morse theory for periodic solutions of hamiltonian systems and the maslov index in this paper we prove morse type inequalities for the contractible 1 periodic solutions of time dependent hamiltonian differential equations on those compact symplectic manifolds m for which the symplectic form and the first chern class of the tangent bundle vanish over q m the proof is based on a version of infinite dimensional morse theory which is due to floer the key point is an index theorem for the fredholm operator which plays a central role in floer homology the index formula involves the maslov index of nondegenerate contractible periodic solutions this maslov index plays the same role as the morse index of a nondegenerate critical point does in finite dimensional morse theory we shall use this connection between floer homology and maslov index to establish the existence of infinitely many periodic solutions having integer periods provided that every i periodic solution has at least one floquet multiplier which is not equal to 1

on the maslov index in this paper we give four definitions of maslov index and show that they all satisfy the same system of axioms and hence are equivalent to each other moreover relationships of several symplectic and differential geometric analytic and topological invariants including triple maslov indices eta invariants spectral flow and signatures of quadratic forms to the maslov index are developed and formulae relating them are given the broad presentation is designed with a view to applications both in geometry and in analysis 1994 john wiley sons inc

accurate projection methods for the incompressible navier stokes equations abstract this paper considers the accuracy of projection method approximations to the initial boundary value problem for the incompressible navier stokes equations the issue of how to correctly specify numerical boundary conditions for these methods has been outstanding since the birth of the second order methodology a decade and a half ago it has been observed that while the velocity can be reliably computed to second order accuracy in time and space the pressure is typically only first order accurate in the l norm this paper identifies the source of this problem in the interplay of the global pressure update formula with the numerical boundary conditions and presents an improved projection algorithm which is fully second order accurate as demonstrated by a normal mode analysis and numerical experiments in addition a numerical method based on a gauge variable formulation of the incompressible navier stokes equations which provides another option for obtaining fully second order convergence in both velocity and pressure is discussed the connection between the boundary conditions for projection methods and the gauge method is explained in detail

fast and high accuracy multigrid solution of the three dimensional poisson equation we employ a fourth order compact finite difference scheme fos with the multigrid algorithm to solve the three dimensional poisson equation we test the influence of different orderings of the grid space and different grid transfer operators on the convergence and efficiency of our high accuracy algorithm fourier smoothing analysis is conducted to show that fos has a smaller smoothing factor than the traditional second order central difference scheme cds a new method of fourier smoothing analysis is proposed for the partially decoupled red black gauss seidel relaxation with fos numerical results are given to compare the computed accuracy and the computational efficiency of fos with multigrid against cds with multigrid

cluster analysis for cognitive diagnosis theory and applications latent class models for cognitive diagnosis often begin with specification of a matrix that indicates which attributes or skills are needed for each item then by imposing restrictions that take this into account along with a theory governing how subjects interact with items parametric formulations of item response functions are derived and fitted cluster analysis provides an alternative approach that does not require specifying an item response model but does require an item by attribute matrix after summarizing the data with a particular vector of sum scores k means cluster analysis or hierarchical agglomerative cluster analysis can be applied with the purpose of clustering subjects who possess the same skills asymptotic classification accuracy results are given along with simulations comparing effects of test length and method of clustering an application to a language examination is provided to illustrate how the methods can be implemented in practice

a finite difference galerkin formulation for the incompressible navier stokes equations abstract the development of a new computational method for solving the incompressible navier stokes equations in primitive variable form is presented it is found that certain finite difference approximations for these equations can be transformed into an equivalent system which efficiently determines the discrete velocity field and which completely eliminates the pressure two such difference schemes for two dimensional problems are examined and some preliminary numerical results are discussed for the steady driven cavity problem

