global existence in l1 for the enskog equation and convergence of the solutions to solutions of the boltzmann equation for the enskog equation in a box an existence theorem is proved for initial data with finite mass energy and entropy then by letting the diameter of the molecules go to zero the weak convergence of solutions of the enskog equation to solutions of the boltzmann equation is proved

l1 and bv type stability of the boltzmann equation with external forces abstract based on the existence theory on the boltzmann equation with external forces in infinite vacuum in this paper we will study the l 1 and bv type stability of the classical solutions for small initial data the stability results generalize those for the boltzmann equation without force to the case with external force in particular we show that the stability can be established for the soft potentials directly while the stability for the hard potentials and hard sphere model is obtained through the construction of some nonlinear functionals the functionals thus constructed generalize those constructed in s y ha nonlinear functionals of the boltzmann equation and uniform stability estimates j differential equations 215 2005 178 205 for the case without force to capture the effect of the force term on the time evolution of the solutions

on the inelastic enskog equation near vacuum the cauchy problem for the inelastic enskog equation is considered for near vacuum data the global existence of mild and classical solutions of the inelastic enskog equation is obtained then based on some new functionals we give the uniform l1 x v stability of solutions for the inelastic enskog equation

the enskog boltzmann equation in the whole space r3 some global existence uniqueness and stability results abstract the enskog boltzmann equation a partial differential integral equation of the hyperbolic type is a model which generalizes the classical boltzmann equation to high gas densities and is here considered with an analysis of the well posedness of the initial value problem in unbounded domains some new global existence and uniqueness results for the solutions of the initial value problem and a discussion on the asymptotic stability are provided under suitable assumptions about the size of the norm of the initial data and about the rate of decay to zero at infinity in the phase space

an improved unsteady unstructured artificial compressibility finite volume scheme for viscous incompressible flows part i theory and implementation a robust artificial compressibility scheme has been developed for modelling laminar steady state and transient incompressible flows over a wide range of reynolds and rayleigh numbers artificial compressibility is applied in a consistant manner resulting in a system of preconditioned governing equations a locally generalized preconditioner is introduced designed to be robust and offer good convergence rates free artificial compressibility parameters in the equations are automated to allow ease of use while facilitating improved or comparable convergence rates as compared with the standard artificial compressibility scheme memory efficiency is achieved through a multistage pseudo time explicit time marching solution procedure a node centred dual cell edge based finite volume discretization technique suitable for unstructured grids is used due to its computational efficiency and high resolution spatial accuracy in the interest of computational efficiency and ease of implementation stabilization is achieved via a scalar valued artificial dissipation scheme temporal accuracy is facilitated by employing a second order accurate dual time stepping method in this part of the paper the theory and implementation details are discussed in part 11 the scheme will be applied to a number of example problems to solve flows over a wide range of reynolds and rayleigh numbers

l 1 stability of the boltzmann equation for the hard sphere model we study the l1 stability of classical solutions to the boltzmann equation for a hard sphere model when initial datum is a small perturbation of a vacuum and tends to zero exponentially fast at infinity in the phase space for this we introduce nonlinear functionals measuring potential interactions between particles with different velocities and l1 distance between classical solutions we use pointwise estimates for a solution and the gain term of a collision operator to control the time evolution of nonlinear functionals

spectrum analysis of the linearized relativistic landau equation in this work we prove the complete spectrum structure of the linearized relativistic landau equation in l 2 by using the semigroup theory and the linear operator perturbation theory our results include the physical interesting coulombic interaction

a cut cell non conforming cartesian mesh method for compressible and incompressible flow this paper details a multigrid accelerated cut cell non conforming cartesian mesh methodology for the modelling of inviscid compressible and incompressible flow this is done via a single equation set that describes sub trans and supersonic flows cut cell technology is developed to furnish body fitted meshes with an overlapping mesh as starting point and in a manner which is insensitive to surface definition inconsistencies spatial discretization is effected via an edge based vertex centred finite volume method an alternative dual mesh construction strategy similar to the cell centred method is developed incompressibility is dealt with via an artificial compressibility algorithm and stabilization achieved with artificial dissipation in compressible flow shocks are captured via pressure switch activated upwinding the solution process is accelerated with full approximation storage fas multigrid where coarse meshes are generated automatically via a volume agglomeration methodology this is the first time that the proposed discretization and solution methods are employed to solve a single compressible incompressible equation set on cut cell cartesian meshes the developed technology is validated by numerical experiments the standard discretization and alternative methods were found equivalent in accuracy and computational cost the multigrid implementation achieved decreases in cpu time of up to one order of magnitude copyright 2007 john wiley sons ltd

