adaptive unstructured volume remeshing ii application to two and three dimensional level set simulations of multiphase flow in part i adaptive unstructured volume remeshing i the method j comput phys in press we presented an adaptive remeshing algorithm that automatically adjusts the size of the elements of meshes of unstructured triangles 2d and unstructured tetrahedra 3d with time and position in the computational domain in order to efficiently resolve the relevant physical scales here we illustrate the performance of an implementation of the algorithm in finite element level set simulations of deformable droplet and fluid fluid interface interactions breakup and coalescence in multiphase flows the wide range of length scales characterizing the dynamics are accurately resolved as demonstrated by comparison to experiments and to theoretical and sharp interface boundary integral numerical results the computational cost is found to be competitive even with respect to boundary integral methods for the first time using an interface capturing level set method we successfully simulate the inertia driven impact and rebound of a liquid droplet from a liquid interface and find agreement with recent experimental results

geometric significance of toeplitz kernels abstract let l 2 be the lebesgue space of square integrable functions on the unit circle we show that the injectivity problem for toeplitz operators is linked to the existence of geodesics in the grassmann manifold of l 2 we also investigate this connection in the context of restricted grassmann manifolds associated to p schatten ideals and essentially commuting projections

three dimensional volume conserving immersed boundary model for two phase fluid flows abstract we present a volume preserving scheme for two phase immiscible incompressible flows using an immersed boundary method ibm in a three dimensional space the two phase ibm employs a mixture of eulerian and lagrangian variables where the fluid interface is represented by discrete lagrangian markers exerting surface tension forces to the eulerian fluid domain and the markers are advected by the fluid velocity the interactions between the lagrangian markers and the fluid variables are linked by the discretized dirac delta function the present study extends the previous two dimensional research li et al volume preserving immersed boundary methods for two phase fluid flows int j numer meth fluids 69 2012 842 858 to the three dimensional space the key idea of the proposed method is relocating surface points along the normal directions to conserve the total volume we perform a number of numerical experiments to show the efficiency and accuracy of the proposed method

self consistent field theory simulations of polymers on arbitrary domains we introduce a framework for simulating the mesoscale self assembly of block copolymers in arbitrary confined geometries subject to neumann boundary conditions we employ a hybrid finite difference volume approach to discretize the mean field equations on an irregular domain represented implicitly by a level set function the numerical treatment of the neumann boundary conditions is sharp i e it avoids an artificial smearing in the irregular domain boundary this strategy enables the study of self assembly in confined domains and enables the computation of physically meaningful quantities at the domain interface in addition we employ adaptive grids encoded with quad oc trees in parallel to automatically refine the grid where the statistical fields vary rapidly as well as at the boundary of the confined domain this approach results in a significant reduction in the number of degrees of freedom and makes the simulations in arbitrary domains using effective boundary conditions computationally efficient in terms of both speed and memory requirement finally in the case of regular periodic domains where pseudo spectral approaches are superior to finite differences in terms of cpu time and accuracy we use the adaptive strategy to store chain propagators reducing the memory footprint without loss of accuracy in computed physical observables

simulations of multiphase flows with multiple length scales using moving mesh interface tracking with adaptive meshing in multiphase flows the length scales of thin regions such as thin films between nearly touching drops and thin threads formed during the interface pinch off are usually several orders of magnitude smaller than the size of the drops in this paper a number of extra length criteria for adaptive meshes are developed and implemented in the moving mesh interface tracking method to solve these multiple length scale problems with high fidelity a nominal length scale based on the solutions of laplace s equations with the unit normal vectors of surfaces as the boundary conditions is proposed for the adaptive mesh refinement in the thin regions for almost flat interfaces boundaries which are near to the thin regions the averaged length of the interior edges sharing the two nodes with the boundary edge is introduced for the mesh adaptation the averaged length of the interfacial edges is used for the interior elements near the interfaces but outside of the thin regions for the interior mesh away from the interfaces boundaries different averaged length scales based on the initial mesh are employed for the adaptive mesh refining and coarsening numerous cases are simulated to demonstrate the capability of the proposed schemes in handling multiple length scales which include the relaxation and necking of an elongated droplet droplet droplet head on approaching droplet wall interactions and a droplet pair in a shear flow the smallest length resolved for the thin regions is three orders of magnitude smaller than the largest characteristic length of the problem

active contours without edges we propose a new model for active contours to detect objects in a given image based on techniques of curve evolution mumford shah 1989 functional for segmentation and level sets our model can detect objects whose boundaries are not necessarily defined by the gradient we minimize an energy which can be seen as a particular case of the minimal partition problem in the level set formulation the problem becomes a mean curvature flow like evolving the active contour which will stop on the desired boundary however the stopping term does not depend on the gradient of the image as in the classical active contour models but is instead related to a particular segmentation of the image we give a numerical algorithm using finite differences finally we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable also the initial curve can be anywhere in the image and interior contours are automatically detected