a coarse grid projection method for accelerating incompressible flow computations we present a coarse grid projection cgp method for accelerating incompressible flow computations which is applicable to methods involving poisson equations as incompressibility constraints the cgp methodology is a modular approach that facilitates data transfer with simple interpolations and uses black box solvers for the poisson and advection diffusion equations in the flow solver after solving the poisson equation on a coarsened grid an interpolation scheme is used to obtain the fine data for subsequent time stepping on the full grid a particular version of the method is applied here to the vorticity stream function primitive variable and vorticity velocity formulations of incompressible navier stokes equations we compute several benchmark flow problems on two dimensional cartesian and non cartesian grids as well as a three dimensional flow problem the method is found to accelerate these computations while retaining a level of accuracy close to that of the fine resolution field which is significantly better than the accuracy obtained for a similar computation performed solely using a coarse grid a linear acceleration rate is obtained for all the cases we consider due to the linear cost elliptic poisson solver used with reduction factors in computational time between 2 and 42 the computational savings are larger when a suboptimal poisson solver is used we also find that the computational savings increase with increasing distortion ratio on non cartesian grids making the cgp method a useful tool for accelerating generalized curvilinear incompressible flow solvers

effects of the computational time step on numerical solutions of turbulent flow effects of large computational time steps on the computed turbulence were investigated using a fully implicit method in turbulent channel flow computations the largest computational time step in wall units which led to accurate prediction of turbulence statistics was determined turbulence fluctuations could not be sustained if the computational time step was near or larger than the kolmogorov time scale

application of a fractional step method to incompressible navier stokes equations a numerical method for computing three dimensional time dependent incompressible flows is presented the method is based on a fractional step or time splitting scheme in conjunction with the approximate factorization technique it is shown that the use of velocity boundary conditions for the intermediate velocity field can lead to inconsistent numerical solutions appropriate boundary conditions for the intermediate velocity field are derived and tested numerical solutions for flows inside a driven cavity and over a backward facing step are presented and compared with experimental data and other numerical results

an unsplit higher order godunov method for scalar conservation laws in multiple dimensions abstract in this paper we develop an unsplit higher order godunov method for scalar conservation laws in two dimensions the method represents an extension for the special case being considered of methods developed by colella and by van leer in our method we begin with a piecewise bilinear representation of the solution on each grid cell a new piecewise bilinear representation at the next time level is then obtained from a two step procedure in the first step a conservative predictor corrector scheme derived from the integral form of the differential equation and characteristic considerations is used to obtain average values of the solution over grid cells at the new time level next these new average values are then used to construct a limited piecewise bilinear profile for each cell at the new time level the resulting method is shown to satisfy a maximum principle for constant coefficient linear advection computational results are presented comparing the new method to colella s method for linear advection the method is also applied to two model problems from porous media flow miscible and immiscible displacement the new scheme provides accurate resolution of sharp fronts without any significant distortion

implicit solutions of incompressible navier stokes equations using the pressure gradient method a modified pressure gradient method is developed for solving the incompressible twoand three dimensional navier stokes equations in primitive variables velocity and pressure gradient vectors rather than the velocity and pressure are considered as dependent variables this choice of the dependent variables is consistent with the flow physics as the velocity field of incompressible flows is not dependent on the pressure but rather the pressure gradient this introduces one and two additional dependent variables for two and three dimensions respectively to close the system of equations additional equations are obtained from the identity that the curl of the pressure gradient is zero this choice of dependent variables also leads to dirichlet boundary conditions for the pressure gradient which improves numerical stability and convergence rates the modified pressure gradient method includes a pressure gradient averaging term in the momentum equations to stabilize the solution this term is extended here to general curvilinear coordinates the system of equations is discritized using a conservative finite volume formulation time integration is achieved with a fully implicit scheme including implicit boundary conditions the implicit scheme guarantees that continuity is satisfied to machine zero numerical results compare well with solutions available in the literature for the cavity flow problem and flow about a circular cylinder at reynolds number 40

the accuracy of the fractional step method we analyze the accuracy of the fractional step method of kim and moin j comput phys 59 1985 pp 308 323 for the incompressible navier stokes equations we show that the boundary conditions cannot be exactly satisfied in the projection step and that this limits the accuracy of the method we also show that the pressure in any projection method can be at best first order accurate our analysis is simpler and more direct than the previous analyses of this method we also show that there is no numerical boundary layer for velocity or pressure but there is one for the auxiliary pressure variable

on convergence of block centered finite differences for elliptic problems we consider linear selfadjoint elliptic problems with neumann boundary conditions in rectangular domains we demonstrate that with sufficiently smooth data the discrete l 2 norm errors for tensor product block centered finite differences in both the approximate solution and its first derivatives are second order for all nonuniform grids extensions to nonselfadjoint and parabolic problems are discussed