a representation of curved boundaries for the solution of the navier stokes equations on a staggered three dimensional cartesian grid a method is presented for representing curved boundaries for the solution of the navier stokes equations on a non uniform staggered three dimensional cartesian grid the approach involves truncating the cartesian cells at the boundary surface to create new cells which conform to the shape of the surface we discuss in some detail the problems unique to the development of a cut cell method on a staggered grid methods for calculating the fluxes through the boundary cell faces for representing pressure forces and for calculating the wall shear stress are derived and it is verified that the new scheme retains second order accuracy in space in addition a novel cell linking method is developed which overcomes problems associated with the creation of small cells while avoiding the complexities involved with other cell merging approaches techniques are presented for generating the geometric information required for the scheme based on the representation of the boundaries as quadric surfaces the new method is tested for flow through a channel placed oblique to the grid and flow past a cylinder at re 40 and is shown to give significant improvement over a staircase boundary formulation finally it is used to calculate unsteady flow past a hemispheric protuberance on a plate at a reynolds number of 800 good agreement is obtained with experimental results for this flow

the boltzmann equation for weakly inhomogeneous data we solve the initial value problem associated to the nonlinear boltzmann equation in the case in which the initial distribution has sufficiently small spatial gradients

cartesian cut cell method for axisymmetric separating body flows a method for the calculation of unsteady axisymmetric compressible flows involving both fixed and separating bodies is presented the method uses a cartesian cut cell mesh approach and high resolution upwind finite volume scheme a stationary background cartesian mesh is generated on the computational domain with complex solid geometries represented by different types of cut cell solid bodies are allowed to move across the mesh using a finite volume scheme modified to deal with moving boundary problems the flow solver employed is a muscl hancock godunov type scheme in conjunction with an approximate riemann solver of the harten lax and van leer type for flow interfaces and an exact riemann solver for a moving piston for fixed or moving solid faces a cell merging technique is used to maintain numerical stability in the presence of arbitrarily small cut cells and to retain strict conservation at moving boundaries the method is applied to a muzzle blast flow and muzzle break problems involving both fixed and separating bodies

global existence inl1 for the generalized enskog equation various existence theorems are given for the generalized enskog equation inr3 and in a bounded spatial domain with periodic boundary conditions a very general form of the geometric factory is allowed including an explicit space velocity and time dependence the method is based on the existence of a liapunov functional an analog of theh function in the boltzmann equation and utilizes a weak compactness argument inl1

stability of global solution for the relativistic enskog equation near vacuum the cauchy problem of the relativistic enskog equation with near vacuum data is considered in this paper under the same assumption as that in jiang j stat phys 127 805 812 2007 for the relativistic enskog equation we obtain the uniform l stability of the solution what s more important is that for two new types of the scattering cross section we give the global existence and l1 x v stability for mild solution when the initial data lies in the space l1 x v as a corollary we have a bv type estimate it is worth mentioning that the stability results in this paper can be applied to the case in jiang j stat phys 127 805 812 2007

classical solution of the nonlinear boltzmann equation in all r 3 asymptotic behavior of solutions proof is given of the existence of a classical solution to the nonlinear boltzmann equation in allr3 the solution which is global in time exists if the initial data go to zero fast enough at infinity and the mean free path is sufficiently large the solution is smooth in the space variable if the initial value is smooth the asymptotic behavior of solutions is also given it is shown that ast the solution to the boltzmann equation can be approximated by the solution to the free motion problem

on the linearized relativistic boltzmann equation i existence of solutions the linearized relativistic boltzmann equation inl 2 r p is investigated the detailed analysis of the collision operatorl is carried out for a wide class of scattering cross sections l is proved to have a form of the multiplication operatorv p plus the compact inl 2 p perturbationk the collisional frequencyv p is analysed to discriminate between relativistic soft and hard interactions finally the existence and uniqueness of the solution to the linearized relativistic boltzmann equation is proved

l 1 stability of multi dimensional discrete velocity boltzmann equations we study the l 1 stability of multi dimensional discrete velocity boltzmann equations under suitable smallness assumption on initial data we show that bounded mild solutions are l 1 stable for a stability estimate we employ bony s multi dimensional analysis for total interactions over characteristic planes

