a fast algorithm for simulating vesicle flows in three dimensions vesicles are locally inextensible fluid membranes that can sustain bending in this paper we extend the study of veerapaneni et al s k veerapaneni d gueyffier g biros d zorin a numerical method for simulating the dynamics of 3d axisymmetric vesicles suspended in viscous flows journal of computational physics 228 19 2009 7233 7249 to general non axisymmetric vesicle flows in three dimensions although the main components of the algorithm are similar in spirit to the axisymmetric case spectral approximation in space semi implicit time stepping scheme important new elements need to be introduced for a full 3d method in particular spatial quantities are discretized using spherical harmonics and quadrature rules for singular surface integrals need to be adapted to this case an algorithm for surface reparameterization is needed to ensure stability of the time stepping scheme and spectral filtering is introduced to maintain reasonable accuracy while minimizing computational costs to characterize the stability of the scheme and to construct preconditioners for the iterative linear system solvers used in the semi implicit time stepping scheme we perform a spectral analysis of the evolution operator on the unit sphere by introducing these algorithmic components we obtain a time stepping scheme that circumvents the stability constraint on the time step and achieves spectral accuracy in space we present results to analyze the cost and convergence rates of the overall scheme to illustrate the applicability of the new method we consider a few vesicle flow interaction problems a single vesicle in relaxation sedimentation shear flows and many vesicle flows

a new mesh generation scheme for arbitrary planar domains this paper describes a new algorithm to generate interior nodes within any arbitrary multi connected regions the boundary nodes and the interior nodes are then linked up to form the best possible triangular elements by a completely revised technique in an efficient and stable manner owing to the generality of the central generation program the global domain is allowed to be divided into as many irregular subdomains as desired in order to model closely the actual physical situation moreover the boundaries of the sub domains are updated from time to time when necessary to include the possibilities of progressive refinement around a sharp corner generating radiating mesh from a prescribed node generating mesh between two circular arcs etc despite its flexibility and capabilities data for triangulation have been kept to a minimum by a logical input module no connectivity information between subregions is needed and common boundaries are defined once only all these features have contributed to a powerful method to generate 3 node or 6 node triangular element meshes of great variety within the most irregular heterogeneous regions

quarter fraction factorial designs constructed via quaternary codes submitted quarter fraction factorial designs constructed via quaternary codes by frederick k h phoa and hongquan xu university of california los angeles the research of developing a general methodology for the con struction of good nonregular designs has been very active in the last decade recent research by xu and wong 2007 suggested a new class of nonregular designs constructed from quaternary codes this paper explores the properties and uses of quaternary codes towards the construction of quarter fraction nonregular designs some theo retical results are obtained regarding the aliasing structure of such designs optimal designs are constructed under the maximum resolu tion minimum aberration and maximum projectivity criteria these designs often have larger generalized resolution and larger projectiv ity than regular designs of the same size it is further shown that some of these designs have generalized minimum aberration and maximum projectivity among all possible designs 1 introduction in many scienti c researches and investigations the interests lie in the study of e ects of many factors simultaneously frac tional factorial designs especially two level fractional factorial designs are the most commonly used experimental plans for this type of investigations designs that can be constructed through de ning relations among factors are called regular designs any two factorial e ects in a regular design are supported in part by nsf grant dms 05 05728 ams 2000 subject classi cations primary 62k15 keywords and phrases aliasing index fractional factorial design generalized minimum aberration generalized resolution nonregular design projectivity

some projection properties of orthogonal arrays the definition of an orthogonal array imposes an important geometric property the projection of an oa 2 t 2 k t a 2 t run orthogonal array with k two level factors and strength t onto any t factors consists of copies of the complete 2 t factorial in this article projections of an oa n 2 k t onto t 1 and t 2 factors are considered the projection onto any t 1 factors must be one of three types one or more copies of the complete 2 t 1 factorial one or more copies of a half replicate of 2 t 1 or a combination of both it is also shown that for k t 2 only when n is a multiple of 2 t 1 can the projection onto some t 1 factors be copies of a half replicate of 2 t 1 therefore if n is not a multiple of 2 t 1 then the projection of an oa n 2 k t with k t 2 onto any t 1 factors must contain at least one complete 2 t 1 factorial some properties of projections onto t 2 factors are established and are applied to show that if n is not a multiple of 8 then for any oa n 2 k 2 with k 4 the projection onto any four factors has the property that all the main effects and two factor interactions of these four factors are estimable when the higher order interactions are negligible