a quadratic spline based interface quasi reconstruction algorithm for accurate tracking of two phase flows a new quadratic spline based interface quasi reconstruction algorithm is presented which provides an accurate and continuous representation of the interface in a multiphase domain and facilitates the direct estimation of local interfacial curvature the fluid interface in each of the mixed cells is represented by piecewise parabolic curves and an initial discontinuous plic approximation of the interface is progressively converted into a smooth quadratic spline made of these parabolic curves the conversion is achieved by a sequence of predictor corrector operations enforcing function c 0 and derivative c 1 continuity at the cell boundaries using simple analytical expressions for the continuity requirements the efficacy and accuracy of the current algorithm has been demonstrated using standard test cases involving reconstruction of known static interface shapes and dynamically evolving interfaces in prescribed flow situations these benchmark studies illustrate that the present algorithm performs excellently as compared to the other interface reconstruction methods available in literature quadratic rate of error reduction with respect to grid size has been observed in all the cases with curved interface shapes only in situations where the interface geometry is primarily flat the rate of convergence becomes linear with the mesh size the flow algorithm implemented in the current work is designed to accurately balance the pressure gradients with the surface tension force at any location as a consequence it is able to minimize spurious flow currents arising from imperfect normal stress balance at the interface this has been demonstrated through the standard test problem of an inviscid droplet placed in a quiescent medium finally the direct curvature estimation ability of the current algorithm is illustrated through the coupled multiphase flow problem of a deformable air bubble rising through a column of water

application of time iterative schemes to incompressible flow the computation of steady incompressible flows by an euler implicit algorithm is studied using both the incompressible equations and the low mach number compressible equations the incompressible equations are handled by adding an artificial time derivative to the continuity equation this allows both the pressure and velocity to be obtained implicitly in one dimensional problems both systems converge rapidly even at low mach numbers where the eigenvalues are very stiff in two dimensions where approximate factorization is required the presence of stiff eigenvalues is highly detrimental stiffness can be avoided in the incompressible equations by selecting an appropriate pseudo mach number this insures reliable convergence and results in an efficient incompressible flow algorithm in the case of compressible equations the mach number cannot be chosen arbitrarily and the contamination introduced by approximate factorization must be removed a matrix preconditioning factor that accomplishes this is developed and demonstrated with this modification the convergence rate is the same as in the incompressible case and is independent of mach number rapid convergence is observed at mach numbers as low as 6 05

a new family of 5 5 cc 4oc schemes applicable for unsteady navier stokes equations in this paper a new family of implicit compact finite difference schemes for computation of unsteady convection diffusion equation with variable convection coefficient is proposed the schemes which are fourth order accurate in space and second or lower order accurate in time depending on the choice of weighted time average parameter are then applied to unsteady navier stokes system the proposed schemes where transport variable and its first derivatives are carried as the unknowns combine virtues of compact discretization and pade scheme for spatial derivative these schemes which are based on a five point stencil with constant coefficients named as 5 5 constant coefficient 4th order compact 5 5 cc 4oc give rise to a diagonally dominant system of equations and shows higher accuracy and better phase and amplitude error characteristics than some of the standard methods these schemes are capable of using a grid aspect ratio other than unity and are unconditionally stable they efficiently capture both transient and steady solutions of linear and nonlinear convection diffusion equations with dirichlet as well as neumann boundary conditions subsequently the proposed schemes are applied to problems governed by the incompressible navier stokes equations the results obtained are in excellent agreement with analytical and available numerical results in all cases establishing efficiency and accuracy of the proposed schemes

stable and accurate pressure approximation for unsteady incompressible viscous flow how to properly specify boundary conditions for pressure is a longstanding problem for the incompressible navier stokes equations with no slip boundary conditions an analytical resolution of this issue stems from a recently developed formula for the pressure in terms of the commutator of the laplacian and leray projection operators here we make use of this formula to a improve the accuracy of computing pressure in two kinds of existing time discrete projection methods implicit in viscosity only and b devise new higher order accurate time discrete projection methods that extend a slip correction idea behind the well known finite difference scheme of kim and moin we test these schemes for stability and accuracy using various combinations of c 0 finite elements for all three kinds of time discretization one can obtain third order accuracy for both pressure and velocity without a time step stability restriction of diffusive type furthermore two kinds of projection methods are found stable using piecewise linear elements for both velocity and pressure

