finite element computation of unsteady viscous compressible flows in this article we present our results for computation of unsteady viscous transonic flows past cylinders and airfoils stabilized finite element methods are employed to solve the compressible navier stokes equations in their conservation law form the nonlinear equations resulting from the finite element discretizations are solved using gmres technique to test the accuracy of the formulation mach 2 flow past a circular cylinder is computed with a mesh that is fine enough to resolve the shock structure for reynolds number 50 the computational results agree quite well with the analytical and theoretical results the methodology is applied to compute unsteady transonic flows past cylinders and airfoils several cases involving flows past a naca0012 airfoil are computed and compared with numerical results from other researchers interesting flow patterns are observed for all the cases it is observed that flow past an airfoil in a channel of width 8 5 chord lengths at mach 0 85 and re 10 000 is unsteady when it is placed at zero incidence to the flow while it reaches a steady state when the angle of attack of the airfoil is 10

a semiparametric bootstrap technique for simulating extreme order statistics abstract we propose a technique for simulating the joint distribution of the j largest order statistics of a very large sample we assume that the parent population is in the domain of attraction of the type 1 gumbel extreme value distribution the bootstrap variates are generated by resampling the normalized spacings of the k largest observed values in the original data where k is larger than j we compare the bootstrap distribution to the fitted extremal distribution of weissman both distributions have the same means conditional on the k largest observed values in the data set if k is large and the normalized spacings behave as independent and identically distributed exponential random variables then the bootstrap variates behave as though sampled from the extremal distribution we propose several procedures for estimating k and give a numerical example

massively parallel finite element computation of incompressible flows involving fluid body interactions abstract we describe our massively parallel finite element computations of unsteady incompressible flows involving fluid body interactions these computations are based on the deforming spatial domain stabilized space time dsd sst finite element formulation unsteady flows past a stationary naca 0012 airfoil are computed for reynolds numbers 1000 5000 and 100 000 significantly different flow patterns are observed for these three cases the method is then applied to computation of the dynamics of an airfoil falling in a viscous fluid under the influence of gravity it is observed that the location of the center of gravity of the airfoil plays an important role in determining its pitch stability computations are reported also for simulation of the dynamics of a two dimensional projectile that has a certain initial velocity specially designed mesh moving schemes are employed to eliminate the need for remeshing all these computations were carried out on the thinking machines cm 200 and cm 5 supercomputers with major speed ups compared to traditional supercomputers the implicit equation systems arising from the finite element discretizations of these large scale problems are solved iteratively by using the gmres update technique with diagonal preconditioners the finite element formulations and their parallel implementations assume unstructured meshes

a coupled momentum method for modeling blood flow in three dimensional deformable arteries abstract blood velocity and pressure fields in large arteries are greatly influenced by the deformability of the vessel moreover wave propagation phenomena in the cardiovascular system can only be described considering wall deformability since blood is usually described as an incompressible fluid however computational methods for simulating blood flow in three dimensional models of arteries have either considered a rigid wall assumption for the vessel or significantly simplified or reduced geometries computing blood flow in deformable domains using standard techniques like the ale method remains a formidable problem for large realistic anatomic and physiologic models of the cardiovascular system we have developed a new method to simulate blood flow in three dimensional deformable models of arteries the method couples the equations of the deformation of the vessel wall at the variational level as a boundary condition for the fluid domain we consider a strong coupling of the degrees of freedom of the fluid and the solid domains and a linear membrane model enhanced with transverse shear for the vessel wall the effect of the vessel wall boundary is therefore added in a monolithic way to the fluid equations resulting in a remarkably robust scheme we present here the mathematical formulation of the method and discuss issues related to the fluid solid coupling membrane formulation time integration method and boundary and initial conditions implementation is discussed and results with simple geometries as well as large subject specific models are presented

vector bundles and regulous maps let x be a compact nonsingular affine real algebraic variety we prove that every pre algebraic vector bundle on x becomes algebraic after finitely many blowing ups using this theorem we then prove that the stiefel whitney classes of any pre algebraic mathbb r vector bundle on x are algebraic we also derive that the chern classes of any pre algebraic mathbb c vector bundles and the pontryagin classes of any pre algebraic mathbb r vector bundle are blow mathbb c algebraic we also provide several results on line bundles on x

