truncation strategies in matching markets roth and rothblum roth a e u g rothblum 1999 truncation strategies in matching markets in search of advice for participants econometrica67 21 43 showed that for matching markets using the deferred acceptance algorithm a physician with symmetric incomplete information possibly gains only by truncating her true ranking we show that in symmetric information environments this result is identical for all priority mechanisms and all linear programming mechanisms introduced in british entry level medical markets and in public school choice in some american cities

conflict and coincidence of interest in job matching some new results and open questions the game theoretic solution to certain job assignment problems allows the interests of agents on the same side of the market e g firms or workers to be simultaneously maximized this is shown to follow from the lattice structure of the set of stable outcomes however it is shown that in a more general class of problems the optimality results persist but the lattice structures do not thus this paper raises as many questions as it answers

acceleration of steady state lattice boltzmann simulations for exterior flows the simulation of a stationary fluid flow past an obstacle by the lattice boltzmann method lbm in two dimensions is discussed the combination of second order expressions for far field boundary conditions and a suitable treatment of the no slip boundary condition at the obstacle surface with the nested grid refinement technique can be applied to the lbm resulting in a highly efficient method for the treatment of exterior flows furthermore via replacing the nested time stepping by local time stepping the resolution process can be substantially accelerated a highly accurate drag coefficient was used to make an error assessment for various no slip boundary conditions imposed on the obstacle surface the analysis showed that the equilibrium method for treating the no slip conditions is superior to halfway bounce back and full way bounce back no slip conditions when the relaxation time ensuremath tau 1 also a ensuremath tau dependence test was made to evaluate the performance of different methods in the treatment of the no slip boundary conditions

numerical analysis of the lattice boltzmann method for simulation of linear acoustic waves we analyze a linear lattice boltzmann lb formulation for simulation of linear acoustic wave propagation in heterogeneous media we employ the single relaxation time bhatnagar gross krook as well as the general multirelaxation time collision operators by calculating the dispersion relation for various 2d lattices we show that the d2q5 lattice is the most suitable model for the linear acoustic problem we also implement a grid refinement algorithm for the lb scheme to simulate waves propagating in a heterogeneous medium with velocity contrasts our results show that the lb scheme performance is comparable to the classical second order finite difference schemes given its efficiency for parallel computation the lb method can be a cost effective tool for the simulation of linear acoustic waves in complex geometries and multiphase media

grid refinement for lattice bgk models lattice boltzmann models proposed at the end of the 1980s as the noise free version of lattice gas models are based on gas kinetic representation of fluid flow their recent modifications the lattice bgk models provide especially simple effective and stable algorithms for the solution of hydrodynamical problems a local second order grid refinement scheme for the lattice bgk model is proposed in this work the refinement scheme and a boundary fitting scheme for complicated geometries are applied to simulate a benchmark problem of flow past a cylinder in a channel with small and moderate reynolds numbers

stable matchings optimal assignments and linear programming vande vate 1989 described the polytope whose extreme points are the stable core matchings in the marriage problem rothblum 1989 simplified and extended this result this paper explores a corresponding linear program its dual and consequences of the fact that the dual solutions have an unusually direct relation to the primal solutions this close relationship allows us to provide simple proofs both of vande vate and rothblum s results and of other important results about the core of marriage markets these proofs help explain the structure shared by the marriage problem without sidepayments and the assignment game with sidepayments the paper further explores fractional matchings which may be interpreted as lotteries over possible matches or as time sharing arrangements we show that those fractional matchings in the stable marriage polytope form a lattice with respect to a partial ordering that involves stochastic dominance thus all expected utility functions corresponding to the same ordinal preferences will agree on the relevant comparisons finally we provide linear programming proofs of slightly stronger versions of known incentive compatibility results

