hamiltonian formulation of surfaces with constant gaussian curvature dirac s method for constrained hamiltonian systems is used to describe surfaces of constant gaussian curvature a geometrical free energy for which these surfaces are equilibrium states is introduced and interpreted as an action an equilibrium surface can then be generated by the evolution of a closed space curve since the underlying action depends on second derivatives the velocity of the curve and its conjugate momentum must be included in the set of phase space variables furthermore the action is linear in the acceleration of the curve and possesses a local symmetry reparametrization invariance which implies primary constraints in the canonical formalism these constraints are incorporated into the hamiltonian through lagrange multiplier functions that are identified as the components of the acceleration of the curve the formulation leads to four first order partial differential equations one for each canonical variable with the appropriate choice of parametrization only one of these equations has to be solved to obtain the surface which is swept out by the evolving space curve to illustrate the formalism several evolutions of pseudospherical surfaces are discussed

analysis of multiple scattering iterations for high frequency scattering problems i the two dimensional case we present an analysis of a recently proposed integral equation method for the solution of high frequency electromagnetic and acoustic scattering problems that delivers error controllable solutions in frequency independent computational times within single scattering configurations the method is based on the use of an appropriate ansatz for the unknown surface densities and on suitable extensions of the method of stationary phase the extension to multiple scattering configurations in turn is attained through consideration of an iterative neumann series that successively accounts for further geometrical wave reflections as we show for a collection of two dimensional cylindrical convex obstacles this series can be rearranged into a sum of periodic orbits of increasing period each corresponding to contributions arising from waves that reflect off a fixed subset of scatterers when these are transversed sequentially in a periodic manner here we analyze the properties of these periodic orbits in the high frequency regime by deriving precise asymptotic expansions for the currents i e the normal derivative of the fields that they induce on the surface of the obstacles as we demonstrate these expansions can be used to provide accurate estimates of the rate at which their magnitude decreases with increasing number of reflections which defines the overall rate of convergence of the multiple scattering series moreover we show that the detailed asymptotic knowledge of these currents can be used to accelerate this convergence and thus to reduce the number of iterations necessary to attain a prescribed accuracy

hamilton s equations for a fluid membrane consider a homogeneous fluid membrane described by the helfrich canham energy quadratic in the mean curvature of the membrane surface the shape equation that determines equilibrium configurations is fourth order in derivatives and cubic in the mean curvature we introduce a hamiltonian formulation of this equation which dismantles it into a set of coupled first order equations this involves interpreting the helfrich canham energy as an action equilibrium surfaces are generated by the evolution of space curves two features complicate the implementation of a hamiltonian framework i the action involves second derivatives this requires treating the velocity as a phase space variable and the introduction of its conjugate momentum the canonical hamiltonian is constructed on this phase space ii the action possesses a local symmetry reparametrization invariance the two labels we use to parametrize points on the surface are themselves physically irrelevant this symmetry implies primary constraints one for each label that need to be implemented within the hamiltonian the two lagrange multipliers associated with these constraints are identified as the components of the acceleration tangential to the surface the conservation of the primary constraints implies two secondary constraints fixing the tangential components of the momentum conjugate to the position hamilton s equations are derived and the appropriate initial conditions on the phase space variables are identified finally it is shown how the shape equation can be reconstructed from these equations

analytic preconditioners for the electric field integral equation since the advent of the fast multipole method large scale electromagnetic scattering problems based on the electric field integral equation efie formulation are generally solved by a krylov iterative solver a well known fact is that the dense complex non hermitian linear system associated to the efie becomes ill conditioned especially in the high frequency regime as a consequence this slows down the convergence rate of krylov subspace iterative solvers in this work a new analytic preconditioner based on the combination of a finite element method with a local absorbing boundary condition is proposed to improve the convergence of the iterative solver for an open boundary some numerical tests precise the behaviour of the new preconditioner moreover comparisons are performed with the analytic preconditioner based on the calderon s relations for integral equations for several kinds of scatterers copyright 2004 john wiley sons ltd