implicit velocity correction based immersed boundary lattice boltzmann method and its applications a version of immersed boundary lattice boltzmann method ib lbm is proposed in this work it is based on the lattice boltzmann equation with external forcing term proposed by guo et al z guo c zheng b shi discrete lattice effects on the forcing term in the lattice boltzmann method phys rev e 65 2002 046308 which can well consider the effect of external force to the momentum and momentum flux as well as the discrete lattice effect in this model the velocity is contributed by two parts one is from the density distribution function and can be termed as intermediate velocity and the other is from the external force and can be considered as velocity correction in the conventional ib lbm the force density external force is explicitly computed in advance as a result we cannot manipulate the velocity correction to enforce the non slip boundary condition at the boundary point in the present work the velocity corrections force density at all boundary points are considered as unknowns which are computed in such a way that the non slip boundary condition at the boundary points is enforced the solution procedure of present ib lbm is exactly the same as the conventional ib lbm except that the non slip boundary condition can be satisfied in the present model while it is only approximately satisfied in the conventional model numerical experiments for the flows around a circular cylinder and an airfoil show that there is no any penetration of streamlines to the solid body in the present results this is not the case for the results obtained by the conventional ib lbm another advantage of the present method is its simple calculation of force on the boundary the force can be directly calculated from the relationship between the velocity correction and the force density

a velocity pressure streamline diffusion finite element method for navier stokes equations a streamline diffusion finite element method is introduced for the time dependent incompressible navier stokes equations in a bounded domain in r squared and r cubed in the case of a flow with a high reynolds number an error estimate is proved and numerical results are given the method is based on a mixed velocity pressure formulation using the same finite element discretization of space time for the velocity and the pressure spaces which consist of piecewise linear functions together with certain least squares modifications of the galerkin variational formulation giving added stability without sacrificing accuracy

on the asymptotic joint distribution of an unbounded number of sample extremes convergence of the sample maximum to a nondegenerate random variable as the sample sizen implies the convergence in distribution of thek largest sample extremes to ak dimensional random vectormk for all fixedk if we letk k n k n 0 then a question arises in a natural way how fast cank grow so that asymptotic probability statements are unaffected when sample extremes are replaced bymk we answer this question for two classes of events the class of all lebesgue sets inrk and the class of events of the form left x in r k sum limits 1 k x i leqq a right

the topology of real algebraic sets with isolated singularities in this paper we give a topological classification of real algebraic sets with isolated singularities showing that they are exactly smooth closed manifolds with smooth subpolyhedra crushed to points the question of which topological spaces are homeomorphic to real algebraic sets solutions of polynomial equations in euclidean space has been long studied in 1936 seifert showed that any smooth compact stably parallelizable manifold is diffeomorphic to a component of an algebraic set 121 and in 1952 nash extended this result to all smooth compact manifolds 11 in 1973 tognoli showed that any smooth compact manifold is diffeomorphic to a nonsingular algebraic set 13 so at least compact nonsingular algebraic sets are classified little has been done with singular algebraic sets however since the transversality arguments used by seifert nash and tognoli no longer apply except in some special cases one could use stability of singularities such as kuiper 71 and akbulut 1 used to show certain nonsmoothable pl manifolds are algebraic sets or one could use the projective version of seifert nash tognoli as king did 6 but one could still not hope these techniques would allow even a characterization of isolated singularities to get around this problem we take a cue from hironaka s resolution of singularities 4 the idea is to take a topological resolution of a space if it exists we can apply transversality techniques seifertnash tognoli to the resolved space and then blow down algebraically and end up with the original space as an algebraic set it seems likely that this technique allows one to classify all algebraic sets but in any case we show that it classifies all algebraic sets with isolated singularities in future papers we will use this technique to show for instance that all compact pl manifolds are homeomorphic to real algebraic sets 17 and that 2 dimensional real algebraic sets are topologically characterized as polyhedra satisfying sullivan s even local euler characteristic condition 16

real algebraic morphisms represent few homotopy classes we study the problem of representing homotopy classes of maps between real algebraic varieties of regular maps

