the em algorithm an old folk song sung to a fast new tune celebrating the 20th anniversary of the presentation of the paper by dempster laird and rubin which popularized the em algorithm we investigate after a brief historical account strategies that aim to make the em algorithm converge faster while maintaining its simplicity and stability e g automatic monotone convergence in likelihood first we introduce the idea of a working parameter to facilitate the search for efficient data augmentation schemes and thus fast em implementations second summarizing various recent extensions of the em algorithm we formulate a general alternating expectation conditional maximization algorithm aecm that couples flexible data augmentation schemes with model reduction schemes to achieve efficient computations we illustrate these methods using multivariate t models with known or unknown degrees of freedom and poisson models for image reconstruction we show through both empirical and theoretical evidence the potential for a dramatic reduction in computational time with little increase in human effort we also discuss the intrinsic connection between em type algorithms and the gibbs sampler and the possibility of using the techniques presented here to speed up the latter the main conclusion of the paper is that with the help of statistical considerations it is possible to construct algorithms that are simple stable and fast

coupling an eulerian fluid calculation to a lagrangian solid calculation with the ghost fluid method we propose a numerical method for modeling multimaterial flows where the domain is decomposed into separate eulerian and lagrangian subdomains that is the equations are written in eulerian form in one subdomain and in lagrangian form in the other subdomain this is of interest for example when considering the effect of underwater explosions on the hull of a ship or the impact of a low speed projectile on a soft explosive target on the one hand high speed fluid flows are traditionally modeled by applying shock capturing schemes to the compressible euler equations to avoid problems associated with tangling of a lagrangian mesh on the other hand solid dynamics calculations are traditionally carried out using lagrangian numerical methods to avoid problems associated with numerical smearing in eulerian calculations we use the ghost fluid method to create accurate discretizations across the eulerian lagrangian interface the numerical method is presented in both one and two spatial dimensions three dimensional extensions to the interface coupling method are straightforward

generators and defining relations for the ring of differential operators on a smooth affine algebraic variety in prime characteristic abstract for the ring of differential operators d o x on a smooth affine algebraic variety x over a perfect field of characteristic p 0 explicit algebra generators and defining relations are found a finite set of generators and a finite set of defining relations are given explicitly for the module der k o x of derivations on the algebra o x of regular functions on the variety x

computational methods for multiphase flow and reactive transport problems arising in subsurface contaminant remediation a mathematical formulation and some numerical approximation techniques are described for a system of coupled partial differential and algebraic equations describing multiphase flow transport and interactions of chemical species in the subsurface a parallel simulator parsim has been developed based on these approximation techniques and is being used to study contaminant remediation strategies numerical results for a highly complex geochemistry problem involving strontium disposal in a pit at oak ridge national laboratory are presented

global f regularity of schubert varieties with applications to d modules a projective algebraic variety x over an algebraically closed field k of positive characteristic is called globally f regular if the section ring s c 0n o h x cn of an ample line bundle c on x is strongly f regular in the sense of h chster and huneke 9 cf definition 1 1 this important notion was introduced by karen smith in 18 in this paper we prove that schubert varieties are globally f regular an im mediate consequence is that local rings of schubert varieties are strongly f regular and thereby f rational another consequence is that local rings of varieties like de terminantal varieties that can be identified with open subsets of schubert varieties cf 13 are strongly f regular let x denote a flag variety and y c x a schubert variety over k then the local cohomology sheaves hjy ox are equivariant for the action of the borel subgroup and holonomic in the sense of 4 x x niodules as an application of ir rationality of schubert varieties we apply recent results of blickle cf 2 to prove that the simple objects in the category of equivariant and holonomic px modules are precisely the local cohomology sheaves hy ox where c is the codimension of y in x using a local grothendieck cousin complex from 11 we prove that the decomposition of the local cohomology modules with support in bruhat cells is multiplicity free see 4 2 in characteristic zero the local cohomology modules with support in bruhat cells correspond to dual verma modules in this setting the decomposition behavior and the simple t x modules arise from intersection cohomology complexes of schubert varieties by the riemann hilbert correspondence if we pick the singular codi mension one schubert variety y in the full flag variety z for sl4 in characteristic zero computations in kazhdan lusztig theory show that hy oz is not a simple z module see 4 1