analysis of multiple scattering iterations for high frequency scattering problems ii the three dimensional scalar case in this paper we continue our analysis of the treatment of multiple scattering effects within a recently proposed methodology based on integral equations for the numerical solution of scattering problems at high frequencies in more detail here we extend the two dimensional results in part i of this work to fully three dimensional geometries as in the former case our concern here is the determination of the rate of convergence of the multiple scattering iterations for a collection of three dimensional convex obstacles that are inherent in the aforementioned high frequency schemes to this end we follow a similar strategy to that we devised in part i first we recast the iterated neumann multiple scattering series in the form of a sum of periodic orbits of increasing period corresponding to multiple reflections that periodically bounce off a series of scattering sub structures then we proceed to derive a high frequency recurrence that relates the normal derivatives of the fields induced on these structures as the waves reflect periodically and finally we analyze this recurrence to provide an explicit rate of convergence associated with each orbit while the procedure is analogous to its two dimensional counterpart the actual analysis is significantly more involved and perhaps more interestingly it uncovers new phenomena that cannot be distinguished in two dimensional configurations e g the further dependence of the convergence rate on the relative orientation of interacting structures as in the two dimensional case and beyond their intrinsic interest we also explain here how the results of our analysis can be used to accelerate the convergence of the multiple scattering series and thus to provide significant savings in computational times

on a class of preconditioning methods for dense linear systems from boundary elements in this paper we discuss several sparse matrix based preconditioners suitable for preconditioning dense linear systems of boundary element equations all preconditioners involve only o n nonzeros we provide a framework for constructing operator splitting based preconditioners and use it to analyze a class of sparse preconditioners for singular integral equations a more efficient preconditioner is proposed that has a band 2 structure

minimizing late jobs in the general one machine scheduling problem abstract in this paper the problem of minimizing the number of late jobs on one machine is investigated the general problem is considered i e with release dates and different due dates a lower bound is first proposed based on the relaxation of a mixed integer linear programming formulation of the problem a heuristic is then presented its effectiveness is computationally studied by comparison with the lower bound

a branch and bound algorithm to minimize the number of late jobs in a permutation flow shop abstract the problem of scheduling n jobs in an m machine permutation flow shop is considered each job requires processing on machines 1 m in that order the processing order of jobs is to be the same for each machine a due date for each job is specified that represents the time by which it should ideally be completed the objective is to schedule the jobs so that the number completed after their due dates is minimized a lower bound which is obtained by solving a single machine subproblem is derived also two improvement procedures which consider all subproblems together are developed a branch and bound algorithm that uses these lower bounds is described computational experience with the algorithm is reported

on the numerical approximation of high frequency acoustic multiple scattering problems by circular cylinders the aim of this paper is to propose a numerical strategy for computing the solution of two dimensional time harmonic acoustic multiple scattering problems at high frequency the scatterers are assumed to be circular leading therefore to semi analytical representation formulae of the scattered field through the solution of a large linear system of equations taking advantage of the special block toeplitz structure of the matrix of the linear system a fast iterative and preconditioned numerical method yielding large memory savings is proposed several numerical experiments for general configurations are presented to show the efficiency of the numerical method

balancing torques in membrane mediated interactions exact results and numerical illustrations torques on interfaces can be described by a divergence free tensor which is fully encoded in the geometry this tensor consists of two terms one originating in the couple of the stress the other capturing an intrinsic contribution due to curvature in analogy to the description of forces in terms of a stress tensor the torque on a particle can be expressed as a line integral along a contour surrounding the particle interactions between particles mediated by a fluid membrane are studied within this framework in particular torque balance places a strong constraint on the shape of the membrane symmetric two particle configurations admit simple analytical expressions which are valid in the fully nonlinear regime in particular the problem may be solved exactly in the case of two membrane bound parallel cylinders this apparently simple system provides some flavor of the remarkably subtle nonlinear behavior associated with membrane mediated interactions