on approximating submanifolds by algebraic sets and a solution to the nash conjecture in n nash showed that any compact smooth submanifold m of ir is e isotopic to a union of connected components of a real algebraic variety if n 2 dim m e isotopic just means that there are arbitrarily small smooth isotopies to components of real algebraic varieties for smaller n however he was not able to get such a strong result but conjectured it was still true in w a proof of this conjecture was given which unfortunately had a gap later i and t2 gave correct proofs in the case where n is bigger than roughly 3 dim m 2 among other results in this paper we give a proof of this conjecture of nash in particular we will show

selection of the k largest order statistics for the domain of attraction of the gumbel distribution abstract statistical modeling of the largest k observations or the exceedances over a high threshold based on extreme value theory has produced powerful methods for drawing inferences about the tail behavior of a distribution however a method for selecting k has not been established we suggest using a forward selection procedure based on a suitable goodness of fit statistic to search for the optimal k when the sample is of finite size and from a distribution in the domain of attraction of the gumbel distribution two criteria are examined generalized least squares and the shapiro wilk goodness of fit simulation studies indicate that the latter is preferable in terms of variation extension of the selection procedure to distributions in the domains of attraction of the frechet and weibull distributions is also discussed the use of the proposed method is illustrated through two examples based on real data

on the estimation of the extreme value index and large quantile estimation l article se constitue de deux parties on donne une preuve simple de la convergence faible de l estimation de pickand pour le parametre principal d une loi de valeurs extremes on donne d autres conditions naturelles pour la convergence forte et pour la normalite asymptotique de l estimation ensuite une grande quantile d une loi est estimee par une combinaison de statistiques d ordre intermediaires ou extremes ceci mene a un intervalle de confiance asymptotique

a space time formulation for multiscale phenomena abstract we develop subgrid scale models for a class of nonsymmetric linear evolution operators by applying the variational multiscale method in space time the results generalize those of hughes 14 which were confined to the steady case the subgrid scale models are shown to be a paradigm for bubble function finite element methods and provide a theoretical and practical framework for the development of so called stabilized methods

extreme precipitation events generated by periodic processes a procedure for the estimation of large quantile daily precipitation totals is developed the technique draws on the statistical properties of extremes generated by processes with periodic variances forty one years of records at homestead florida are used to calibrate the model and are incorporated into the simulation procedure that compares the proposed technique to standard methods of analyzing annual series results indicate that the procedure yields reasonable estimates of large quantile precipitation and performs as reliably or more so than the standard techniques the physical and theoretical bases of the procedure are maintained throughout the study

a statistical distribution with an unbounded hazard function and its application to a theory from demography we introduce a statistical distribution with hazard function mu t proportional to psi t beta 1 for 0 less than or equal to t less than psi and shape parameter beta satisfying 0 less than beta less than 1 this hazard function is suggested by a theory of aging in demography we discuss properties of this distribution and maximum likelihood estimates of its parameters mixture distributions are considered to account for pooling across dissimilar populations this model is compared with the gompertz and generalized pareto distributions and used to estimate a finite limit on human lifespan based on the survival of a group of female centenarians

a new finite element formulation for computational fluid dynamics viii the galerkin least squares method for advective diffusive equations abstract galerkin least squares finite element methods are presented for advective diffusive equations galerkin least squares represents a conceptual simplification of supg and is in fact applicable to a wide variety of other problem types a convergence analysis and error estimates are presented

arbitrary lagrangian eulerian formulation for fluid rigid body interaction a new formulation for two dimensional fluid rigid body interaction problems is developed in particular vortex induced oscillations of a rigid body in viscous incompressible flow are studied the incompressible navier stokes equations are used to describe the motion of the fluid while it is assumed that the rigid body is mounted on a system consisting of a spring and a dashpot an arbitrary lagrangian eulerian formulation ale is used in order to account for large boundary motion a general formulation for the coupled problem is obtained by uncoupling the translation motion of the body from its rotational motion and developing a specific algorithm to efficiently handle the nonlinear dependence of the rotations this general formulation can be easily applied to multi body problems two numerical examples involving either translations and rotations are presented as an illustration of the proposed methodologies for fluid rigid body interaction

