between and within cluster covariate effects in the analysis of clustered data standard methods for the regression analysis of clustered data postulate models relating covariates to the response without regard to between and within cluster covariate effects implicit in these analyses is the assumption that these effects are identical example data show that this is frequently not the case and that analyses that ignore differential between and within cluster covariate effects can be misleading consideration of between and within cluster effects also helps to explain observed and theoretical differences between mixture model analyses and those based on conditional likelihood methods in particular we show that conditional likelihood methods estimate purely within cluster covariate effects whereas mixture model approaches estimate a weighted average of between and within cluster covariate effects

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 modified higher order godunov s scheme for stiff source conservative hydrodynamics we present an efficient second order accurate scheme to treat stiff source terms within the framework of higher order godunov s methods we employ duhamel s formula to devise a modified predictor step which accounts for the effects of stiff source terms on the conservative fluxes and recovers the correct isothermal behavior in the limit of an infinite cooling reaction rate source term effects on the conservative quantities are fully accounted for by means of a one step second order accurate semi implicit corrector scheme based on the deferred correction method of dutt et al we demonstrate the accurate stable and convergent results of the proposed method through a set of benchmark problems for a variety of stiffness conditions and source types

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

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

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

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

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

on error estimates of the projection methods for the navier stokes equations second order schemes we present in this paper a rigorous error analysis of several projection schemes for the approximation of the unsteady incompressible navier stokes equations the error analysis is accomplished by interpreting the respective projection schemes as second order time discretizations of a perturbed system which approximates the navier stokes equations numerical results in agreement with the error analysis are also presented

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

a cartesian grid embedded boundary method for hyperbolic conservation laws we present a second order godunov algorithm to solve time dependent hyperbolic systems of conservation laws on irregular domains our approach is based on a formally consistent discretization of the conservation laws on a finite volume grid obtained from intersecting the domain with a cartesian grid we address the small cell stability problem associated with such methods by hybridizing our conservative discretization with a stable nonconservative discretization at irregular control volumes and redistributing the difference in the mass increments to nearby cells in a way that preserves stability and local conservation the resulting method is second order accurate in l 1 for smooth problems and is robust in the presence of large amplitude discontinuities intersecting the irregular boundary

application of the natural stress formulation for solving unsteady viscoelastic contraction flows abstract we present a numerical scheme for a previously unexploited formulation of the equations for unsteady viscoelastic flow the formulation aligns the polymer stress along particle paths streamlines utilising the characteristic curves associated with the hyperbolic part of the constitutive equations we illustrate the approach for the oldroyd b model in the benchmark 4 1 contraction for moderate elasticity numbers we show that the scheme is able to accurately capture the re entrant corner singularity for the polymer stresses and the pressure the latter variable being inaccurately determined by schemes using the traditional formulation in terms of cartesian polymer stresses a space step restriction for stability is derived which can be numerically limiting in certain recirculation regions this contrasts with the equivalent space step restriction for the formulation in cartesian stresses which is limiting in flow regions of high velocity gradients for example at sharp corners in contraction flows

two phase viscoelastic jetting a coupled finite difference algorithm on rectangular grids is developed for viscoelastic ink ejection simulations the ink is modeled by the oldroyd b viscoelastic fluid model the coupled algorithm seamlessly incorporates several things 1 a coupled level set projection method for incompressible immiscible two phase fluid flows 2 a higher order godunov type algorithm for the convection terms in the momentum and level set equations 3 a simple first order upwind algorithm for the convection term in the viscoelastic stress equations 4 central difference approximations for viscosity surface tension and upper convected derivative terms and 5 an equivalent circuit model to calculate the inflow pressure or flow rate from dynamic voltage

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

conditional generalized estimating equations for the analysis of clustered and longitudinal data a common and important problem in clustered sampling designs is that the effect of within cluster exposures i e exposures that vary within clusters on outcome may be confounded by both measured and unmeasured cluster level factors i e measurements that do not vary within clusters when some of these are ill not accounted for estimation of this effect through population averaged models or random effects models may introduce bias we accommodate this by developing a general theory for the analysis of clustered data which enables consistent and asymptotically normal estimation of the effects of within cluster exposures in the presence of cluster level confounders semiparametric efficient estimators are obtained by solving so called conditional generalized estimating equations we compare this approach with a popular proposal by neuhaus and kalbfleisch 1998 biometrics 54 638 645 who separate the exposure effect into a within and a between cluster component within a random intercept model we find that the latter approach yields consistent and efficient estimators when the model is linear but is less flexible in terms of model specification under nonlinear models this approach may yield inconsistent and inefficient estimators though with little bias in most practical settings

