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

theory and methodologyminimax regret solution to linear programming problems with an interval objective function this paper deals with a linear programming problem with interval objective function coefficients a new treatment of an interval objective function is presented by introducing the minimax regret criterion as used in decision theory the properties of minimax regret solution and the relations with possibly and necessarily optimal solutions are investigated next the minimax regret criterion is applied to the final determination of the solution when a reference solution set is given a method of solution by a relaxation procedure is proposed the solution is obtained by repetitional use of the simplex method the minimax regret solution is obtained by the proposed solution method when the reference solution set is the set of possibly optimal solutions in order to illustrate the proposed solution method a numerical example is given

the numerical solution of laplace s equation in three dimensions we consider the dirichlet problem for laplace s equation on a simply connected three dimensional region with a smooth boundary this problem is easily converted to the solution of a fredholm integral equation of the second kind based on representing the harmonic solution as a double layer potential function we solve this integral equation formulation by using galerkin s method with spherical harmonics as the basis functions this approach leads to small linear systems and once the galerkin coefficients for the region have been calculated the computation time is small for any particular boundary function the major disadvantage of the method is the calculation of the galerkin coefficients each of which is a four fold integral with a singular integrand theoretical and computational details of the method are presented

distributionally robust optimization and its tractable approximations in this paper we focus on a linear optimization problem with uncertainties having expectations in the objective and in the set of constraints we present a modular framework to obtain an approximate solution to the problem that is distributionally robust and more flexible than the standard technique of using linear rules our framework begins by first affinely extending the set of primitive uncertainties to generate new linear decision rules of larger dimensions and is therefore more flexible next we develop new piecewise linear decision rules that allow a more flexible reformulation of the original problem the reformulated problem will generally contain terms with expectations on the positive parts of the recourse variables finally we convert the uncertain linear program into a deterministic convex program by constructing distributionally robust bounds on these expectations these bounds are constructed by first using different pieces of information on the distribution of the underlying uncertainties to develop separate bounds and next integrating them into a combined bound that is better than each of the individual bounds

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

a boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2d we present a new method for the evolution of inextensible vesicles immersed in a stokesian fluid we use a boundary integral formulation for the fluid that results in a set of nonlinear integro differential equations for the vesicle dynamics the motion of the vesicles is determined by balancing the non local hydrodynamic forces with the elastic forces due to bending and tension numerical simulations of such vesicle motions are quite challenging on one hand explicit time stepping schemes suffer from a severe stability constraint due to the stiffness related to high order spatial derivatives and a milder constraint due to a transport like stability condition on the other hand an implicit scheme can be expensive because it requires the solution of a set of nonlinear equations at each time step we present two semi implicit schemes that circumvent the severe stability constraints on the time step and whose computational cost per time step is comparable to that of an explicit scheme we discretize the equations by using a spectral method in space and a multistep third order accurate scheme in time we use the fast multipole method fmm to efficiently compute vesicle vesicle interaction forces in a suspension with a large number of vesicles we report results from numerical experiments that demonstrate the convergence and algorithmic complexity properties of our scheme

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

nonlinear preservers of pseudospectral radius on banach spaces abstract given a complex banach space x we denote by l x the algebra of all linear bounded operators on it for e 0 let r e t denote the e pseudospectral radius of t l x for an infinite dimensional space x we characterize surjective maps l x l x such that r e t 1 t 2 r e t 1 t 2 for all t 1 t 2 l x an analogous result is obtained in the finite dimensional case with no surjectivity assumption on the map

minimax regret solution to linear programming problems with an interval objective function in this paper a linear programming problem with an interval objective function is treated first the previous approaches to this problem are reviewed and the drawbacks are pointed out to improve the drawbacks a new approach to this problem is proposed by introducing the minimax regret criterion as used in decision theory the properties of minimax regret solution are investigated in order to obtain the minimax regret solution a method of solution by a relaxation procedure is proposed it is shown that the solution is obtained by repetitional use of the simplex method a numerical example is given to illustrate the proposed solution method

