stabilization of a class of stochastic differential equations with markovian switching stability of stochastic differential equations with markovian switching has been studied quite extensively for a number of years for example by basak et al j math anal appl 202 1996 604 622 ji and chizeck ieee trans automat control 35 1990 777 788 mariton jump linear systems in automatic control marcel dekker new york 1990 mao et al stochastic process appl 79 1999 45 67 bernoulli 6 2000 73 90 and yuan and lygeros in r alur g pappas eds hybrid systems computation and control seventh international workshop hscc 2004 lecture notes in computer science vol 2993 springer berlin 2004 pp 646 659 by contrast the problem of designing controllers to stabilize systems of this type has received relatively little attention in this paper we study the problem of mean square exponential stabilization for a class of stochastic differential equations with markovian switching

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

algorithm for direct numerical simulation of emulsion flow through a granular material a multipole accelerated 3d boundary integral algorithm capable of modelling an emulsion flow through a granular material by direct multiparticle multidrop simulations in a periodic box is developed and tested the particles form a random arrangement at high volume fraction rigidly held in space including the case of an equilibrium packing in mechanical contact deformable drops with non deformed diameter comparable with the particle size squeeze between the particles under a specified average pressure gradient the algorithm includes recent boundary integral desingularization tools especially important for drop solid and drop drop interactions the hebeker representation for solid particle contributions and unstructured surface triangulations with fixed topology multipole acceleration with two levels of mesh node decomposition entire drop solid surfaces and patches is a significant improvement over schemes used in previous purely multidrop simulations it remains efficient at very high resolutions 10 4 10 5 triangular elements per surface and has no lower limitation on the number of particles or drops such resolutions are necessary in the problem to alleviate lubrication difficulties especially for near critical squeezing conditions as well as using 10 4 time steps and an iterative solution at each step both for contrast and matching viscosities examples are shown for squeezing of 25 40 drops through an array of 9 14 solids with the total volume fraction of 70 for particles and drops the flow rates for the drop and continuous phases are calculated extensive convergence testing with respect to program parameters triangulation multipole truncation etc is made

accurate projection methods for the incompressible navier stokes equations abstract this paper considers the accuracy of projection method approximations to the initial boundary value problem for the incompressible navier stokes equations the issue of how to correctly specify numerical boundary conditions for these methods has been outstanding since the birth of the second order methodology a decade and a half ago it has been observed that while the velocity can be reliably computed to second order accuracy in time and space the pressure is typically only first order accurate in the l norm this paper identifies the source of this problem in the interplay of the global pressure update formula with the numerical boundary conditions and presents an improved projection algorithm which is fully second order accurate as demonstrated by a normal mode analysis and numerical experiments in addition a numerical method based on a gauge variable formulation of the incompressible navier stokes equations which provides another option for obtaining fully second order convergence in both velocity and pressure is discussed the connection between the boundary conditions for projection methods and the gauge method is explained in detail

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

a projection algorithm for general variational inequalities with perturbed constraint sets we consider the problem of general variational inequalities gvi with nonmonotone operator in a finite dimensional space we propose a method to solve gvi that at each iteration considers only one projection on an easy approximation of the constraint set which is important from a practical point of view we analyse the convergence of the algorithm under a weak cocoercivity condition using variational metric analysis computational experience is reported and comparative analysis with other two algorithms is also given for the monotone case

an extended pressure finite element space for two phase incompressible flows with surface tension we consider a standard model for incompressible two phase flows in which a localized force at the interface describes the effect of surface tension if a level set or vof method is applied then the interface which is implicitly given by the zero level of the level set function is in general not aligned with the triangulation that is used in the discretization of the flow problem this non alignment causes severe difficulties w r t the discretization of the localized surface tension force and the discretization of the flow variables in cases with large surface tension forces the pressure has a large jump across the interface in standard finite element spaces due to the non alignment the functions are continuous across the interface and thus not appropriate for the approximation of the discontinuous pressure in many simulations these effects cause large oscillations of the velocity close to the interface so called spurious velocities in this paper for a simplified model problem we give an analysis that explains why known standard methods for discretization of the localized force term and for discretization of the pressure variable often yield large spurious velocities in the paper s grosz a reusken finite element discretization error analysis of a surface tension force in two phase incompressible flows preprint 262 igpm rwth aachen siam j numer anal accepted for publication we introduce a new and accurate method for approximation of the surface tension force in the present paper we use the extended finite element space xfem presented in n moes j dolbow t belytschko a finite element method for crack growth without remeshing int j numer meth eng 46 1999 131 150 t belytschko n moes s usui c parimi arbitrary discontinuities in finite elements int j numer meth eng 50 2001 993 1013 for the discretization of the pressure we show that the size of spurious velocities is reduced substantially provided we use both the new treatment of the surface tension force and the extended pressure finite element space

phase field simulations of interfacial dynamics in viscoelastic fluids using finite elements with adaptive meshing this paper describes a novel numerical algorithm for simulating interfacial dynamics of non newtonian fluids the interface between two immiscible fluids is treated as a thin mixing layer across which physical properties vary steeply but continuously the property and evolution of the interfacial layer is governed by a phase field variable that obeys a cahn hilliard type of convection diffusion equation this circumvents the task of directly tracking the interface and produces the correct interfacial tension from the free energy stored in the mixing layer viscoelasticity and other types of constitutive equations can be incorporated easily into the variational phase field framework the greatest challenge of this approach is in resolving the sharp gradients at the interface this is achieved by using an efficient adaptive meshing scheme governed by the phase field variable the finite element scheme easily accommodates complex flow geometry and the adaptive meshing makes it possible to simulate large scale two phase systems of complex fluids in two dimensional and axisymmetric three dimensional implementations the numerical toolkit is applied here to drop deformation in shear and elongational flows rise of drops and retraction of drops and torii some of these solutions serve as validation of the method and illustrate its key features while others explore novel physics of viscoelasticity in the deformation and evolution of interfaces