efficient implementation of thinc scheme in this paper we improve the multi dimensional thinc tangent of hyperbola for interface capturing scheme f xiao y honma t kono a simple algebraic interface capturing scheme using hyperbolic tangent function int j numer meth fluid 48 2005 1023 the thinc scheme is a vof volume of fluid type method in the original thinc scheme one dimensional thinc scheme was straightforwardly used for multi dimensional cases in this paper we propose the wlic weighed line interface calculation method to extend the thinc scheme to multi dimension in the wlic method the interface is reconstructed by taking an average of line interfaces along x y and z coordinates with the weights calculated from surface normal the wlic method can extend the thinc scheme to multi dimension while maintaining simplicity of implementation and achieve a higher accuracy than the original thinc scheme the wlic method can readily extend the thinc scheme to three dimension

essential independence and likelihood based ability estimation for polytomous items a definition ofessential independence is proposed for sequences of polytomous items for items satisfying the reasonable assumption that the expected amount of credit awarded increases with examinee ability we develop a theory ofessential unidimensionality which closely parallels that of stout essentially unidimensional item sequences can be shown to have a unique up to change of scale dominant underlying trait which can be consistently estimated by a monotone transformation of the sum of the item scores in more general polytomous response latent trait models with or without ordered responses anm estimator based upon maximum likelihood may be shown to be consistent for under essentially unidimensional violations of local independence and a variety of monotonicity identifiability conditions a rigorous proof of this fact is given and the standard error of the estimator is explored these results suggest that ability estimation methods that rely on the summation form of the log likelihood under local independence should generally be robust under essential independence but standard errors may vary greatly from what is usually expected depending on the degree of departure from local independence an index of departure from local independence is also proposed

the unregularized gradient flow of the symplectic action the symplectic action can be defined on the space of smooth paths in a symplectic manifold p which join two lagrangian submanifolds of p to pursue a new approach to the variational theory of this function we define on a subset of the path space the flow whose trajectories are given by the solutions of the cauchy riemann equation with respect to a suitable almost complex structure on p in particular we prove compactness and transversality results for the set of bounded trajectories

comparison of second and fourth order discretizations for multigrid poisson solvers we combine a compact high order difference approximation with multigrid v cycle algorithm to solve the two dimensional poisson equation with dirichlet boundary conditions this scheme along with several different orderings of grid space and projection operators is compared with the five point formula to show the dramatic improvement in computed accuracy on serial and vector machines

a high order discontinuous galerkin method for 2d incompressible flows in this paper we introduce a high order discontinuous galerkin method for two dimensional incompressible flow in the vorticity stream function formulation the momentum equation is treated explicitly utilizing the efficiency of the discontinuous galerkin method the stream function is obtained by a standard poisson solver using continuous finite elements there is a natural matching between these two finite element spaces since the normal component of the velocity field is continuous across element boundaries this allows for a correct upwinding gluing in the discontinuous galerkin framework while still maintaining total energy conservation with no numerical dissipation and total enstrophy stability the method is efficient for inviscid or high reynolds number flows optimal error estimates are proved and verified by numerical experiments

a module structure on the symplectic floer cohomology the aim of this paper is to offer an affirmative answer to the floer conjectures in 2 p 589 which states that there is a module structure on the z 2 n graded symplectic floer cohomology for monotone symplectic manifolds by constructing a z graded symplectic floer cohomology as an integral lift of the z 2 n graded symplectic floer cohomology we gain control of the holomorphic bubbling spheres this makes a module structure on the z graded floer cohomology there is a spectral sequence with e 1 given by the z graded symplectic floer cohomology such a spectral sequence converges to the z 2 n graded symplectic floer cohomology hence we induce a module structure for the z 2 n graded symplectic floer cohomology by the spectral sequence and algebraic topology methods

