convergence of dziuk s linearly implicit parametric finite element method for curve shortening flow convergence of dziuk s fully discrete linearly implicit parametric finite element method for curve shortening flow on the plane still remains open since it was proposed in 1991 though the correspo

an unfitted finite element method for the numerical approximation of void electromigration microelectronic circuits usually contain small voids or cracks and if those defects are large enough to sever the line they cause an open circuit we present a numerical method for investigating the migration of voids in the presence of both surface diffusion and electric loading our mathematical model involves a bulk interface coupled system with a moving interface governed by a fourth order geometric evolution equation and a bulk where the electric potential is computed thanks to a novel approximation of the interface equidistribution of its vertices is guaranteed and no remeshing is necessary in addition the used curvature approximation means that our method is unconditionally stable for the evolution by surface diffusion only various examples are performed to demonstrate the accuracy of the method

the inverse mean curvature flow and the riemannian penrose inequality let m be an asymptotically flat 3 manifold of nonnegative scalar curvature the riemannian penrose inequality states that the area of an outermost minimal surface n in m is bounded by the adm mass m according to the formula n 16 m 2 we develop a theory of weak solutions of the inverse mean curvature flow and employ it to prove this inequality for each connected component of n using geroch s monotonicity formula for the adm mass our method also proves positivity of bartnik s gravitational capacity by computing a positive lower bound for the mass purely in terms of local geometry

a method of finite element tearing and interconnecting and its parallel solution algorithm a novel domain decomposition approach for the parallel finite element solution of equilibrium equations is presented the spatial domain is partitioned into a set of totally disconnected subdomains each assigned to an individual processor lagrange multipliers are introduced to enforce compatibility at the interface nodes in the static case each floating subdomain induces a local singularity that is resolved in two phases first the rigid body modes are eliminated in parallel from each local problem and a direct scheme is applied concurrently to all subdomains in order to recover each partial local solution next the contributions of these modes are related to the lagrange multipliers through an orthogonality condition a parallel conjugate projected gradient algorithm is developed for the solution of the coupled system of local rigid modes components and lagrange multipliers which completes the solution of the problem when implemented on local memory multiprocessors this proposed method of tearing and interconnecting requires less interprocessor communications than the classical method of substructuring it is also suitable for parallel vector computers with shared memory moreover unlike parallel direct solvers it exhibits a degree of parallelism that is not limited by the bandwidth of the finite element system of equations

finite element matrices in congruent subdomains and their effective use for large scale computations the structure of finite element matrices in congruent subdomains is studied when a domain has a form of symmetries and or periodicities it is decomposed into a union of congruent subdomains each of which is an image of a reference subdomain by an affine transformation with an orthogonal matrix whose components consist of 1 0 and 1 stiffness matrices in subdomains are expressed by one in the reference subdomain with renumbering indices and changing signs corresponding to the orthogonal matrices the memory requirements for a finite element solver are reduced by the domain decomposition which is useful in large scale computations reducing rates of memory requirements to store matrices are reported with examples of domains both applicability and limitations of the algorithm are discussed with an application to the earth s mantle convection problem

on the variational approximation of combined second and fourth order geometric evolution equations we present a variational formulation of combined motion by minus the laplacian of curvature and mean curvature flow as well as related flows the proposed scheme covers both the closed curve case and the case of curves that are connected via triple or quadruple junction points or intersect the external boundary on introducing a parametric finite element approximation we prove stability bounds and compare our scheme with existing approaches the presented scheme has very good properties with respect to the equidistribution of mesh points and if applicable area conservation

outlier detection and time series modeling some statistics used in regression analysis are considered for detection of outliers in time series approximations and asymptotic distributions of these statistics are considered a method is proposed for distinguishing an observational outlier from an innovational one a four step procedure for modeling time series in the presence of outliers is also proposed and an example is presented to illustrate the methodology