some unitary similarity invariant sets preservers of skew lie products abstract let h and k be complex separable hilbert spaces with dimensions at least three and b h the banach algebra of all bounded linear operators on h let denote w or e where for a w a stands for the numerical range of a b h and e a the e pseudospectrum of a it is shown that a bijective map no algebraic structure assumed b h b k satisfies that a b b a a b b a for all a b b h if and only if there exists a unitary operator u b h k such that a u a u for all a b h where 1 1 if w then the injectivity assumption on can be omitted

unitary similarity invariant function preservers of skew products of operators abstract let b h denote the banach algebra of all bounded linear operators on a complex hilbert space h with dim h 3 and let a and b be subsets of b h which contain all rank one operators suppose f is a unitary invariant norm the pseudo spectra the pseudo spectral radius the c numerical range or the c numerical radius for some finite rank operator c the structure is determined for surjective maps a b satisfying f a b f a b for all a b a to establish the proofs some general results are obtained for functions f f 1 h 0 0 where f 1 h is the set of rank one operators in b h satisfying a f u a u f a for a complex unit a f 1 h and unitary u b h b for any rank one operator x f 1 h the map t f t x on 0 is strictly increasing and c the set f x x f 1 h and x 1 attains its maximum and minimum

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

a divergence free spectral expansions method for three dimensional flows in spherical gap geometries abstract a spectral method for the solution of the incompressible navier stokes equations in spherical gap geometries is presented the method uses divergence free vector expansions which inherently satisfy the boundary conditions 1 basis and test functions are constructed from chebyshev polynomials and vector spherical harmonics vsh yielding a petrov galerkin weighted residual method that produces spectral convergence no rotational nor equatorial symmetry of the flow field is implicitly imposed the approach makes extensive use of the convenient properties of the vsh which are presented in a computationally suitable form whenever possible the alias free implementation of the method rests upon a standard explicit implicit time integration technique a vsh chebyshev vector transform with two fast directions is also developed and briefly presented several test cases are used to validate the resulting initial boundary value code axisymmetric basic spherical couette flow computations are compared with available numerical results while a three dimensional spiral taylor gortler vortex flow simulation is tested against experimental measurements very good agreement is found in all cases

viscous regularization and r adaptive remeshing for finite element analysis of lipid membrane mechanics as two dimensional fluid shells lipid bilayer membranes resist bending and stretching but are unable to sustain shear stresses this property gives membranes the ability to adopt dramatic shape changes in this paper a finite element model is developed to study static equilibrium mechanics of membranes in particular a viscous regularization method is proposed to stabilize tangential mesh deformations and improve the convergence rate of nonlinear solvers the augmented lagrangian method is used to enforce global constraints on area and volume during membrane deformations as a validation of the method equilibrium shapes for a shape phase diagram of lipid bilayer vesicle are calculated these numerical techniques are also shown to be useful for simulations of three dimensional large deformation problems the formation of tethers long tube like extensions and ginzburg landau phase separation of a two lipid component vesicle to deal with the large mesh distortions of the two phase model modification of viscous regularization is explored to achieve r adaptive mesh optimization

dynamic simulation of locally inextensible vesicles suspended in an arbitrary two dimensional domain a boundary integral method we consider numerical algorithms for the simulation of hydrodynamics of two dimensional vesicles suspended in a viscous stokesian fluid the motion of vesicles is governed by the interplay between hydrodynamic and elastic forces continuum models of vesicles use a two phase fluid system with interfacial forces that include tension to maintain local surface inextensibility and bending vesicle flows are challenging to simulate on the one hand explicit time stepping schemes suffer from a severe stability constraint due to the stiffness related to high order spatial derivatives in the bending term on the other hand implicit time stepping schemes can be expensive because they require the solution of a set of nonlinear equations at each time step our method is an extension of the work of veerapaneni et al s k veerapaneni d gueyffier d zorin g biros a boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2d journal of computational physics 228 7 2009 2334 2353 in which a semi implicit time marching scheme based on a boundary integral formulation of the stokes problem for vesicles in an unbounded medium was proposed in this paper we consider two important generalizations i confined flows within arbitrary shaped stationary moving geometries and ii flows in which the interior to the vesicle and exterior fluids have different viscosity in the rest of the paper we will refer to this as the viscosity contrast these two problems require solving additional integral equations and cause nontrivial modifications to the previous numerical scheme our method does not have severe time step stability constraints and its computational cost per time step is comparable to that of an explicit scheme the discretization is pseudo spectral in space and multistep bdf in time we conduct numerical experiments to investigate the stability accuracy and the computational cost of the algorithm overall our method achieves several orders of magnitude speed up compared to standard explicit schemes as a preliminary validation of our scheme we study the dependence of the inclination angle of a single vesicle in shear flow on the viscosity contrast and the reduced area of the vesicle the lateral migration of vesicles in shear flow the dispersion of two vesicles and the effective viscosity of a dilute suspension of vesicles