a stable and convergent scheme for viscoelastic flow in contraction channels we present a new algorithm to simulate unsteady viscoelastic flows in abrupt contraction channels in our approach we split the viscoelastic terms of the oldroyd b constitutive equation using duhamel s formula and discretize the resulting pdes using a semi implicit finite difference method based on a lax wendroff method for hyperbolic terms in particular we leave a small residual elastic term in the viscous limit by design to make the hyperbolic piece well posed a projection method is used to impose the incompressibility constraint we are able to compute the full range of unsteady elastic flows in an abrupt contraction channel from the viscous limit to the elastic limit in a stable and convergent manner we demonstrate the range of our method for unsteady flow of a maxwell fluid with and without viscosity in planar contraction channels we also demonstrate stable and convergent results for benchmark high weissenberg number problems at we 1 and we 10

a cartesian grid method for modeling multiple moving objects in 2d incompressible viscous flow we present an efficient method for solving 2d incompressible viscous flows around multiple moving objects our method employs an underlying regular cartesian grid to solve the system using a streamfunction vorticity formulation and with discontinuities representing the embedded objects the no penentration condition for the moving geometry is satisfied by superposing a homogenous solution to the poisson s equation for the streamfunction the no slip condition is satisfied by generating vorticity on the surfaces of the objects both the initial poisson solution and the evaluation of the homogenous solution require embedding irregular discontinuities in a fast poisson solver computation time is dictated by the time required to do a fast poisson solution plus solve an integral form of laplace s equation there is no significant increase in computational cost if the geometry of the embedded objects is variable and moving relative to the underlying grid we test the method against the canonical example of flow past a cylinder and obtained new results on the flow and forces of two cylinders moving relative to each other

a high order immersed interface method for simulating unsteady incompressible flows on irregular domains immersed boundary methods and immersed interface methods are becoming increasingly popular for the computation of unsteady flows around complex geometries using a cartesian grid while good results both qualitative and quantitative have been obtained most of the methods rely on low order corrections to account for the immersed boundary the objective of the present work is to present as an alternative a high order modified immersed interface method for the 2d unsteady incompressible navier stokes equations in stream function vorticity formulation the method employs an explicit fourth order runge kutta time integration scheme fourth order compact finite differences for computation of spatial derivatives and a nine point fourth order compact discretization of the poisson equation for computation of the stream function corrections to the finite difference schemes are used to maintain high formal accuracy at the immersed boundary as confirmed by analytical tests to validate the method in its application to incompressible flows several physically relevant test cases are computed including uniform flow past a circular cylinder and tollmien schlichting waves in a boundary layer

consistency of nonparametric classification in cognitive diagnosis latent class models for cognitive diagnosis have been developed to classify examinees into one of the 2 k attribute profiles arising from a k dimensional vector of binary skill indicators these models recognize that response patterns tend to deviate from the ideal responses that would arise if skills and items generated item responses through a purely deterministic conjunctive process an alternative to employing these latent class models is to minimize the distance between observed item response patterns and ideal response patterns in a nonparametric fashion that utilizes no stochastic terms for these deviations theorems are presented that show the consistency of this approach when the true model is one of several common latent class models for cognitive diagnosis consistency of classification is independent of sample size because no model parameters need to be estimated simultaneous consistency for a large group of subjects can also be shown given some conditions on how sample size and test length grow with one another

discrete exterior calculus discretization of incompressible navier stokes equations over surface simplicial meshes a conservative discretization of incompressible navier stokes equations is developed based on discrete exterior calculus dec a distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product the governing equations are first rewritten using the exterior calculus notation replacing vector calculus differential operators by the exterior derivative hodge star and wedge product operators the discretization is then carried out by substituting with the corresponding discrete operators based on the dec framework numerical experiments for flows over surfaces reveal a second order accuracy for the developed scheme when using structured triangular meshes and first order accuracy for otherwise unstructured meshes by construction the method is conservative in that both mass and vorticity are conserved up to machine precision the relative error in kinetic energy for inviscid flow test cases converges in a second order fashion with both the mesh size and the time step