a variational formulation of anisotropic geometric evolution equations in higher dimensions we present a novel variational formulation of fully anisotropic motion by surface diffusion and mean curvature flow in mathbb r d d 2 this new formulation leads to an unconditionally stable fully discrete parametric finite element approximation in the case d 2 or 3 the resulting scheme has very good properties with respect to the distribution of mesh points and if applicable volume conservation this is demonstrated by several numerical experiments for d 3 including regularized crystalline mean curvature flow and regularized crystalline surface diffusion

geometric solution strategy of laplace problems with free boundary summary this paper introduces a geometric solution strategy for laplace problems our main interest and emphasis is on efficient solution of the inverse problem with a boundary with cauchy condition and with a free boundary this type of problem is known to be sensitive to small errors we start from the standard laplace problem and establish the geometric solution strategy on the idea of deforming equipotential layers continuously along the field lines from one layer to another this results in exploiting ordinary differential equations to solve any boundary value problem that belongs to the class of laplace s problem interpretation in terms of a geometric flow will provide us with stability considerations the approach is demonstrated with several examples copyright 2015 john wiley sons ltd

the polyharmonic heat flow of closed plane curves abstract in this paper we consider the polyharmonic heat flow of a closed curve in the plane our main result is that closed initial data with initially small normalised oscillation of curvature and isoperimetric defect flows exponentially fast in the c topology to a simple circle our results yield a characterisation of the total amount of time during which the flow is not strictly convex quantifying in a sense the failure of the maximum principle

flow of nonconvex hypersurfaces into spheres the flow of surfaces by functions of their principal curvatures has been intensively studied it started with the work of brakke 1 who used the formalism of geometric measure theory a more classical approach had been chosen by huisken who looked at the so called inward flow in 5 the outward flow of surfaces this term will be explained in the sequel is scaling invariant and therefore more natural than the inward flow producing more general results so far huisken 6 and urbas 8 proved that the outward flow of convex surfaces by suitable functions of their principal curvatures converges to spheres the convexity assumption is essential in their work in this paper we would like to present a different method for proving the convergence of star shaped surfaces into spheres via the outward flow let be a symmetric positive function homogeneous of degree one being defined on an open cone of rn with vertex in the origin which contains the positive diagonal i e all tuples of the form

influence measures for logistic regression another point of view summary several measures of influence for logistic regression have been suggested these measures have been developed for the purpose of identifying observations which are influential relative to the estimation of the regression coefficients vector and the deviance we propose measures for detecting influence relative to the determination of probabilities and the classification of future observations the relationships among measures are indicated

on affine plane curve evolution abstract an affine invariant curve evolution process is presented in this work the evolution studied is the affine analogue of the euclidean curve shortening flow evolution equations for both affine and euclidean invariants are developed an affine version of the classical euclidean isoperimetric inequality is proved this inequality is used to show that in the case of affine evolution of convex plane curves the affine isoperimetric ratio is a non decreasing function of time convergence of this affine isoperimetric ratio to the ellipse s value 8 2 as well as convergence in the hausdorff metric of the evolving curve to an ellipse is also proved

variational discretization of axisymmetric curvature flows we present natural axisymmetric variants of schemes for curvature flows introduced earlier by the present authors and analyze them in detail although numerical methods for geometric flows have been used frequently in axisymmetric settings numerical analysis results so far are rare in this paper we present stability equidistribution existence and uniqueness results for the introduced approximations numerical computations show that these schemes are very efficient in computing numerical solutions of geometric flows as only a spatially one dimensional problem has to be solved the good mesh properties of the schemes also allow them to compute in very complex axisymmetric geometries

finite element discretization of the navier stokes equations with a free capillary surface the instationary navier stokes equations with a free capillary boundary are considered in 2 and 3 space dimensions a stable finite element discretization is presented the key idea is the treatment of the curvature terms by a variational formulation in the context of a discontinuous in time space time element discretization stability in weak energy norms can be proved numerical examples in 2 and 3 space dimensions are given