a test for extreme value domain of attraction abstract a simple statistic is proposed to test the hypothesis that a sample comes from a distribution in the domain of attraction of the gumbel distribution it is based on the top k order statistics and is a generalization of the shapiro wilk goodness of fit statistic the critical region of the test and its power against the alternative that the sample comes from a distribution in another domain of attraction are studied theoretically and by simulation the power turns out to be superior to that of other tests previously proposed

a finite element method for fluid structure interaction with surface waves using a finite calculus formulation abstract a stabilized semi implicit fractional step finite element method fem for solving coupled fluid structure interaction problems involving free surface waves is presented the stabilized governing equations for the viscous incompressible fluid and the free surface are derived at a differential level via a finite calculus fic procedure a mesh updating technique based on solving a fictitious elastic problem on the moving mesh is described examples of the efficiency of the stabilized semi implicit algorithm for the analysis of fluid structure interaction problems in totally or partially submerged bodies is presented

using extreme value theory to estimate large percentiles weissman 1978 suggested percentile estimators based on the joint limiting distribution of the k largest order statistics the present work identifies situations where weissman s estimators are a significant improvement over the usual sample percentile estimators and gives practical advice on how to use these new estimators effectively in particular large reductions in mean squared error can be made when the tails of the distributions are approximately exponential and p 95

algebraic realization of manifolds with group actions abstract let g be a compact lie group and m a closed smooth g manifold with some restrictions on g or on the isotropy groups of the action we show that m is algebraically realized i e there exists a non singular real algebraic g variety which is equivariantly diffeomorphic to m

estimation of high conditional quantiles for heavy tailed distributions estimation of conditional quantiles at very high or low tails is of interest in numerous applications quantile regression provides a convenient and natural way of quantifying the impact of covariates at different quantiles of a response distribution however high tails are often associated with data sparsity so quantile regression estimation can suffer from high variability at tails especially for heavy tailed distributions in this article we develop new estimation methods for high conditional quantiles by first estimating the intermediate conditional quantiles in a conventional quantile regression framework and then extrapolating these estimates to the high tails based on reasonable assumptions on tail behaviors we establish the asymptotic properties of the proposed estimators and demonstrate through simulation studies that the proposed methods enjoy higher accuracy than the conventional quantile regression estimates in a real application involving statistical downscaling of daily precipitation in

computation of incompressible flows with implicit finite element implementations on the connection machine two implicit finite element formulations for incompressible flows have been implemented on the connection machine supercomputers and successfully applied to a set of time dependent problems the stabilized space time formulation for moving boundaries and interfaces and a new stabilized velocity pressure stress formulation are both described and significant aspects of the implementation of these methods on massively parallel architectures are discussed several numerical results for flow problems involving moving as well as fixed cylinders and airfoils are reported the parallel implementation taking full advantage of the computational speed of the new generation of supercomputers is found to be a significant asset in fluid dynamics research its current capability to solve large scale problems especially when coupled with the potential for growth enjoyed by massively parallel computers make the implementation a worthwhile enterprise

on real algebraic models of smooth manifolds an affine nonsingular real algebraic variety x diffeomorphic to a smooth manifold m is said to be an algebraic model of m the remarkable theorem of nash tognoli asserts that each compact smooth manifold m has an algebraic model 16 or 6 theorem 14 1 10 in fact there exists an infinite family x n of irreducible algebraic models of m such that xt and xj are birationally nonisomorphic for i j 10 cf also 7 for a proof in a special case in view of these results it seems natural and interesting to investigate algebro geometric properties of various algebraic models of a given smooth manifold this paper addresses a few questions of this type for notions and results of real algebraic geometry we refer the reader to the book 6 given a compact affine nonsingular real algebraic variety x denote by h x z 2 the subgroup of hk x z 2 of the homology classes represented by zariski closed fc dimensional algebraic subvarieties of x 6 chapter 11 or 11 let h x z 2 be the image of h k xfz 2 9 d dimx under the poincare duality isomorphism hd k x z 2 h x z 2 although the groups hlg x z 2 are one of the most important invariants of x a sample of applications can be found in 1 2 3 6 8 9 our knowledge of their behavior is still rather limited here we consider the following problem let m be a compact smooth manifold and let g be a subgroup of h m z 2 when are there an algebraic model x of m and a diffeomorphism c x m such that the induced isomorphism p h m z 2 h x z 2