an efficient algorithm for hydrodynamical interaction of many deformable drops an efficient and accurate 3d algorithm for dynamical simulations of many deformable drops with strong hydrodynamical interactions at zero reynolds numbers is developed the drop to medium viscosity ratio and the bond number are arbitrary and the drops are subject to gravity with stationary triply periodic boundary conditions the algorithm at each step is a hybrid of boundary integral and economical multipole techniques with extensive use of rotational transformations and economical truncation of multipole expansions to optimize near field interactions a significant part of the code is the new best paraboloid spline technique for calculating the normal vectors and curvatures on drop surfaces which greatly improves the quality of long time simulations examples show the phenomenon of clustering in a concentrated sedimenting emulsion for 0 25 and 1 which leads to an increase in the average sedimentation velocity with time a high efficiency of the method is demonstrated with two orders of magnitude gains over the standard o n2n2 boundary integral technique for n 102 drops in a periodic cell with n 103 triangular boundary elements per drop so that typical long time dynamical simulations can be performed in a few days or weeks on a standard workstation as compared to the several years which would be required for the same simulations using standard boundary integral techniques the effects of drop triangulation and truncation of multipole expansions on dynamical simulations are assessed

the efficiencies of fractional factorial designs a frequently stated advantage of fractional factorial ff designs over one factor at a time 1fat designs is their high relative efficiency we study k factor 2k run designs where k is a power of 2 or is divisible by 4 for which the usually stated relative efficiency is k in favor of the resolution iv ff design over an orthogonal 1fat design we examine other ways to measure efficiency under main effects only modeling in the case when all factors are quantitative which enables rescaling of their settings if both designs are restricted to lie in smallest sized hypercubes or hyperspheres of equal volume then the relative efficiency of the ff design is 1 under the full model k effects active we also show that the designs are identical in an important sense the 1fat design can be rescaled and rotated to become a resolution iv ff design the primary advantage of the ff design lies in its projection properties if at most k factors are expected to be active then under equal volume designs the ef

comments on information theoretic key agreement of multiple terminals part i theorem 5 of a gohari v anantharam ieee transactions on information theory vol 56 no 8 pp 3973 3996 2010 states an upper bound on the secrecy capacity for the source model problem it has a three page proof given in appendix b of the paper unfortunately we show that this bound does not provide any improvement over the simpler bound given in corollary 1 of the paper we also provide an example of a family of two agent source model problems where the one way secrecy rate in each direction is zero but the secrecy rate is nonzero and can be determined exactly as a conditional mutual information

some hidden projection properties of orthogonal arrays with strength three summary it is shown that a two level orthogonal array with strength three whose run size is not a multiple of 16 has the hidden projection property that in its projection on to any five factors all the main effects and two factor interactions are estimable if the higher order interactions are negligible the result applies to the fold over of any strength two orthogonal array whose run size is not a multiple of 8 this extends diamond s 1995 result on the fold over of the 12 run plackett burman design some connections with search designs are also presented

adaptive triangulation of evolving closed or open surfaces by the advancing front method the advancing front method is adapted to describe the evolution of open or closed three dimensional surfaces in terms of an unstructured grid consisting of quadratic triangular elements in science and engineering applications the surface may be identified with a material interface a free boundary or a moving front in the numerical method the geometrical properties of the surface and the coordinates of the triangle vertices are computed either in terms of available analytical expressions or by means of interpolation through an underlying coarse grid the shape and size of the curved triangular elements are determined by the maximum magnitude of the mean or directional local surface curvature two algorithms are implemented the first one for simply connected open surfaces bounded by closed lines and for closed surface with plane symmetry and the second for closed surfaces in the case of open surfaces the discretization front advances from a one dimensional boundary grid that traces the bounding curve the boundary grid is generated either by a one dimensional version of the advancing front method or by requiring a set of criteria based on local line representation with circular arcs in the case of closed surfaces the discretization front emanates from the point of the maximum mean curvature in both cases the algorithm also interpolates to generate the values of surface geometrical or physical variables such as temperature or concentration of a surface active agent the method was tested by following the motion of several passive and active surfaces evolving under the action of specified fields of flow while performing occasional regridding to ensure adequate spatial resolution in one test the large deformation of a viscous drop subjected to an infinite simple shear flow at vanishing reynolds number was computed into the regime where a cigar like shape is established thereby extending previous numerical computations for small and moderate deformations and reproducing experimentally observed shapes overall the adaptive front method emerges as an important tool in numerical studies of free boundaries or moving fronts and should be useful in a broad range of applications