using powerdomains to generalize relational databases abstract much of relational algebra and the underlying principles of relational database design have a simple representation in the theory of domains that is traditionally used in the denotational semantics of programming languages by investigating the possible orderings on powerdomains that are well known in the study of nondeterminism and concurrency it is possible to show that many of the ideas in relational databases apply to structures that are much more general than relations this also suggests a method of representing database objects as typed objects in programming languages in this paper we show how operations such as natural join and projection which are fundamental to relational database design can be generalized and we use this generalized framework to give characterizations of several relational database concepts including functional dependencies and universal relations all of these have a simple minded semantics in terms of the underlying domains which can be thought of as domains of partial descriptions of real world objects we also discuss the applicability of relational database theory to nonrelational structures such as records with variants higher order relations recursive structures and other ordered spaces

completeness and spectral synthesis of nonselfadjoint one dimensional perturbations of selfadjoint operators abstract we study spectral properties of nonselfadjoint rank one perturbations of compact selfadjoint operators the problems under consideration include completeness of eigenvectors relations between completeness of the perturbed operator and its adjoint and the spectral synthesis problem we obtain new criteria for completeness and spectral synthesis in this class as well as a series of counterexamples which show that the spectral structure of rank one perturbations is in general unexpectedly rich and complicated a parallel spectral theory is developed for one dimensional singular perturbations of unbounded selfadjoint operators our approach is based on a functional model for this class which translates the properties of operators to completeness problems for systems of reproducing kernels and their biorthogonals in some spaces of analytic entire functions

a model space approach to some classical inequalities for rational functions we consider the set mathcal r n of rational functions of degree at most n geq1 with no poles on the unit circle mathbb t and its subclass mathcal r n r consisting of rational functions without poles in the annulus left xi r leq xi leq frac 1 r right we discuss an approach based on the model space theory which brings some integral representations for functions in mathcal r n and their derivatives using this approach we obtain l p analogs of several classical inequalities for rational functions including the inequalities by p borwein and t erdelyi the spijker lemma and s m nikolskii s inequalities these inequalities are shown to be asymptotically sharp as n tends to infinity and the poles of the rational functions approach the unit circle mathbb t

asymptotically orthonormal basis and toeplitz operators abstract recently m mitkovski 13 gave a criterion for basicity of a sequence of complex exponentials in terms of the invertibility properties of a certain naturally associated toeplitz operator in the spirit of work of khrushchev nikolski pavlov 9 in our paper we extend the results of mitkovski to model spaces associated with meromorphic inner functions and we also give an analogue for the property of being an asymptotically orthonormal basis

differentiation in star invariant subspaces i boundedness and compactness abstract given a discrete set c r let r p denote the subspace of lp r generated by rational functions with poles in we determine for which s the differentiation operator d dx r p lp r is bounded or compact

efficient implementation of thinc scheme in this paper we improve the multi dimensional thinc tangent of hyperbola for interface capturing scheme f xiao y honma t kono a simple algebraic interface capturing scheme using hyperbolic tangent function int j numer meth fluid 48 2005 1023 the thinc scheme is a vof volume of fluid type method in the original thinc scheme one dimensional thinc scheme was straightforwardly used for multi dimensional cases in this paper we propose the wlic weighed line interface calculation method to extend the thinc scheme to multi dimension in the wlic method the interface is reconstructed by taking an average of line interfaces along x y and z coordinates with the weights calculated from surface normal the wlic method can extend the thinc scheme to multi dimension while maintaining simplicity of implementation and achieve a higher accuracy than the original thinc scheme the wlic method can readily extend the thinc scheme to three dimension

a simple level set method for solving stefan problems a simple level set method for solving stefan problems is presented this method can be applied to problems involving dendritic solidification our method consists of an implicit finite difference scheme for solving the heat equation and a level set approach for capturing the front between solid and liquid phases of a pure substance our method is accurate with respect to some exact solutions of the stefan problem results indicate that this method can handle topology changes and complicated interfacial shapes and that it can numerically simulate many of the physical features of dendritic solidification

a level set approach for computing solutions to incompressible two phase flow a level set approach for computing solutions to incompressible two phase flow is presented the interface between the two fluids is considered to be sharp and is described as the zero level set of a smooth function a new treatment of the level set method allows us to efficiently maintain the level set function as the signed distance from the interface we never have to explicitly reconstruct or find the zero level set consequently we are able to handle arbitrarily complex topologies large density and viscosity ratios and surface tension on relatively coarse grids we use a second order projection method along with a second order upwinded procedure for advecting the momentum and level set equations we consider the motion of air bubbles and water drops we also compute flows with multiple fluids such as air oil and water

differentiation in star invariant subspaces ii schatten class criteria abstract given an inner function on the upper half plane c let k h 2 h 2 be the corresponding star invariant subspace of the hardy space h 2 earlier we showed that the differentiation operator d dx k l 2 r is bounded iff l r and compact iff c 0 r the current problem is to determine when the above operator belongs to the schatten von neumann class s p the most important cases are p 1 and p 2 and for these p s we solve the problem completely the s 1 and s 2 criteria that arise involve the decay rate of at infinity or alternatively the distribution of the zero sequence z j of moreover explicit formulae for the trace and the hilbert schmidt norm are provided for other values of p we point out some necessary and some sufficient conditions in order that d dx s p the gap is presumably quite small and we are able to eliminate it for special classes of zero sequences z j