proteus a coupled iterative force correction immersed boundary multi domain cascaded lattice boltzmann solver abstract most realistic fluid flow problems are characterized by high reynolds numbers and complex boundaries over the last ten years immersed boundary methods that are able to cope with realistic geometries have been applied to lattice boltzmann lb methods these methods however have normally been applied to low reynolds number problems here we present a novel coupling between an iterative force correction immersed boundary zhang et al 2016 and a multi domain cascaded lb method the iterative force correction immersed boundary method has been selected due to the improved accuracy of the computation while the cascaded lb formulation is used due to its superior stability at high reynolds numbers the coupling is shown to improve both the stability and numerical accuracy of the solution the resulting solver has been applied to viscous flow up to a reynolds number of 100000 passed a naca 0012 airfoil at a 10 degree angle of attack good agreement with results obtained using a body fitted navier stokes solver has been obtained the formulation provides a straight forward and efficient method for modeling realistic geometries and could easily be extended to problems with moving boundaries

conditional quantile estimation for generalized autoregressive conditional heteroscedasticity models conditional quantile estimation is an essential ingredient in modern risk management although generalized autoregressive conditional heteroscedasticity garch processes have proven highly successful in modeling financial data it is generally recognized that it would be useful to consider a broader class of processes capable of representing more flexibly both asymmetry and tail behavior of conditional returns distributions in this article we study estimation of conditional quantiles for garch models using quantile regression quantile regression estimation of garch models is highly nonlinear we propose a simple and effective two step approach of quantile regression estimation for linear garch time series in the first step we use a quantile autoregression sieve approximation for the garch model by combining information over different quantiles then second stage estimation for the garch model is carried out based on the first stage minimum distance estimation of the scale process of the time series

on the integral hodge conjecture for real varieties i we formulate the real integral hodge conjecture a version of the integral hodge conjecture for real varieties and raise the question of its validity for cycles of dimension 1 on uniruled and calabi yau threefolds and on rationally connected varieties we relate it to the problem of determining the image of the borel haefliger cycle class map for 1 cycles with the problem of deciding whether a real variety with no real point contains a curve of even geometric genus and with the problem of computing the torsion of the chow group of 1 cycles of real threefolds new results about these problems are obtained along the way

confidence regions for high quantiles of a heavy tailed distribution estimating high quantiles plays an important role in the context of risk management this involves extrapolation of an unknown distribution function in this paper we propose three methods namely the normal approximation method the likelihood ratio method and the data tilting method to construct confidence regions for high quantiles of a heavy tailed distribution a simulation study prefers the data tilting method

a note on the estimation of a distribution function and quantiles by a kernel method there has recently been extensive work on the estimation by kernel methods of probability densities and their derivatives for a review see wertz 1978 for estimating the cumulative distribution function the empirical distribution function f is in a sense already quite smooth although it is known that further smoothing can be an advantage the object of the present note is to report briefly an investigation of kernel estimation applied to distribution function and quantiles further details are available from the author for independent and identically distributed random variables x1 x the usual kernel estimator of the density f is

a space time galerkin least squares finite element formulation of the navier stokes equations for moving domain problems a space time galerkin least squares finite element formulation of the navier stokes equations is presented for the analysis of free surface flows moving spatial configurations and deforming fluid structure interfaces the variational equation is based on the time discontinuous galerkin method employing the physical entropy variables the space time elements are oriented in time to accommodate the spatial deformations if the elements are oriented along the particle paths the formulation is lagrangian and if they are fixed in time it is eulerian consequently this formulation is analogous to the arbitrary lagrangian eulerian ale technique a novel mesh rezoning strategy is presented to orient the elements in time and adapt the fluid mesh to the changing spatial configuration numerical results are presented to show the performance of the method

