a density corrected quantum boltzmann equation binary correlations are a recognized part of the pair density operator but the influence of binary correlations on the singlet density operator is usually not emphasized here free motion and binary correlations are taken as independent building blocks for the structure of the nonequilibrium singlet and pair density operators binary correlations are assumed to arise from the collision of twofree particles together with the first bbgky equation and a retention of all terms that are second order in gas density a generalization of the boltzmann equation is obtained this is an equation for thefree particle density operator rather than for the full singlet density operator the form for the pressure tensor calculated from this equation reduces at equilibrium to give the correct beth uhlenbeck second virial coefficient in contrast to a previous quantum boltzmann equation which gave only part of the quantum second virial coefficient generalizations to include higher order correlations and collision types are indicated

domain dependence of solutions to compressible navier stokes equations the minimization of the drag functional for the stationary isentropic compressible navier stokes equations nse in three spatial dimensions is considered in order to establish the existence of an optimal shape the general result on compactness of families of generalized solutions to the nse is established within in the framework of the modern theory of nonlinear pdes p l lions mathematical topics in fluid dynamics vol 2 compressible models oxford university press clarendon press new york 1998 e feireisl dynamics of viscous compressible fluids oxford university press oxford uk 2004 the family of generalized solutions to the nse is constructed over a family of admissible domains mathcal u ad any admissible domain omega b setminus s contains an obstacle s e g a wing profile compactness properties of the family of admissible domains in the form of the condition mathcal h omega is imposed roughly speaking the condition mathcal h omega is satisfied provided that for any sequence of admissible domains omega n subset mathcal u ad there is a subsequence convergent both in hausdorff metrics and in the sense of kuratowski and mosco the analysis is performed for the adiabatic constant gamma 1 in the pressure law p rho rho gamma and it is based on the technique used in p i plotnikov and j sokolowski comm math phys 258 2005 pp 567 608 in the case of discretized nse the result is a generalization to the stationary equations with gamma 1 of the results obtained in e feireisl a h novotny and h petzeltova math methods appl sci 25 2002 pp 1045 1073 e feireisl appl math optim 47 2003 pp 59 78 for evolution equations within the range gamma 3 2 for the adiabatic ratio

benchmarking optimization software with performance profiles we propose performance profiles distribution functions for a performance metric as a tool for benchmarking and comparing optimization software we show that performance profiles combine the best features of other tools for performance evaluation

what is the optimal shape of a pipe we consider an incompressible fluid in a three dimensional pipe following the navier stokes system with classical boundary conditions we are interested in the following question is there any optimal shape for the criterion energy dissipated by the fluid moreover is the cylinder the optimal shape we prove that there exists an optimal shape in a reasonable class of admissible domains but the cylinder is not optimal for that purpose we explicit the first order optimality condition thanks to adjoint state and we prove that it is impossible that the adjoint state be a solution of this over determined system when the domain is the cylinder at last we show some numerical simulations for that problem

globally convergent polak ribiere polyak conjugate gradient methods under a modified wolfe line search it is well known that global convergence has not been established for the polak ribiere polyak prp conjugate gradient method using the standard wolfe conditions in the convergence analysis of prp method with wolfe line search the sufficient descent condition and the restriction b k 0 are indispensable see 4 7 this paper shows that these restrictions could be relaxed under some suitable conditions by using a modified wolfe line search global convergence results were established for the prp method some special choices for b k which can ensure the search direction s descent property were also discussed in this paper preliminary numerical results on a set of large scale problems were reported to show that the prp method s computational efficiency is encouraging