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

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

condition spectra of special operators and condition spectra preservers abstract let h be a complex hilbert space and let l h be the algebra of all bounded linear operators on h descriptions of the condition spectra of various special classes of operators are established as application characterization is obtained for maps on l h leaving invariant the condition spectrum or the condition spectral radius of the product of operators analogous results are obtained for jordan triple product of operators

preservers of unitary similarity functions on lie products of matrices abstract denote by m n the set of n n complex matrices let f m n 0 be a continuous map such that f u a u f a for any complex unit a m n and unitary u m n f x 0 if and only if x 0 and the induced map t f t x is monotonically increasing on 0 for any rank one nilpotent x m n characterization is given for surjective maps on m n satisfying f a b b a f a b b a the general theorem is then used to deduce results on special cases when the function is the pseudo spectrum and the pseudo spectral radius

random yield and random demand in a production system with downward substitution in this paper we present and solve a single period multiproduct downward substitution model our model has one raw material as the production input and produces n different products as outputs the demands and yields for the products are random we determine the optimal production input and allocation of the n products to satisfy demands the problem is modeled as a two stage stochastic program which we show can be decomposed into a parameterized network flow problem we present and compare three different solution methods a stochastic linear program a decomposition resulting in a series of network flow subproblems and a decomposition where the same network flow subproblems are solved by a new greedy algorithm

a linear decision based approximation approach to stochastic programming stochastic optimization especially multistage models is well known to be computationally excruciating moreover such models require exact specifications of the probability distributions of the underlying uncertainties which are often unavailable in this paper we propose tractable methods of addressing a general class of multistage stochastic optimization problems which assume only limited information of the distributions of the underlying uncertainties such as known mean support and covariance one basic idea of our methods is to approximate the recourse decisions via decision rules we first examine linear decision rules in detail and show that even for problems with complete recourse linear decision rules can be inadequate and even lead to infeasible instances hence we propose several new decision rules that improve upon linear decision rules while keeping the approximate models computationally tractable specifically our approximate models are in the forms of the so called second order cone soc programs which could be solved efficiently both in theory and in practice we also present computational evidence indicating that our approach is a viable alternative and possibly advantageous to existing stochastic optimization solution techniques in solving a two stage stochastic optimization problem with complete recourse

a high order algorithm for obstacle scattering in three dimensions in this work we describe implement and analyse in detail a high order fully discrete spectral algorithm for solving the helmholtz equation exterior to a bounded sound soft sound hard or absorbing obstacle in three space dimensions with dirichlet neumann or robin impedance boundary conditions our algorithm may be thought of as a discrete glerkin method but it is also equivalent to a nystrom method after a simple transformation we test our algorithm with extensive computational experiments on a variety of three dimensional smooth and non smooth obstacles with conical singularities our tests include the computation of scattered and far fields induced by incident plane waves our method is shown to be very accurate for scattering from surfaces which are globally parameterised by spherical coordinates and tests show that it performs very much better than several of the well established fast algorithms for obstacle sattering on a range of such surfaces even some which are non smooth further we prove superalgebraic convergence of the scattered and far fields obtained using our algorithm in the case of smooth scatterers