locally univalent approximations of analytic functions abstract in the present paper we introduce a measure of the non univalency of an analytic function and we use it in order to find the best approximation of analytic function by a locally univalent normalized analytic function

an unsplit cell centered godunov method for ideal mhd we present a second order godunov algorithm for multidimensional ideal mhd our algorithm is based on the unsplit formulation of colella j comput phys 87 1990 with all of the primary dependent variables centered at the same location to properly represent the divergence free condition of the magnetic fields we apply a discrete projection to the intermediate values of the field at cell faces and apply a filter to the primary dependent variables at the end of each time step we test the method against a suite of linear and nonlinear tests to ascertain accuracy and stability of the scheme under a variety of conditions the test suite includes rotated planar linear waves mhd shock tube problems low beta flux tubes and a magnetized rotor problem for all of these cases we observe that the algorithm is second order accurate for smooth solutions converges to the correct weak solution for problems involving shocks and exhibits no evidence of instability or loss of accuracy due to the possible presence of non solenoidal fields

estimating exposure effects by modelling the expectation of exposure conditional on confounders in order to estimate the causal effects of one or more exposures or treatments on an outcome of interest one has to account for the effect of confounding factors which both covary with the exposures or treatments and are independent predictors of the outcome in this paper we present regression methods which in contrast to standard methods adjust for the confounding effect of multiple continuous or discrete covariates by modelling the conditional expectation of the exposures or treatments given the confounders in the special case of a univariate dichotomous exposure or treatment this conditional expectation is identical to what rosenbaum and rubin have called the propensity score they have also proposed methods to estimate causal effects by modelling the propensity score our methods generalize those of rosenbaum and rubin in several ways first our approach straightforwardly allows for multivariate exposures or treatments each of which may be continuous ordinal or discrete second even in the case of a single dichotomous exposure our approach does not require subclassification or matching on the propensity score so that the potential for residual confounding i e bias due to incomplete matching is avoided third our approach allows a rather general formalization of the idea that it is better to use the estimated propensity score than the true propensity score even when the true score is known the additional power of our approach derives from the fact that we assume the causal effects of the exposures or treatments can be described by the parametric component of a semiparametric regression model to illustrate our methods we reanalyze the effect of current cigarette smoking on the level of forced expiratory volume in one second in a cohort of 2 713 adult white males we compare the results with those obtained using standard methods

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 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 wave propagation algorithm for viscoelastic fluids with spatially and temporally varying properties an algorithm is presented for simulating the fluid and stress equations that arise in a continuum model of platelet aggregation a l fogelson r d guy platelet wall interactions in continuum models of platelet thrombosis formulation and numerical solution math med biol 21 2004 293 334 the model is equivalent to models of viscoelastic fluids with spatially and temporally varying material parameters a subsystem containing the elastic terms is handled using a wave propagation algorithm two different methods for propagating waves are compared in computational tests one method linearizes the equations about cell edges and the other is based on the propagation of waves in a heterogeneous elastic medium when the viscoelastic fluid is in contact with a newtonian fluid the method based on linearization about the edges gives more accurate results no high weissenberg number instabilities were observed as long as the time step is chosen to obey a cfl condition the algorithm is stable and no unphysical oscillations appear in the solution 2007 elsevier b v all rights reserved

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

physically motivated domain decomposition for singularly perturbed equations a domain decomposition algorithm suitable for the efficient and accurate solution of a parabolic reaction convection diffusion equation with small parameter multiplying the diffusion term is presented convergence is established via maximum principle arguments the equation arises in the modeling of laminar transonic flow decomposition into subdomains is accomplished via singular perturbation analysis which dictates regions where certain reduced equations may be solved in place of the full equation effectively preconditioning the problem this paper concentrates on the theoretical basis of the method establishing local and global a priori error bounds