global and superlinear convergence of the smoothing newton method and its application to general box constrained variational inequalities the smoothing newton method for solving a system of nonsmooth equations f x 0 which may arise from the nonlinear complementarity problem the variational inequality problem or other problems can be regarded as a variant of the smoothing method at the kth step the nonsmooth function f is approximated by a smooth function f and the derivative of f at x k is used as the newton iterative matrix the merits of smoothing methods and smoothing newton methods are global convergence and convenience in handling in this paper we show that the smoothing newton method is also superlinearly convergent if f is semismooth at the solution and f satisfies a jacobian consistency property we show that most common smooth functions such as the gabriel more function have this property as an application we show that for box constrained variational inequalities if the involved function is p uniform the iteration sequence generated by the smoothing newton method will converge to the unique solution of the problem globally and superlinearly quadratically

on error estimates of the projection methods for the navier stokes equations second order schemes we present in this paper a rigorous error analysis of several projection schemes for the approximation of the unsteady incompressible navier stokes equations the error analysis is accomplished by interpreting the respective projection schemes as second order time discretizations of a perturbed system which approximates the navier stokes equations numerical results in agreement with the error analysis are also presented

brief paper on almost sure stability of continuous time markov jump linear systems in this paper we study the almost sure stability of continuous time jump linear systems with a finite state markov form process a sufficient condition for almost sure stability is derived that refers to the statistics of the transition matrix over m switches it is shown that if the system is exponentially almost sure stable there exists a finite m such that the criterion is satisfied in order to evaluate the expected value appearing in the condition an efficient monte carlo algorithm is worked out

a gradient augmented level set method for unstructured grids we present and test a gradient augmented level set method for unstructured grids which has been designed to allow for easy integration in parallel flow solvers the means to this end is a hermite formulation where the gradient is stored and advected as an independent variable along with the level set function the method uses narrow band storage in conjunction with a fast marching method which is also designed to take advantage of the gradient augmentation we demonstrate through standard passive advection test cases that the proposed method is able to compute interface motion with performance comparable to popular high performing methods on structured grids

new finite element finite volume level set formulation for modelling two phase incompressible flows we present a new level set method for modelling two phase incompressible flows with moving interface boundaries the method is based on a finite element fe treatment of the equations governing the motion of the interface separating two immiscible phases and a finite volume fv description of the fluid flow equations the performance of the method is demonstrated and validated using several sample problems involving two phase isothermal flows with density ratios of the order of 102 103 and viscosity ratios as high as 7 104 surface tension effects are included the present formulation displays good convergence properties and it is relatively simple to program this allows the method to be implemented into existing commercial fv based computational fluid dynamics cfd software thereby extending their application range we have successfully implemented the method in the code cfx 4

on a generalization of a normal map and equation the class of normal maps was recently investigated by robinson and ralph in connection with the study of a variational inequality defined on a polyhedral set in this paper a generalization of such a map is considered and the associated generalized normal equation is studied the latter provides a unified formulation of several generalized variational inequality and complementarity problems using degree theory some sufficient conditions for the existence of a zero of a generalized normal map are established and the stability of a generalized normal equation at a solution is analyzed specializations of the results to various applications are discussed

implicit tracking for multi fluid simulations in this work we introduce a new method for tracking the interfaces among several immiscible fluids to advance the solution in time we use a muscl type scheme which couples a partial volume representation with a level set one to build the numerical fluxes in particular we show the positiveness and conservation properties of this method some numerical tests are given to demonstrate the conservativeness and the performances of our method

stochastic versions of the lasalle theorem the main aim of this paper is to establish stochastic versions of the well known lasalle stability theorem from these stochastic versions follow many classical results on stochastic stability this shows clearly the power of our new results

local remeshing for large amplitude grid deformations fluid structure interaction fsi modelling can involve large deformations in the fluid domain which could lead to degenerating mesh quality and numerical inaccuracies or instabilities if allowed to amplify unchecked complete remeshing of the entire domain during the solution process is computationally expensive and can require interpolation of solution variables between meshes as an alternative we investigate a local remeshing algorithm with two emphases a the identification and remedy of flat degenerate tetrahedra and b the avoidance of node motion and hence associated interpolation errors initially possible topological changes are examined using a dynamic programming algorithm to maximise the minimum local element quality through edge reconnection in the 3d situation it was found that reconnection improvements tend to be limited to long edges and those with few three or four element neighbours the remaining degenerate elements are classified into one of four types using three proposed metrics the minimum edge to edge distance ee the minimum node to edge distance ne and the shortest edge length se and removed according to the best manner for their type optimised thresholds for identifying and classifying elements for removal were found to be ee 0 18 ne 0 21 se 0 2

an accurate adaptive solver for surface tension driven interfacial flows a method combining an adaptive quad octree spatial discretisation geometrical volume of fluid interface representation balanced force continuum surface force surface tension formulation and height function curvature estimation is presented the extension of these methods to the quad octree discretisation allows adaptive variable resolution along the interface and is described in detail the method is shown to recover exact equilibrium to machine accuracy between surface tension and pressure gradient in the case of a stationary droplet irrespective of viscosity and spatial resolution accurate solutions are obtained for the classical test case of capillary wave oscillations an application to the capillary breakup of a jet of water in air further illustrates the accuracy and efficiency of the method the source code of the implementation is freely available as part of the gerris flow solver