accuracy enhancement for higher derivatives using chebyshev collocation and a mapping technique a new method is investigated to reduce the roundoff error in computing derivatives using chebyshev collocation methods by using a grid mapping derived by kosloff and tal ezer and the proper choice of the parameter alpha the roundoff error of the k th derivative can be reduced from o n 2k to o n lge k where epsilon is the machine precision and n is the number of collocation points this drastic reduction of roundoff error makes mapped chebyshev methods competitive with any other algorithm in computing second or higher derivatives with large n several other aspects of the mapped chebyshev differentiation matrix are also studied revealing that the mapped chebyshev methods require much less than pi points to resolve a wave the eigenvalues are less sensitive to perturbation by roundoff error and larger time steps can be used for solving pdes all these advantages of the mapped chebyshev methods can be achieved while maintaining spectral accuracy

adaptive finite element method for a phase field bending elasticity model of vesicle membrane deformations in this paper a three dimensional adaptive finite element method is developed for a variational phase field bending elasticity model of vesicle membrane deformations using a mixed finite element formulation residual type a posteriori error estimates are derived for the associated nonlinear system of equations and they are used to introduce the mesh refinement and coarsening the resulting mesh adaptivity significantly improves the efficiency of the phase field simulation of vesicle membranes and enhances its capability in handling complex shape and topological changes the effectiveness of the adaptive method is further demonstrated through numerical examples

a fast high order algorithm for the solution of surface scattering problems basic implementation tests and applications we present a new algorithm for the numerical solution of problems of acoustic scattering by surfaces in three dimensional space this algorithm evaluates scattered fields through fast high order solution of the corresponding boundary integral equation the high order accuracy of our solver is achieved through use of partitions of unity together with analytical resolution of kernel singularities the acceleration in turn results from use of a novel approach which based on high order two face equivalent source approximations reduces the evaluation of far interactions to evaluation of 3 d fast fourier transforms ffts this approach is faster and substantially more accurate and it runs on dramatically smaller memories than other fft and k space methods the present algorithm computes one matrix vector multiplication in o n6 5logn to o n4 3logn operations where n is the number of surface discretization points the latter estimate applies to smooth surfaces for which our high order algorithm provides accurate solutions with small values of n the former more favorable count is valid for highly complex surfaces requiring significant amounts of subwavelength sampling further our approach exhibits super algebraic convergence it can be applied to smooth and nonsmooth scatterers and it does not suffer from accuracy breakdowns of any kind in this paper we introduce the main algorithmic components in our approach and we demonstrate its performance with a variety of numerical results in particular we show that the present algorithm can evaluate accurately in a personal computer scattering from bodies of acoustical sizes of several hundreds

method for efficient shape parametrization of fluid membranes and vesicles in this paper we describe a method for the parametrization of the shapes adopted by fluid membranes and vesicles the method is based upon a boundary value approach to geometry description in which smooth surfaces are produced as the solution to an elliptic partial differential equations shape parameters are introduced through the boundary conditions which control the shape of the vesicle models in combination with a model for the surface energy and a method for numerical minimization it is shown how the method can accurately approximate the shapes of both axisymmetric and nonaxisymmetric vesicles over a wide range of control parameters the particular value of the method lies in its ability to parametrize complicated shapes efficiently a feature that becomes especially valuable when seeking shapes of minimal energy using direct optimization techniques

robust convex optimization we study convex optimization problems for which the data is not specified exactly and it is only known to belong to a given uncertainty set u yet the constraints must hold for all possible values of the data from u the ensuing optimization problem is called robust optimization in this paper we lay the foundation of robust convex optimization in the main part of the paper we show that if u is an ellipsoidal uncertainty set then for some of the most important generic convex optimization problems linear programming quadratically constrained programming semidefinite programming and others the corresponding robust convex program is either exactly or approximately a tractable problem which lends itself to efficientalgorithms such as polynomial time interior point methods

properties and preservers of the pseudospectrum abstract the interplay between the algebraic and analytic properties of a matrix and the geometric properties of its pseudospectrum is investigated it is shown that one can characterize hermitian matrices positive semi definite matrices orthogonal projections unitary matrices etc in terms of the pseudospectrum also characterizations are given to maps on matrices leaving invariant the pseudospectrum of the sum difference or product of matrix pairs it is shown that such a map is always a unitary similarity transform followed by some simple operations such as adding a constant matrix taking the matrix transpose or multiplying by a scalar in 1 1

