculate magnetic field b and iv the projection method by solving a poisson solver after each time marching step to demonstrate the capabilities of these methods two benchmark mhd flows are calculated i a rotated one dimensional mhd shock tube problem and ii a mhd vortex problem the results show no differences between different approaches and all results compare favorably with previously reported data

on the wave interactions in the drift flux equations of two phase flows abstract in the present work we investigate the riemann problem and interaction of weak shocks for the widely used isentropic drift flux equations of two phase flows the complete structure of solution is analyzed and with the help of rankine hugoniot jump condition and lax entropy conditions we establish the existence and uniqueness condition for elementary waves the explicit form of the shock waves contact discontinuities and rarefaction waves are derived analytically within this respect we develop an exact riemann solver to present the complete solution structure a necessary and sufficient condition for the existence of solution to the riemann problem is derived and presented in terms of initial data furthermore we present a necessary and sufficient condition on initial data which provides the information about the existence of a rarefaction wave or a shock wave for one or three family of waves to validate the performance and the efficiency of the developed exact riemann solver a series of test problems selected from the open literature are presented and compared with independent numerical methods simulation results demonstrate that the present exact solver is capable of reproducing the complete wave propagation using the current drift flux equations as the numerical resolution the provided computations indicate that accurate results be accomplished efficiently and in a satisfactory agreement with the exact solution

application of the space time conservation element and solution element method to one dimensional convection diffusion problems abstract in the space time conservation element and solution element ce se method the independent marching variables used comprise not only the mesh values of the physical dependent variables but also in contrast to a typical numerical method the mesh values of the spatial derivatives of these physical variables the use of the extra marching variables results from the need to construct the two level explicit and nondissipative schemes which are at the core of the ce se development it also results from the need to minimize the stencil while maintaining accuracy in this paper using the 1d a scheme as an example the effect of this added complication on consistency accuracy and operation count is assessed as part of this effort an equivalent yet more efficient form of the a scheme in which the independent marching variables are the local fluxes tied to each mesh point is introduced also the intriguing relations that exist among the a leapfrog and dufort frankel schemes are further explored in addition the redundancy of the leapfrog dufort frankel and lax schemes and the remedy for this redundancy are discussed this paper is concluded with the construction and evaluation of a ce se solver for the inviscid burgers equation

mode coupling theory of the glass transition for confined fluids we present a detailed derivation of a microscopic theory for the glass transition of a liquid enclosed between two parallel walls relying on a mode coupling approximation this geometry lacks translational invariance perpendicular to the walls which implies that the density profile and the density density correlation function depends explicitly on the distances to the walls we discuss the residual symmetry properties in slab geometry and introduce a symmetry adapted complete set of two point correlation functions since the currents naturally split into components parallel and perpendicular to the walls the mathematical structure of the theory differs from the established mode coupling equations in bulk we prove that the equations for the nonergodicity parameters still display a covariance property similar to bulk liquids

central upwind schemes for the system of shallow water equations with horizontal temperature gradients we introduce a central upwind scheme for one and two dimensional systems of shallow water equations with horizontal temperature gradients the ripa system the scheme is well balanced positivity preserving and does not develop spurious pressure oscillations in the neighborhood of temperature jumps that is near the contact waves such oscillations would typically appear when a conventional godunov type finite volume method is applied to the ripa system and the nature of the oscillation is similar to the ones appearing at material interfaces in compressible multifluid computations the idea behind the proposed approach is to utilize the interface tracking method originally developed in chertock et al m2an math model numer anal 42 991 1019 2008 for compressible multifluids the resulting scheme is highly accurate preserves two types of lake at rest steady states and is oscillation free across the temperature jumps as it is illustrated in a number of numerical experiments

diffuse interface model for compressible fluid compressible elastic plastic solid interaction an eulerian hyperbolic diffuse interface model for elastic plastic solid fluid interaction is constructed the system of governing equations couples euler equations of compressible fluids and a visco plastic model of maxwell type materials the deviatoric part of the stress tensor decreases during plastic deformations in the same manner as models of multicomponent fluids in particular the model is able to create interfaces which were not present initially the model is thermodynamically compatible it verifies the entropy inequality however a numerical treatment of the model is particularly challenging indeed the model is non conservative so a special numerical splitting is proposed to overcome this difficulty the numerical algorithm contains two relaxation procedures one of them is physical and is related to the plastic relaxation mechanism relaxation toward the yield surface the second one is numerical it consists in replacing the algebraic equation expressing a mechanical equilibrium between components by a partial differential equation with a short relaxation time the numerical method was tested in 1d case wilkins flying plate problem 2d plane case impact of a projectile on a plate and axisymmetrical case taylor test problem impact with penetration effects etc numerical examples show the ability of the model to deal with real physical phenomena