resolving the shock induced combustion by an adaptive mesh redistribution method an adaptive mesh method is presented for numerical simulation of shock induced combustion the method is composed of two independent ingredients a flow solver and a mesh redistribution algorithm the flow solver is a finite volume based second order upwind tvd scheme together with a lower upper symmetric gauss seidel relaxation scheme for solving the multispecies navier stokes equations with finite rate chemistry the adaptive mesh is determined by a grid generation method based on solving poisson equations with the monitor function carefully designed to resolve both sharp fronts and the induction zone between them numerically it is found that the resolution of the induction zone is particularly critical to the combustion problems and an under resolved numerical method may cause excessive energy release and spurious runaway reactions the monitor function proposed in this paper which is based on the relative rate of change of mass fraction covered this issue satisfactorily numerical simulations of supersonic flows past an axisymmetric projectile in a premixed hydrogen oxygen or air mixture are carried out the results show that the spurious runaway chemical reactions appearing on coarse grids can be eliminated by using adaptive meshes without invoking any ad hoc treatment for reaction rates the adaptive mesh approach is more effective than the fixed mesh one in obtaining grid independent results finally discrepancies between the numerical and benchmark experimental results and difficulties in simulating the detonation waves are delineated which appeal for further investigation

finite time stability and stabilization of nonlinear stochastic hybrid systems this paper deals with the problem of finite time stability and stabilization of nonlinear markovian switching stochastic systems which exist impulses at the switching instants using multiple lyapunov function theory a sufficient condition is established for finite time stability of the underlying systems furthermore based on the state partition of continuous parts of systems a feedback controller is designed such that the corresponding impulsive stochastic closed loop systems are finite time stochastically stable a numerical example is presented to illustrate the effectiveness of the proposed method

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

a multi level adaptive mesh refinement for an integrated finite element level set formulation to simulate multiphase flows with surface tension abstract a multi level adaptive mesh refinement technique for an integrated finite element level set formulation was implemented to simulate the incompressible interfacial flows with surface tension by using unstructured p2p1 triangular and tetrahedral meshes linear quadratic elements near the interface were dynamically refined as an interface evolves in order to produce an accurate solution with a lower computational cost an adaptive mesh refinement algorithm for a linear element has been extended to a quadratic element by using a node reordering the proposed algorithm was successfully validated by solving several benchmark problems simulation of a static bubble problem was found to give an accurate solution with negligible spurious currents compared with existing results simulation results of rising bubble problems in 2d and 3d were also compared against existing numerical and experimental results in terms of terminal rising speed and terminal bubble shape we have found that the present algorithm provided stable and accurate solutions even for a high density ratio and that the solution accuracy strongly depended on the mesh resolution near the interface further the present algorithm was shown to be very efficient because the computational overhead by mesh refinement algorithm was very small compared to the elapsed times consumed for solving the incompressible navier stokes equations and the advection re initialization equations of level set method lastly the coalescence scenario of two oblique bubbles was well reproduced by the present 3d simulation

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

an adaptive coupled level set volume of fluid interface capturing method for unstructured triangular grids we present an adaptive coupled level set volume of fluid aclsvof method for interfacial flow simulations on unstructured triangular grids at each time step we evolve both the level set function and the volume fraction the level set function is evolved by solving the level set advection equation using a discontinuous galerkin finite element method the volume fraction advection is performed using a lagrangian eulerian method the interface is reconstructed based on both the level set and the volume fraction information in particular the interface normal vector is calculated from the level set function while the line constant is determined by enforcing mass conservation based on the volume fraction different from previous works we have developed an analytic method for finding the line constant on triangular grids which makes interface reconstruction efficient and conserves volume of fluid exactly the level set function is finally reinitialized to the signed distance to the reconstructed interface since the level set function is continuous the normal vector calculation is easy and accurate compared to a classic volume of fluid method while tracking the volume fraction is essential for enforcing mass conservation the method is also coupled to a finite element based stokes flow solver the code validation shows that our method is second order and mass is conserved very accurately in addition owing to the adaptive grid algorithm we can resolve complex interface changes and interfaces of high curvature efficiently and accurately

a balanced force refined level set grid method for two phase flows on unstructured flow solver grids a balanced force refined level set grid method for two phase flows on structured and unstructured flow solver grids is presented to accurately track the phase interface location an auxiliary high resolution equidistant cartesian grid is introduced in conjunction with a dual layer narrow band approach this refined level set grid method allows for parallel efficient grid convergence and error estimation studies of the interface tracking method the navier stokes equations are solved on an unstructured flow solver grid with a novel balanced force algorithm for level set methods based on the recently proposed method by francois et al m m francois s j cummins e d dendy d b kothe j m sicilian m w williams a balanced force algorithm for continuous and sharp interfacial surface tension models within a volume tracking framework j comput phys 213 2006 141 173 for volume of fluid methods on structured grids to minimize spurious currents a second order converging curvature evaluation technique for level set methods is presented the results of several different test cases demonstrate the effectiveness of the proposed method showing good mass conservation properties and second order converging spurious current magnitudes

a dual neural network for redundancy resolution of kinematically redundant manipulators subject to joint limits and joint velocity limits in this paper a recurrent neural network called the dual neural network is proposed for online redundancy resolution of kinematically redundant manipulators physical constraints such as joint limits and joint velocity limits together with the drift free criterion as a secondary task are incorporated into the problem formulation of redundancy resolution compared to other recurrent neural networks the dual neural network is piecewise linear and has much simpler architecture with only one layer of neurons the dual neural network is shown to be globally exponentially convergent to optimal solutions the dual neural network is simulated to control the pa10 robot manipulator with effectiveness demonstrated