a spectral boundary integral method for flowing blood cells a spectral boundary integral method for simulating large numbers of blood cells flowing in complex geometries is developed and demonstrated the blood cells are modeled as finite deformation elastic membranes containing a higher viscosity fluid than the surrounding plasma but the solver itself is independent of the particular constitutive model employed for the cell membranes the surface integrals developed for solving the viscous flow and thereby the motion of the massless membrane are evaluated using an o nlogn particle mesh ewald pme approach the cell shapes which can become highly distorted under physiologic conditions are discretized with spherical harmonics the resolution of these global basis functions is of course excellent but more importantly they facilitate an approximate de aliasing procedure that stabilizes the simulations without adding any numerical dissipation or further restricting the permissible numerical time step complex geometry no slip boundaries are included using a constraint method that is coupled into an implicit system that is solved as part of the time advancement routine the implementation is verified against solutions for axisymmetric flows reported in the literature and its accuracy is demonstrated by comparison against exact solutions for relaxing surface deformations it is also used to simulate flow of blood cells at 30 volume fraction in tubes between 4 9 and email protected in diameter for these it is shown to reproduce the well known non monotonic dependence of the effective viscosity on the tube diameter

pseudospectra of special operators and pseudospectrum preservers abstract denote by b h the banach algebra of all bounded linear operators on a complex hilbert space h let a b h and denote by a the spectrum of a for e 0 define the e pseudospectrum e a of a as e a z a e e b h e e in this paper the pseudospectra of several special classes of operators are characterized as an application complete descriptions are given of the maps of b h leaving invariant the pseudospectra of a b for different kinds of binary operations on operators such as the difference a b the operator product ab and the jordan product a b b a

on the complexity of minmax regret linear programming abstract we consider linear programming problems with uncertain objective function coefficients for each coefficient of the objective function an interval of uncertainty is known and it is assumed that any coefficient can take on any value from the corresponding interval of uncertainty regardless of the values taken by other coefficients it is required to find a minmax regret solution this problem received considerable attention in the recent literature but its computational complexity status remained unknown we prove that the problem is strongly np hard this gives the first known example of a minmax regret optimization problem that is np hard in the case of interval data representation of uncertainty but is polynomially solvable in the case of discrete scenario representation of uncertainty

preservers of radial unitary similarity functions on products of operators abstract let s be a subset of the algebra l h of all bounded linear operators on an infinite dimensional complex hilbert space h and let f s 0 be a radial unitary similarity invariant function under some assumption on s and f characterizations are obtained for surjective maps on s satisfying f t s f t s t s s where the binary operation stands for the product or the jordan semi triple product on operators analogous descriptions are obtained for the finite dimensional case without the surjectivity assumption on

robust regret for uncertain linear programs with application to co production models abstract this paper considers the regret optimization criterion for linear programming problems with uncertainty in the data inputs the problems of study are more challenging than those considered in previous works that address only interval objective coefficients and furthermore the uncertainties are allowed to arise from arbitrarily specified polyhedral sets to this end a safe approximation of the regret function is developed so that the maximum regret can be evaluated reasonably efficiently by leveraging on previous established results and solution algorithms the proposed approach is then applied to a two stage co production newsvendor problem that contains uncertainties in both supplies and demands computational experiments demonstrate that the proposed regret approximation is reasonably accurate and the corresponding regret optimization model performs competitively well against other optimization approaches such as worst case and sample average optimization across different performance measures

the n ϵ pseudospectrum of an element of a banach algebra abstract let a be a complex unital banach algebra a a n z and 0 the n pseudospectrum n a of a is defined as n a a a a 2 n 1 2 n 1 here a denotes the spectrum of a the usual pseudospectrum a of a is a special case of this namely 0 a it is proved that n pseudospectrum approximates the closed neighbourhood of spectrum for large n further it has been shown that n pseudospectrum has no isolated points has a finite number of connected components and each component contains an element from a some examples are given to illustrate these results

an improved algorithm for selecting p items with uncertain returns according to the minmax regret criterion we consider the problem of selecting a subset of p investments of maximum total return out of a set of n available investments with uncertain returns where uncertainty is represented by interval estimates for the returns and the minmax regret objective is used we develop an algorithm that solves this problem in o min p n p n time this improves the previously known complexity o min p n p 2n