acceleration of steady state lattice boltzmann simulations on non uniform mesh using local time step method in this paper the local time step method is applied to the lattice boltzmann method lbm on non uniform grid generalized form of interpolation supplemented lbm gilbm for steady flow simulations the local time step method is known to be an effective technique to accelerate the solution to the converged steady state on non uniform grid first code validation for global time step method is performed by solving flow around a cylinder at low reynolds numbers our results show good agreement with previous studies two dimensional flow simulations around an airfoil were performed in order to validate the code using the local time step method and the results are compared with the global time step solutions the pressure distribution and the aerodynamic coefficients of global and local time step results are in good agreement they are also consistent with the previous studies at the same time cpu time required to obtain the steady state solutions using the local time step are reduced by 70 80 compared with that using global time step

matching with indifferences a comparison of algorithms in the context of course allocation abstract we evaluate six one and eight two sided matching mechanisms with preferences based on a collection of 28 field data sets although important properties of matching mechanisms such as strategy proofness or pareto efficiency can be shown by formal proofs the size the average rank and the popularity of matchings ask for an empirical evaluation we introduce different metrics to compare the results the study shows trade offs between various design desiderata which are relevant in the field the results provide guidelines for the selection of matching mechanisms

volumetric formulation of the lattice boltzmann method for fluid dynamics basic concept a lattice boltzmann algorithm based on a volumetric representation is formulated for achieving properties consistent with the standard form at finer resolution in contrast to pointwise interpolation schemes this approach can be applied to arbitrary meshes without compromising exact conservation or equilibrium properties

flow simulation around cambered airfoil by using conformal mapping and intermediate domain in lattice boltzmann method in this paper the developed interpolation lattice boltzmann method is used for simulation of unsteady fluid flow it combines the desirable features of the lattice boltzmann and the joukowski transformation methods this approach has capability to simulate flow around curved boundary geometries such as airfoils in a body fitted grid system simulation of unsteady flow around a cambered airfoil in a non uniform grid for the first time is considered to show the capability of this method for modeling of fluid flow around complex geometries and complicated long term periodic flow phenomena the developed solver is also coupled with a fast adaptive grid generator in addition the new approach retains all the advantages of the standard lattice boltzmann method the strouhal number the pressure the drag and the lift coefficients obtained from the simulations agree well with classical computational fluid dynamics simulations numerical studies for various test cases illustrate the strength of this new approach

flow simulation around an airfoil by lattice boltzmann method on generalized coordinates flow simulations around an airfoil naca0012 using lattice boltzmann method lbm are performed in this paper originally lbm is an incompressible flow solver on orthogonal coordinates however in order to resolve the boundary layer of the airfoil accurately the algorithm is extended to generalized coordinates also suitable wall boundary condition is introduced for generalized coordinates first of all the present numerical method is validated at relatively small reynolds number re 500 the velocity profile of the boundary layer is compared in detail with the cfl3d results and consistent results are obtained second the present method is combined with the baldwin lomax turbulence model and results at relatively high reynolds number re 5x10 5 are shown the results are in good agreement with the experimental data with the same grid resolution the present method can solve high reynolds

buchi context free languages we define context free grammars with buchi acceptance condition generating languages of countable words we establish several closure properties and decidability results for the class of buchi context free languages generated by these grammars we also define context free grammars with muller acceptance condition and show that there is a language generated by a grammar with muller acceptance condition which is not a buchi context free language

locally finite languages we investigate properties of locally finite languages introduced by ressayre j symbolic logic 53 4 1988 1009 1026 these languages are defined by locally finite sentences and generalize languages recognized by automata or defined by monadic second order sentences we give many examples showing that numerous context free languages are locally finite then we study closure properties of the family loc of locally finite languages and show that most undecidability results that hold for context free languages may be extended to locally finite languages in a second part we consider an extension of these languages to infinite and transfinite length words we prove that each language which is recognized by a buchi automaton where is an ordinal and is defined by a locally finite sentence this result combined with a preceding one of finkel and ressayre j symbolic logic 61 2 1996 563 585 provides a generalization of buchi s result about decidability of monadic second order theory of the structure