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

stability of hybrid stochastic delay systems whose discrete components have a large state space a two time scale approach abstract this work is concerned with stability of stochastic differential delay equations with markovian switching where the modulating markov chain has a large state space and is subject to both fast and slow movements under simple conditions we demonstrate that if the limit systems are p th moment exponentially stable then the original systems are p th moment exponentially stable in an appropriate sense in addition the exponential stability is also investigated moreover stability in distribution is obtained for such hybrid systems

prost a parabolic reconstruction of surface tension for the volume of fluid method volume of fluid vof methods are popular for the direct numerical simulation of time dependent viscous incompressible flow of multiple liquids as in any numerical method however it has its weaknesses namely for flows in which the capillary force is the dominant physical mechanism the lack of convergence with spatial refinement or convergence to a solution that is slightly different from the exact solution has been documented in the literature a well known limiting case for this is the existence of spurious currents for the simulation of a spherical drop with zero initial velocity these currents are present in all previous versions of vof algorithms in this paper we develop an accurate representation of the body force due to surface tension which effectively eliminates spurious currents we call this algorithm prost parabolic reconstruction of surface tension there are several components to this procedure including the new body force algorithm improvements in the projection method for the navier stokes solver and a higher order interface advection scheme the curvature to the interface is calculated from an optimal fit for a quadratic approximation to the interface over groups of cells

alternative theorems for nonlinear projection equations and applications to generalized complementarity problems let k be a closed convex subset in rn and let f g and h be three functions from rn into itself we consider the following nonlinear projection equation npe h x k g x f x x r 1 where k is the orthogonal projection operator onto the set k this equation provides a uni ed formulation of several interesting and important special cases in the case when h x g x for any x rn then 1 reduces to the equation studied by pang and yao 17 under the name of generalized normal equation which is equivalent to the following generalized variational inequality gvi g x k y g x f x 0 for all y k 2

regular article a pde based fast local level set method we develop a fast method to localize the level set method of osher and sethian 1988 j comput phys 79 12 and address two important issues that are intrinsic to the level set method a how to extend a quantity that is given only on the interface to a neighborhood of the interface b how to reset the level set function to be a signed distance function to the interface efficiently without appreciably moving the interface this fast local level set method reduces the computational effort by one order of magnitude works in as much generality as the original one and is conceptually simple and easy to implement our approach differs from previous related works in that we extract all the information needed from the level set function or functions in multiphase flow and do not need to find explicitly the location of the interface in the space domain the complexity of our method to do tasks such as extension and distance reinitialization is o n where n is the number of points in space not o n log n as in works by sethian 1996 proc nat acad sci 93 1591 and helmsen and co workers 1996 spie microlithography ix p 253 this complexity estimation is also valid for quite general geometrically based front motion for our localized method

an alternative theorem for generalized variational inequalities and solvability of nonlinear quasi p m complementarity problems in this paper an alternative theorem and hence a sufficient solution condition is established for generalized variational inequality problems the concept of exceptional family for generalized variational inequality is introduced this concept is general enough to include as special cases the notions of exceptional family of elements and the d orientation sequence for continuous functions particularly we apply the alternative theorem for investigating the solvability of the nonlinear complementarity problems with so called quasi p m maps which are broad enough to encompass the quasi monotone maps and p maps as the special cases an existence theorem for this class of complementarity problems is established which significantly generalizes several previous existence results in the literature

stability of a random diffusion with linear drift we consider a linear system with markovian switching which is perturbed by gaussian type noise if the linear system is mean square stable then we show that under certain conditions the perturbed system is also stable we also show that under certain conditions the linear system with markovian switching can be stabilized by such noisy perturbation

piecewise smoothness local invertibility and parametric analysis of normal maps this paper is concerned with properties of the euclidean projection map onto a convex set defined by finitely many smooth convex inequalities and affine equalities under a constant rank constraint qualification we show that the projection map is piecewise smooth pc1 hence bouligand differentiable or directionally differentiable and a relatively simple formula is given for the b derivative these properties of the projection map are used to obtain inverse and implicit function theorems for associated normal maps using a new characterization of invertibility of a pc1 function in terms of its b derivative an extension of the implicit function theorem which does not require local uniqueness is also presented degree theory plays a major role in the analysis of both the locally unique case and its extension

numerical simulation of drop impact on a liquid liquid interface with a multiple marker front capturing method the gravity driven motion of a droplet impacting on a liquid liquid interface is studied the full navier stokes equations are solved on a fixed uniform grid using a finite difference front capturing method for the representation of fluid fluid interfaces a coupled level set volume of fluid method m sussman e g puckett a coupled level set and volume of fluid method for computing 3d and axisymmetric incompressible two phase flows j comp phys 162 2000 301 337 is used in which we introduce the novel approach of describing separate interfaces with different marker functions as a consequence we prevent numerical coalescence of the droplet and the liquid liquid interface without excessive local grid refinement to validate our method numerical simulations of the drop impact event are compared with experiments z mohamed kassim e k longmire drop impact on a liquid liquid interface phys fluids 15 2003 3263 3273 furthermore a comparison is made with the numerical results of a esmaeeli g tryggvason direct numerical simulations of bubbly flows part 2 moderate reynolds number arrays j fluid mech 385 1999 325 358 for an array of rising bubbles the investigation shows that the multiple marker approach successfully prevents numerical coalescence of interfaces and adequately captures the effect of surface tension