an adaptive mesh algorithm for evolving surfaces simulation of drop breakup and coalescence abstract an algorithm is presented for the adaptive restructuring of meshes on evolving surfaces the resolution of the relevant local length scale is maintained everywhere with prescribed accuracy through the minimization of an appropriate mesh energy function by a sequence of local restructuring operations the resulting discretization depends on the instantaneous configuration of the surface but is insensitive to the deformation history application of the adaptive discretization algorithm is illustrated with three dimensional boundary integral simulations of deformable drops in stokes flow the results show that the algorithm can accurately resolve detailed features of deformed fluid interfaces including slender filaments associated with drop breakup and dimpled regions associated with drop coalescence our algorithm should be useful in a variety of fields including computational fluid dynamics image processing geographical information systems and biomedical engineering problems

a moving mesh finite element algorithm for singular problems in two and three space dimensions a framework for adaptive meshes based on the hamilton schoen yau theory was proposed by dvinsky in a recent work 2001 j comput phys 170 562 588 we extended dvinsky s method to provide an efficient moving mesh algorithm which compared favorably with the previously proposed schemes in terms of simplicity and reliability in this work we will further extend the moving mesh methods based on harmonic maps to deal with mesh adaptation in three space dimensions in obtaining the variational mesh we will solve an optimization problem with some appropriate constraints which is in contrast to the traditional method of solving the euler lagrange equation directly the key idea of this approach is to update the interior and boundary grids simultaneously rather than considering them separately application of the proposed moving mesh scheme is illustrated with some two and three dimensional problems with large solution gradients the numerical experiments show that our methods can accurately resolve detail features of singular problems in 3d

theory of j characteristics for fractional factorial designs and projection justification of minimum g2 aberration deng tang 1999 introduced the generalised resolution and minimum g aberration criteria for assessing nonregular fractional factorials in tang deng 1999 a relaxed variant of minimum g aberration called minimum g 2 aberration is proposed and studied these criteria are defined using a set of j values called j characteristics in this paper we show that a factorial design is uniquely determined by its j characteristics just as a regular factorial design is uniquely determined by its defining relation the theorem is given through an explicit formula that relates the set of design points to that of j characteristics through this formula projection justification of minimum g 2 aberration is established

self adaptive grid method with application to airfoil flow a self adaptive grid method that is suitable for multidimensional steady and unsteady computations is described based on variational principles a spring analogy is used to redistribute grid points in an optimal sense to reduce the overall solution error user specified parameters denoting both maximum and minimum permissible grid spacings are used to define the all important constants thereby minimizing the empiricism and making the method self adaptive operator splitting and one sided controls for orthogonality and smoothness are used to make the method practical robust and efficient examples are included for both steady and unsteady viscous flow computations about airfoils in two dimensions as well as for a steady inviscid flow computation and a one dimensional case these examples illustrate the precise control the user has with the self adaptive method and demonstrate a significant improvement in accuracy and quality of the solutions

lagrange galerkin methods on spherical geodesic grids the weak lagrange galerkin finite element method for the 2d shallow water equations on the sphere is presented this method offers stable and accurate solutions because the equations are integrated along the characteristics the equations are written in 3d cartesian conservation form and the domains are discretized using linear triangular elements the use of linear triangular elements permits the construction of accurate by virtue of the second order spatial and temporal accuracies of the scheme and efficient by virtue of the less stringent cfl condition of lagrangian methods schemes on unstructured domains using linear triangles in 3d cartesian space allows for the explicit construction of area coordinate basis functions thereby simplifying the calculation of the finite element integrals the triangular grids are constructed by a generalization of the icosahedral grids that have been typically used in recent papers an efficient searching strategy for the departure points is also presented for these generalized icosahedral grids which involves very few floating point operations in addition a high order scheme for computing the characteristic curves in 3d cartesian space is presented a general family of runge kutta schemes results for six test cases are reported in order to confirm the accuracy of the scheme