random paths to stability in two sided matching empirical studies of two sided matching have so far concentrated on markets in which certain kinds of market failures were addressed by resorting to centralized deterministic matching procedures loosely speaking the results of these studies are that those centralized procedures which achieved stable outcomes resolved the market failures while those markets organized through procedures that yielded unstable outcomes continued to fail 2 so the market failures seem to be associated with instability of the outcomes but many entry level labor markets and other two sided matching situations don t employ centralized matching procedures and yet aren t observed to experience such failures so we can conjecture that at least some of these markets may reach stable outcomes by means of decentralized decision making and decentralized decision making in complex environments presumably introduces some randomness into what matchings are achieved however as far as we are aware no nondeterministic models leading to stable outcomes have yet been studied the present paper demonstrates that starting from an arbitrary matching the process of allowing randomly chosen blocking pairs to match will converge to a stable matching with probability one this resolves an open question raised by knuth 1976 who showed that such a process may cycle furthermore every stable matching can arise

acceleration of lattice bgk schemes with grid refinement abstract the lbgk method with local grid refinement has been shown to be an efficient and accurate tool for the simulation of incompressible viscous flows over complex geometries in the present study further improvement of this concept is proposed enabling the use of smaller amount of time steps on refined grids without impairing the spatial or temporal accuracy this extension of the lbgk method has been proved by analytical and numerical investigations the gain in computational time was found to be significant

lattice boltzmann method on curvilinear coordinates system using an interpolation based strategy the lattice boltzmann method is extended to apply to general curvilinear coordinate systems as an example a cylindrical coordinate system is used to simulate two dimensional flow around a circular cylinder numerical simulations are carried out for impulsive initial conditions with reynolds numbers up to 104 the agreement of our results with previous computational and experimental results is satisfactory compared with previous lattice boltzmann simulations of the same problem our new approach greatly enhances the computational efficiency

finite automata and ordinals abstract several definitions of automata on words indexed by ordinals have been proposed previously the first one was introduced by buchi to prove the decidability of the monadic second order theory of denumerable ordinals wojciechowski studied the properties of these automata independently of the length of the input the second definition proposed by choueka works only on words of length less than n in this paper we restrict the domain of wojciechowski automata to the domain of choueka s ones that is given n we keep only sequences for n 1 in the language defined by a wojciechowski automaton in order to prove the equivalence between choueka automata and wojciechowski automata then we obtain the closure under complementation of the class of wojciechowski s definable sets and finally we give an algorithm for determinizing wojciechowski automata

optimal preconditioning of lattice boltzmann methods a preconditioning technique to accelerate the simulation of steady state problems using the single relaxation time srt lattice boltzmann lb method was first proposed by guo et al z guo t zhao y shi preconditioned lattice boltzmann method for steady flows phys rev e 70 2004 066706 1 the key idea in this preconditioner is to modify the equilibrium distribution function in such a way that by means of a chapman enskog expansion a time derivative preconditioner of the navier stokes ns equations is obtained in the present contribution the optimal values for the free parameter c of this preconditioner are searched both numerically and theoretically the later with the aid of linear stability analysis and with the condition number of the system of ns equations the influence of the collision operator single versus multiple relaxation times mrt is also studied three steady state laminar test cases are used for validation namely the two dimensional lid driven cavity a two dimensional microchannel and the three dimensional backward facing step finally guidelines are suggested for an a priori definition of optimal preconditioning parameters as a function of the reynolds and mach numbers the new optimally preconditioned mrt method derived is shown to improve simultaneously the rate of convergence the stability and the accuracy of the lattice boltzmann simulations when compared to the non preconditioned methods and to the optimally preconditioned srt one additionally direct time derivative preconditioning of the lb equation is also studied