minimax regret treatment choice with missing outcome data i use the minimax regret criterion to study choice between two treatments when some outcomes in the study population are unobservable and the distribution of missing data is unknown i first assume that observable features of the study population are known and derive the treatment rule that minimizes maximum regret over all possible distributions of missing data when no treatment is dominant this rule allocates positive fractions of persons to both treatments i then assume that the data are a random sample of the study population and show that in some instances treatment rules that estimate certain point identified population means by sample averages are finite sample minimax regret

short note a fast and stable method for rotating spherical harmonic expansions in this paper we present a simple and efficient method for rotating a spherical harmonic expansion this is a well studied problem arising in classical scattering theory quantum mechanics and numerical analysis usually addressed through the explicit construction of the wigner rotation matrices we show that rotation can be carried out easily and stably through pseudospectral projection without ever constructing the matrix entries themselves existing fast algorithms based on recurrence relations are subject to a variety of instabilities limiting the effectiveness of the approach for expansions of high degree

robust multi market newsvendor models with interval demand data we present a robust model for determining the optimal order quantity and market selection for short life cycle products in a single period newsvendor setting due to limited information about demand distribution in particular for short life cycle products stochastic modeling approaches may not be suitable we propose the minimax regret multi market newsvendor model where the demands are only known to be bounded within some given interval in the basic version of the problem a linear time solution method is developed for the capacitated case we establish some structural results to reduce the problem size and then propose an approximation solution algorithm based on integer programming finally we compare the performance of the proposed minimax regret model against the typical average case and worst case models our test results demonstrate that the proposed minimax regret model outperformed the average case and worst case models in terms of risk related criteria and mean profit respectively

maps leaving functional values of operator products invariant abstract let a be a standard operator algebra on a complex hilbert space h of dimension greater than 2 by invariants of certain functional values of operator products we characterize some surjective maps on a furthermore several kinds of general preserver problems on standard operator algebras are solved when we take respectively the functional as for example k numerical radius k 1 operator norm ky fan k norm schatten p norm 1 p and so on

regret in the newsvendor model with partial information traditional stochastic inventory models assume full knowledge of the demand probability distribution however in practice it is often difficult to completely characterize the demand distribution especially in fast changing markets in this paper we study the newsvendor problem with partial information about the demand distribution e g mean variance symmetry unimodality in particular we derive the order quantities that minimize the newsvendor s maximum regret of not acting optimally most of our solutions are tractable which makes them attractive for practical application our analysis also generates insights into the choice of the demand distribution as an input to the newsvendor model in particular the distributions that maximize the entropy perform well under the regret criterion our approach can be extended to a variety of problems that require a robust but not conservative solution

deterministic approximations to co production problems with service constraints and random yields we study production planning problems where multiple item categories are produced simultaneously the items have random yields and are used to satisfy the demands of many products these products have specification requirements that overlap an item originally targeted to satisfy the demand of one product may be used to satisfy the demand of other products when it conforms to their specifications customers demand must be satisfied from inventory 100 of the time we formulate the problem with service constraints and provide near optimal solution to the problem with fixed planning horizon we also propose simple heuristics for the problem solved with a rolling horizon some of the heuristics performed very well over a wide range of parameters

preservers of pseudo spectral radius of operator products abstract let h be an infinite dimensional complex hilbert space and let l h be the algebra of all bounded linear operators on h for e 0 and t l h let r e t denote the e pseudo spectral radius of t we characterize surjective maps on l h which satisfy r e t s r e t s for all t s l h we also obtain analogous result for the finite dimensional case without the surjectivity assumption on