a globally convergent version of the polak ribiere conjugate gradient method in this paper we propose a new line search algorithm that ensures global convergence of the polak ribiere conjugate gradient method for the unconstrained minimization of nonconvex differentiable functions in particular we show that with this line search every limit point produced by the polak ribiere iteration is a stationary point of the objective function moreover we define adaptive rules for the choice of the parameters in a way that the first stationary point along a search direction can be eventually accepted when the algorithm is converging to a minimum point with positive definite hessian matrix under strong convexity assumptions the known global convergence results can be reobtained as a special case from a computational point of view we may expect that an algorithm incorporating the step size acceptance rules proposed here will retain the same good features of the polak ribiere method while avoiding pathological situations

on the snider equation we study the physical content of the snider quantum transport equation and the origin of a puzzling feature of this equation which implies contradictory values for the one particle density operator we discuss in detail why the two values are in fact not very different provided that the studied particles have sufficiently large wave packets and only a small interaction probability a condition which puts a limit on the validity of the snider equation in order to improve its range of application we propose a reinterpretation of the equation as a mixed equation relating the real one particle distribution function on the left hand side of the equation to the free distribution on the right hand side which we have introduced in a recent contribution in its original form the snider equation is valid only when used to generate boltzmann type equations where collisions are treated as point processes in space and time no range no duration in this approximation virial corrections are not included so that the real and free distributions coincide if the equation is used beyond this approximation to generate nonlocal and density corrections we conclude that the results are not necessarily correct

concentrations of solutions to time discretizied compressible navier stokes equations the compactness properties of solutions to time discretization of compressible navier stokes equations are investigated in three dimensions the existence of generalized solutions is established

state constrained optimal control of the three dimensional stationary navier stokes equations abstract in this paper an optimal control problem for the stationary navier stokes equations in the presence of state constraints is investigated existence of optimal solutions is proved and first order necessary conditions are derived the regularity of the adjoint state and the state constraint multiplier is also studied lipschitz stability of the optimal control state and adjoint variables with respect to perturbations is proved and a second order sufficient optimality condition for the case of pointwise state constraints is stated

a new conjugate gradient method with guaranteed descent and an efficient line search a new nonlinear conjugate gradient method and an associated implementation based on an inexact line search are proposed and analyzed with exact line search our method reduces to a nonlinear version of the hestenes stiefel conjugate gradient scheme for any inexact line search our scheme satisfies the descent condition bf g k sf t bf d k le frac 7 8 bf g k 2 moreover a global convergence result is established when the line search fulfills the wolfe conditions a new line search scheme is developed that is efficient and highly accurate efficiency is achieved by exploiting properties of linear interpolants in a neighborhood of a local minimizer high accuracy is achieved by using a convergence criterion which we call the approximate wolfe conditions obtained by replacing the sufficient decrease criterion in the wolfe conditions with an approximation that can be evaluated with greater precision in a neighborhood of a local minimum than the usual sufficient decrease criterion numerical comparisons are given with both l bfgs and conjugate gradient methods using the unconstrained optimization problems in the cute library

second order methods for optimal control of time dependent fluid flow second order methods for open loop optimal control problems governed by the two dimensional instationary navier stokes equations are investigated optimality systems based on a lagrangian formulation and adjoint equations are derived the newton and quasi newton methods as well as various variants of sqp methods are developed for applications to optimal flow control and their complexity in terms of system solves is discussed local convergence and rate of convergence are proved a numerical example illustrates the feasibility of solving optimal control problems for two dimensional instationary navier stokes equations by second order numerical methods in a standard workstation environment

a practical pr conjugate gradient method only using gradient abstract in this paper we consider the polak ribiere or polak ribiere plus conjugate gradient method for solving optimality condition of an unconstrained minimization problem we give two new steplength rules only using gradient and under gradient lipschitz assumption prove this method s global convergence correspondingly then we develop a practical polak ribiere plus method whose steplength is located by one inequality only using gradient and report promising numerical results on high accuracy solution for some standard test problems when compared to the state of art methods in this research direction importantly our work provides a new idea of devising a practical version of the celebrated polak ribiere or polak ribiere plus method