the kinetic theory of simple reacting spheres i global existence result in a dilute gas case existence of global in time spatially inhomogeneous and l 1 renormalized solutions is proven for the model of simple reacting spheres under the assumptions that initially the system has a finite total mass energy and entropy

on solutions of fuzzy random multiobjective quadratic programming with applications in portfolio problem in this paper a multiobjective quadratic programming problem fuzzy random coefficients matrix in the objectives and constraints and the decision vector are fuzzy variables is considered first we show that the efficient solutions fuzzy quadratic multiobjective programming problems series optimal solutions of relative scalar fuzzy quadratic programming some theorems are to find an optimal solution of the relative scalar quadratic multiobjective programming with fuzzy coefficients having decision vectors as fuzzy variables an application fuzzy portfolio optimization problem as a convex quadratic programming approach is discussed and an acceptable solution to such problem is given at the end numerical examples are illustrated in the support of the obtained results

spectrum analysis of some kinetic equations we analyze the spectrum structure of some kinetic equations qualitatively by using semigroup theory and linear operator perturbation theory the models include the classical boltzmann equation for hard potentials with or without angular cutoff and the landau equation with gamma geqq 2 as an application we show that the solutions to these two fundamental equations are asymptotically equivalent mod time decay rate t 5 4 as t to infty to that of the compressible navier stokes equations for initial data around an equilibrium state

an efficient artificial compressibility ac scheme based on the characteristic based split cbs method for incompressible flows in this paper an artificial compressibility scheme using the finite element method is introduced 2002 zienkiewicz silver medal and prize winning paper the multi purpose cbs scheme is implemented in its fully explicit form to solve incompressible fluid dynamics problems it is important to note that the scheme developed here includes split and velocity correction the proposed method takes advantage of good features from both velocity correction and standard artificial compressibility schemes unlike many other artificial compressibility schemes the proposed one works on a variety of grids and gives results for a wide range of reynold s numbers the paper presents some bench mark two and three dimensional steady and unsteady incompressible flow solutions obtained from the proposed scheme copyright 2003 john wiley sons ltd

new properties of a class of generalized kinetic equations we give some properties of a new class of hard sphere kinetic equations of great generality introduced earlier by polewczak the assumptions used to obtain the general class are very weak and the equations include not only the standard and revised enskog equations but also generalizations thereof that can be expected to yield essentially exact transport coefficients in particular there is a natural two particle realization that is obtained from maximizing the information entropy subject to prescribed two particle and one particle probability distribution functions k particle analogs fork 2 also naturally follow we obtain liapunov functionals for the whole class of equations under consideration and discuss the question of which of these functionals can be expected to play the role ofh functions we also obtain several more special results that include new lower bounds on the potential part of theh function for the revised enskog equation the bounds are instrumental in obtaining global existence theorems and also imply that the necessary condition for invertibility of the nonequilibrium extension of local activity as a functional of local density is satisfied

small data existence for the enskog equation in l 1 an existence theorem for the enskog equation with small initial data is proved in anl1 setting this type of result is not available for the boltzmann equation

global validity of the boltzmann equation for a three dimensional rare gas in vacuum we consider a system ofn hard disks in 2 in the boltzmann grad limit i e n d 0 n d 1 0 whered is the diameter of the disks if is sufficiently small and if the joint distribution densities factorize at time zero we prove that the time evolved one particle distribution converges for all times to the solution of the boltzmann equation with the same initial datum

computation of solid liquid phase fronts in the sharp interface limit on fixed grids a finite difference formulation is applied to track solid liquid boundaries on a fixed underlying grid the interface is not of finite thickness but is treated as a discontinuity and is explicitly tracked the imposition of boundary conditions exactly on a sharp interface that passes through the cartesian grid is performed using simple stencil readjustments in the vicinity of the interface attention is paid to formulating difference schemes that are globally second order accurate in x and t error analysis and grid refinement studies are performed for test problems involving the diffusion and convection diffusion equations and for stable solidification problems issues concerned with stability and change of phase of grid points in the evolution of solid liquid phase fronts are also addressed it is demonstrated that the field calculation is second order accurate while the position of the phase front is calculated to first order accuracy furthermore the accuracy estimates hold for the cases where there is a property jump across the interface unstable solidification phenomena are simulated and an attempt is made to compare results with previously published work the results indicate the need to begin an effort to benchmark computations of instability phenomena