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

multiscale simulations for suspensions of rod like molecules we study the doi model for suspensions of rod like molecules the doi model couples a microscopic fokker planck type equation smoluchowski equation to the macroscopic stokes equation the smoluchowski equation describes the evolution of the distribution of the rod orientations it comes as a drift diffusion equation on the sphere at every point in physical space for sufficiently high macroscopic shear rates high deborah numbers the solution of the coupled system develops internal layers in the macroscopic strain rate the spurt phenomenon in the high deborah numbers regime the drift term in the smoluchowski equation is dominant we thus introduce a finite volume type discretization of the microscopic smoluchowski equation which is motivated by transport dominated pdes we carry out direct numerical simulations of the spurt phenomenon both in the dilute and concentrated regimes below the isotropic nematic transition the solution structure is identical to the one described by purely macroscopic models jso model for higher concentrations we observe the formation of microstructure coming from a position dependent tumbling rate we also investigate the 2 d stability of the spurted solution

a cartesian grid embedded boundary method for poisson s equation on irregular domains we present a numerical method for solving poisson s equation with variable coefficients and dirichlet boundary conditions on two dimensional regions the approach uses a finite volume discretization which embeds the domain in a regular cartesian grid we treat the solution as a cell centered quantity even when those centers are outside the domain cells that contain a portion of the domain boundary use conservative differencing of second order accurate fluxes on each cell volume the calculation of the boundary flux ensures that the conditioning of the matrix is relatively unaffected by small cell volumes this allows us to use multigrid iterations with a simple point relaxation strategy we have combined this with an adaptive mesh refinement amr procedure we provide evidence that the algorithm is second order accurate on various exact solutions and compare the adaptive and nonadaptive calculations

convex approximations of analytic functions abstract we introduce a method for constructing the best approximation of an analytic function in a subclass k k of convex functions in the sense of the l 2 norm the construction is based on solving a certain semi infinite quadratic programming problem which may be of independent interest

efforts to adjust for confounding by neighborhood using complex survey data in social epidemiology one often considers neighborhood or contextual effects on health outcomes in addition to effects of individual exposures this paper is concerned with the estimation of an individual exposure effect in the presence of confounding by neighborhood effects motivated by an analysis of national health interview survey nhis data in the analysis we operationalize neighborhood as the secondary sampling unit of the survey which consists of small groups of neighboring census blocks thus the neighborhoods are sampled with unequal probabilities as are individuals within neighborhoods we develop and compare several approaches for the analysis of the effect of dichotomized individual level education on the receipt of adequate mammography screening in the analysis neighborhood effects are likely to confound the individual effects due to such factors as differential availability of health services and differential neighborhood culture the approaches can be grouped into three broad classes ordinary logistic regression for survey data with either no effect or a fixed effect for each cluster conditional logistic regression extended for survey data and generalized linear mixed model glmm regression for survey data standard use of glmms with small clusters fails to adjust for confounding by cluster e g neighborhood this motivated us to develop an adaptation we use theory simulation and analyses of the nhis data to compare and contrast all of these methods one conclusion is that all of the methods perform poorly when the sampling bias is strong more research and new methods are clearly needed

computation of viscoelastic fluid flows using continuation methods the numerical simulation of viscoelastic fluid flow becomes more difficult as a physical parameter the weissenberg number increases specifically at a weissenberg number larger than a critical value the iterative nonlinear solver fails to converge a phenomenon known as the high weissenberg number problem in this work we describe the application and implementation of continuation methods to the nonlinear johnson segalman model for steady state viscoelastic flows simple natural and pseudo arclength continuation approaches in weissenberg number are investigated for a discontinuous galerkin finite element discretization of the equations computations are performed for a benchmark contraction flow and several aspects of the performance of the continuation methods including high weissenberg number limits are discussed

causal inference with generalized structural mean models summary we estimate cause effect relationships in empirical research where exposures are not completely controlled as in observational studies or with patient non compliance and self selected treatment switches in randomized clinical trials additive and multiplicative structural mean models have proved useful for this but suffer from the classical limitations of linear and log linear models when accommodating binary data we propose the generalized structural mean model to overcome these limitations this is a semiparametric two stage model which extends the structural mean model to handle non linear average exposure effects the first stage structural model describes the causal effect of received exposure by contrasting the means of observed and potential exposure free outcomes in exposed subsets of the population for identification of the structural parameters a second stage nuisance model is introduced this takes the form of a classical association model for expected outcomes given observed exposure under the model we derive estimating equations which yield consistent asymptotically normal and efficient estimators of the structural effects we examine their robustness to model misspecification and construct robust estimators in the absence of any exposure effect the double logistic structural mean model is developed in more detail to estimate the effect of observed exposure on the success of treatment in a randomized controlled blood pressure reduction trial with self selected non compliance