shape derivative of drag functional in this paper compressible stationary navier stokes equations are considered the model is well posed and there exist weak solutions in bounded domains subject to inhomogeneous boundary conditions the shape sensitivity analysis is performed for navier stokes boundary value problems in the framework of small perturbations of the so called approximate solutions the approximate solutions are determined from the stokes problem and the small perturbations are given by the unique solutions to the full nonlinear model the differentiability of small perturbations of the approximate solutions with respect to the coefficients of differential operators implies the shape differentiability of the drag functional the shape gradient of the drag functional is derived in a form convenient for computations and an appropriate adjoint state is introduced to this end the shape derivatives of solutions to the navier stokes equations are given by smooth functions however the shape differentiability of the solutions is shown in a weak norm the proposed method of shape sensitivity analysis is general the differentiability of solutions to the navier stokes equations with respect to the data leads to the first order necessary conditions for a broad class of optimization problems the boundary shape gradient as well as the boundary value problems for the shape derivatives of solutions to state equations and the adjoint state equations are obtained in the form of singular limits of volume integrals this method of shape sensitivity analysis seems to be new and is appropriate for nonlinear problems it is an important contribution in the field of numerical methods of shape optimization in fluid mechanics

shape optimization with stokes constraints over the set of axisymmetric domains in this paper we are interested in the study of shape optimizations problems with stokes constraints within the class of axisymmetric domains represented by the graph of a function existence results with weak assumptions on the regularity of the graph are provided we strongly use these assumptions to get some topological properties we formulate the shape optimization problem using different constraints formulations uniform bound constraints on the function and its derivative and or volume global constraint writing the first order optimality conditions allows to provide quasi explicit solutions in some particular cases and to give some hints for the treatment of the generic problem furthermore we extend the negative result of 16 dealing with the non optimality of the cylinder

global convergence properties of conjugate gradient methods for optimization this paper explores the convergence of nonlinear conjugate gradient methods without restarts and with practical line searches the analysis covers two classes of methods that are globally convergent on smooth nonconvex functions some properties of the fletcher reeves method play an important role in the first family whereas the second family shares an important property with the polak ribiere method numerical experiments are presented

steady compressible navier stokes flow in a square abstract we investigate a steady flow of compressible fluid with inflow boundary condition on the density and slip boundary conditions on the velocity in a square domain q r 2 we show existence if a solution v w p 2 q w p 1 q that is a small perturbation of a constant flow v 1 0 1 we also show that this solution is unique in a class of small perturbations of the constant flow v in order to show the existence of the solution we adapt the techniques known from the theory of weak solutions we apply the method of elliptic regularization and a fixed point argument

global convergence of the polak ribiere polyak conjugate gradient method with an armijo type inexact line search for nonconvex unconstrained optimization problems we propose two algorithms for nonconvex unconstrained optimization problems that employ polak ribiere polyak conjugate gradient formula and new inexact line search techniques we show that the new algorithms converge globally if the function to be minimized has lipschitz continuous gradients preliminary numerical results show that the proposed methods for particularly chosen line search conditions are very promising

convergence properties of nonlinear conjugate gradient methods recently important contributions on convergence studies of conjugate gradient methods were made by gilbert and nocedal siam j optim 2 1992 pp 21 42 they introduce a sufficient descent condition to establish global convergence results although this condition is not needed in the convergence analyses of newton and quasi newton methods gilbert and nocedal hint that the sufficient descent condition which was enforced by their two stage line search algorithm may be crucial for ensuring the global convergence of conjugate gradient methods this paper shows that the sufficient descent condition is actually not needed in the convergence analyses of conjugate gradient methods consequently convergence results on the fletcher reeves and polak ribiere type methods are established in the absence of the sufficient descent condition to show the differences between the convergence properties of fletcher reeves and polak ribiere type methods two examples are constructed showing that neither the boundedness of the level set nor the restriction beta k geq 0 can be relaxed for the polak ribiere type methods