global stability of traveling waves for an area preserving curvature flow with contact angle condition abstract we consider an evolving plane curve with two endpoints that can move freely on the x axis with generating constant contact angles we discuss the asymptotic behavior of global in time solutions when the evolution of this plane curve is governed by the area preserving curvature flow equation the main result shows that any moving curve converges to a traveling wave if the moving curve starts from an embedded convex curve and remains bounded in global time

finite element modeling of a linear membrane shell problem using tangential differential calculus we construct a new galerkin finite element method for the membrane elasticity problem on a meshed surface by using two dimensional elements extended into three dimensions the membrane finite element model is established using a tangential differential calculus approach that avoids the use of classical differential geometric methods the finite element method generalizes the classical flat element shell method where standard plane stress elements are used for membrane problems this makes our method applicable to a wider range of problems and of surface descriptions including surfaces defined by distance functions

stabilized mixed methods for the stokes problem the solution of the stokes problem is approximated by three stabilized mixed methods one due to hughes balestra and franca and the other two being variants of this procedure in each case the bilinear form associated with the saddle point problem of the standard mixed formulation is modified to become coercive over the finite element space error estimates are derived for each procedure

diagnosing shocks in time series abstract efficient means of modeling aberrant behavior in times series are developed our methods are based on state space forms and allow test statistics for various interventions to be computed from a single run of the kalman filter smoother the approach encompasses existing detection methodologies departures commonly observed in practice such as outlying values level shifts and switches are readily dealt with new diagnostic statistics are proposed implications for structural models autoregressive integrated moving average models and models with explanatory variables are given

balancing neumann neumann methods for incompressible stokes equations this paper describes the unerlying mathematical model and the balancing neumann neumann methods are introduced and studied for incompressible stokes equations discretized with mixed finite or spectral elements with discontinuous pressures after decomposing the original domain of the problem into nonoverlapping subdomains the interior unknowns which are the interior velocity component and all except the constant pressure component of each subdomain problem are implicitly eliminated the resulting saddle point schur complement is solved with a krylov space method with a balancing neumann neumann preconditioner based on the solution of a coarse stokes problem with a few degrees of freedom per subdomain and on the solution of local stokes problems with natural neumann velocity and essential boundary conditions on the subdomains this preconditioner is of hybrid form in which the coarse problem is treated multiplicatively while the local problems are treated additively the condition number of the preconditioned operator is independent of the number of subdomains and is bounded from above by the product of the square of the logarithm of the local number of unknowns in each subdomain and the inverse of the inf sup constants of the discrete problem and of the coarse subproblem numerical results show that the method is quite fast they are also fully consistent with the theory

a convergent evolving finite element algorithm for mean curvature flow of closed surfaces a proof of convergence is given for semi and full discretizations of mean curvature flow of closed two dimensional surfaces the numerical method proposed and studied here combines evolving finite elements whose nodes determine the discrete surface like in dziuk s method and linearly implicit backward difference formulae for time integration the proposed method differs from dziuk s approach in that it discretizes huisken s evolution equations for the normal vector and mean curvature and uses these evolving geometric quantities in the velocity law projected to the finite element space this numerical method admits a convergence analysis in the case of finite elements of polynomial degree at least two and backward difference formulae of orders two to five the error analysis combines stability estimates and consistency estimates to yield optimal order h 1 norm error bounds for the computed surface position velocity normal vector and mean curvature the stability analysis is based on the matrix vector formulation of the finite element method and does not use geometric arguments the geometry enters only into the consistency estimates numerical experiments illustrate and complement the theoretical results

on the affine heat equation for non convex curves 1998 american mathematical society first published in journal of the american mathematical society vol 11 no 3 july 1998 published by the american mathematical society