estimation of regression models for the mean of repeated outcomes under nonignorable nonmonotone nonresponse we propose a new class of models for making inference about the mean of a vector of repeated outcomes when the outcome vector is incompletely observed in some study units and missingness is nonmonotone each model in our class is indexed by a set of unidentified selection bias functions which quantify the residual association of the outcome at each occasion t and the probability that this outcome is missing after adjusting for variables observed prior to time t and for the past nonresponse pattern in particular selection bias functions equal to zero encode the investigator s a priori belief that nonresponse of the next outcome does not depend on that outcome after adjusting for the observed past we call this assumption sequential explainability since each model in our class is nonparametric it fits the data perfectly well as such our models are ideal for conducting sensitivity analyses aimed at evaluating the impact that different degrees of departure from sequential explainability have on inference about the marginal means of interest although the marginal means are identified under each of our models their estimation is not feasible in practice because it requires the auxiliary estimation of conditional expectations and probabilities given high dimensional variables we henceforth discuss the estimation of the marginal means under each model in our class assuming additionally that at each occasion either one of the following two models holds a parametric model for the conditional probability of nonresponse given current outcomes and past recorded data or a parametric model for the conditional mean of the outcome on the nonrespondents given the past recorded data we call the resulting procedure 2 t multiply robust as it protects at each of the t time points against misspecification of one of these two working models although not against simultaneous misspecification of both we extend our proposed class of models and estimators to incorporate data configurations which include baseline covariates and a parametric model for the conditional mean of the vector of repeated outcomes given the baseline covariates

a discontinuous galerkin method for the simulation of compressible gas gas and gas water two medium flows abstract in this paper we develop a new discontinuous galerkin method for the simulation of shocks and interfaces in compressible gas gas and gas water two medium flows by solving the based model the spatial discretization is carefully designed to possess the following features discrete conservation in terms of the total mass total momentum and total energy high order accuracy and consistency for smooth flows free of oscillations at an isolated material interface in order to handle potential discontinuities arising in the simulation a nonlinear limiter based on the weighted essentially non oscillatory weno strategy is employed to suppress numerical oscillations and to preserve high order of accuracy in regions of smooth flows the weno reconstruction is imposed on suitably selected quantities rather than the conserved ones in case for discontinuities with large pressure ratio low density and dramatic change of material property where unphysical variables may be encountered a posteriori solution correction on the subcell level is locally adopted to enhance the robustness a series of typical test cases for both one and two dimensional problems are provided to demonstrate the performance of the proposed method

the optimal convergence rate of the p version of the finite element method optimal error estimates for the p version of the finite element method in two dimensions are proven for the case when u in h k omega or u has singularities induced by the corners of the domain the case of nonhomogenous essential boundary conditions is also analyzed

analysis of discontinuous galerkin methods for multicomponent reactive transport problems primal discontinuous galerkin dg methods including the oden babuska baumann version of dg are formulated for solving multicomponent reactive transport problems in porous media using the information of chemical stoichiometry an efficient approach is proposed for a special case of multicomponent reactive transport without immobile species a priori error analysis is conducted to establish the convergence of dg methods for multicomponent reactive transport systems which is optimal in h and nearly optimal in p

a posteriori error estimation and dynamic adaptivity for symmetric discontinuous galerkin approximations of reactive transport problems a symmetric discontinuous galerkin scheme is applied for solving reactive transport problems an explicit a posteriori error estimator in l 2 l 2 is derived for the semi discrete scheme applied to transport with general kinetic reactions explicit a posteriori error estimators in terms of linear functionals and negative norms are also obtained for transport problems with simple reactions an adaptive approach based on the a posteriori error estimators is proposed to modify the mesh dynamically numerical examples demonstrate the efficiency and effectivity of the estimators moreover it is shown in this study that the proposed adaptivity eliminates the need of slope limiters 2005 elsevier b v all rights reserved