spectral gaps for sets and measures if x is a closed subset of the real line denote by gx the supremum of the size of the gap in the fourier spectrum of a measure taken over all non trivial finite complex measures supported on x in this paper we attempt to find gx in terms of x

hereditary completeness for systems of exponentials and reproducing kernels abstract we solve the spectral synthesis problem for exponential systems on an interval namely we prove that any complete and minimal system of exponentials e i n t n n in l 2 a a is hereditarily complete up to a one dimensional defect this means that for any partition n n 1 n 2 of the index set the orthogonal complement to the system e i n t n n 1 e n n n 2 where e n is the system biorthogonal to e i n t is at most one dimensional however this one dimensional defect is possible and thus there exist nonhereditarily complete exponential systems analogous results are obtained for systems of reproducing kernels in de branges spaces for a wide class of de branges spaces we construct nonhereditarily complete systems of reproducing kernels thus answering a question posed by n nikolski

an algebraic synthesis of the foundations of logic and probability abstract this paper develops a unified algebraic theory of logic and probability based upon an initial boolean algebra logic of propositions together with its extensionally associated boolean algebra of models probabilistic events that satisfy the axioms of the boolean algebra of propositions a proposition may be true in some models and false in others but each model must unambiguously assign true or false to each proposition thus the examples models in which different propositions are true may be all some or none according as those propositions are necessary possible or impossible a probability measure p on the collection of models events induces a probability measure on the propositions the crucial if then relation is defined so that p if p then q equals p q p the conditional probability of q given p this conditional probability is less than the probability of the material conditional q or not p unless p p 1 or p q p 1 at these two extremes the two propositional constructions coalesce thus an additional relation q p is needed in logic and probability namely q given p this is accomplished in the algebraic logic generated by the various sum ideals entailments of various propositions that may serve as the explicit condition of a conditional proposition q p the corresponding relation b a in the model realm defines the notion of a conditional event in this context of algebraic logic and model theory a new algebraic structure called the conditional closure l l of a boolean logic l is defined consisting of the ordered pairs q p of all propositions of l excluding those for which the condition p is equivalent to 0 that is impossible the conditional closure is not altogether a boolean algebra not altogether distributive for instance but it has many subalgebras that are boolean including l itself this paper contains partially assumed formulas for operating on the conditional propositions q p using and or not and of course if then this allows complex conditional expressions to be reduced to simple conditionals of boolean propositions which have a conditional probability an example calculation from the dice table illustrates how to simplify a compound conditional proposition and compute its probability the structure of l l is explored including the finite conditional closures of finite boolean logics formulas are given for the probabilistic difference between familiar conditional propositions that are equivalent in the two valued logic where all propositions are either necessary or impossible but not equivalent in the conditional closure of a logic with possible propositions the probability that a proposition p is a theorem true in all models is contrasted from the probability of the models in which the proposition is true the latter being p p while the former is p p 1 this leads to a natural connection with fuzzy set theory since p 1 can also be expressed as p 1 where 1 is the sum ideal filter of necessary propositions given the boolean axioms this paper ends with a representation of each conditional proposition q p as the p measurable two valued truth function of q restricted to those models that satisfy p

deduction with uncertain conditionals uncertain conditional propositions or conditional events pose a special problem for deduction due to their three valued nature true false or inapplicable this three valued ness gives rise to several different kinds of deduction between conditionals depending upon the particular deductive relation being employed there is a hierarchy of 13 deductive relations between conditionals built up from four elementary ones which can be expressed in terms of boolean relations on the components of the conditionals these different but interrelated deductive relations on conditionals in turn give rise to various deductively closed systems of conditionals theorems are proved relating the deductive relations with each other and with their associated deductively closed sets dcss the principal dcs generated by a single conditional using any of the deductive relations is completely characterized except for two of the deductive relations deduction with a finite number of conditionals or with additional conditional information is also completely characterized as the union of associated principal dcss examples of finite sets of deductively closed conditionals are exhibited including many unlike boolean algebra which are finite and yet non principal that is not generated by any one conditional an introductory section carefully provides motivations and a complete algebraic characterization of the four chosen operations on conditional events results are applied to the famous penguin problem

binary level set shape optimization model and algorithm for volumetric modulated arc therapy in radiotherapy treatment we introduce in this paper a variational framework for the construction of improved treatment plans in volumetric modulated arc therapy for cancer treatment this framework consists of a shape optimization component from the molding of beam shapes as well as strong constraints from the equipment involved on both beam shapes and intensities we apply the binary level set method to handle complex shape topologies and the fast sweeping method to handle beam intensity constraints the result is a fast flow based algorithm in a simplified setting that guarantees energy decrease we include numerical simulations of clinical cases to demonstrate the efficacy of the approach