truncation error analysis of lattice boltzmann methods a truncation error analysis is performed for models based on the lattice boltzmann lb equation this analysis involves two steps the recursive application of the lb equation and a taylor series expansion unlike previous analytical studies of lb methods the present work does not assume an asymptotic relationship between the temporal and spatial discretization parameters or between the probability distribution function f and its equilibrium distribution feq effective finite difference stencils are derived for both the distribution function and the primitive variables i e density and velocity the governing partial differential equations are also recovered the associated truncation errors are derived and the results are validated by numerical simulation of analytic flows analysis of the truncation errors elucidates the roles of the kinetic theory relaxation parameter and the discretization parameters x and t the effects of initial and boundary conditions are also addressed and are shown to significantly affect the overall accuracy of the method

an eulerian description of the streaming process in the lattice boltzmann equation this paper presents a novel strategy for solving discrete boltzmann equation dbe for simulation of fluid flows this strategy splits the solution procedure into streaming and collision steps as in the lattice boltzmann equation lbe method the streaming step can then be carried out by solving pure linear advection equations in an eulerian framework this offers two significant advantages over previous methods first the relationship between the relaxation parameter and the discretization of the collision term developed from the lbe method is directly applicable to the dbe method the resulting dbe collision step remains local and poses no constraint on time step second decoupling of the advection step from the collision step facilitates implicit discretization of the advection equation on arbitrary meshes an implicit unstructured dbe method is constructed based on this strategy and is evaluated using several test cases of flow over a backward facing step lid driven cavity flow and flow past a circular cylinder the speedup of convergence for some cases improves by a factor of about 20

some progress in lattice boltzmann method part i nonuniform mesh grids a new lattice boltzmann algorithm is proposed to simulate the navier stokes equation on arbitrary nonuniform mesh grids the new algorithm retains the advantages of the lattice boltzmann method parallel of algorithm ease of programming and ability to incorporate microscopic interactions a simulation of flow in a two dimensional symmetric channel with sudden expansion is carried out using the new algorithm on a nonuniform mesh the results of the simulation are in excellent agreement with previous experimental and numerical results

on the finite difference based lattice boltzmann method in curvilinear coordinates the lattice boltzmann method is a microscopic based approach for solving the fluid flow problems at the macroscopic scales the presently popular method uses regularly spaced lattices and cannot handle curved boundaries with desirable flexibility to circumvent such difficulties a finite difference based lattice boltzmann method fdlbm in curvilinear coordinates is explored using body fitted coordinates with non uniform grids several test cases including the impulsively started cylindrical couette flow steady state cylindrical couette flow steady flow over flat plates and steady flow over a circular cylinder are used to examine various issues related to the fdlbm the effect of boundary conditions for the distribution functions on the solution the merits between second order central difference and upwind schemes for advection terms and the effect of the reynolds number are investigated favorable results are obtained using fdlbm in curvilinear coordinates indicating that the method is potentially capable of solving finite reynolds number flow problems in complex geometries

multiscale lattice boltzmann schemes with turbulence modeling abstract the viability of multiscale lattice boltzmann schemes for the numerical simulation of turbulent flows is discussed and numerically demonstrated for turboaxial machine applications the extension of boundary fitting formulas based on wall functions is proposed which enables the efficient computation of turbulent flows in complex curvilinear geometry using a simple cartesian grid examples of two dimensional turbulent flows in an axial compressor cascade are presented

a characteristic galerkin method for discrete boltzmann equation abstract the characteristic galerkin finite element method for the discrete boltzmann equation is presented to simulate fluid flows in complex geometries the inherent geometric flexibility of the finite element method permits the easy use of simple cartesian variables on unstructured meshes and the mesh clustering near large gradients the characteristic galerkin procedure with appropriate boundary condition results in accurate solutions with little numerical diffusion several test cases are conducted including unsteady couette flows lid driven cavity flows and steady flow past a circular cylinder on unstructured meshes the numerical results are in good agreement with previous analytical if applicable numerical and experimental results