multicomponent flow calculations by a consistent primitive algorithm the dynamics of inviscid multicomponent fluids may be modelled by the euler equations augmented by one or more additional species equation s attempts to compute solutions for extended euler models in conservation form show strong oscillations and other computational inaccuracies near material interfaces these are due to erroneous pressure fluctuations generated by the conservative wave model this problem does not occur in single component computations and arises only in the presence of several species a nonconservative primitive euler formulation is proposed which results in complete elimination of the oscillations the numerical algorithm uses small viscous perturbations to remove leading order conservation errors and is conservative to the order of numerical approximation numerical experiments show clean monotonic solution profiles with acceptably small conservation error for shocks of weak to moderate strengths

d module structure of local cohomology modules of toric algebras let s be a toric algebra over a field k of characteristic 0 and let i be a monomial ideal of s we show that the local cohomology modules h i i s are of finite length over the ring of differential operators d s k generalizing the classical case of a polynomial algebra s as an application we compute the characteristic cycles of some local cohomology modules

estimation of parasitic infection dynamics when detectability is imperfect the simultaneous estimation of infection rate cure rate and detectability of parasitic infections is considered a new method for this estimation based on a simple statistical model assuming constant transition rates between parasite states is proposed repeated observations on the infection status of the same individuals is required for this method a maximum likelihood approach is used for parameter estimation and the calculation of standard errors of the estimates the method is illustrated by a longitudinal study of the presence of giardia lamblia infection in kenyan children

bayesian estimation of movement and survival probabilities from capture recapture data summary the arnason schwarz model is usually used for estimating survival and movement probabilities of animal populations from capture recapture data the missing data structure of this capture recapture model is exhibited and summarised via a directed graph representation taking advantage of this structure we implement a gibbs sampling algorithm from which bayesian estimates and credible intervals for survival and movement probabilities are derived convergence of the algorithm is proved using a duality principle we illustrate our approach through a real example

large sample theory for parametric multiple imputation procedures we consider the asymptotic behaviour of various parametric multiple imputation procedures which include but are not restricted to the proper imputation procedures proposed by rubin 1978 the asymptotic variance structure of the resulting estimators is provided this result is used to compare the relative efficiencies of different imputation procedures it also provides a basis to understand the behaviour of two monte carlo iterative estimators stochastic em celeux diebolt 1985 wei tanner 1990 and simulated em ruud 1991 we further develop properties of these estimators when they stop at iteration k with imputation size m an application to a mcasurement error problem is used to illustrate the results

runge kutta discontinuous galerkin methods for compressible two medium flow simulations one dimensional case the runge kutta discontinuous galerkin rkdg method for solving hyperbolic conservation laws is a high order finite element method which utilizes the useful features from high resolution finite volume schemes such as the exact or approximate riemann solvers tvd runge kutta time discretizations and limiters in this paper we investigate using the rkdg finite element method for compressible two medium flow simulation with conservative treatment of the moving material interfaces numerical results for both gas gas and gas water flows in one dimension are provided to demonstrate the characteristic behavior of this approach

a discontinuous hp finite element method for convection diffusion problems this paper presents a new method which exhibits the best features of both finite volume and finite element techniques special attention is given to the issues of conservation flexible accuracy and stability the method is elementwise conservative the order of polynomial approximation can be adjusted element by element and the stability is not based on the introduction of artificial diffusion but on the use of a very particular finite element formulation with discontinuous basis functions the method supports h p and hp approximations and can be applied to any type of meshes including non matching grids a priori error estimates and numerical experiments on representative model problems indicate that the method is robust and capable of delivering high accuracy

anisotropic and dynamic mesh adaptation for discontinuous galerkin methods applied to reactive transport mesh adaptation strategies are proposed for discontinuous galerkin methods applied to reactive transport problems with emphasis on dynamic and anisotropic adaptation they include an anisotropic mesh adaptation scheme and two isotropic methods using an l 2 l 2 norm error estimator and a hierarchic error indicator these dynamic mesh adaptation approaches are investigated using benchmark cases numerical results demonstrate that the three approaches resolve time dependent transport adequately without slope limiting for both long term and short term simulations it is shown that these results apply to problems where either diffusion or advection dominates in different subdomains moreover for these schemes mass conservation is retained locally during dynamic mesh modification comparison studies indicate that the anisotropic mesh adaptation provides the most efficient meshes and has the least numerical diffusion among the three adaptation approaches 2005 elsevier b v all rights reserved