a numerical method for simulating the dynamics of 3d axisymmetric vesicles suspended in viscous flows we extend shravan k veerapaneni denis gueyffier denis zorin george biros a boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2d journal of computational physics 228 7 2009 2334 2353 to the case of three dimensional axisymmetric vesicles of spherical or toroidal topology immersed in viscous flows although the main components of the algorithm are similar in spirit to the 2d case spectral approximation in space semi implicit time stepping scheme the main differences are that the bending and viscous force require new analysis the linearization for the semi implicit schemes must be rederived a fully implicit scheme must be used for the toroidal topology to eliminate a cfl type restriction and a novel numerical scheme for the evaluation of the 3d stokes single layer potential on an axisymmetric surface is necessary to speed up the calculations by introducing these novel components we obtain a time scheme that experimentally is unconditionally stable has low cost per time step and is third order accurate in time we present numerical results to analyze the cost and convergence rates of the scheme to verify the solver we compare it to a constrained variational approach to compute equilibrium shapes that does not involve interactions with a viscous fluid to illustrate the applicability of method we consider a few vesicle flow interaction problems the sedimentation of a vesicle interactions of one and three vesicles with a background poiseuille flow

a kernel independent adaptive fast multipole algorithm in two and three dimensions we present a new fast multipole method for particle simulations the main feature of our algorithm is that it does not require the implementation of multipole expansions of the underlying kernel and it is based only on kernel evaluations instead of using analytic expansions to represent the potential generated by sources inside a box of the hierarchical fmm tree we use a continuous distribution of an equivalent density on a surface enclosing the box to find this equivalent density we match its potential to the potential of the original sources at a surface in the far field by solving local dirichlet type boundary value problems the far field evaluations are sparsified with singular value decomposition in 2d or fast fourier transforms in 3d we have tested the new method on the single and double layer operators for the laplacian the modified laplacian the stokes the modified stokes the navier and the modified navier operators in two and three dimensions our numerical results indicate that our method compares very well with the best known implementations of the analytic fmm method for both the laplacian and modified laplacian kernels its advantage is the relative simplicity of the implementation and its immediate extension to more general kernels

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

a heuristic to minimax absolute regret for linear programs with interval objective function coefficients decision makers faced with uncertain information often experience regret upon learning that an alternative action would have been preferable to the one actually selected models that minimize the maximum regret can be useful in such situations especially when decisions are subject to ex post review of particular interest are those decision problems that can be modeled as linear programs with interval objective function coefficients the minimax regret solution for these formulations can be found using an algorithm that at each iteration solves first a linear program to obtain a candidate solution and then a mixed integer program mip to maximize the corresponding regret the exact solution of the mip is computationally expensive and becomes impractical as the problem size increases in this paper we develop a heuristic for the mip and investigate its performance both alone and in combination with exact procedures the heuristic is shown to be effective for problems that are significantly larger than those previously reported in the literature

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

simulating the dynamics and interactions of flexible fibers in stokes flows the dynamics of slender filaments or fibers suspended in stokesian fluids are fundamental to understanding many flows arising in physics biology and engineering such filaments can have aspect ratios of length to radius ranging from a few tens to several thousands full discretizations of such 3d flows are very costly instead we employ a nonlocal slender body theory that yields an integral equation along the filament centerline relating the force exerted on the body to the filament velocity this hydrodynamical description takes into account the effect of the filament on the fluid and is extended to capture the interaction of multiple filaments as mediated by the intervening fluid we consider filaments that are inextensible and elastic replacing the force in the slender body integral equation by an explicit expression that uses euler bernoulli theory to model bending and tensile forces yields an integral expression for the velocity of the filament centerlines coupled to auxiliary integro differential equations for the filament tensions based on a regularized version of these slender body equations that is asymptotically equivalent to the original formulation we construct a numerical method which uses a combination of finite differences implicit time stepping to avoid severe stability constraints and special quadrature methods for nearly singular integrals we present simulations of single flexible filaments as well as multiple interacting filaments evolving in a background shear flow these simulations show shear induced buckling and relaxation of the filaments leading to the storage and release of elastic energy these dynamics are responsible for the development of positive first normal stress differences commonly associated with visco elastic fluids that are suspensions of microscopic elastic fibers

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

portfolio selection under independent possibilistic information this paper deals with a portfolio selection problem with independently estimated possibilistic return rates under such a circumstance a distributive investment has been regarded as a good solution in the traditional portfolio theory however the conventional possibilistic approach yields a concentrated investment solution considering the reason why a distributive investment is advocated a new approach to the possibilistic portfolio selection is proposed