volume of fluid interface tracking with smoothed surface stress methods for three dimensional flows motivated by the need for three dimensional methods for interface calculations that can deal with topology changes we describe a numerical scheme built from a volume of fluid interface tracking technique that uses a piecewise linear interface calculation in each cell momentum balance is computed using explicit finite volume finite differences on a regular cubic grid surface tension is implemented by the continuous surface stress or continuous surface force method examples and verifications of the method are given by comparing simulations to analytical results and experiments for sedimenting droplet arrays and capillary waves at finite reynolds number in the case of a pinching pendant drop both three dimensional and axisymmetric simulations are compared to experiments agreement is found both before and after the reconnections

solving generally constrained generalized linear variational inequalities using the general projection neural networks generalized linear variational inequality glvi is an extension of the canonical linear variational inequality in recent years a recurrent neural network nn called general projection neural network gpnn was developed for solving glvis with simple bound often box type or sphere type constraints the aim of this paper is twofold first some further stability results of the gpnn are presented second the gpnn is extended for solving glvis with general linear equality and inequality constraints a new design methodology for the gpnn is then proposed furthermore in view of different types of constraints approaches for reducing the number of neurons of the gpnn are discussed which results in two specific gpnns moreover some distinct properties of the resulting gpnns are also explored based on their particular structures numerical simulation results are provided to validate the results

transient adaptivity applied to two phase incompressible flows an anisotropic adaptation process is applied to a three dimensional incompressible two phase flow solver the solver uses a level set finite element method on unstructured tetrahedral meshes we show how the level set function can be used to build an anisotropic mesh with good properties some computations with a strong transient character and large densities ratios 1 1000 are presented we show that the efficiency of the computations can be deeply enhanced by mesh adaptations

a high order and interface preserving discontinuous galerkin method for level set reinitialization abstract a high order numerical method for interface preserving level set reinitialization is presented in this paper in the interface cells the gradient of the level set function is determined by a weighted local projection scheme and the missing additive constant is determined such that the position of the zero level set is preserved in the non interface cells we compute the gradient of the level set function by solving a hamilton jacobi equation as a conservation law system using the discontinuous galerkin method following the work by hu and shu siam j sci comput 21 1999 660 690 the missing constant is then recovered by the continuity of the level set function while taking into account the characteristics to handle highly distorted initial conditions we develop a hybrid numerical flux that combines the lax friedrichs flux and the penalty flux our method is stable for non trivial test cases and handles singularities away from the interface very well when derivative singularities are present on the interface a second derivative limiter is designed to suppress the oscillations at least n 1 th order accuracy in the interface cells and nth order in the whole domain are observed for smooth solutions when nth degree polynomials are used two dimensional test cases are presented to demonstrate superior properties such as accuracy long term stability interface preserving capability and easy treatment of contact lines we also show some preliminary results on the pinch off process of a pendant drop where topological changes of the fluid interface are involved our method is readily extendable to three dimensions and adaptive meshes

a level set formulation of eulerian interface capturing methods for incompressible fluid flows a level set formulation is derived for incompressible immiscible navier stokes equations separated by a free surface the interface is identified as the zero level set of a smooth function eulerian finite difference methods based on this level set formulation are proposed these methods are robust and efficient and are capable of computing interface singularities such as merging and reconnection numerical experiments are presented to demonstrate the effectiveness of the methods

an arbitrary lagrangian eulerian method for three phase flows with triple junction points we present a moving mesh method suitable for solving two dimensional and axisymmetric three liquid flows with triple junction points this method employs a body fitted unstructured mesh where the interfaces between liquids are lines of the mesh system and the triple junction points if exist are mesh nodes to enhance the accuracy and the efficiency of the method the mesh is constantly adapted to the evolution of the interfaces by refining and coarsening the mesh locally dynamic boundary conditions on interfaces in particular the triple points are therefore incorporated naturally and accurately in a finite element formulation in order to allow pressure discontinuity across interfaces double values of pressure are necessary for interface nodes and triple values of pressure on triple junction points the resulting non linear system of mass and momentum conservation is then solved by an uzawa method with the zero resultant condition on triple points reinforced at each time step the method is used to investigate the rising of a liquid drop with an attached bubble in a lighter liquid

an improved goldstein s type method for a class of variant variational inequalities this paper aims at presenting an improved goldstein s type method for a class of variant variational inequalities in particular the iterate computed by an existing goldstein s type method he a goldstein s type projection method for a class of variant variational inequalities j comput math 17 4 1999 425 434 is used to construct a descent direction and thus the new method generates the new iterate by searching the optimal step size along the descent direction some restrictions on the involving functions of the existing goldstein s type methods are relaxed while the global convergence of the new method is proved without additional assumptions the computational superiority of the new method is verified by the comparison to some existing methods

a discrete time neural network for optimization problems with hybrid constraints recurrent neural networks have become a prominent tool for optimizations including linear or nonlinear variational inequalities and programming due to its regular mathematical properties and well defined parallel structure this brief presents a general discrete time recurrent network for linear variational inequalities and related optimization problems with hybrid constraints in contrary to the existing discrete time networks this general model can operate not only on bound constraints but also on hybrid constraints comprised of inequality equality and bound constraints the model has dynamical properties of global convergence asymptotical and exponential convergences under some weaker conditions numerical examples demonstrate its efficacy and performance