how to preserve the mass fractions positivity when computing compressible multi component flows abstract we are interested in the numerical investigation of the compressible flow of a gaseous mixture considering a hyperbolic system including the euler equations for the mixture and a mass conservation equation for each species we propose a new approximation scheme for the convective term of the species equations this approximation relies on some properties of the exact solution of the riemann problem for the multi component system and applies when an upwind godunov type scheme is used for the euler equations its main interest lies in the fact that it preserves the positivity and monotonicity of the mass fractions of all species

a priori error estimates for finite element methods based on discontinuous approximation spaces for elliptic problems we analyze three discontinuous galerkin approximations for solving elliptic problems in two or three dimensions in each one the basic bilinear form is nonsymmetric the first one has a penalty term on edges the second has one constraint per edge and the third is totally unconstrained for each of them we prove hp error estimates in the h1 norm optimal with respect to h the mesh size and nearly optimal with respect to p the degree of polynomial approximation we establish these results for general elements in two and three dimensions for the unconstrained method we establish a new approximation result valid on simplicial elements l2 estimates are also derived for the three methods

model based inference for categorical survey data subject to non ignorable non response we consider non response models for a single categorical response with categorical covariates whose values are always observed we present bayesian methods for ignorable models and a particular non ignorable model and we argue that standard methods of model comparison are inappropriate for comparing ignorable and non ignorable models uncertainty about ignorability of non response is incorporated by introducing parameters describing the extent of non ignorability into a pattern mixture specification and integrating over the prior uncertainty associated with these parameters our approach is illustrated using polling data from the 1992 british general election panel survey we suggest sample size adjustments for surveys when non ignorable non response is expected

a fully coupled upwind discontinuous galerkin method for incompressible porous media flows high order computations of viscous fingering instabilities in complex geometry we present a new approach to the simulation of viscous fingering instabilities in incompressible miscible displacement flows in porous media in the past high resolution computational simulations of viscous fingering instabilities have always been performed using high order finite difference or fourier spectral methods which do not posses the flexibility to compute very complex subsurface geometries our approach instead by means of a fully coupled nonlinear implementation of the discontinuous galerkin method possesses a fundamental differentiating feature in that it maintains high order accuracy on fully unstructured meshes in addition the proposed method shows very low sensitivity to mesh orientation in contrast with classical finite volume approximation used in porous media flow simulations the robustness and accuracy of the method are demonstrated in a number of challenging computational problems

the ghost fluid method for compressible gas water simulation an analysis is carried out for the ghost fluid method gfm based algorithm as applied to the gas water riemann problems which can be construed as two single medium gfm riemann problems it is found that the inability to provide correct and consistent riemann waves in the respective real fluids by these two gfm riemann problems may lead to inaccurate numerical results based on this finding two conditions are suggested and imposed for the ghost fluid status in order to ensure that correct and consistent riemann waves are provided in the respective real fluids during the numerical decomposition of the singularity using these two conditions to analyse some of the existing gfm based algorithms such as the original gfm j comput phys 152 1999 457 the new version gfm j comput phys 166 2001 1 j comput phys 175 2002 200 and the modified gfm mgfm j comput phys 190 2003 651 it is found that there are ranges of conditions for each type of solution where either the original gfm or the new version gfm or both are unable to provide correct or consistent riemann waves in one of the real fluids within these ranges examples can be found such that either the original gfm or the new version gfm or both are unable to provide accurate results the mgfm is also found to encounter difficulties when applied to nearly cavitating flow various examples are presented to demonstrate the conclusions obtained the mgfm with proposed modification when applied to nearly cavitating flow is then found to be quite robust and can provide relatively reasonable results

a numerical method for two phase flow consisting of separate compressible and incompressible regions abstract we propose a numerical method for modeling two phase flow consisting of separate compressible and incompressible regions this is of interest for example when the combustion of fuel droplets or the shock induced mixing of liquids is numerically modeled we use the level set method to track the interface between the compressible and incompressible regions as well as the ghost fluid method gfm to create accurate discretizations across the interface the gfm is particularly effective here since the equations differ in both number and type across the interface the numerical method is presented in two spatial dimensions with numerical examples in both one and two spatial dimensions while three dimensional extensions are straightforward