a fast algorithm for signal extraction influence and cross validation in state space models summary a fast algorithm is developed for computing the conditional mean and variance of the signal given the observations in a signal plus noise model the resulting recursions can be applied immediately to provide new and efficient formulae for smoothing part or all of the state vector the ideas of studentized residuals and leverage from regression analysis are generalized to state space models and the new algorithm is used to compute the various measures the results are also applied to obtain a new efficient algorithm for polynomial spline smoothing suppose observations are generated by a gaussian signal plus noise process with the signal described by a state space model such a model for the signal occurs often in practice for example when the signal is the output of a stochastic difference or differential equation this paper presents a new algorithm for signal extraction that is the computa tion of the conditional mean and variance of the signal given the observations the usual method for signal extraction is to use the kalman filter see for example anderson moore 1979 p 105 followed by a smoothing step using an algorithm such as the fixed interval smoothing algorithm anderson moore 1979 p 187 our approach also uses the kalman filter but for the smoothing step introduces a new set of recursions which are more efficient than those for the fixed interval smoothing algorithm as for the fixed interval smoothing algorithm recursions for estimating the signal and its variance are carried out separately so that considerable additional savings can be made if the signal estimate alone is required the development uses ideas introduced by ansley kohn 1987a a remarkable property of the new recursions is that they can be applied immediately

a stabilized finite element method for the rayleigh benard equations with infinite prandtl number in a spherical shell abstract a finite element scheme is developed and analyzed for a thermal convection problem of boussinesq fluid with infinite prandtl number in a spherical shell this problem is a mathematical model of the earth s mantle movement and has been a topic of interest for geophysicists it is described by the rayleigh benard equations with infinite prandtl number that is a system of the stokes equations and the convection diffusion equation coupled with the buoyancy and the convection terms a stabilized finite element scheme with p1 p1 p1 element is presented and an error estimate is established the obtained theoretical convergence order is also recognized by a numerical result another numerical result is shown as an example of the earth s mantle movement simulation

on the approximation of the unsteady navier stokes equations by finite element projection methods this paper provides an analysis of a fractional step projection method to compute incompressible viscous flows by means of finite element approximations the analysis is based on the idea that the appropriate functional setting for projection methods must accommodate two different spaces for representing the velocity fields calculated respectively in the viscous and the incompressible half steps of the method such a theoretical distinction leads to a finite element projection method with a poisson equation for the incremental pressure unknown and to a very practical implementation of the method with only the intermediate velocity appearing in the numerical algorithm error estimates in finite time are given an extension of the method to a problem with unconventional boundary conditions is also considered to illustrate the flexibility of the proposed method

detection of influential observation in linear regression a new measure based on confidence ellipsoids is developed for judging the contribution of each data point to the determination of the least squares estimate of the parameter vector in full rank linear regression models it is shown that the measure combines information from the studentized residuals and the variances of the residuals and predicted values two examples are presented

singularities of the area preserving curve shortening flow with a free boundary condition we consider the area preserving curve shortening flow with neumann free boundary conditions outside of a convex domain or at a straight line we give a criterion on initial curves that guarantees the appearance of a singularity in finite time we prove that the singularity is of type ii furthermore if these initial curves are convex then an appropriate rescaling at the finite maximal time of existence yields a grim reaper or half a grim reaper as limit flow we construct examples of initial curves satisfying the mentioned criterion

a parametric finite element method for fourth order geometric evolution equations we present a finite element approximation of motion by minus the laplacian of curvature and related flows the proposed scheme covers both the closed curve case and the case of curves that are connected via triple junctions on introducing a parametric finite element approximation we prove stability bounds and compare our scheme with existing approaches it turns out that the new scheme has very good properties with respect to area conservation and the equidistribution of mesh points we state also an extension of our scheme to willmore flow of curves and discuss possible further generalizations