the advancing front mesh generation method revisited this paper presents a mesh generation method of the advancing front type which is designed in such a way that the well known difficulties of the classical advancing front method are not present the retained solution consists of using the first steps of a voronoi delaunay method to construct a background mesh which is then used to govern the algorithm the two dimensional case is considered in detail and possible extensions to adaption problems and three dimensions are indicated

k circulant supersaturated designs a class of supersaturated designs called k circulant designs is explored these designs are constructed from cyclic generators by cycling k elements at a time the class of designs includes many es2 optimal designs some of which are already known and some of which are more efficient than known designs for model estimation under factor sparsity generators for the most efficient designs are listed and projection properties of some of the designs are explored we also illustrate that some k circulant supersaturated designs can be augmented with interaction columns to produce efficient designs for a larger number of factors or for estimating interactions

one hundred years of the design of experiments on and off the pages of biometrika the earliest important papers on planned experiments in biometrika appeared within a year of each other in 1917 and 1918 roughly speaking one was concerned with design optimality and industrial experiments the other with agricultural trials and blocking we find this approximate division of the subject into two parts helpful in describing its development and growth as a result of the hostility between fisher and karl pearson much of the development of designs for agriculture in the 1920s and 1930s occurred off the pages of biometrika despite this we are able to trace a coherent history of the development of the subject from field trials and response surface methods to clinical trials and bayesian versions of design optimality

another look at first order saturated designs the p efficient designs the problem of constructing first order saturated designs that are optimal in some sense has received a great deal of attention in the literature since these saturated designs are frequently used in screening situations the focus will be on the potential projective models rather than the full model this article discusses some practical concerns in choosing a design and presents some first order saturated designs having two desirable properties near equal occurrence and near orthogonality these saturated designs are shown to be reasonably efficient for estimating the parameters of projective submodels and thus are called p efficient designs comparisons with the efficiency of d optimal designs are given for designs for all n from 3 to 30

numerical study of flows of two immiscible liquids at low reynolds number we review our recent results on fingering bamboo waves and drop breakup in low reynolds number flows composed of two viscous liquids under shear

moment aberration projection for nonregular fractional factorial designs nonregular fractional factorial designs such as plackett burman designs are widely used in industrial experiments for run size economy and flexibility a novel criterion called moment aberration projection is proposed to rank and classify nonregular designs it measures the goodness of a design through moments of the number of coincidences between the rows of its projection designs the new criterion is used to rank and classify designs of 16 20 and 27 runs examples are given to illustrate that the ranking of designs is supported by other design criteria

comparison of two mathematical models for solving the dam break problem using the fem method abstract this paper describes and compares two mathematical models for solving the dam break problem using the fem the first method solves the navier stokes equations considering two immiscible and incompressible fluids assigning the density and viscosity according to an indicator function whose zero level set determines the interface position the second method is based on solving the shallow water equations using the well known two step taylor galerkin method in this case the problem becomes one of a drying and wetting one this problem is simply handled by assigning null depth and velocity of the calculated dry nodes when performing the integrals over the elements in the mesh the comparison of the results from the two methods for a number of test cases reveals the shortcomings of the shallow water approach however when considering the computational effort required by each method the shallow water approach should be considered as a major candidate for computations involving large domains leaving the navier stokes approach for fine calculations where knowledge of the 3d structure of the flow is required

projective properties of certain orthogonal arrays summary a question of importance in factor screening is when a two level orthogonal design for a multifactor experiment can be projected into lower dimension typically p 2 or 3 new results relate to the projectivity p of saturated designs in which n 1 factors are tested in n runs it is shown that a design obtained by doubling an n x n orthogonal array is always of projectivity p 2 a twolevel cyclic design is either a factorial array and hence has p 2 or it has p 3 a two level orthogonal design with 4m runs m odd has p 3 in particular these results allow the designs derived by plackett burman 1946 to be categorised in terms of these projective properties