sensitivity analysis of composite piecewise smooth equations this paper is a contribution to the sensitivity analysis of piecewise smooth equations a piecewise smooth function is a lipschitzian homeomorphism near a given point if and only if it is coherently oriented and has an invertible b derivative at this point we emphasise the role of functions of the typef g h whereg is piecewise smooth andh is smooth and present verifiable conditions which ensure that the functionf g tilde h is a lipschitzian homeomorphism near a given point for every tilde h sufficiently close toh with respect to thec1 topology

high resolution flux based level set method a new high resolution flux based finite volume method for general advection equations in nondivergent form including a level set equation for moving interfaces is introduced the method is applicable to the case of nondivergence free velocity and to general unstructured grids in higher dimensions we show that the method is consistent and that the numerical solution fulfills the discrete minimum maximum principle numerical experiments show its second order accuracy for smooth solutions as well as for solutions with discontinuous derivatives and on general unstructured meshes numerical examples for passive transport and shrinking of dynamic interfaces including examples with topological changes are presented using locally adapted two dimensional and three dimensional grids

controllability stabilizability and continuous time markovian jump linear quadratic control consideration is given to the control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes the relationship between appropriately defined controllability stabilizability properties and the solution of the infinite time jump linear quadratic jlq optimal control problems is also examined although the solution of the continuous time markov jlq problem with finite or infinite time horizons is known only sufficient conditions for the existence of finite cost constant stabilizing controls for the infinite time problem appear in the literature in this paper necessary and sufficient conditions are established these conditions are based on new definitions of controllability observability stabilizability and detectability that are appropriate for continuous time markovian jump linear systems these definitions play the same role for the jlq problem as the deterministic properties do for the linear quadratic regulator lqr problem

degree theory for generalized variational inequalities and applications in this paper a degree theory for finite dimensional generalized variational inequalities is built and employed to prove some results on solution existence and solution stability

modeling merging and breakup in the moving mesh interface tracking method for multiphase flow simulations the three dimensional moving mesh interface tracking mmit method coupled with local mesh adaptations by quan and schmidt s p quan d p schmidt a moving mesh interface tracking method for 3d incompressible two phase flows j comput phys 221 2007 761 780 demonstrated the capability to accurately simulate multiphase flows to handle large deformation and also to perform interface pinch off for some specific cases however another challenge i e how to handle interface merging such as droplet coalescence has not been addressed in this paper we present a mesh combination scheme for interface connection and a more general mesh separation algorithm for interface breakup these two schemes are based on the conversion of liquid cells in one phase to another fluid by changing the fluid properties of the cells in the combination or separation region after the conversion the newly created interface is usually ragged and a local projection method is employed to smooth the interface extra mesh adaptation criteria are introduced to handle colliding interfaces with almost zero curvatures as the distance between the interfaces diminishes simulations of droplet pair collisions including both head on and off center coalescences show that the mesh adaptations are capable of resolving very small length scales and the mesh combination and mesh separation schemes can handle the topological transitions in multiphase flows the potential of our method to perform detailed investigations of droplet coalescence and breakup is also displayed

a new regression estimator with neural network realization a new regression estimator viewed as the solution of a strictly convex quadratic programming problem is introduced in this paper two recurrent neural networks in continuous time and discrete time respectively are proposed to solve the quadratic programming problem in real time the continuous time neural network is shown to have a global stability including the global asymptotic and exponential stability the discrete time neural network is shown to have a global convergence with a fixed step length this fixed step length can be independent of the regression problem size by scaling a design parameter since the sizes of the proposed neural networks depend only on the constraints of the optimization problems the proposed new regression estimator can obtained by two novel neural networks with lower implementation costs than the conventional methods our simulation results confirm that the proposed neural networks are effective in solving various kind of regression problems

some developments in general variational inequalities general variational inequalities provide us with a unified natural novel and simple framework to study a wide class of equilibrium problems arising in pure and applied sciences in this paper we present a number of new and known numerical techniques for solving general variational inequalities using various techniques including projection wiener hopf equations updating the solution auxiliary principle inertial proximal penalty function dynamical system and well posedness we also consider the local and global uniqueness of the solution and sensitivity analysis of the general variational inequalities as well as the finite convergence of the projection type algorithms our proofs of convergence are very simple as compared with other methods our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems since the general variational inequalities include quasi variational inequalities and quasi implicit complementarity problems as special cases results presented here continue to hold for these problems several open problems have been suggested for further research in these areas

brief paper new results on stabilization of markovian jump systems with time delay this paper studies the problem of stochastic stabilization for a class of markovian jump systems with time delay a new delay dependent stochastic stability criterion on the stochastic stability of the system is derived based on a novel lyapunov krasovskii functional lkf approach the equivalence and superiority to existing results are demonstrated then a state feedback controller which guarantees the stochastic stability of the closed loop system is designed illustrative examples are provided to show the reduced conservatism and effectiveness of the proposed techniques

stochastic population dynamics under regime switching ii this is a continuation of our paper q luo x mao stochastic population dynamics under regime switching j math anal appl 334 2007 69 84 on stochastic population dynamics under regime switching in this paper we still take both white and color environmental noise into account we show that a sufficient large white noise may make the underlying population extinct while for a relatively small noise we give both asymptotically upper and lower bound for the underlying population in some special but important situations we precisely describe the limit of the average in time of the population