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

a darcy law for the drift velocity in a two phase flow model this work deals with the design and numerical approximation of an eulerian mixture model for the simulation of two phase dispersed flows in contrast to the more classical two fluid or drift flux models the influence of the velocity disequilibrium is taken into account through dissipative second order terms characterized by a darcy law for the relative velocity as a result the convective part of the model is always unconditionally hyperbolic we show that this model corresponds to the first order equilibrium approximation of classical two fluid models a finite volume approximation of this system taking advantage of the hyperbolic nature of the convective part of the model and of the particular structural form of the dissipative part is proposed numerical applications are presented to assess the capabilities of the model

the space time cese scheme for shallow water equations incorporating variable bottom topography and horizontal temperature gradients abstract the effects of bottom topography and horizontal temperature gradients on the shallow water flows are theoretically investigated the considered systems of partial differential equations pdes are non strictly hyperbolic and non conservative due to the presence of non conservative differential terms on the right hand side the solutions of these model equations are very challenging for a numerical scheme thus our primary goal is to introduce an improved numerical scheme which can handle the non conservative differential terms efficiently and accurately in this paper the space time conservation element and solution element cese method is extended to approximate these model equations the proposed scheme has capability to overcome all difficulties posed by this nonlinear system of pdes the performance of the scheme is analyzed by considering several case studies of practical interest and the results of suggested scheme are compared with those of central nt scheme the accuracy of the scheme is verified qualitatively and quantitatively

risk sensitive control of discrete time markov processes with infinite horizon in this paper we study existence of solutions to the bellman equation corresponding to risk sensitive ergodic control of discrete time markov processes using three different approaches also for particular classes of systems asymptotics for vanishing risk factor is investigated showing that in the limit the optimal value for an average cost per unit time is obtained

an approximate linearized riemann solver for a two fluid model an approximate linearized riemann solver is presented for the numerical simulation of two phase flows this new solver is based on a linearization of nonconservative products and uses an extension of roe s approximate riemann solver the scheme is applied to shock tube problem and to a standard test for two fluid codes

controlling a process to a goal in finite time a player starts at x in 0 1 and seeks to reach 1 by time t0 the process xt 0 t t0 of the player s positions is a diffusion process or an ito process whose infinitesimal parameters are chosen by the player at each instant of time from a set depending on the current position the probability of reaching 1 by time t0 is maximized if the player can and does choose the parameters so that and 2 are maximized at least when these maxima are sufficiently regular this result implies that bold play is optimal for subfair continuous time red and black and roulette when there is a limit on playing time

multi period mean variance portfolio optimization with high order coupled asset dynamics this paper is concerned with a multi period portfolio management problem over a finite horizon the objective is to seek the optimal investment policy series which maximizes the weighted sum of a linear combination of the expected return and the variance of portfolio over all the investment periods this formulation enables the investor to adjust weights for any period and have full freedom and control over their best tradeoff between return and risk over each period we show that such a problem is a convex quadratic programming problem in terms of the decision variables regardless of price dynamic nature either linear or nonlinear cases by solving the stationary equation directly an optimal solution is developed for its original problem without using embedding method the solution is simplified for a general linear price model with high order and coupled asset dynamics and shown to be implementable with historical price data simulation is carried out on usa and china stock markets with real data which demonstrates feasibility and better performance of the proposed solution than the special case considered in the literature in particular the proposed solution with suitable nonzero weights on intermediate time periods offers higher return at the same risk level compared with one involving the terminal wealth only in the objective function

an all speed relaxation scheme for interface flows with surface tension we consider interface flows where compressibility and capillary forces surface tension are significant these flows are described by a non conservative unconditionally hyperbolic multiphase model the numerical approximation is based on finite volume method for unstructured grids at the discrete level the surface tension is approximated by a volume force csf formulation the interface physical properties are recovered by designing an appropriate linearized riemann solver relaxation scheme that prevents spurious oscillations near material interfaces for low speed flows a preconditioning linearization is proposed and the low mach asymptotic is formally recovered numerical computations for a bubble equilibrium converge to the required laplace law and the dynamic of a drop falling under gravity is in agreement with experimental observations

optimal control of favorable games with expected loss constraint using a forward backward iterative method we maximize the expected profit of a gambling strategy for an arbitrary finite sequence of independent favorable gambles with payoffs in l1 under an expected loss constraint the solution is explicit up to solving a finite sequence of deterministic optimization problems over mathbf r 2