semi implicit second order schemes for numerical solution of level set advection equation on cartesian grids abstract a new parametric class of semi implicit numerical schemes for a level set advection equation on cartesian grids is derived and analyzed an accuracy and a stability study is provided for a linear advection equation with a variable velocity using partial lax wendroff procedure and numerical von neumann stability analysis the obtained semi implicit scheme is 2nd order accurate in space and time in any dimensional case when using a dimension by dimension extension of the one dimensional scheme that is not the case for analogous fully explicit or fully implicit schemes a further improvement is obtained by using so called corner transport upwind extension in two dimensional case the extended semi implicit scheme with a specific velocity dependent value of is 3rd order accurate in space and time for a constant advection velocity and it is unconditional stable according to the numerical von neumann stability analysis for the linear advection equation in general

new cartesian grid methods for interface problems using the finite element formulation new finite element methods based on cartesian triangulations are presented for two dimensional elliptic interface problems involving discontinuities in the coefficients the triangulations in these methods do not need to fit the interfaces the basis functions in these methods are constructed to satisfy the interface jump conditions either exactly or approximately both non conforming and conforming finite element spaces are considered corresponding interpolation functions are proved to be second order accurate in the maximum norm the conforming finite element method has been shown to be convergent with cartesian triangulations these new methods can be used as finite difference methods numerical examples are provided to support the methods and the theoretical analysis

the mixed powerdomain this paper introduces an operator m called the mixed powerdomain which generalizes the convex plotkin powerdomain the construction is based on the idea of representing partial information about a set of data items using a pair of sets one representing partial information in the manner of the upper smyth powerdomain and the other in the manner of the lower hoare powerdomain where the components of such pairs are required to satisfy a consistency condition this provides a richer family of meaningful partial descriptions than are available in the convex powerdomain and also makes it possible to include the empty set in a satisfactory way the new construct is given a rigorous mathematical treatment like that which has been applied to the known powerdomains it is proved that m is a continuous functor on bifinite domains which is left adjoint to the forgetful functor from a category of continuous structures called mix algebras for a domain d with a coherent scott topology elements of md can be represented as pairs u v where u d is a compact upper set v d is a closed set and the downward closure of u v is equal to v a stone dual characterization of m is also provided

classification using geometric level sets a variational level set method is developed for the supervised classification problem nonlinear classifier decision boundaries are obtained by minimizing an energy functional that is composed of an empirical risk term with a margin based loss and a geometric regularization term new to machine learning the surface area of the decision boundary this geometric level set classifier is analyzed in terms of consistency and complexity through the calculation of its e entropy for multicategory classification an efficient scheme is developed using a logarithmic number of decision functions in the number of classes rather than the typical linear number of decision functions geometric level set classification yields performance results on benchmark data sets that are competitive with well established methods

conditional logic and the principle of entropy abstract the conditional three valued logic of calabrese is applied to the language l of conditionals on propositional variables with finite domain the conditionals in l serve as a means for the construction and manipulation of probability distributions respecting the principle of maximum entropy and of minimum relative entropy this principle allows a sound inference even in the presence of uncertain evidence the inference is directed it respects a probabilistic version of modus ponens not of modus tollens it permits transitive chaining and supports a cautious monotony conjunctive conditional and material deduction are manageable in this probabilistic logic too the concept is not merely theoretical but enables large scale applications in the expert system shell spirit

a spectral szegő theorem on the real line abstract we characterize even measures w d x s on the real line r with finite entropy integral r log w t 1 t 2 d t in terms of 2 2 hamiltonians generated by in the sense of the inverse spectral theory as a corollary we obtain criterion for spectral measure of krein string to have converging logarithmic integral

geometry of reproducing kernels in model spaces near the boundary we study two geometric properties of reproducing kernels in model spaces k theta where theta is an inner function in the disc overcompleteness and existence of uniformly minimal systems of reproducing kernels which do not contain riesz basic sequences both of these properties are related to the notion of the ahern clark point it is shown that uniformly minimal non riesz sequences of reproducing kernels exist near each ahern clark point which is not an analyticity point for theta while overcompleteness may occur only near the ahern clark points of infinite order and is equivalent to a zero localization property in this context the notion of quasi analyticity appears naturally and as a by product of our results we give conditions in the spirit of ahern clark for the restriction of a model space to a radius to be a class of quasi analyticity

a self adaptive oriented particles level set method for tracking interfaces a new method for tracking evolving interfaces by lagrangian particles in conjunction with a level set approach is introduced this numerical technique is based on the use of time evolution equations for fundamental vector and tensor quantities defined on the front and represents a new and convenient way to couple the advantages of the eulerian description given by a level set function f to the use of lagrangian massless particles the term oriented points out that the information advected by the particles not only concern the spatial location but also the local outward normal vector n to the interface c and the second fundamental tensor the shape operator n the particles are exactly located upon c and provide all the requested information for tracking the interface on their own in addition a self adaptive mechanism suitably modifies at each time step the markers distribution in the numerical domain each particle behaves both as a potential seeder of new markers on c so as to guarantee an accurate reconstruction of the interface and a de seeder to avoid any useless gathering of markers and to limit the computational effort the algorithm is conceived to avoid any transport equation for f and to confine the level set function to the role of a mere post processing tool thus all the numerical diffusion problems usually affecting the level set methodology are removed the method has been tested both on 2d and 3d configurations it carries out a fast reconstruction of the interface and its accuracy is only limited by the spatial resolution of the mesh