unsteady solution of incompressible navier stokes equations abstract a new time accurate finite difference numerical method for solving incompressible navier stokes equations is presented with primitive variables as the unknowns the numerical scheme is a crank nicolson implicit treatment of all terms of the equations with central differencing for space derivatives the pressure and the nonlinearities in convection terms are not lagged to obtain the incompressible solution at the advanced time level a continuous auxiliary system is introduced in pseudo time with artificial compressibility time accurate solutions are presented for two dimensional fluid flows in a square cavity with an impulsively starting lid and with an oscillating lid

a note on exploratory item factor analysis by singular value decomposition we revisit a singular value decomposition svd algorithm given in chen et al psychometrika 84 124 146 2019b for exploratory item factor analysis ifa this algorithm estimates a multidimensional ifa model by svd and was used to obtain a starting point for joint maximum likelihood estimation in chen et al 2019b thanks to the analytic and computational properties of svd this algorithm guarantees a unique solution and has computational advantage over other exploratory ifa methods its computational advantage becomes significant when the numbers of respondents items and factors are all large this algorithm can be viewed as a generalization of principal component analysis to binary data in this note we provide the statistical underpinning of the algorithm in particular we show its statistical consistency under the same double asymptotic setting as in chen et al 2019b we also demonstrate how this algorithm provides a scree plot for investigating the number of factors and provide its asymptotic theory further extensions of the algorithm are discussed finally simulation studies suggest that the algorithm has good finite sample performance

a second order projection method for the incompressible navier stokes equations in this paper we describe a second order projection method for the time dependent incom pressible navier stokes equations as in the original projection method developed by chorin we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields by introducing more coupling between the diffusion onvection step and the projection step we obtain a temporal discretiza tion that is second order accurate our treatment of the diffusion convection step uses a specialized higher order godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high reynolds number the godunov procedure is second order accurate for smooth flow and remains stable for discontinuous initial data even in the zero viscosity limit we approximate the projection directly using a galerkin procedure that uses a local basis for discretely divergence free vector fields numerical results are presented validating the convergence properties of the method we also apply the method to doubly periodic shear layers to assess the performance of the method on more difficult

transversality in elliptic morse theory for the symplectic action our goal in this paper is to settle some transversality question for the perturbed nonlinear cauchy riemann equations on the cylinder these results play a central role in the denition of symplectic floer homology and hence in the proof of the arnold conjecture there is currently no other reference to these transversality results in the open literature our approach does not require aronszajn s theorem instead we derive the unique continuation theorem from a generalization of the carleman similarity principle

the generalized dina model framework the g dina generalized deterministic inputs noisy and gate model is a generalization of the dina model with more relaxed assumptions in its saturated form the g dina model is equivalent to other general models for cognitive diagnosis based on alternative link functions when appropriate constraints are applied several commonly used cognitive diagnosis models cdms can be shown to be special cases of the general models in addition to model formulation the g dina model as a general cdm framework includes a component for item by item model estimation based on design and weight matrices and a component for item by item model comparison based on the wald test the paper illustrates the estimation and application of the g dina model as a framework using real and simulated data it concludes by discussing several potential implications of and relevant issues concerning the proposed framework

computational design for long term numerical integration of the equations of fluid motion the integral constraints on quadratic quantities of physical importance such as conservation of mean kinetic energy and mean square vorticity will not be maintained in finite difference analogues of the equation of motion for two dimensional incompressible flow unless the finite difference jacobian expression for the advection term is restricted to a form which properly represents the interaction between grid points as derived in this paper it is shown that the derived form of the finite difference jacobian prevents nonlinear computational instability and thereby permits long term numerical integrations

a non staggered grid fractional step method for time dependent incompressible navier stokes equations in curvilinear coordinates a numerical method for solving three dimensional time dependent incompressible navier stokes equations in curvilinear coordinates is presented the non staggered grid method originally developed by c m rhie and w l chow aiaaj 21 1525 1983 for steady state problems is extended to compute unsteady flows in the computational space the cartesian velocity components and the pressure are defined at the center of a control volume while the volume fluxes are defined at the mid point on their corresponding cell faces the momentum equations are integrated semi implicitly by the approximate factorization technique the intermediate velocities are interpolated onto the faces of the control volume to form the source terms of the pressure poisson equation which is solved iteratively with a multigrid method the compatibility condition of the pressure poisson equation is satisfied in the same manner as in a staggered grid method mass conservation can be satisfied to machine accuracy the pressure boundary condition is derived from the momentum equations solutions of both steady and unsteady problems including the large eddy simulation of a rotating and stratified upwelling flow in an irregular container established the favorable accuracy and efficiency of the present method