an efficient interface preserving level set redistancing algorithm and its application to interfacial incompressible fluid flow in sussman smereka and osher j comp phys 94 1994 pp 146 159 a numerical scheme was presented for computing incompressible air water flows using the level set method crucial to the above method was a new iteration method for maintaining the level set function as the signed distance from the zero level set in this paper we implement a constraint along with higher order difference schemes in order to make the iteration method more accurate and efficient accuracy is measured in terms of the new computed signed distance function and the original level set function having the same zero level set we apply our redistancing scheme to incompressible flows with noticeably better resolved results at reduced cost we validate our results with experiment and theory we show that our distance level set scheme with the added constraint competes well with available interface tracking schemes for basic advection of an interface we perform basic accuracy checks and more stringent tests involving complicated interfacial structures as with all level set schemes our method is easy to implement

exceptional families and finite dimensional variational inequalities over polyhedral convex sets a new concept of exceptional family for nonlinear variational inequalities over polyhedral sets is introduced in this paper it generalizes the concepts for complementarity problem introduced by smith and isac we applied the new analytical tool to the study of existence problem for variational inequalities it is shown that our existence condition is weaker than most of the sufficient conditions which have been known

an auxiliary grid method for computations of multiphase flows in complex geometries a method is developed for computations of interfacial flows in complex geometries the method combines a front tracking method with a newly developed finite volume fv scheme and utilizes an auxiliary grid for computationally efficient tracking of interfaces in body fitted curvilinear grids the tracking algorithm reduces particle tracking in a curvilinear grid to tracking on a uniform cartesian grid with a look up table the algorithm is general and can be used for other applications where lagrangian particles have to be tracked in curvilinear or unstructured grids the spatial and temporal errors are examined and it is shown that the method is globally second order accurate both in time and space the method is implemented to solve two dimensional planar or axisymmetric interfacial flows and is validated for a buoyancy driven drops in a straight tube and the motion of buoyancy driven drops in a periodically constricted channel

explicit conditions for asymptotic stability of stochastic lienard type equations with markovian switching this paper deals with the boundedness in probability and convergence for solutions of stochastic lienard type equations some explicit conditions to ensure that all solution is bounded in probability and convergent to some fixed sets are obtained we also show that white noise can affect the boundedness of corresponding deterministic lienard equations

computing minimal surfaces via level set curvature flow given a fixed closed curve or curves in r sp3 there is an associated problem of finding a surface with mean curvature zero which has that curve or curves as its boundary in this paper a new approach to numerically solving the minimal surface problem is introduced the surface is represented as a level set of a global function phi r sp3 to r the family of surfaces evolve in time according to mean curvature flow a solution is found when a steady state condition is achieved a new system of interpolatory boundary conditions are used to maintain the connection between the surface and the fixed boundary contour several computer surfaces are shown including examples of topological changes

stabilization and destabilization of hybrid systems of stochastic differential equations this paper aims to determine whether or not a stochastic feedback control can stabilize or destabilize a given nonlinear hybrid system new methods are developed and sufficient conditions on the stability and instability for hybrid stochastic differential equations are provided these results are then used to examine stochastic stabilization and destabilization

a coupled level set and volume of fluid method for computing 3d and axisymmetric incompressible two phase flows we present a coupled level set volume of fluid clsvof method for computing 3d and axisymmetric incompressible two phase flows this method combines some of the advantages of the volume of fluid method with the level set method to obtain a method which is generally superior to either method alone we present direct comparisons between computations made with the clsvof method and computations made with the level set method the volume of fluid method and the boundary integral method we also compare our computations to the exact solution for an oscillating ellipse due to lamb and experimental results obtained for a rising gas bubble in liquid obtained by hnat and buckmaster our computational examples focus on flows in which surface tension forces and changes in topology are dominant features of the flow

tracking discontinuities in hyperbolic conservation laws with spectral accuracy it is well known that the spectral solutions of conservation laws have the attractive distinguishing property of infinite order convergence also called spectral accuracy when they are smooth e g c canuto m y hussaini a quarteroni t a zang spectral methods for fluid dynamics springer verlag heidelberg 1988 j p boyd chebyshev and fourier spectral methods second ed dover new york 2001 c canuto m y hussaini a quarteroni t a zang spectral methods fundamentals in single domains springer verlag berlin heidelberg 2006 if a discontinuity or a shock is present in the solution this advantage is lost there have been attempts to recover exponential convergence in such cases with rather limited success the aim of this paper is to propose a discontinuous spectral element method coupled with a level set procedure which tracks discontinuities in the solution of nonlinear hyperbolic conservation laws with spectral convergence in space spectral convergence is demonstrated in the case of the inviscid burgers equation and the one dimensional euler equations

finite element discretization error analysis of a surface tension force in two phase incompressible flows we consider a standard model for a stationary two phase incompressible flow with surface tension in the variational formulation of the model a linear functional which describes the surface tension force occurs this functional depends on the location and the curvature of the interface in a finite element discretization method the functional has to be approximated for an approximation method based on a laplace beltrami representation of the curvature we derive sharp bounds for the approximation error a new modified approximation method with a significantly smaller error is introduced