a matrix free implicit incompressible fractional step algorithm for fluid structure interaction applications in this paper we detail a fast fully coupled partitioned fluid structure interaction fsi scheme for the incompressible fluid new fractional step algorithms are proposed which make possible the fully implicit but matrix free parallel solution of the entire coupled fluid solid system these algorithms include artificial compressibility pressure poisson solution in conjunction with upwind velocity stabilisation as well as simplified pressure stabilisation for improved computational efficiency a dual timestepping approach is proposed where a jacobi method is employed for the momentum equations while the pressures are concurrently solved via a matrix free preconditioned gmres methodology this enables efficient sub iteration level coupling between the fluid and solid domains parallelisation is effected for distributed memory systems the accuracy and efficiency of the developed technology is evaluated by application to benchmark problems from the literature the new schemes are shown to be efficient and robust with the developed preconditioned gmres solver furnishing speed ups ranging between 50 and 80

on the initial boundary value problems for the enskog equation in irregular domains the paper is concerned with the enskog equation with a constant high density factor for large initial data in l1 rn the initial boundary value problem is investigated for bounded domains with irregular boundaries the proof of an h theorem for the case of general domains and boundary conditions is given the main result guarantees the existence of global solutions of boundary value problems for large initial data with all v moments initially finite and domains having boundary with finite hausdorff measure and satisfying a cone condition existence and uniqueness are first proved for the case of bounded velocities the solution has finite norm int sup 0 leqslant t leqslant t f t 0 t x vt sqrt 1 v 2 dq text dv where q t0 x is taken on all possible n dimensional planes q v in rn l intersecting a fixed point and orthogonal to vectors 1 v v rn

on the classical solutions of the boltzmann equation on etudie le probleme aux valeurs initiales pour l equation de boltzmann on montre que des solutions au sens classique existent pour tout temps si la donnee initiale est assez proche de l equilibre on se restreint a un domaine cubique et on considere seulement la condition aux limites periodique

on the asymptotic equivalence between the enskog and the boltzmann equations an asymptotic equivalence theorem is proven between the solutions of the initial value problem in all space for the boltzmann and enskog equations for initial data which assure global existence for the solutions to the initial value problem for one of the two equations the proof is given starting from the solution of the boltzmann equation then the proof line is simply indicated when one starts from the enskog equation the proof holds for knudsen numbers of the order of unity and equivalence is proven when the scale of the dimensions of the gas particles characterizing the enskog equation tends to zero

uniform stability of the solutions to the relativistic enskog equation abstract we present the uniform stability of classical solutions to the relativistic enskog equation under the locally lipschitz assumption of the collision factors given by polewczak this stability is an extension of the result given by ha and xiao for the relativistic boltzmann equation and it is very useful for the study of the cauchy problem for the relativistic enskog equation

a cartesian grid method with transient anisotropic adaptation a cartesian grid method with solution adaptive anisotropic refinement and coarsening is developed for simulating time dependent incompressible flows the cartesian grid cells and faces are managed using an unstructured data approach and algorithms are described for the time accurate transient anisotropic refinement and coarsening of the cells the governing equations are discretized using a collocated cell centered arrangement of velocity and pressure and advanced in time using the fractional step method significant savings in the memory requirement of the method can be realized by advancing the velocity field using a novel approximate factorization technique although an iterative technique is also presented the pressure poisson equation is solved using additive correction multigrid and an efficient coarse grid selection algorithm is presented finally the cartesian cell geometry allows the development of relatively simple analytic expressions for the optimal cell dimensions based on limiting the velocity interpolation error the overall method is validated by solving several benchmark flows including the 2d and 3d lid driven cavity flows and the 2d flow around a circular cylinder in this latter case an immersed boundary method is used to handle the embedded cylinder boundary

on the cauchy problem for the nonlinear boltzmann equation global existence uniqueness and asymptotic stability the analysis of the initial value problem for the nonlinear boltzmann equation is considered in this paper a theorem defining global existence and uniqueness for initial data which decay at infinity with an inverse power law is the main result of this work and is obtained by suitable application of fixed point theorems in banach spaces the theorem also defines the asymptotic stability of the solutions

the grad limit for a system of soft spheres a model describing the dynamics of a system of soft spheres is introduced the model contains a random mechanism which mollifies the deterministic model of hard sphere molecules it allows a rigorous deduction of the corresponding boltzmann equation for a wide class of initial data and arbitrarily long times