a novel dynamic framework for subgrid scale parametrization of mesoscale eddies in quasigeostrophic turbulent flows abstract this paper puts forth a modular dynamic subgrid scale modeling framework for large eddy simulation of quasigeostrophic turbulence based on minimizing the errors between structural and functional subgrid scale models the approximate deconvolution ad procedure is used to estimate the free modeling parameters for the eddy viscosity coefficient parameterized in space and time using the smagorinsky and leith models the novel idea here is to estimate the modeling parameters using the ad method rather than the traditionally used test filtering approach first a priori and a posteriori analyses are presented for solving a canonical homogeneous isotropic decaying turbulence problem the proposed model is then applied to a wind driven quasigeostrophic four gyre ocean circulation problem which is a standard prototype of more realistic ocean dynamics results show that the proposed model captures the quasi stationary ocean dynamics and provides the time averaged four gyre circulation patterns taking locally resolved flow characteristics into account the model dynamically provides higher eddy viscosity values for lower resolutions

numerical investigation of the three dimensional development in boundary layer transition a numerical method for solving the complete navier stokes equations for incompressible flows is introduced that is applicable for investigating three dimensional transition phenomena in a spatially growing boundary layer results are discussed for a test case with small three dimensional disturbances for which detailed comparison to linear stability theory is possible the validity of our numerical model for investigating nonlinear transition phenomena is demonstrated by realistic spatial simulations of the experiments by kachanov and levchenko1 for a subharmonic resonance breakdown and of the experiments of klebanoff et al 2 for a fundamental resonance breakdown

joint maximum likelihood estimation for diagnostic classification models joint maximum likelihood estimation jmle is developed for diagnostic classification models dcms jmle has been barely used in psychometrics because jmle parameter estimators typically lack statistical consistency the jmle procedure presented here resolves the consistency issue by incorporating an external statistically consistent estimator of examinees proficiency class membership into the joint likelihood function which subsequently allows for the construction of item parameter estimators that also have the consistency property consistency of the jmle parameter estimators is established within the framework of general dcms the jmle parameter estimators are derived for the loglinear cognitive diagnosis model lcdm two consistency theorems are proven for the lcdm using the framework of general dcms makes the results and proofs also applicable to dcms that can be expressed as submodels of the lcdm simulation studies are reported for evaluating the performance of jmle when used with tests of varying length and different numbers of attributes as a practical application jmle is also used with real world educational data collected with a language proficiency test

an overview of projection methods for incompressible flows a series of numerical issues related to the analysis and implementation of fractional step methods for incompressible flows are addressed in this paper these methods are often referred to in the literature as projection methods and can be classified into three classes namely the pressure correction methods the velocity correction methods and the consistent splitting methods for each class of schemes theoretical and numerical convergence results available in the literature are reviewed and open questions are discussed the essential results are summarized in a table which could serve as a useful reference to numerical analysts and practitioners published by elsevier b v msc 65n35 65n22 65f05 35j05

a time integration method using artificial compressibility for unsteady viscous flows abstract a time accurate integration method for the study of unsteady incompressible viscous flows is presented based on a three point backward implicit discretization of the navier stokes equations in real time and a pseudo time relaxation with artificial compressibility to advance the solution between consecutive real time levels the spatial discretization uses central differencing based on a stretched staggered grid a factored adi scheme with lagged non linearities is used to reduce the problem to the solution of scalar tridiagonal systems this method displays very good computing efficiency and accuracy when applied for validation to several typical steady and unsteady flow problems