isogeometric analysis of geometric partial differential equations abstract we consider the numerical approximation of geometric partial differential equations pdes defined on surfaces in the 3d space in particular we focus on the geometric pdes deriving from the minimization of an energy functional by l 2 gradient flow we analyze two energy functionals the area which leads to the mean curvature flow a nonlinear second order pde and the willmore energy leading to the willmore flow a nonlinear fourth order pde we consider surfaces represented by single patch tensor product nurbs and discretize the pdes by means of nurbs based isogeometric analysis in the framework of the galerkin method to approximate the high order geometric pdes we use high order continuous nurbs basis functions for the time discretization of the nonlinear geometric pdes we use backward differentiation formulas bdf with extrapolation of the geometric quantities involved in the weak formulation of the problem in this manner we solve a linear problem at each time step we report numerical results concerning the mean curvature and willmore flows on different geometries of interest and we show the accuracy and efficiency of the proposed approximation scheme

smoothing and interpolation with the state space model abstract a new result dealing with smoothing and interpolation in the state space model is developed and explored the result simplifies the derivation of existing smoothing algorithms and provides alternate forms that have analytic and practical computing advantages the connection to signal extraction and interpolation is explored and diffuse specifications are considered

fast reaction slow diffusion and curve shortening the reaction diffusion problem u 1 varepsilon delta u varepsilon 1 v n u quad u x 0 varepsilon g x quad partial n u 0 text on partial omega for a vector u x t varepsilon is considered in a domain omega in r m an asymptotic solution is constructed for varepsilon small it shows that at each x u tends quickly to a minimum of v u when v has several minima when u tends to a piecewise constant function boundary layer expansions are constructed around the resulting surfaces of discontinuity or fronts each front is found to move along its normal with a constant velocity determined by the discontinuity v in v across it when v 0 the front s normal velocity is varepsilon kappa where kappa is its mean curvature the motion of fronts in this manner is studied for arcs in the plane which are normal to partial omega at their endpoints and for fronts that are closed curves it is shown a front can shrink to a point in

a finite element method for surface diffusion the parametric case surface diffusion is a fourth order highly nonlinear geometric driven motion of a surface with normal velocity proportional to the surface laplacian of mean curvature we present a novel variational formulation for parametric surfaces with or without boundaries the method is semi implicit requires no explicit parametrization and yields a linear system of elliptic pde to solve at each time step we next develop a finite element method propose a schur complement approach to solve the resulting linear systems and show several significant simulations some with pinch off in finite time we introduce a mesh regularization algorithm which helps prevent mesh distortion and discuss the use of time and space adaptivity to increase accuracy while reducing complexity

axisymmetric surface diffusion dynamics and stability of self similar pinchoff the dynamics of surface diffusion describes the motion of a surface with its normal velocity given by the surface laplacian of its mean curvature this flow conserves the volume enclosed inside the surface while minimizing its surface area we review the axisymmetric equilibria the cylinder sphere and the delaunay unduloid the sphere is stable while the cylinder is long wave unstable a subcritical bifurcation from the cylinder produces a continuous family of unduloid solutions we present computations that suggest that the stable manifold of the unduloid forms a separatrix between states that relax to the cylinder in infinite time and those that tend toward finite time pinchoff we examine the structure of the pinchoff showing it has self similar structure using asymptotic numerical and analytical methods in addition to a previously known similarity solution we find a countable set of similarity solutions each with a different asymptotic cone angle we develop a stability theory in similarity variables that selects the original similarity solution as the only linearly stable one and consequently the only observable solution we also consider similarity solutions describing the dynamics after the topological transition

dynamic linear model diagnostics summary in time series analysis using dynamic linear models retrospective analysis involves the calculation of filtered or smoothed distributions for state parameters in the past we develop and illustrate novel results that are useful in retrospective assessment of the influence of individual observations on such distributions in particular new and computationally simple filtering equations are derived for past state parameters based on leaving out one observation at a time providing dynamic model based versions of methods currently used in standard static regression diagnostics