stochastic algorithms for markov models estimation with intermittent missing data summary multistate markov models are frequently used to characterize disease processes but their estimation from longitudinal data is often hampered by complex patterns of incompleteness two algorithms for estimating markov chain models in the case of intermittent missing data in longitudinal studies a stochastic em algorithm and the gibbs sampler are described the first can be viewed as a random perturbation of the em algorithm and is appropriate when the m step is straightforward but the e step is computationally burdensome it leads to a good approximation of the maximum likelihood estimates the gibbs sampler is used for a full bayesian inference the performances of the two algorithms are illustrated on two simulated data sets a motivating example concerned with the modelling of the evolution of parasitemia by plasmodium falciparum malaria in a cohort of 105 young children in cameroon is described and briefly analyzed

the d module structure of r f modules let r be a regular ring essentially of finite type over a perfect field k an r module m is called a unit r f module if it comes equipped with an isomorphism f e m m where f denotes the frobenius map on spec r and f e is the associated pullback functor it is well known that m then carries a natural d r module structure in this paper we investigate the relation between the unit r f structure and the induced d r structure on m in particular it is shown that if k is algebraically closed and m is a simple finitely generated unit r f module then it is also simple as a d r module an example showing the necessity of k being algebraically closed is also given

how to prevent pressure oscillations in multicomponent flow calculations a new numerical scheme for computing multicomponent flows is presented it is able to handle strong shocks is pressure oscillation free through the contact discontinuities and guarantees the posi tivity of mass fractions some numerical experiments on shock tubes indicate the convergence to the correct weak solution comparisons with classical finite volume schemes are also proposed

level set methods an overview and some recent results the level set method was devised by s osher and j a sethian 1988 j comput phys 79 12 49 as a simple and versatile method for computing and analyzing the motion of an interface in two or three dimensions bounds a possibly multiply connected region the goal is to compute and analyze the subsequent motion of under a velocity field v this velocity can depend on position time the geometry of the interface and the external physics the interface is captured for later time as the zero level set of a smooth at least lipschitz continuous function x t i e t x x t 0 is positive inside negative outside and is zero on t topological merging and breaking are well defined and easily performed in this review article we discuss recent variants and extensions including the motion of curves in three dimensions the dynamic surface extension method fast methods for steady state problems diffusion generated motion and the variational level set approach we also give a user s guide to the level set dictionary and technology and couple the method to a wide variety of problems involving external physics such as compressible and incompressible possibly reacting flow stefan problems kinetic crystal growth epitaxial growth of thin films vortex dominated flows and extensions to multiphase motion we conclude with a discussion of applications to computer vision and image processing

the intersection homology d module in finite characteristic for y a closed normal subvariety of codimension c of a smooth variety x brylinski and kashiwara showed that the local cohomology module c y x x contains a unique simple x submodule denoted by y x in this paper the analogous result is shown for x and y defined over a perfect field of finite characteristic moreover a local construction of y x is given relating it to the theory of tight closure from the construction one obtains a criterion for the x simplicity of c y x x

a discontinuoushpfinite element method for diffusion problems we present an extension of the discontinuous galerkin method which is applicable to the numerical solution of diffusion problems the method involves a weak imposition of continuity conditions on the solution values and on fluxes across interelement boundaries within each element arbitrary spectral approximations can be constructed with different orderspin each element we demonstrate that the method is elementwise conservative a property uncharacteristic of high order finite elements for clarity we focus on a model class of linear second order boundary value problems and we developpriorierror estimates convergence proofs and stability estimates the results of numerical experiments onh andp convergence rates for representative two dimensional problems suggest that the method is robust and capable of delivering exponential rates of convergence

finding the observed information matrix when using the em algorithm a procedure is derived for extracting the observed information matrix when the em algorithm is used to find maximum likelihood estimates in incomplete data problems the technique requires computation of a complete data gradient vector or second derivative matrix but not those associated with the incomplete data likelihood in addition a method useful in speeding up the convergence of the em algorithm is developed two examples are presented