numerical schemes for the hamilton jacobi and level set equations on triangulated domains borrowing from techniques developed for conservation law equations numerical schemes which discretize the hamilton jacobi h j level set and eikonal equations on triangulated domains are presented the first scheme is a provably monotone discretization for the h j equations unfortunately the basic scheme lacks lipschitz continuity of the numerical hamiltonian by employing a virtual edge flipping technique local lipschitz continuity of the numerical flux is restored on acute triangulations next schemes are introduced and developed based on the weaker concept of positive coefficient approximations for homogeneous hamiltonians these schemes possess a discrete maximum principle on arbitrary triangulations and exhibit local lipschitz continuity of the numerical hamiltonian finally a class of petrov galerkin approximations is considered these schemes are stabilized via a least squares bilinear form the petrov galerkin schemes do not possess a discrete maximum principle but generalize to high order accuracy discretization of the level set equation also requires the numerical approximation of a mean curvature term a simple mass lumped galerkin approximation is presented in section 6 and analyzed using maximum principle analysis the use of unstructured meshes permits several forms of mesh adaptation which have been incorporated into numerical examples these numerical examples include discretizations of convex and nonconvex forms of the h j equation the eikonal equation and the level set equation

an adaptive level set method with enhanced volume conservation for simulations in multiphase domains while implicit interface methods such as the level set method have the main advantage of avoiding explicit interface meshing they raise important volume conservation issues that can be handled by local mesh refinement this refinement is then performed multiple times throughout the simulation in order to follow the interface nevertheless mesh adaptation itself is a process that generates a volume conservation problem due to field transfer in this work multiphase simulations are addressed using a new lagrangian level set method that relies on an automatic mesh motion and topological mesh adaptation procedure remeshing is hence activated only when element flipping is detected this procedure is extended in order to take into account local phase distributions during remeshing so that volume conservation can be controlled 2 this method relies on a robust level set reinitialization technique also developed in this work 1 this constraint on volume conservation is automatically relaxed when necessary in order to take into account complex topological events such as apperance disappearance and coalescence of objects during the simulation numerical results show that the proposed method is competitive in terms of cost and accuracy with respect to standard eulerian and lagrangian level set methods while still enabling large displacements and deformations some examples concerning the modeling of evolutive microstructures will be detailed references 1 m shakoor b scholtes p o bouchard and m bernacki an efficient and parallel level set reinitialization method application to micromechanics and microstructural evolutions applied mathematical modelling 39 23 24 7291 7302 2015 2 m shakoor p o bouchard and m bernacki an adaptive level set method with enhanced volume conservation for simulations in multiphase domains international journal for numerical methods in engineering volume 109 issue 4 27 january 2017 555 576

inverse variational inequalities with projection based solution methods abstract an inverse variational inequality is defined as to find a vector u r n such that f u v f u t u 0 v if an inverse function u f 1 x exists the above inverse variational inequality could be transformed as a regular variational inequality however in reality it is not uncommon that the inverse function of f 1 x does not have explicit form although its functional values can be observed existing line search algorithms cannot be applied directly to solve such inverse variational inequalities in this paper we propose two projection based methods using the co coercivity of mapping f a self adaptive strategy is developed to determine the step sizes efficiently when the co coercivity modulus is unknown the convergence of the proposed methods is proved rigorously

resolving small scale structures in boussinesq convection by adaptive grid methods inviscid boussinesq convection is a challenging problem both analytically and numerically due to the complex dynamic development of small scales and the rapid loss of solution regularity the boussinesq convection pushes any numerical strategy to the limit in e and shu phys fluids 6 1994 49 a detailed numerical study of the boussinesq convection in the absence of viscous effects is carried out using filtered pseudospectral method and a high order accurate eno schemes in their computations very fine grids have to be used in order to resolve the small structures of the boussinesq fluid in this work we will develop an efficient adaptive grid method for solving the inviscid incompressible flows which can be useful in resolving extremely small structures with reasonably small number of grid points to demonstrate the effectiveness of the proposed method the boussinesq convection problem will be computed using the adaptive grid method

a front tracking method for the computations of multiphase flow direct numerical simulations of multiphase flows using a front tracking method are presented the method is based on writing one set of governing equations for the whole computational domain and treating the different phases as one fluid with variable material properties interfacial terms are accounted for by adding the appropriate sources as functions at the boundary separating the phases the unsteady navier stokes equations are solved by a conventional finite volume method on a fixed structured grid and the interface or front is tracked explicitly by connected marker points interfacial source terms such as surface tension are computed on the front and transferred to the fixed grid advection of fluid properties such as density is done by following the motion of the front the method has been implemented for fully three dimensional flows as well as for two dimensional and axisymmetric ones first the method is described for the flow of two or more isothermal phases the representation of the moving interface and its dynamic restructuring as well as the transfer of information between the moving front and the fixed grid are discussed applications and extensions of the method to homogeneous bubbly flows atomization flows with variable surface tension solidification and boiling are then presented

population dynamical behavior of lotka volterra system under regime switching in this paper we investigate a lotka volterra system under regime switching dx t diag x 1 t x n t b r t a r t x t dt s r t db t where b t is a standard brownian motion the aim here is to find out what happens under regime switching we first obtain the sufficient conditions for the existence of global positive solutions stochastic permanence and extinction we find out that both stochastic permanence and extinction have close relationships with the stationary probability distribution of the markov chain the limit of the average in time of the sample path of the solution is then estimated by two constants related to the stationary distribution and the coefficients finally the main results are illustrated by several examples

the asymptotic stability and exponential stability of nonlinear stochastic differential systems with markovian switching and with polynomial growth abstract this paper discusses the asymptotic stability and exponential stability of nonlinear stochastic differential systems with markovian switching sdswmss the systems coefficients are assumed to satisfy local lipschitz condition and polynomial growth condition by applying some novel techniques we propose some conditions under which such sdswmss are asymptotically stable and exponentially stable nontrivial examples are provided to illustrate our results