linking anisotropic sharp and diffuse surface motion laws via gradient flows we compare four surface motion laws for sharp surfaces with their diffuse interface counterparts by means of gradient flows on corresponding energy functionals the energy functionals can be defined to give the same dependence on normal direction for the energy of sharp plane surfaces as for their diffuse counterparts the anisotropy of the kinetics can be incorporated into the inner product without affecting the energy functional

on the parametric finite element approximation of evolving hypersurfaces in r 3 we present a variational formulation of motion by minus the laplacian of curvature and mean curvature flow as well as related second and fourth order flows of a closed hypersurface in r 3 on introducing a parametric finite element approximation we prove stability bounds and compare our scheme with existing approaches the presented scheme has very good properties with respect to the distribution of mesh points and if applicable volume conservation

on stable parametric finite element methods for the stefan problem and the mullins sekerka problem with applications to dendritic growth we introduce a parametric finite element approximation for the stefan problem with the gibbs thomson law and kinetic undercooling which mimics the underlying energy structure of the problem the proposed method is also applicable to certain quasi stationary variants such as the mullins sekerka problem in addition fully anisotropic energies are easily handled the approximation has good mesh properties leading to a well conditioned discretization even in three space dimensions several numerical computations including for dendritic growth and for snow crystal growth are presented

assessment of local influence summary statistical models usually involve some degree of approximation and therefore are nearly always wrong because of this inexactness an assessment of the influence of minor perturbations of the model is important we discuss a method for carrying out such an assessment the method is not restricted to linear regression models and it seems to provide a relatively simple unified approach for handling a variety of problems

eliminating spurious velocities with a stable approximation of viscous incompressible two phase stokes flow abstract we present a parametric finite element approximation of two phase flow this free boundary problem is given by the stokes equations in the two phases which are coupled via jump conditions across the interface using a novel variational formulation for the interface evolution gives rise to a natural discretization of the mean curvature of the interface in addition the mesh quality of the parametric approximation of the interface does not deteriorate in general over time and an equidistribution property can be shown for a semidiscrete continuous in time variant of our scheme in two space dimensions moreover on using a simple xfem pressure space enrichment we obtain exact volume conservation for the two phase regions furthermore our fully discrete finite element approximation can be shown to be unconditionally stable we demonstrate the applicability of our method with some numerical results which in particular demonstrate that spurious velocities can be avoided in the classical test cases

alternative algorithms for the estimation of dynamic factor mimic and varying coefficient regression models this paper provides a general approach to the formulation and estimation of dynamic unobserved component models after introducing the general model two methods for estimating the unknown parameters are presented both are algorithms for maximizing the likelihood function the first is based on the method of scoring the second is the em algorithm a derivative free method each iteration of em requires a kalman filter and smoother followed by straightforward regression calculations the paper suggests using the em methods to quickly locate a neighborhood of the maximum scoring can then be used to pinpoint the maximum and calculate the information matrix

detecting outliers in time series data abstract occasional large errors in data can have drastic effects on estimates for such quantities as correlation coefficients regression coefficients and spectral density estimates in this article we investigate the effect of outliers on time series data by considering the influence function for the autocorrelations p k of a stationary time series this influence function matrix is applied to simulated data to power plant data and to inventory data on nuclear materials

an algorithm for evolutionary surfaces an algorithm is presented which allows to split the calculation of the mean curvature flow of surfaces with or without boundary into a series of poisson problems on a series of surfaces this gives a new method to solve plateau s problem forh surfaces

some dynamic properties of volume preserving curvature driven flows this paper is concerned with the following three types of geometric evolution equations the volume preserving mean curvature flow the intermediate surface diffusion flow and the surface diffusion flow important common properties of these flows are the preservation of volume and the decrease of perimeter it is shown in this paper that the intermediate surface diffusion flow can lose convexity hence the volume preserving mean curvature flow is the only flow among the evolution equations under consideration which preserves convexity cf 11 16 14 17 moreover several sufficient conditions are presented which illustrate that each of the above mentioned flows can move smooth initial configurations into singularities in finite time