global existence and asymptotic behavior for the discrete velocity models of the boltzmann equation by using fixed point techniques some theorems which supply local and global existence uniqueness and asymptotic behavior of the solution of a general discrete velocity model of the boltzmann equation in three dimensions are given

a stochastic model associated with enskog equation and its kinetic limit we examine a system of particles in which the particles travel deterministically in between stochastic collisions the collisions are elastic and occur with probability d when two particles are at a distance when the number of particles n goes to infinity and n d goes to a nonzero constant we show that the particle density converges to a solution of the enskog equation

spectral properties of the linearized boltzmann operator in l p for 1 p the spectrum of both classical and relativistic boltzmann operator for hard interactions in a whole space is shown to be independent of p in l p for 1 p it consists of a half plane operatorname re lambda leq nu 0 and countably many branches in the strip nu 0 operatorname re lambda leq0 moreover the resolvent set is independent of p for all 1 p but in l this operator possesses in addition to the continuous also an uncountable set of point spectrum

application of fuzzy calculations for improving portfolio matrices in this paper we draw upon portfolio analysis to develop and implement a strategic decision making model we consider the limitations and problems of classic portfolio analysis approach and resolve these problems by using fuzzy set theory in the proposed method both internal and external factors are evaluated in linguistic terms and in terms of fuzzy triangular numbers the fuzzy numbers are fed into an industry attractiveness business analysis matrix the novelty of the proposed approach comes from the fact that fuzzy numbers are processed without using conventional methods allowing for strategies to be ranked

existence and conditional energetic stability of capillary gravity solitary water waves by minimisation firstly the two dimensional stationary water wave problem is considered existence of capillary gravity solitary waves is proved by minimising a functional related to smale s amended potential we first establish the existence of periodic solutions of arbitrarily large periods leading to a minimising sequence in l2 that stays away from the boundary of the neighbourhood of 0 w2 2 in which the analysis is carried out with the help of the concentration compactness principle we then show that every minimising sequence has a subsequence that after possible shifts in the propagation direction converges in l2 to a minimiser secondly for the evolutionary problem we prove that the set of minimal solitary waves as a whole is energetically conditionally stable energetically means that the distance to the set of all minimisers is defined in terms of the total energy and conditionally means that we consider solutions to the evolutionary problem that do not explode instantaneously but could perhaps explode in finite time e g via the explosion of another norm we work in some bounded set in w2 2 that contains the quiescent state and we are not interested in the fate of solutions that leave this set

global existence proof for relativistic boltzmann equation the existence and causality of solutions to the relativistic boltzmann equation inl1 and inl loc 1 are proved the solutions are shown to satisfy physically naturala priori bounds time independent inl1 the results rely upon new techniques developed for the nonrelativistic boltzmann equation by diperna and lions

hypocoercivity of the relativistic boltzmann and landau equations in the whole space abstract we study the hypocoercivity property for some kinetic equations in the whole space and obtain the optimal convergence rates of solutions to the equilibrium state in some function spaces the analysis relies on the basic energy method and the compensating function introduced by kawashima to the classical boltzmann equation and developed by glassey and strauss in the relativistic setting it is also motivated by the recent work duan et al 2008 8 on the boltzmann equation by combining the spectrum analysis and energy method the advantage of the method introduced in this paper is that it can be applied to some complicated system whose detailed spectrum is not known in fact only some estimates through the fourier transform on the conservative transport operator and the dissipation of the linearized operator on the subspace orthogonal to the collision invariants are needed

the relativistic boltzmann equation for soft potentials abstract the paper concerns the cauchy problem on the relativistic boltzmann equation for soft potentials in a periodic box we show that the global in time solutions around relativistic maxwellians exist in the weighted l perturbation framework and also approach equilibrium states in large time in the weighted l 2 framework at the rate of exp t for some 0 and 0 1 the proof is based on the nonlinear l 2 energy method and nonlinear l pointwise estimate with appropriate exponential weights in momentum the results extend those on the classical boltzmann equation by caflisch 2 3 and strain and guo 31 to the relativistic version and also improve the recent result on almost exponential time decay by strain 28 to the exponential rate moreover we study the propagation of spatial regularity for the obtained solutions and also the large time behavior in the corresponding regular sobolev space provided that the spatial derivatives of initial data are bounded not necessarily small