an interface treating technique for compressible multi medium flow with runge kutta discontinuous galerkin method the high order accurate runge kutta discontinuous galerkin rkdg method is applied to the simulation of compressible multi medium flow generalizing the interface treating method given in chertock et al 2008 9 in mixed cells where the interface is located riemann problems are solved to define the states on both sides of the interface the input states to the riemann problem are obtained by extrapolation to the cell boundary from solution polynomials in the neighbors of the mixed cell the level set equation is solved by using a high order accurate rkdg method for hamilton jacobi equations resulting in a unified dg solver for the coupled problem the method is conservative if we include the states in the mixed cells which are however not used in the updating of the numerical solution in other cells the states in the mixed cells are plotted to better evaluate the conservation errors manifested by overshoots undershoots when compared with states in neighboring cells these overshoots undershoots in mixed cells are problem dependent and change with time numerical examples show that the results of our scheme compare well with other methods for one and two dimensional problems in particular the algorithm can capture well complex flow features of the one dimensional shock entropy wave interaction problem and two dimensional shock bubble interaction problem

accuracy of operator splitting for advection dispersion reaction problems an operator splitting approach is often used for the numerical solution of advection dispersion reaction problems operationally this approach advances the solution over a single time step in two stages one involving the solution of the nonreactive advection dispersion equation and the other the solution of the reaction equations the first stage is usually solved with a finite difference finite element or related technique while the second stage is normally solved with an ordinary differential equation integrator the only generally published guidelines on numerical accuracy suggest that the discretization errors associated with each stage must be small in order to achieve high accuracy of the overall solution however in this note we demonstrate that there is an inherent mass balance error present in the operator splitting algorithm for problems involving continuous mass influx boundary conditions the mass balance error does not exist for instantaneous mass input problems these conclusions are based upon analysis of a simple first order decay problem for which each stage of the calculation can be performed analytically i e without discretization error for this linear decay problem we find that the product of the first order decay coefficient k times t must be less than approximately 0 1 in order for the mass balance error to be less than 5 we also present a variant of the normal operator splitting algorithm in which the order of solving the advection dispersion and reaction operators is reversed at each time step this modification reduces the mass balance error by more than a factor of 10 for a wide range of k t values

a runge kutta discontinuous galerkin approach to solve reactive flows a runge kutta discontinuous galerkin method to solve the hyperbolic part of reactive navier stokes equations written in conservation form is presented complex thermodynamics laws are taken into account particular care has been taken to solve the stiff gaseous interfaces correctly with no restrictive hypothesis 1d and 2d test cases are presented

a discontinuous galerkin method for gravity driven viscous fingering instabilities in porous media we present a new approach to the simulation of gravity driven viscous fingering instabilities in porous media flow these instabilities play a very important role during carbon sequestration processes in brine aquifers our approach is based on a nonlinear implementation of the discontinuous galerkin method and possesses a number of key features first the method developed is inherently high order and is therefore well suited to study unstable flow mechanisms secondly it maintains high order accuracy on completely unstructured meshes the combination of these two features makes it a very appealing strategy in simulating the challenging flow patterns and very complex geometries of actual reservoirs and aquifers this article includes an extensive set of verification studies on the stability and accuracy of the method and also features a number of computations with unstructured grids and non standard geometries

riemann problem and level set approaches for homentropic two fluid flow computations a finite volume method is presented for the computation of compressible flows of two immiscible fluids at very different densities a novel ingredient in the method is a linearized two fluid osher scheme allowing for flux computations in the case of different fluids e g water and air left and right of a cell face a level set technique is employed to distinguish between the two fluids the level set equation is incorporated into the system of hyperbolic conservation laws fixes are presented for the solution errors pressure oscillations that may occur near two fluid interfaces when applying a capturing method the fixes are analyzed and tested for two fluid flows with arbitrarily large density ratios a simple variant of the ghost fluid method appears to be a perfect remedy computations for compressible water air flows yield perfectly sharp pressure oscillation free interfaces the masses of the separate fluids appear to be conserved up to first order accuracy