disturbance smoother for state space models summary this paper develops a method to evaluate the smoothed estimator of the disturbance vector in a state space model together with its mean squared error matrix this disturbance smoother also leads to an efficient smoother for the state vector applications include a method to calculate auxiliary residuals for unobserved components time series models and an em algorithm for estimating covariance parameters in a state space model

phase field approximations of the willmore functional and flow we discuss in this paper phase field approximations of the willmore functional and the associated mathrm l 2 l2 flow after recollecting known results on the approximation of the willmore energy and its mathrm l 1 l1 relaxation we derive the expression of the flows associated with various approximations and we show their behavior by formal arguments based on matched asymptotic expansions we introduce an accurate numerical scheme whose local convergence is proved to describe with more details the behavior of two flows the classical and the flow associated with an approximation model due to mugnai we propose a series of numerical simulations in 2d and 3d to illustrate their behavior in both smooth and singular situations

leave k out diagnostics for time series abstract the authors propose diagnostics for arima model fitting for time series formed by deleting observations from the data and measuring the change in the estimates of the parameters the use of leave one out diagnostics is a well established tool in regression analysis this document demonstrates the efficacy of observation deletion based diagnostics for arima models addressing issues special to the time diagnostics based on the innovations variance it is shown that the dependency aspect of time series data gives rise to a smearing effect which confounds the diagnostics for the coefficients it is also shown that the diagnostics based on the innovations variance are much clearer and more sensitive than those for the coefficients a leave k out diagnostics approach is proposed to deal with patches of outliers and problems caused by masking are handled by use of iterative deletion an overall strategy for arima model fitting is given and applied to two data sets

a predictive view of the detection and characterization of influential observations in regression analysis abstract assuming a set of observations is available from the general linear model and assuming prior information about parameters we propose a method of assessing the influence of specified subsets of the data when the goal is to predict future observations

parametric approximation of willmore flow and related geometric evolution equations we present various variational approximations of willmore flow in mathbb r d d 2 3 as well as the classic willmore flow we also consider variants that are a volume preserving and b volume and area preserving the latter evolution law is the so called helfrich flow in addition we consider motion by gaus curvature the presented fully discrete schemes are easy to solve as they are linear at each time level and they have good properties with respect to the distribution of mesh points finally we present numerous numerical experiments including simulations for energies appearing in the modeling of biological cell membranes

detecting over influential observations in time series summary the purpose of this paper is to develop a tool for identifying over influential observations in time series when they are viewed in the time domain we present a method for obtaining various measures of influence for the autocorrelation function as well as thresholds for declaring an observation over influential an example of the use of these thresholds is also presented

capturing the behavior of bubbles and drops using the variational level set approach we reproduce the general behavior of complicated bubble and droplet motions using the variational level set formulation introduced by the authors earlier our approach here ignores inertial effects thus the motion is only correct as an approximation for very viscous problems however the steady states are true equilibrium solutions inertial forces will be added in future work the problems include soap bubbles colliding and merging drops falling or remaining attached to a generally irregular ceiling and liquid penetrating through a funnel in both two and three dimensions each phase is identified with a particular level set function the zero level set of this function is that particular phase boundary the level set functions all evolve in time through a constrained gradient descent procedure so as to minimize an energy functional the functions are coupled through physical constraints and through the requirements that different phases do not overlap and vacuum regions do not develop both boundary conditions and inequality constraints are cast in terms of either local or global equality constraints the gradient projection method leads to a system of perturbed by curvature if surface tension is involved hamilton jacobi equations coupled through a constraint the coupling is enforced using the lagrange multiplier associated with this constraint the numerical implementation requires much of the modern level set technology in particular we achieve a significant speed up by using the fast localization algorithm of h k zhao m kang b merriman d peng and s osher