strategy proofness makes the difference deferred acceptance with responsive priorities in college admissions and student placements at public schools the admission decision can be thought of as assigning indivisible objects with capacity constraints to a set of students such that each student receives at most one object and monetary compensations are not allowed in these important market design problems the agent proposing deferred acceptance da mechanism with responsive strict priorities performs well and economists have successfully implemented da mechanisms or slight variants thereof we show that almost all real life mechanisms used in such environments including the large classes of priority mechanisms and linear programming mechanisms satisfy a set of simple and intuitive properties once we add strategy proofness to these properties da mechanisms are the only ones surviving in market design problems that are based on weak priorities like school choice generally multiple tie breaking mtb procedures are used and then a mechanism is implemented with the obtained strict priorities by adding stability with respect to the weak priorities we establish the rst normative foundation

stable matching with incomplete information we formulate a notion of stable outcomes in matching problems with one sided asymmetric information the key conceptual problem is to formulate a notion of a blocking pair that takes account of the inferences that the uninformed agent might make from the hypothesis that the current allocation is stable we show that the set of stable outcomes is nonempty in incomplete information environments and is a superset of the set of complete information stable outcomes we then provide sucient conditions for incomplete information stable matchings to be ecient lastly we dene a notion of price sustainable allocations and show that the set of incomplete information stable matchings is a subset of the set of such allocations

the economics of matching stability and incentives this paper considers some game theoretic aspects of matching problems and procedures of the sort which involve matching the members of one group of agents with one or more members of a second disjoint group of agents ail of whom have preferences over the possible resulting matches the main focus of this paper is on determining the extent to which matching procedures can be designed which give agents the incentive to honestly reveal their preferences and which produce stable matches two principal results are demonstrated the first is that no matching procedure exists which always yields a stable outcome and gives players the incentive to reveal their true preferences even though procedures exist which accomplish either of these goals separately the second result is that matching procedures do exist however which always yield a stable outcome and which always give all the agents in one of the two disjoint sets of agents the incentive to reveal their true preferences

least squares finite element scheme for the lattice boltzmann method on an unstructured mesh a numerical model of the lattice boltzmann method lbm utilizing least squares finite element method in space and the crank nicolson method in time is developed this method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using the flexibility and numerical stability of a finite element method while employing accurate least squares optimization fourth order accuracy in space and second order accuracy in time are derived for a pure advection equation on a uniform mesh while high stability is implied from a von neumann linearized stability analysis implemented on unstructured mesh through an innovative element by element approach the proposed method requires fewer grid points and less memory compared to traditional lbm accurate numerical results are presented through two dimensional incompressible poiseuille flow couette flow and flow past a circular cylinder finally the proposed method is applied to estimate the permeability of a randomly generated porous media which further demonstrates its inherent geometric flexibility

direct and large eddy simulation of turbulent flows on composite multi resolution grids by the lattice boltzmann method in order to properly address the simulation of complex weakly compressible turbulent flows the lattice boltzmann method originally designed for uniform structured grids needs to be extended to composite multi domain grids displaying various levels of spatial resolution therefore physical conditions must be specified to determine the mapping of statistical information about the populations of moving particles at the interface between two domains of different resolutions quite simply in terms of the probability distributions of the underlying discrete velocity boltzmann equation namely the continuity of the mass density and fluid momentum is fulfilled by imposing the continuity of the equilibrium part of these distributions whereas the discontinuity of the rate of strain tensor is ensured by applying a spatial transformation to the collision term of the discrete velocity boltzmann equation the latter condition allows us to explicitly account for the subgrid scale modeling in the treatment of resolution changes test computations of a turbulent plane channel flow have been carried out the lattice boltzmann scheme relies on the standard d3q19 lattice in a cell vertex representation and uses the bgk approximation for the collision term a shear improved variant of the smagorinsky viscosity is used to account for possible subgrid scale dynamics in a quasi direct numerical simulation at re t 180 with two levels of grid resolution the results are found in excellent agreement with reference data obtained by a high resolution pseudo spectral simulation in a large eddy simulation les at re t 395 with three levels of grid resolution the results compare reasonably well with high resolution reference data the accuracy is improved in comparison with a standard finite volume les performed with the same subgrid scale viscosity and comparable grid resolution by combining the simplicity and physical relevance of the shear improved smagorinsky model and the computational efficiency of the lattice boltzmann scheme here extended to composite multi resolution grids we believe that our proposal offers a high potential for the simulation of complex turbulent flows