stable power domains abstract in the category of stable dcpo s free constructions w r t algebraic theories exist from this we obtain various stable power domain constructions after handling their properties in general we concentrate on the stable plotkin power construction for continuous ground domains it is explicitly described in terms of saturated compact sets in case of algebraic ground domains this description is isomorphic to buneman s lossless power domains

topology optimization of steady navier stokes flow with body force abstract this paper presents the topology optimization of steady navier stokes flows with body forces that influence the optimal shape and topology of fluid flows based on the implicit expression of the fluid flow with the level set method an optimization problem is formulated and analyzed using the continuous adjoint method the shape and topological sensitivities are computed based on the adjoint and asymptotic analysis of the optimization problem in the optimization procedure the level set surface is evolved based on the shape sensitivity and nucleated based on the topological sensitivity simultaneously three kinds of body forces that are commonly used in the design of fluid devices i e constant nonuniform and solution dependent body forces are considered in the two dimensional and three dimensional numerical examples numerical results demonstrate that this method can effectively achieve the topology optimization of the navier stokes flows with body forces

a binary level set model and some applications to mumford shah image segmentation in this paper we propose a pde based level set method traditionally interfaces are represented by the zero level set of continuous level set functions instead we let the interfaces be represented by discontinuities of piecewise constant level set functions each level set function can at convergence only take two values i e it can only be 1 or 1 thus our method is related to phase field methods some of the properties of standard level set methods are preserved in the proposed method while others are not using this new method for interface problems we need to minimize a smooth convex functional under a quadratic constraint the level set functions are discontinuous at convergence but the minimization functional is smooth we show numerical results using the method for segmentation of digital images

bernstein type inequalities for shift coinvariant subspaces and their applications to carleson embeddings abstract we study weighted norm inequalities for the derivatives bernstein type inequalities in the shift coinvariant subspaces k p of the hardy class h p in the upper half plane it is shown that the differentiation operator acts from k p to certain spaces of the form l p w where the weight w x depends on the density of the spectrum of near the point x of the real line we discuss an application of the bernstein type inequalities to the problems of the description of measures for which k p l p and of compactness of such embeddings new versions of carleson type embedding theorems are obtained generalizing the theorems due to w s cohn and a l volberg s r treil

a contoured continuum surface force model for particle methods a surface tension model is essential to simulate multiphase flows with deformed interfaces this study develops a contoured continuum surface force ccsf model for particle methods a color function that varies sharply across the interface to mark different fluid phases is smoothed in the transition region where the local contour curvature can be regarded as the interface curvature the local contour passing through each reference particle in the transition region is extracted from the local profile of the smoothed color function the local contour curvature is calculated based on the taylor series expansion of the smoothed color function whose derivatives are calculated accurately according to the definition of the smoothed color function two schemes are proposed to specify the smooth radius fixed scheme where 2 r e r e particle interaction radius is assigned to all particles in the transition region and varied scheme where r e and 2 r e are assigned to the central and edged particles in the transition region respectively numerical examples including curvature calculation for static circle and ellipse interfaces deformation of square droplet to a circle 2d and 3d droplet deformation in shear flow and droplet coalescence are simulated to verify the ccsf model and compare its performance with those of other methods the ccsf model with the fixed scheme is proven to produce the most accurate curvature and lowest parasitic currents among the tested methods

a semi lagrangian particle level set finite element method for interface problems we present a quasi monotone semi lagrangian particle level set qmsl pls method for moving interfaces the qmsl method is a blend of first order monotone and second order semi lagrangian methods the qmsl pls method is easy to implement efficient and well adapted for unstructured either simplicial or hexahedral meshes we prove that it is unconditionally stable in the maximum discrete norm parallel cdot parallel h infty and the error analysis shows that when the level set solution u t is in the sobolev space w r 1 infty d r geq 0 the convergence in the maximum norm is of the form kt delta t min 1 delta t parallel v parallel h infty h 1 alpha h p h q p min 2 r 1 and q min 3 r 1 where v is a velocity this means that at high cfl numbers that is when delta t h the error is o frac 1 alpha h p h q delta t whereas at cfl numbers less than 1 the error is o 1 alpha h p 1 h q 1 we have tested our method with satisfactory results i

weighted norm inequalities for de branges rovnyak spaces and their applications let h b denote the de branges rovnyak space associated with a function b in the unit ball of h 1 c we study the boundary behavior of the derivatives of functions in h b and obtain weighted norm estimates of the form k f n k l2 ck f k h b where f h b and is a carleson type measure on c r we provide several applications of these inequalities we apply them to obtain embedding theorems for h b spaces these results extend cohn and volberg treil embedding theorems for the model star invariant subspaces which are special classes of de branges rovnyak spaces we also exploit the inequalities for the derivatives to study stability of riesz bases of reproducing kernels k bn in h b under small perturbations of the pointsn