effect of omitted confounders on the analysis of correlated binary data summary marginal analysis using the generalized estimating equation approach is widely applied to correlated observations as occur in studies with clusters and in longitudinal follow up of individuals in this article we investigate the effect of confounding in such models we assume that a risk factor x and a confounder z are related by a generalized linear model to the outcome y which can be binary or ordinal in order to investigate confounding arising from the omission of z a joint structure for x and z must be specified modeling normally distributed x z as sums of between and within individual or cluster components allows us to incorporate different degrees of betweenand within individual correlation such a structure includes as special cases cohort and period effects in longitudinal settings and random intercept models the latter situation corresponds to allowing z to vary only on the between individual or cluster level and to be uncorrelated with x and leads to attenuation of the coefficient of x in marginal models with the logit and probit links more complex situations occur when z is allowed to also vary on the within individual or cluster level and when z is correlated with x we examine the model specification and the expected bias when fitting a marginal model in the presence of the omitted confounder z we derive general formulas and interpret the parameters and results in an ongoing cohort study testing for omitted covariates is also discussed

between within models for survival analysis a popular way to control for confounding in observational studies is to identify clusters of individuals e g twin pairs such that a large set of potential confounders are constant shared wit

multiply robust inference for statistical interactions a primary focus of an increasing number of scientific studies is to determine whether two exposures interact in the effect that they produce on an outcome of interest interaction is commonly assessed by fitting regression models in which the linear predictor includes the product between those exposures when the main interest lies in the interaction this approach is not entirely satisfactory because it is prone to possibly severe bias when the main exposure effects or the associations between outcome and extraneous factors are misspecified in this article we consider conditional mean models with identity or log link that postulate the statistical interaction in terms of a finite dimensional parameter but are otherwise unspecified we show that estimation of the interaction parameter often is not feasible in this model because it requires nonparametric estimation of auxiliary conditional expectations given high dimensional variables we thus consider multiply robust estimation under a union model th

partitioned gmm logistic regression models for longitudinal data correlation is inherent in longitudinal studies due to the repeated measurements on subjects as well as due to time dependent covariates in the study in the national longitudinal study of adolescent to adult health add health data were repeatedly collected on children in grades 7 12 across four waves thus observations obtained on the same adolescent were correlated while predictors were correlated with current and future outcomes such as obesity status among other health issues previous methods such as the generalized method of moments gmm approach have been proposed to estimate regression coefficients for time dependent covariates however these approaches combined all valid moment conditions to produce an averaged parameter estimate for each covariate and thus assumed that the effect of each covariate on the response was constant across time this assumption is not necessarily optimal in applications such as add health or health related data thus we depart from this assumption and instead use the partitioned gmm approach to estimate multiple coefficients for the data based on different time periods these extra regression coefficients are obtained using a partitioning of the moment conditions pertaining to each respective relationship this approach offers a deeper understanding and appreciation into the effect of each covariate on the response we conduct simulation studies as well as analyses of obesity in add health rehospitalization in medicare data and depression scores in a clinical study the partitioned gmm methods exhibit benefits over previously proposed models with improved insight into the nonconstant relationships realized when analyzing longitudinal data

starlike approximations of analytic functions abstract when an analytic function is not univalent it is often of interest to approximate it by univalent functions in this paper we introduce a measure of the non univalency of a function and we derive a method for constructing the best starlike univalent approximations of analytic functions with respect to it suitable for both practical problems and numerical implementation

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

numerical modeling of viscoelastic flows using equal low order finite elements a mixed finite element scheme abbreviated as i ps devss cnbs scheme for modeling viscoelastic flow problems is presented the finite incremental calculus fic pressure stabilization process and the discrete elastic viscous stress splitting method devss are introduced into the general framework of the iterative version of the fractional step algorithm with the use of the crank nicolson based splitting inconsistent streamline upwinding method su is employed to spatially discretize the constitutive equation of viscoelastic fluids equal low order finite elements which violate the lbb compatibility conditions are successfully used in the proposed scheme in addition the oldroyd b and the ptt models have been integrated into the proposed scheme to solve the 4 1 sudden contraction flow problem the numerical results demonstrate prominent stability and accuracy of both pressure and stress distributions over the flow domains provided by the proposed scheme within the weissenberg number range studied in the present work as compared with the reference solutions reported in the literatures

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

hyperbolicity and change of type in the flow of viscoelastic fluids the equations governing the flow of viscoelastic liquids are classified according to the symbol of their differential operators propagation of singularities is discussed and conditions for a change of type are investigated the vorticity equation for steady flow can change type when a critical condition involving speed and stresses is satisfied this leads to a partitioning of the field of flow into subcritical and supercritical regions as in the problem of transonic flow