the inverse conjecture for the revised enskog equation it is shown that the pair correlation function which is by definition the high density factor in the revised enskog theory is not always a well defined functional of the local density moreover for a finite system with periodic boundary conditions and in the space homogeneous case this function computed at the contact value is bounded at the maximum allowed density i e a densitynmax such that in one dimension 1 a 1 l nmax 1 a equality sign which corresponds to the usual close packing density for whichl a is an integer being included as a particular case at least for the one dimensional gas model this finite value is shown to approach infinity in the thermodynamic and in the hydrodynamic limits a new form for the revised enskog equation which does not depend on the inverse conjecture is finally given

analytical solution methods for the fuzzy weighted average for the fuzzy weighted average fwa despite various discrete solution algorithms and their improvements attempts at analytical solutions are very rare this paper provides an analytical solution method for the fwa based on the conclusions of the karnik mendel km algorithm compared with the two current popular kinds of a cut based computational methods for the fwa mathematical programming transformations and direct iterate computations our method is precise and has a concise structure efficient computation process and sound theoretical proofs we propose two algorithms for computing the analytical solution of the fwa two numerical examples illustrate our proposed approach

global existence and asymptotic behavior for the nonlinear enskog equation the existence of a classical solution to the nonlinear enskog equation in all mathbb r 3 is proved the solution which is global in time exists if the initial data go to zero fast enough at infinity and the mean path is sufficiently large the solution is smooth in space variable if the initial value is smooth the asymptoticbehavior of solutions is also given it is shown that as t to infty the solution to the enskog equation can be approximated by the solution to the free motion problem key words partial differential equations nonlinear integral equation asymptotic behavior kinetic theory boltzmann equation

global weak solutions and uniform lp stability of the boltzmann enskog equation abstract we present the regularity theory of renormalized solutions and uniform l p stability estimates of the boltzmann enskog model we use a multi dimensional bony type functional to control the time phase space integral of a truncated collision operator we employ cercignani s arguments and a bony type functional to show that the renormalized solutions to the boltzmann enskog model are weak solutions in usual distributional sense for the uniform l p stability estimate we use lu s trick together with the holder inequality

numerical analysis of a shock wave solution of the enskog equation obtained via a monte carlo method in this paper a planar stationary shock wave like solution of the enskog equation obtained via a monte carlo technique is studied both the algorithm used to obtain the solution and the qualitative behavior of the macroscopic quantities are discussed in comparison with the corresponding solution of the boltzmann equation

regular article an accurate cartesian grid method for viscous incompressible flows with complex immersed boundaries a cartesian grid method has been developed for simulating two dimensional unsteady viscous incompressible flows with complex immersed boundaries a finite volume method based on a second order accurate central difference scheme is used in conjunction with a two step fractional step procedure the key aspects that need to be considered in developing such a solver are imposition of boundary conditions on the immersed boundaries and accurate discretization of the governing equation in cells that are cut by these boundaries a new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the second order spatial accuracy of the underlying solver the presence of immersed boundaries alters the conditioning of the linear operators and this can slow down the iterative solution of these equations the convergence is accelerated by using a preconditioned conjugate gradient method where the preconditioner takes advantage of the structured nature of the underlying mesh the accuracy and fidelity of the solver is validated by simulating a number of canonical flows and the ability of the solver to simulate flows with very complicated immersed boundaries is demonstrated

gerris a tree based adaptive solver for the incompressible euler equations in complex geometries an adaptive mesh projection method for the time dependent incompressible euler equations is presented the domain is spatially discretised using quad octrees and a multilevel poisson solver is used to obtain the pressure complex solid boundaries are represented using a volume of fluid approach second order convergence in space and time is demonstrated on regular statically and dynamically refined grids the quad octree discretisation proves to be very flexible and allows accurate and efficient tracking of flow features the source code of the method implementation is freely available

invertible matrices and semilinear spaces over commutative semirings this paper deals with invertible matrices and semilinear spaces over commutative semirings some necessary and sufficient conditions for matrices to be invertible over commutative semirings are obtained the condition under which the cardinality of each basis of semilinear space of n dimensional vectors is n is given in the end the factor rank of matrices over semirings is investigated

the boltzmann equation global existence for a rare gas in an infinite vacuum solutions of the boltzmann equation are proved to exist globally in time under conditions that include the case of a finite volume of gas in an infinite vacuum when the mean free path of the gas is large enough it is also proved as might be expected in this case that the density of the gas at each point in space goes to zero as time goes to infinity