level set reinitialization at a contact line when a level set signed distance function is reinitialized in the vicinity of a contact line there is a blind spot that prevents an accurate reconstruction of a signed distance function the numerical method can create parasitic velocity currents near this region if additional contact line physics are included the parasitic velocity currents would pollute the solution and alter the physical behavior in this study a modified reinitialization routine is proposed that combines the standard hamilton jacobi equation with a relaxation equation for those grid cells along a wall in the blind spot two test cases an angled fluid wedge zero curvature and a circular fluid arc constant curvature are used to evaluate the numerical error induced by different methods the proposed method has less numerically induced interface distortion than other techniques examined furthermore this routine can be easily extended to three dimensions drops sliding on a wall are simulated in both two and three dimensions to demonstrate the advantages of this method a spreading fluid interface further shows that this method allows contact lines to merge naturally

a weak formulation for solving elliptic interface problems without body fitted grid a typical elliptic interface problem is casted as piecewise defined elliptic partial differential equations pde in different regions which are coupled together with interface conditions such as jumps in solution and flux across the interface in many situations such as the interface is moving the challenge is how to solve such a problem accurately robustly and efficiently without generating a body fitted mesh the key issue is how to capture complex geometry of the interface and jump conditions across the interface effectively on a fixed mesh while the interface is not aligned with the mesh and the pde is not valid across the interface in this work we present a systematic formulation and further study of a second order accurate numerical method proposed in hou and liu 2005 16 for elliptic interface problem the key idea is to decompose the solution into two parts a singular part and a regular part the singular part captures the interface conditions while the regular part belongs to an appropriate space in the whole domain which can be solved by a standard finite element formulation in a general setup the two parts are coupled together we give an explicit study of the construction of the singular part and the discretized system for the regular part one key advantage of using weak formulation is that one can avoid assuming using more regularity than necessary of the solution and the interface we present the numerical algorithm and numerical tests in 3d to demonstrate the accuracy and other properties of our method

kernels and spectrum of toeplitz operators on the dirichlet space abstract in this paper we study the spectrum of toeplitz operators on the dirichlet space d with bounded conjugate analytic symbols and give a characterization of the kernels of toeplitz operators with harmonic symbols in p m d using this characterization we show that the spectrum of a toeplitz operator with symbol the sum of an analytic polynomial with degree at most two and the conjugate of linear polynomial is connected but there are toeplitz operators with general harmonic polynomial symbols having disconnected spectrum

the category theoretic solution of recursive domain equations recursive specifications of domains plays a crucial role in denotational semantics as developed by scott and strachey and their followers the purpose of the present paper is to set up a categorical framework in which the known techniques for solving these equations find a natural place the idea is to follow the well known analogy between partial orders and categories generalizing from least fixed points of continuous functions over cpos to initial ones of continuous functors over omega categories to apply these general ideas we introduce wand s bf o categories where the morphism sets have a partial order structure and which include almost all the categories occurring in semantics the idea is to find solutions in a derived category of embeddings and we give order theoretic conditions which are easy to verify and which imply the needed categorical ones the main tool is a very general form of the limit colimit coincidence remarked by scott in the concluding section we outline how compatibilit

a fast high resolution algorithm for linear convection problems particle transport method the paper is devoted to a novel explicit technique the particle transport method ptm for solving linear convection problems while being a lagrangian characteristic based method ptm has the advantage of eulerian methods to represent the solution on a fixed mesh the proposed approach belongs to the class of monotone high resolution numerical schemes possesses the property of unconditional stability and works with structured and unstructured meshes it is also demonstrated that the method has a linear computational complexity the performance of the presented algorithm is tested on one and two dimensional benchmark problems the numerical results confirm that the method has the 2nd order spatial accuracy and can be significantly faster than the grid based methods of the same order copyright 2006 john wiley sons ltd

on powerdomains and modality abstract this note shows a simple connection between powerdomains and modal assertions that can be made about nondeterministic computations we consider three kinds of powerdomains the plotkin powerdomain the smyth powerdomain and one christened the hoare powerdomain by plotkin because it captures the partial correctness of a nondeterministic program the modal operators are for inevitably and for possibly it is shown in a precise sense how the smyth powerdomain is built up from assertions about the inevitable behaviour of a process the hoare powerdomain is built up from assertions about the possible behaviour of a process while the plotkin powerdomain is built up from both kinds of assertions taken together

free surface flows under impacting droplets a numerical method which fulfils the free surface boundary conditions and extrapolates the fluid velocity into empty grid cells outside the fluid region on a fixed cartesian grid system is presented the complex three dimensional vortex structures formed via surface vortex interaction and induction between vortices have been computed using the proposed technique implemented within a level set method for both vertical and oblique droplet impacts in incompressible fluids the present results have been validated through numerical tests which confirm zero tangential shear at the free surface and comparisons with experimental observations of cavity and vortex ring formation underneath the impact location in some cases transitions from a concentric vortex ring to a fully three dimensional vortex structure has been confirmed whilst the primary vortex ring is initiated at the highly curved contact surface between the droplet and receiving surface azimuthal instabilities are manifested in the shear layer around the cavity crater developing after the vertical impact resulting in axial counter rotating vorticity between the cavity and descending vortex ring underlying mechanisms which induce local deformation of the free surface creating a so called scar due to the sub surface vortices at the oblique impacts are also discussed

new aspects of beurling lax shift invariant subspaces in terms of forward and backward shift invariant subspaces we characterize functions in hardy spaces or analytic signals in the terminology of signal analysis through multiplications between analytic and conjugate analytic signals as applications we give some necessary and sufficient conditions for solutions of the bedrosian equation h fg f hg when f or g is a bandlimited signal we also solve the band preserving problem by means of the shift invariant subspace method which establishes some necessary and sufficient conditions on the functions f that make fg have bandwidth within that of the function g

a quick construction of a retraction of all retractions for stable bifinites in the framework of stable domain theory we show that the space of retractions over a bifinite is a retract of the functional space