analysis of longitudinal data with irregular outcome dependent follow up summary a frequent problem in longitudinal studies is that subjects may miss scheduled visits or be assessed at self selected points in time as a result observed outcome data may be highly unbalanced and the availability of the data may be directly related to the outcome measure and or some auxiliary factors that are associated with the outcome if the follow up visit and outcome processes are correlated then marginal regression analyses will produce biased estimates building on the work of robins rotnitzky and zhao we propose a class of inverse intensity of visit process weighted estimators in marginal regression models for longitudinal responses that may be observed in continuous time this allows us to handle arbitrary patterns of missing data as embedded in a subject s visit process we derive the large sample distribution for our inverse visit intensity weighted estimators and investigate their finite sample behaviour by simulation our approach is illustrated with a data set from a health services research study in which homeless people with mental illness were randomized to three different treatments and measures of homelessness as percentage days homeless in the past 3 months and other auxiliary factors were recorded at follow up times that are not fixed by design

symmetric and nonsymmetric discontinuous galerkin methods for reactive transport in porous media for solving reactive transport problems in porous media we analyze three primal discontinuous galerkin dg methods with penalty namely symmetric interior penalty galerkin sipg nonsymmetric interior penalty galerkin nipg and incomplete interior penalty galerkin iipg a cut off operator is introduced in dg to treat general kinetic chemistry error estimates in l2 h1 are established which are optimal in h and nearly optimal in p we develop a parabolic lift technique for sipg which leads to h optimal and nearly p optimal error estimates in the l2 l2 and negative norms numerical results validate these estimates we also discuss implementation issues including penalty parameters and the choice of physical versus reference polynomial spaces

efficient numerical methods for simulating surface tension of multi component mixtures with the gradient theory of fluid interfaces abstract surface tension significantly impacts subsurface flow and transport and it is the main cause of capillary effect a major immiscible two phase flow mechanism for systems with a strong wettability preference in this paper we consider the numerical simulation of the surface tension of multi component mixtures with the gradient theory of fluid interfaces major numerical challenges include that the system of the euler lagrange equations is solved on the infinite interval and the coefficient matrix is not positive definite we construct a linear transformation to reduce the euler lagrange equations and naturally introduce a path function which is proven to be a monotonic function of the spatial coordinate variable by using the linear transformation and the path function we overcome the above difficulties and develop the efficient methods for calculating the interface and its interior compositions moreover the computation of the surface tension is also simplified the proposed methods do not need to solve the differential equation system and they are easy to be implemented in practical applications numerical examples are tested to verify the efficiency of the proposed methods

an adaptive ghost fluid finite volume method for compressible gas water simulations an adaptive ghost fluid finite volume method is developed for one and two dimensional compressible multi medium flows in this work it couples the real ghost fluid method gfm c w wang t g liu b c khoo a real ghost fluid method for the simulation of multi medium compressible flow siam j sci comput 28 2006 278 302 and the adaptive moving mesh method h z tang t tang moving mesh methods for one and two dimensional hyperbolic conservation laws siam j numer anal 41 2003 487 515 h z tang t tang p w zhang an adaptive mesh redistribution method for non linear hamilton jacobi equations in two and three dimensions j comput phys 188 2003 543 572 and thus combines their advantages this work shows that the local mesh clustering in the vicinity of the material interface can effectively reduce both numerical and conservative errors caused by the gfm around the material interface and other discontinuities besides the improvement of flow field resolution the adaptive gfm also largely increases the computational efficiency several numerical experiments are conducted to demonstrate robustness and efficiency of the current method they include several 1d and 2d gas water flow problems involving a large density gradient at the material interface and strong shock interface interactions the results show that our algorithm can capture the shock waves and the material interface accurately and is stable and robust even for solutions with large density and pressure gradients

joint modeling and analysis of longitudinal data with informative observation times in analysis of longitudinal data it is often assumed that observation times are predetermined and are the same across study subjects such an assumption however is often violated in practice as a result the observation times may be highly irregular it is well known that if the sampling scheme is correlated with the outcome values the usual statistical analysis may yield bias in this article we propose joint modeling and analysis of longitudinal data with possibly informative observation times via latent variables a two step estimation procedure is developed for parameter estimation we show that the resulting estimators are consistent and asymptotically normal and that the asymptotic variance can be consistently estimated using the bootstrap method simulation studies and a real data analysis demonstrate that our method performs well with realistic sample sizes and is appropriate for practical use