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

analysis of longitudinal data with unmeasured confounders confounding in longitudinal or clustered data creates special problems and opportunities because the relationship between the confounder and covariate of interest may differ across and within individuals or clusters a well known example of such confounding in longitudinal data is the presence of cohort and period effects in models of aging in epidemiologic research we first formulate a data generating model with confounding and derive the distribution of the response variable unconditional on the confounder we then examine the properties of the regression coefficient for some analytic approaches when the confounder is omitted from the fitted model the expected value of the regression coefficient differs in across and within individual regression in the multivariate case within and between individual information is combined and weighted according to the assumed covariance structure we assume compound symmetry in the fitted covariance matrix and derive the variance bias and mean squared error of the slope estimate as a function of the fitted within individual correlation we find that even in this simplest multivariate case the trade off between bias and variance depends on a large number of parameters it is generally preferable to fit correlations somewhat above the true correlation to minimize the effect of between individual confounders or cohort effects period effects can lead to situations where it is advantageous to fit correlations that are below the true correlation the results highlight the trade offs inherent in the choice of method for analysis of longitudinal data and show that an appropriate choice can be made only after determining whether within or between individual confounding is the major concern

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

numerical simulation of viscoelastic flows using integral constitutive equations a finite difference approach this work presents a numerical technique for simulating incompressible isothermal viscoelastic flows of fluids governed by the upper convected maxwell ucm and k bkz kaye bernstein kearsley and zapas integral models the numerical technique described herein is an extension of the gensmac method to the solution of the momentum and mass conservation equations to include integral constitutive equations the governing equations are solved by the finite difference method on a staggered grid using a marker and cell approach the finger tensor b t t is computed in an eulerian framework using the ideas of the deformation fields method however improvements to the deformation fields method are introduced the finger tensor b t x t is obtained by a second order accurate method and the stress tensor t x t is computed by a second order quadrature formula the numerical method presented in this work is validated by comparing the predictions of velocity and stress fields in two dimensional fully developed channel flow of a maxwell fluid with the corresponding analytic solutions furthermore the flow through a planar 4 1 contraction is investigated and the numerical results were compared with the corresponding experimental data finally the ucm and the k bkz models were used to simulate the planar 4 1 contraction flow over a wide range of reynolds and weissenberg numbers and the numerical results obtained are in agreement with published data

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

a conservative adaptive projection method for the variable density incompressible navier stokes equations in this paper we present a method for solving the equations governing time dependent variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids the method is based on a projection formulation in which we first solve advection diffusion equations to predict intermediate velocities and then project these velocities onto a space of approximately divergence free vector fields our treatment of the first step uses a specialized second order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high reynolds number flow density and other scalars are advected in such a way as to maintain conservation if appropriate and free stream preservation our approach to adaptive refinement uses a nested hierarchy of logically rectangular girds with simultaneous refinement of the girds in both space and time the integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized the single grid algorithm is described briefly but the emphasis here is on the time stepping procedure for the adaptive hierarchy numerical examples are presented to demonstrate the algorithms s accuracy and convergence properties and illustrate the behavior of the method an additional example demonstrates the performance of the method on a more realistic problem namely a three dimensional variable density shear layer

longitudinal data analysis using generalized linear models summary this paper proposes an extension of generalized linear models to the analysis of longitudinal data we introduce a class of estimating equations that give consistent estimates of the regression parameters and of their variance under mild assumptions about the time dependence the estimating equations are derived without specifying the joint distribution of a subject s observations yet they reduce to the score equations for multivariate gaussian outcomes asymptotic theory is presented for the general class of estimators specific cases in which we assume independence m dependence and exchangeable correlation structures from each subject are discussed efficiency of the proposed estimators in two simple situations is considered the approach is closely related to quasi likelih ood some key ironh estimating equation generalized linear model longitudinal data quasi likelihood repeated measures

separating between and within cluster covariate effects by using conditional and partitioning methods summary we consider the situation where the random effects in a generalized linear mixed model may be correlated with one of the predictors which leads to inconsistent estimators we show that conditional maximum likelihood can eliminate this bias conditional likelihood leads naturally to the partitioning of the covariate into between and within cluster components and models that include separate terms for these components also eliminate the source of the bias another viewpoint that we develop is the idea that many violations of the assumptions including correlation between the random effects and a covariate in a generalized linear mixed model may be cast as misspecified mixing distributions we illustrate the results with two examples and simulations