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

cmv matrices with asymptotically constant coefficients szego blaschke class scattering theory abstract we develop a modern extended scattering theory for cmv matrices with asymptotically constant verblunsky coefficients we show that the traditional faddeev marchenko condition is too restrictive to define the class of cmv matrices for which there exists a unique scattering representation the main results are 1 the class of twosided cmv matrices acting in l 2 whose spectral density satisfies the szego condition and whose point spectrum the blaschke condition corresponds precisely to the class where the scattering problem can be posed and solved that is to a given cmv matrix of this class one can associate the scattering data and the fm space the cmv matrix corresponds to the multiplication operator in this space and the orthonormal basis in it corresponding to the standard basis in l 2 behaves asymptotically as the basis associated with the free system 2 from the point of view of the scattering problem the most natural class of cmv matrices is that one in which a the scattering data determine the matrix uniquely and b the associated gelfand levitan marchenko transformation operators are bounded necessary and sufficient conditions for this class can be given in terms of an a 2 kind condition for the density of the absolutely continuous spectrum and a carleson kind condition for the discrete spectrum similar conditions close to the optimal ones are given directly in terms of the scattering data

notions of computation and monads abstract the calculus is considered a useful mathematical tool in the study of programming languages since programs can be identified with terms however if one goes further and uses conversion to prove equivalence of programs then a gross simplification is introduced programs are identified with total functions from values to values that may jeopardise the applicability of theoretical results in this paper we introduce calculi based on a categorical semantics for computations that provide a correct basis for proving equivalence of programs for a wide range of notions of computation

beurling malliavin theory for toeplitz kernels we consider the family of toeplitz operators t j bar s a acting in the hardy space h2 in the upper halfplane j and s are given meromorphic inner functions and a is a real parameter in the case where the argument of s has a power law type behavior on the real line we compute the critical value c j s inf left a mathop mathrm ker t j bar s a ne0 right the formula for c j s generalizes the beurling malliavin theorem on the radius of completeness for a system of exponentials

power domains and second order predicates abstract lower upper sandwich mixed and convex power domains are isomorphic to domains of second order predicates mapping predicates on the ground domain to logical values in a semiring the various power domains differ in the nature of the underlying semiring logic and in logical constraints on the second order predicates

a problem on completeness of exponentials let be a nite positive measure on the real line for a 0 denote by ea the family of exponential functions ea fe ist j s2 0 a g

finite element simulation of single crystal growth process using gsmac method abstract the characteristics of the melt convection and the melt deformation process in two crystal growth techniques czochralski cz and floating zone fz methods are investigated with three dimensional numerical simulation using generalized simplified marker and cell finite element method gsmac fem large eddy simulation les with the smagorinsky model is applied to calculate the melt convection with high rayleigh numbers in the cz method and level set method lsm is adopted for the computation of liquid bridge deformation first the cz lsm melt convections are investigated with the boundary conditions in terms of the free surface and the rotational rate changed as a result it is found that the heat radiation and the marangoni effect on the free surface encourage the instability of flows and the coriolis force can largely suppress the natural convection second a series of simulations in terms of liquid bridge deformation are carried out with the coil position coil shape and the magnitude of surface tension varied after that it turns out that those are important factors in the melt shape moreover it is proved numerically that the deformation of the liquid bridge is kept small by the skin effect and large surface tension in the real fz crystal growth

numerical simulation of free surface incompressible liquid flows surrounded by compressible gas a numerical model for the three dimensional simulation of liquid gas flows with free surfaces is presented the incompressible navier stokes equations are assumed to hold in the liquid domain in the gas domain the velocity is disregarded the pressure is supposed to be constant in each connected component of the gas domain and follows the ideal gas law the gas pressure is imposed as a normal force on the liquid gas interface an implicit splitting scheme is used to decouple the physical phenomena given the gas pressure on the interface the method described in j comput phys 155 1999 439 int j numer meth fluids 42 7 2003 697 is used to track the liquid domain and to compute the velocity and pressure fields in the liquid then the connected components of the gas domain are found using an original numbering algorithm finally the gas pressure is updated from the ideal gas law in each connected component of gas the implementation is validated in the frame of mould filling numerical results in two and three space dimensions show that the effect of pressure in the bubbles of gas trapped by the liquid cannot be neglected

the extended finite element method xfem for solidification problems an enriched finite element method for the multi dimensional stefan problems is presented in this method the standard finite element basis is enriched with a discontinuity in the derivative of the temperature normal to the interface the approximation can then represent the phase interface and the associated discontinuity in the temperature gradient within an element the phase interface can be evolved without re meshing or the use of artificial heat capacity techniques the interface is described by a level set function that is updated by a stabilized finite element scheme several examples are solved by the proposed method to demonstrate the accuracy and robustness of the method copyright 2001 john wiley sons ltd