computational parametric willmore flow with spontaneous curvature and area difference elasticity effects a new stable continuous in time semidiscrete parametric finite element method for willmore flow is introduced the approach allows for spontaneous curvature and area difference elasticity effects which are important for many applications in particular in the context of membranes the method extends ideas from dziuk and the present authors to obtain an approximation that allows for a tangential redistribution of mesh points which typically leads to better mesh properties moreover we consider volume and surface area preserving variants of these schemes and in particular we obtain stable approximations of helfrich flow we also discuss fully discrete variants and present several numerical computations

evolution of plane curves driven by a nonlinear function of curvature and anisotropy in this paper we study evolution of plane curves satisfying a geometric equation v beta k nu where v is the normal velocity and k and nu are the curvature and tangential angle of a plane curve gamma we follow the direct approach and we analyze the so called intrinsic heat equation governing the motion of plane curves obeying such a geometric equation the intrinsic heat equation is modified to include an appropriate nontrivial tangential velocity functional alpha we show how the presence of a nontrivial tangential velocity can prevent numerical solutions from forming various instabilities from an analytical point of view we present some new results on short time existence of a regular family of evolving curves in the degenerate case when beta k nu gamma nu k m 0 m le 2 and the governing system of equations includes a nontrivial tangential velocity functional

assessing the predictive influence of cases in a state space process an important inferential objective in state space modelling is to recover unobserved states using fixed interval smoothing thus the identification of cases which have a substantial influence on the smoothers is a relevant practical problem to facilitate this identification we propose a case deletion diagnostic which can be easily computed using the outputs of the standard filtering and smoothing algorithms our diagnostic is defined as the kullback leibler directed divergence between two versions of the conditional density which determines the smoothers one based on all the data the other based on all the data except for the case or cases in question we investigate the detection performance of the diagnostic in a practical application

a stable numerical method for the dynamics of fluidic membranes we develop a finite element scheme to approximate the dynamics of two and three dimensional fluidic membranes in navier stokes flow local inextensibility of the membrane is ensured by solving a tangential navier stokes equation taking surface viscosity effects of boussinesq scriven type into account in our approach the bulk and surface degrees of freedom are discretized independently which leads to an unfitted finite element approximation of the underlying free boundary problem bending elastic forces resulting from an elastic membrane energy are discretized using an approximation introduced by dziuk numer math 111 55 80 2008 the obtained numerical scheme can be shown to be stable and to have good mesh properties finally the evolution of membrane shapes is studied numerically in different flow situations in two and three space dimensions the numerical results demonstrate the robustness of the method and it is observed that the conservation properties are fulfilled to a high precision

a diffuse interface model for alloys with multiple components and phases a nonisothermal phase field model for alloys with multiple phases and components is derived the model allows for arbitrary phase diagrams we relate the model to classical sharp interface models by formally matched asymptotic expansions in addition we discuss several examples and relate our model to the ones already existing

finite element approximation of a phase field model for surface diffusion of voids in a stressed solid we consider a fully practical finite element approximation of the degenerate cahn hilliard equation with elasticity find the conserved order parameter theta x t in 1 1 and the displacement field underline u x t in bbb r 2 such that gamma frac partial theta partial t nabla cdot b theta nabla gamma delta theta gamma 1 psi theta tfrac 12 c theta cal c underline underline cal e underline u underline underline cal e underline u quad nabla cdot c theta cal c underline underline cal e underline u underline 0 subject to an initial condition theta 0 cdot in 1 1 on theta and boundary conditions on both equations here gamma in bbb r 0 is the interfacial parameter psi is a nonsmooth double well potential underline underline cal e is the symmetric strain tensor cal c is the possibly anisotropic elasticity tensor c s c 0 frac 12 1 c 0 1 s with c 0 gamma in bbb r 0 and b s 1 s 2 is the degenerate diffusion mobility in addition to showing stability bounds for our approximation we prove convergence and hence existence of a solution to this nonlinear degenerate parabolic system in two space dimensions finally some numerical experiments are presented

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