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

lusternik schnirelmann theory and closed reeb orbits we develop a variant of lusternik schnirelmann theory for the shift operator in equivariant floer and symplectic homology our key result is that the spectral invariants are strictly decreasing under the action of the shift operator when periodic orbits are isolated as an application we prove new multiplicity results for simple closed reeb orbits on the standard contact sphere the unit cotangent bundle to the sphere and some other contact manifolds we also show that the lower conley zehnder index enjoys a certain recurrence property and revisit and reprove from a different perspective a variant of the common jump theorem of long and zhu this is the second combinatorial ingredient in the proof of the multiplicity results

improving the speed and accuracy of projection type incompressible flow solvers abstract superseding so called first generation incompressible flow solvers of the projection type based on taylor galerkin advection second order pressure damping and element based data structures the current second generation solvers based on high order upwind advection fourth order pressure damping and edge based data structures have now been in use for half a decade and have proven remarkably robust and efficient for many large scale problems in order to achieve higher accuracy and speed these solvers have recently been enhanced in a variety of ways a substepping for advection b implicit treatment of advective terms via sgs and gmres lu sgs iterative solvers c fully implicit time accurate advancement of pressure and velocities and d linelet preconditioning for the pressure poisson equation the combined effect of these third generation improvements leads to speedups of the order of o 1 5 1 10 with similar or even better temporal accuracy as demonstrated on a variety of academic and industrial problems

symplectic fixed points and holomorphic spheres letp be a symplectic manifold whose symplectic form integrated over the spheres inp is proportional to its first chern class on the loop space ofp we consider the variational theory of the symplectic action function perturbed by a hamiltonian term in particular we associate to each isolated invariant set of its gradient flow an abelian group with a cyclic grading it is shown to have properties similar to the homology of the conley index in locally compact spaces as an application we show that if the fixed point set of an exact diffeomorphism onp is nondegenerate then it satisfies the morse inequalities onp we also discuss fixed point estimates for general exact diffeomorphisms

a new algorithm for solving some mechanical problems this paper explores the utility of a discrete singular convolution algorithm for solving certain mechanical problems benchmark mechanical systems including plate vibrations and incompressible flows are employed to illustrate the robustness and to test accuracy of the present algorithm numerical results indicate that the present approach is very accurate efficient and reliable for solving the aforementioned problems

uncoupled temporally second order accurate implicit solver of incompressible navier stokes equations an efficient method with temporal second order accuracy for solving the incompressible navier stokes equations in generalized coordinate systems is developed efficiency is obtained by extending an existing fractional step semi implicit solver into an implicit one with implicit approximation of the convection terms a novel three level linearization scheme is proposed to decouple the momentum equations from one another in addition to the fractional step approach that decouples the continuity equation from the momentum equations consequently all of the governing equations are uncoupled without degrading temporal accuracy or stability and without the need for iterations to solve the nonlinear system of equations at each time level the proposed decoupling technique can be used for other systems of nonlinear and time dependent partial differential equations moreover only minor modifications are required to apply the method to existing two level schemes several test cases confirm that the proposed decoupled scheme has temporal second order accuracy and allows the use of large time steps

a well conditioned augmented system for solving navier stokes equations in irregular domains an augmented method based on a cartesian grid is proposed for the incompressible navier stokes equations in irregular domains the irregular domain is embedded into a rectangular one so that a fast poisson solver can be utilized in the projection method unlike several methods suggested in the literature that set the force strengths as unknowns which often results in an ill conditioned linear system we set the jump in the normal derivative of the velocity as the augmented variable the new approach improves the condition number of the system for the augmented variable significantly using the immersed interface method we are able to achieve second order accuracy for the velocity numerical results and comparisons to benchmark tests are given to validate the new method a lid driven cavity flow with multiple obstacles and different geometries are also presented

hierarchical diagnostic classification models a family of models for estimating and testing attribute hierarchies although latent attributes that follow a hierarchical structure are anticipated in many areas of educational and psychological assessment current psychometric models are limited in their capacity to objectively evaluate the presence of such attribute hierarchies this paper introduces the hierarchical diagnostic classification model hdcm which adapts the log linear cognitive diagnosis model to cases where attribute hierarchies are present the utility of the hdcm is demonstrated through simulation and by an empirical example simulation study results show the hdcm is efficiently estimated and can accurately test for the presence of an attribute hierarchy statistically a feature not possible when using more commonly used dcms empirically the hdcm is used to test for the presence of a suspected attribute hierarchy in a test of english grammar confirming the data is more adequately represented by hierarchical attribute structure when compared to a crossed or nonhierarchical structure