global minimum for active contour models a minimal path approach a new boundary detection approach for shape modeling is presented it detects the global minimum of an active contour model s energy between two end points initialization is made easier and the curve is not trapped at a local minimum by spurious edges we modify the snake energy by including the internal regularization term in the external potential term our method is based on finding a path of minimal length in a riemannian metric we then make use of a new efficient numerical method to find this shortest path it is shown that the proposed energy though based only on a potential integrated along the curve imposes a regularization effect like snakes we explore the relation between the maximum curvature along the resulting contour and the potential generated from the image the method is capable to close contours given only one point on the objects boundary by using a topology based saddle search routine we show examples of our method applied to real aerial and medical images

divergence of gradient convolution deformable segmentation with arbitrary initializations in this paper we propose a unified approach to deformable model based segmentation the fundamental force field of the proposed method is based on computing the divergence of a gradient convolution field gcf which makes the full use of directional information of the image gradient vectors and their interactions across image domain however instead of directly using such a vector field for deformable segmentation as in the conventional approaches we derive a more salient representation for contour evolution and very importantly we demonstrate that this representation of image force field not only leads to global minimum through convex relaxation but also can achieve the same result using the conventional gradient descent with an intrinsic regularization thus the proposed method can handle arbitrary initializations the proposed external force field for deformable segmentation has both edge based properties in that the gcf is computed from image gradients and the region based attributes since its divergence can be treated as a region indication function moreover nonlinear diffusion can be conveniently applied to gcf to improve its performance in dealing with noise interference we also show the extension of gcf from 2d to 3d in comparison to the state of the art deformable segmentation techniques the proposed method shows greater flexibility in model initialization and optimization realization as well as better performance toward noise interference and appearance variation

computations of two fluid models based on a simple and robust hybrid primitive variable riemann solver with ausmd this paper is to continue our previous work in 2008 on solving a two fluid model for compressible liquid gas flows we proposed a pressure velocity based diffusion term original derived from ausmd scheme of wada and liou in 1997 to enhance its robustness the proposed ausmd schemes have been applied to gas and liquid fluids universally to capture fluid discontinuities such as the fluid interfaces and shock waves accurately for the ransom s faucet problem air water shock tube problems and 2d shock water liquid interaction problems however the proposed scheme failed at computing liquid gas interfaces in problems under large ratios of pressure density and volume of fraction the numerical instability has been remedied by chang and liou in 2007 using the exact riemann solver to enhance the accuracy and stability of numerical flux across the liquid gas interface here instead of the exact riemann solver we propose a simple ausmd type primitive variable riemann solver pvrs which can successfully solve 1d stiffened water air shock tube and 2d shock gas interaction problems under large ratios of pressure density and volume of fraction without the expensive cost of tedious computer time in addition the proposed approach is shown to deliver a good resolution of the shock front rarefaction and cavitation inside the evolution of high speed droplet impact on the wall

toeplitz operators and arguments of analytic functions for a toeplitz operator t we study the interrelationship between smoothness properties of the symbol and those of the functions annihilated by t for instance it follows from our results that if is a unimodular function on the circle lying in some lipschitz or zygmund space with 0 and if f is an hp function p 1 with t f 0 then f and f lambda a le c varphi d lambda a f p for some c c p and d d p an explicit formula for the optimal exponent d is provided similar and more general results for various smoothness classes are obtained and several approaches are discussed furthermore since a given non null function f hp lies in the kernel of t psi with psi bar z bar f f we derive information on the smoothness of hp functions with smooth arguments this can be viewed as a natural counterpart to the existing theory of analytic functions with smooth moduli

a fixed grid sharp interface method for bubble dynamics and phase change abstract a numerical method has been developed for direct simulation of bubble dynamics with large liquid to vapor density ratio and phase change the numerical techniques are based on a fixed grid finite volume method capable of treating the interface as a sharp discontinuity the unsteady axisymmetric navier stokes equations and energy equation in both liquid and vapor phases are computed the mass momentum and energy conditions are explicitly matched at the phase boundary to determine the interface shape and movement the cubic b spline is used in conjunction with a fairing algorithm to yield smooth and accurate information of curvatures nondimensional parameters including reynolds weber and jakob numbers are varied to offer insight into the physical and numerical characteristics of the bubble dynamics based on the present sharp interface approach bubble dynamics for density ratio of 1600 or higher with and without phase change can be successfully computed

universal profinite domains abstract we introduce a bicartesian closed category of what we call profinite domains study of these domains is carried out through the use of an equivalent category of pre orders in a manner similar to the information systems approach advocated by dana scott and others a class of universal profinite domains is defined and used to derive sufficient conditions for the profinite solution of domain equations involving continuous operators as a special instance of this construction a universal domain for the category sfp is demonstrated necessary conditions for the existence of solutions for domain equations over the profinites are also given and used to derive results about solutions of some equations a new universal bounded complete domain is also demonstrated using an operator which has bounded complete domains as its fixed points