algebraic cycles and approximation theorems in real algebraic geometry let af be a compact c manifold a theorem of nash tognoli asserts that m has an algebraic model that is m is diffeomorphic to a nonsingular real algebraic set x let fv afx z 2 denote the subgroup of hk x z 2 of the cohomology classes determined by algebraic cycles of codi mension k on x assuming that m is connected orientable and dim m 5 we prove in this paper that a subgroup g of h2 m z 2 is isomorphic to h x z 2 for some algebraic model x of m if and only if w2 tm is in g and each element of g is of the form w2k for some real vector bundle over m where w2 stands for the second stiefel whitney class a result of this type was previously known for subgroups g of hx m z 2

a resolution theorem for homology cycles of real algebraic varieties the theorem is the best possible in the sense that the components of nonsingular algebraic subsets in the conclusion cannot be replaced by nonsingular algebraic subsets see remark 14 it is well known that the topology of the singularities of 7 2 homology cycles is closely related to real algebraic structures on v ak 2 ak3 therefore it is natural to study to what extent general homology cycles differ from the cycles induced by submanifolds the main theorem of this paper implies that all the singularities of homology cycles can be smoothed by a blowing up process this result should be viewed as a homology version of the resolution theorem h the reason this result is not an easy consequence of h is that not all homology cycles of v may be represented by algebraic subsets there are real obstructions e g ak2 even if they were the map resolving them may introduce new bad homology cycles upstairs the result turns out to be a useful device in topologically classifying real algebraic sets ak6 it also gives interesting corollaries in algebraic topology ak2 another result of this paper theorem 4 says that any smooth map f w v between nonsingular algebraic sets can be approximated by a rational map after changing w by a rational diffeomorphism if the homotopy class of f contains a rational representative this strengthens proposition 2 3 of aks for given algebraic sets vcf and w e n m a function f v w is called an entire rational function if f x p x q x where p ir and q ir ir

algebraic models of smooth manifolds in fact we conjecture that such a family can be chosen uncountable in view of this theorem it seems natural and interesting to investigate algebrogeometric properties of various algebraic models of a given smooth manifold let us now describe one of these problems which will be the main object of study in this paper for notions definitions and results of real algebraic geometry we refer the reader to the book 9 given a compact nonsingular real affine algebraic variety x denote by h ig x 7z 2 the subgroup of nk x z 2 of homology classes represented by zariski closed k dimensional algebraic subvarieties of x cf 9 chap 1 1 let h lg x z 2 be the image of h a k x 71 2 d dimx under the poincar6 duality isomorphism hd k x 71 2 o hk x 71 2 these groups h ig x 71 2 are undoubtedly one of the most important invariants of an algebraic variety x still our knowledge of the behavior of h g x 71 2 is rather limited the main open problem is the following

methods for 3d computation of fluid object interactions in spatially periodic flows abstract we present computational methods for 3d simulation of fluid object interactions in spatially periodic flows these methods include a stabilized space time finite element formulation for incompressible flows with spatial periodicity automatic mesh generation and update techniques for fluid object mixtures with spatial periodicity and parallel implementations the methods can be applied to uni periodic i e periodic in one direction bi periodic or tri periodic flows the methods are described here in the context of tri periodic flows with fluid object interactions and are applied to the simulation of sedimentation of particles in a fluid we present several case studies where the results obtained provide notable insight into the behavior of fluid particle mixtures during sedimentation

streamline upwind petrov galerkin formulations for convection dominated flows with particular emphasis on the incompressible navier stokes equations abstract a new finite element formulation for convection dominated flows is developed the basis of the formulation is the streamline upwind concept which provides an accurate multidimensional generalization of optimal one dimensional upwind schemes when implemented as a consistent petrov galerkin weighted residual method it is shown that the new formulation is not subject to the artificial diffusion criticisms associated with many classical upwind methods the accuracy of the streamline upwind petrov galerkin formulation for the linear advection diffusion equation is demonstrated on several numerical examples the formulation is extended to the incompressible navier stokes equations an efficient implicit pressure explicit velocity transient algorithm is developed which accomodates several treatments of the incompressibility constraint and allows for multiple iterations within a time step the effectiveness of the algorithm is demonstrated on the problem of vortex shedding from a circular cylinder at a reynolds number of 100