on the cauchy problem for boltzmann equations global existence and weak stability we study the large data cauchy problem for boltzmann equations with general collision kernels we prove that sequences of solutions which satisfy only the physically natural a priori bounds converge weakly in l to a solution from this stability result we deduce global existence of a solution to the cauchy problem our method relies upon recent compactness results for velocity averages a new formulation of the boltzmann equation which involves nonlinear normalization and an analysis of subsolutions and supersolutions it allows us to overcome the lack of strong a priori estimates and define a meaningful collision operator for general configurations

loeb solutions of the boltzmann equation existence problems for the boltzmann equation constitute a main area of research within the kinetic theory of gases and transport theory the present paper considers the spatially periodic case with l1 initial data the main result is that the loeb subsolutions obtained in a preceding paper are shown to be true solutions the proof relies on the observation that monotone entropy and finite energy imply loeb integrability of non standard approximate solutions and uses estimates from the proof of the h theorem two aspects of the continuity of the solutions are also considered

an accelerated fully coupled parallel 3d hybrid finite volume fluid structure interaction scheme abstract in this paper we propose a fast parallel 3d fully coupled partitioned hybrid unstructured finite volume fluid structure interaction fsi scheme spatial discretisation is effected via a vertex centred finite volume method where a hybrid nodal elemental strain procedure is employed for the solid in the interest of accuracy for the incompressible fluid a split step algorithm is presented which allows the entire fluid solid system to be solved in a fully implicit yet matrix free manner the algorithm combines a preconditioned gmres solver for implicit integration of pressures with dual timestepping on the momentum equations thereby allowing strong coupling of the system to occur through the inner solver iterations further acceleration is provided at little additional cost by applying lu sgs relaxation to the viscous and advective terms the solver is parallelised for distributed memory systems using mpi and its scaling efficiency evaluated the developed modelling technology is evaluated by application to two 3d fsi problems the advanced matrix free solvers achieve reductions in overall cpu time of up to 50 times while preserving close to linear parallel computing scaling using up to 128 cpus for the problems considered

hilbert expansion from the boltzmann equation to relativistic fluids we study the local in time hydrodynamic limit of the relativistic boltzmann equation using a hilbert expansion more specifically we prove the existence of local solutions to the relativistic boltzmann equation that are nearby the local relativistic maxwellians the maxwellians are constructed from a class of solutions to the relativistic euler equations that includes a large subclass of near constant non vacuum fluid states in particular for small knudsen number these solutions to the relativistic boltzmann equation have dynamics that are effectively captured by corresponding solutions to the relativistic euler equations

comparison of pressure based and artificial compressibility methods for solving 3d steady incompressible viscous flows pressure based and artificial compressibility methods for calculating three dimensional steady incompressible viscous flows are compared in this work each method is applied to the prediction of three dimensional laminar flows in strongly curved ducts of square and circular cross sections numerical predictions from each method are compared with available experimental data and previously reported predictions using a multigrid numerical method the accuracy grid independence convergence behavior and computational efficiency of each method are critically examined hence some of the merits and demerits of each method are revealed in this study

nonlinear functionals of the boltzmann equation and uniform stability estimates abstract we present nonlinear functionals measuring physical space variation and l 1 distance between two classical solutions for the boltzmann equation with a cut off inverse power potential in the case that initial datum is a small smooth perturbation of vacuum and decays fast enough in the phase space we show that these functionals satisfy stability estimates which lead to bv type estimates and a uniform l 1 stability

regularity of the moments of the solution of a transport equation let u u x v satisfy the transport equation u v xu f x rn v rnwhere f belongs to some space of type lp dx d v where is a positive bounded measure on rn we study the resulting regularity of the moment u x v d v in terms of fractional sobolev spaces for example counter examples are given in order to test the optimality of our results

the inelastic enskog equation with external force in this paper the cauchy problem for the inelastic enskog equation with external force is considered for near vacuum data under the assumptions on the bi characteristic we proved the global existence of mild solution

global existence in l 1 for the modified nonlinear enskog equation in ℝ 3 a global existence theorem with large initial data inl1 is given for the modified enskog equation in 3 the method which is based on the existence of a liapunov functional analog of theh boltzmann theorem utilizes a weak compactness argument inl1 in a similar way to the diperna lions proof for the boltzmann equation the existence theorem is obtained under certain condition on the behavior of the geometric factory the condition ony amounts to the fact that thel1 norm of the collision term grows linearly when the local density tends to infinity