ordinary differential equations transport theory and sobolev spaces we obtain some new existence uniqueness and stability results for ordinary differential equations with coefficients in sobolev spaces these results are deduced from corresponding results on linear transport equations which are analyzed by the method of renormalized solutions

globally convergent modified perry s conjugate gradient method abstract conjugate gradient methods are probably the most famous iterative methods for solving large scale optimization problems in scientific and engineering computation characterized by the simplicity of their iteration and their low memory requirements in this paper we propose a new conjugate gradient method which is based on the mbfgs secant condition by modifying perry s method our proposed method ensures sufficient descent independent of the accuracy of the line search and it is globally convergent under some assumptions numerical experiments are also presented

new approach to the incompressible maxwell boussinesq approximation existence uniqueness and shape sensitivity abstract the boussinesq approximation to the fourier navier stokes f n s flows under the electromagnetic field is considered such a model is the so called maxwell boussinesq approximation we propose a new approach to the problem we prove the existence and uniqueness of weak solutions to the variational formulation of the model some further regularity in w 1 2 0 is obtained for the weak solutions the shape sensitivity analysis by the boundary variations technique is performed for the weak solutions as a result the existence of the strong material derivatives for the weak solutions of the problem is shown the result can be used to establish the shape differentiability for a broad class of shape functionals for the models of fourier navier stokes flows under the electromagnetic field

regularity of solutions to the navier stokes equations for compressible barotropic flows on a polygon the navier stokes system for a steady state barotropic nonlinear compressible viscous flow with an inflow boundary condition is studied on a polygon d a unique existence for the solution of the system is established it is shown that the lowest order corner singularity of the nonlinear system is the same as that of the laplacian in suitable l q spaces let be the interior angle of a vertex p of d if and then the velocity u is split into singular and regular parts near the vertex p if 2 and or if 2 and 2 q it is shown that u h 2 q d 2

a reinterpretation of dense gas kinetic theory in dense gas kinetic theory it is standard to express all reduced distribution functions as functionals of the singlet distribution function since the singlet distribution function includes aspects of correlated particles as well as describing the properties of freely moving particles it is here argued that these aspects should more clearly be distinguished and that it is the distribution function for free particles that is the prime object in terms of which dense gas kinetic theory should be expressed the standard equations of dense gas kinetic theory are rewritten from this point of view and the advantages of doing so are discussed

a descent nonlinear conjugate gradient method for large scale unconstrained optimization in this paper a new nonlinear conjugate gradient method was proposed for large scale unconstrained optimization which possesses the following three properties i the sufficient descent property holds without any line searches ii employing some steplength technique which ensures the zoutendijk condition to be held this method is globally convergent iii this method inherits an important property of the polak ribiere polyak prp method the tendency to turn towards the steepest descent direction if a small step is generated away from the solution preventing a sequence of tiny steps from happening preliminary numerical results show that this method is very promising

three dimensional shape optimization in stokes flow problems an integral equation constrained optimization approach to finding minimum drag shapes for solid bodies of revolution in stokes flows subject to constraints on body s volume and shape has been developed an axially symmetric stokes flow problem has been formulated in the form of an integral equation state equation and finding an optimal shape has been reduced to an integral equation constrained optimization problem the total variation of the lagrangian functional of the problem has been reduced to the variation only with respect to the shape by the adjoint equation based method and the steepest descent direction for the coefficients in the function series representing the shape has been found analytically it has been shown that solutions to the state and adjoint integral equations are related by a simple algebraic formula which eliminates the need for solving the adjoint equation the approach has been illustrated in finding the minimum drag shape for a solid unit volume particle and in finding the

compressible stokes problem on nonconvex polygonal domains abstract the compressible stokes system with the inflow boundary condition is studied on the polygonal domain d it is shown that the lowest order corner singularity of the system is the same as that of the laplacian the velocity u is split into a singular and regular part near each concave vertex if the polygon is convex it is shown that u h 2 d 2