projection properties of plackett and burman designs the projection properties of the 2 r q p fractional factorials are well known and have been used effectively in a number of published examples of experimental investigations the plackett and burman designs also have interesting projective properties knowledge of which allows the experimenter to follow up an initial plackett and burman design with runs that increase the initial resolution for the factors that appear to matter and thus permit efficient separation of effects of interest projections of designs into 2 5 dimensions are discussed and the 12 run case is given in detail a numerical example illustrates the practical uses of these projections

hidden projection properties of some nonregular fractional factorial designs and their applications in factor screening often only a few factors among a large pool of potential factors are active under such assumption of effect sparsity in choosing a design for factor screening it is important to consider projections of the design onto small subsets of factors cheng showed that as long as the run size of a two level orthogonal array of strength two is not a multiple of 8 its projection onto any four factors allows the estimation of all the main effects and two factor interactions when the higher order interactions are negligible this result applies for example to all plackett burman designs whose run sizes are not multiples of 8 it is shown here that the same hidden projection property also holds for paley designs of sizes greater than 8 even when their run sizes are multiples of 8 a key result is that such designs do not have defining words of length three or four applications of this result to the construction of e s 2 optimal supersaturated designs are also discussed in particular certain designs constructed by using wu s method are shown to be e s 2 optimal the article concludes with some three level designs with good projection properties

regridding surface triangulations an advancing front surface gridding technique that operates on discretely defined surfaces i e triangulations is presented different aspects that are required to make the procedure reliable for complex geometries are discussed notable among these are a the recovery of surface features and discrete surface patches from the discrete data b filtering based on point and side normals to remove undesirable data close to cusps and corners c the proper choice of host faces for ridges and d fast interpolation procedures suitable for complex geometries post generation surface recovery or repositioning techniques are discussed several examples ranging from academic to industrial demonstrate the utility of the proposed procedure forab initiosurface meshing from discrete data such as those encountered when the surface description is already given as discrete the improvement of existing surface triangulations as well as remeshing applications during runs exhibiting significant change of domain

projective three level main effects designs robust to model uncertainty this paper is concerned with designing experiments under the assumption that an analysis strategy is used that considers interactions in addition to main effects a criterion which averages an approximation to as efficiency over lower dimensional projections of the design is introduced to compare designs a columnwise design procedure is used to construct three level designs for six factors in 18 runs the projection efficiencies of these designs are explored and compared with designs obtained from the l 18 orthogonal array results are also given for designs with 14 and 17 runs

interfacial dynamics for stokes flow theoretical and computational aspects of the method of interfacial dynamics for flow at vanishing reynolds number are considered the mathematical formulation relies on the boundary integral representation that expresses the flow in terms of distributions of stokes flow singularities over the interfaces the densities of the distributions are identified with the jump in the hydrodynamic traction due to interfacial in plane and transverse tensions the interfacial velocity or the strength of a hydrodynamic potential the numerical procedure involves describing the interfaces in terms of interfacial marker points that reproduce the evolving shapes of the interfaces by global or local interpolation solving integral equations of the second kind for the interfacial velocity or for the density of a hydrodynamic potential and computing the motion of the marker points while simultaneously updating interfacial fields relevant to the dynamics including the concentration of a surfactant and the position of interfacial point particles at an equilibrium configuration interfaces exhibiting isotropic tension elastic tensions viscous and incompressible behavior are considered the mathematical modeling of the tensions and bending moments developing over interfaces with a membrane like constitution is discussed in the context of the theory of thin shells to facilitate the numerical implementation the coupling of the interfacial mechanics to the hydrodynamics by means of interface force and torque balances is formulated in global cartesian coordinates recent progress in the implementation of boundary element methods is reviewed and areas for further research are identified

adaptive remeshing for compressible flow computations an adaptive mesh procedure for improving the quality of steady state solutions of the euler equations in two dimensions is described the procedure is implemented in conjunction with a finite element solution algorithm using linear triangular elements and an explicit time stepping scheme the mesh adaptation is accomplished by regeneration using information provided by the computed solution on the current mesh the meshes produced are characterised by the appearance of stretched elements in the vicinity of one dimensional flow features and can exhibit a large variation in element size this allows solutions of enhanced quality to be produced in a computationally efficient manner