lattice boltzmann method on composite grids a composite block structured lattice boltzmann method is proposed for the simulation of two dimensional incompressible fluid flows the grid structure is composed of a coarse base grid and one or several fine grid s the former covers the entire physical domain the latter are placed at regions where local grid refinement is desirable the simulation is first carried out on the base grid level at a smaller relaxation time allowing a rapid propagation of boundary information throughout the entire domain thus large scale flow features can be resolved efficiently at a relatively low cost at a later time fine grid variables are initiated the dependent variables on both grid levels are then advanced in time simultaneously with the fine grid boundary conditions obtained from the base grid solution at the grid interface as a demonstration the lid driven cavity flow is selected for study the results show good agreement with benchmark numerical data and those calculated from the finite volume u 2 mathrm rans model the proposed method is able to produce accurate solutions on fine grids with a considerable saving in cpu time

tree automatic scattered linear orders tree automatic linear orders on regular tree languages are studied it is shown that there is no tree automatic scattered linear order and therefore no tree automatic well order on the set of all finite labeled trees and that a regular tree language admits a tree automatic scattered linear order if and only if for some n no binary tree of height n can be embedded into the union of the domains of its trees hence the problem whether a given regular tree language can be ordered by a scattered linear order or a well order is decidable moreover sharp bounds for tree automatic well orders on some regular tree languages are computed by connecting tree automata with automata on ordinals the proofs use elementary techniques of automata theory

finite volume lattice boltzmann method we present a finite volume formulation for the lattice boltzmann method fvlbm based on standard bilinear quadrilateral elements in two dimensions the accuracy of this scheme is demonstrated by comparing the velocity field with the analytical solution of the navier stokes equations for time dependent rotating couette flow and taylor vortex flow to demonstrate the flexibility of the scheme we have also simulated a modified rotating couette flow where the inner cylinder has an elliptical shape the results agree with those obtained from the traditional marker and cell method the fvlbm scheme is applicable to arbitrarily shaped two dimensional regions and thus the range of applicability of the lattice boltzmann method has been significantly extended

multi block lattice boltzmann method extension to 3d and validation in turbulence abstract in this paper a multi block method is applied to 3d problems in this application interpolation schemes are carefully addressed to avoid the inconsistency when information is transferred from coarse to fine blocks two test cases are employed to assess information transfer scheme and accuracy improvement with respect to grid refinement

finite volume scheme for the lattice boltzmann method on unstructured meshes department of mathematics and statistics bowling green state university bowling green ohio 43403 received 9 september 1998 a nite volume scheme for the lattice boltzmann method is developed for unstructured triangular meshes intwo dimensions the accuracy of this new scheme is demonstrated by comparing the numerical results with theexact solutions to the navier stokes equations for taylor vortex ow shear ow between two parallel plates shear ow between two rotating cylinders and poiseuille ow the agreement between the numerical andanalytical results is very good for each of these tests s1063 651x 99 07804 6 pacs number s 47 10 1g 47 11 1j 05 20 ddi introduction

implementation of the compact interpolation within the octree based lattice boltzmann solver musubi abstract a sparse octree based parallel implementation of the lattice boltzmann method for non uniform meshes is presented in this paper to couple grids of different resolutions a second order accurate compact interpolation is employed and further extended into three dimensions the compact interpolation requires only four source elements from the adjacent level for both two and three dimensions thus improves the computational efficiency moreover a weight based domain decomposition algorithm and the level wise arrangement of elements is explained in detail the second order convergence for both velocity and strain rate are validated numerically in the taylor green vortex test case additionally the 3d flow around a sphere in the reynolds number range of 100 1000 is investigated good agreement between simulated results and those from literature is observed which provides further evidence for the accuracy of our method