boundary element analysis for the helmholtz eigenvalue problems with a multiply connected domain for a helmholtz eigenvalue problem with a multiply connected domain the boundary integral equation approach as well as the boundary element method is shown to yield spurious eigenvalues even if the complex valued kernel is used in such a case it is found that spurious eigenvalues depend on the geometry of the inner boundary demonstrated as an analytical case the spurious eigenvalue for a multiply connected problem with its inner boundary as a circle is studied analytically by using the degenerate kernels and circulants an annular case can be studied analytically in a discrete system and can be treated as a special case the proof for the general boundary instead of the circular boundary is also derived the burton miller method is employed to eliminate spurious eigenvalues in the multiply connected case moreover a modified method considering only the real part formulation is provided five examples are shown to demonstrate that the spurious eigenvalues depend on the shape of the inner boundary good agreement between analytical prediction and numerical results are found

optimal control for holonomic and nonholonomic mechanical systems with symmetry and lagrangian reduction in this paper we establish necessary conditions for optimal control using the ideas of lagrangian reduction in the sense of reduction under a symmetry group the techniques developed here are designed for lagrangian mechanical control systems with symmetry the benefit of such an approach is that it makes use of the special structure of the system especially its symmetry structure and thus it leads rather directly to the desired conclusions for such systems lagrangian reduction can do in one step what one can alternatively do by applying the pontryagin maximum principle followed by an application of poisson reduction the idea of using lagrangian reduction in the sense of symmetry reduction was also obtained by bloch and crouch proc 33rd cdc ieee 1994 pp 2584 2590 in a somewhat different context and the general idea is closely related to those in montgomery comm math phys 128 1990 pp 565 592 and vershik and gershkovich dynamical systems vii v arnold and s p novikov eds springer verlag 1994 here we develop this idea further and apply it to some known examples such as optimal control on lie groups and principal bundles such as the ball and plate problem and reorientation examples with zero angular momentum such as the satellite with moveable masses however one of our main goals is to extend the method to the case of nonholonomic systems with a nontrivial momentum equation in the context of the work of bloch krishnaprasad marsden and murray arch rational mech anal 1996 to appear the snakeboard is used to illustrate the method

coupling of dirichlet to neumann boundary condition and finite difference methods in curvilinear coordinates for multiple scattering the applicability of the dirichlet to neumann technique coupled with finite difference methods is enhanced by extending it to multiple scattering from obstacles of arbitrary shape the original boundary value problem bvp for the multiple scattering problem is reformulated as an interface bvp a heterogenous medium with variable physical properties in the vicinity of the obstacles is considered a rigorous proof of the equivalence between these two problems for smooth interfaces in two and three dimensions for any finite number of obstacles is given the problem is written in terms of generalized curvilinear coordinates inside the computational region then novel elliptic grids conforming to complex geometrical configurations of several two dimensional obstacles are constructed and approximations of the scattered field supported by them are obtained the numerical method developed is validated by comparing the approximate and exact far field patterns for the scattering from two circular obstacles in this case for a second order finite difference scheme a second order convergence of the numerical solution to the exact solution is easily verified

laplace pressure as a surface stress in fluid vesicles consider a surface enclosing a fixed volume described by a free energy depending only on the local geometry for example the canham helfrich energy quadratic in the mean curvature describes a fluid membrane the stress at any point on the surface is determined completely by geometry in equilibrium its divergence is proportional to the laplace pressure normal to the surface maintaining the constraint on the volume it is shown that this source itself can be expressed as the divergence of a position dependent surface stress as a consequence the equilibrium can be described in terms of a conserved effective surface stress various non trivial geometrical consequences of this identification are explored in a cylindrical geometry the cross section can be viewed as a closed planar euler elastic curve with respect to an appropriate centre the effective stress itself vanishes this provides a remarkably simple relationship between the curvature and the position along the loop in two or higher dimensions it is shown that the only geometry consistent with the vanishing of the effective stress is spherical it is argued that the appropriate generalization of the loop result will involve null stresses

interface mediated interactions between particles a geometrical approach particles bound to an interface interact because they deform its shape the stresses that result are fully encoded in the geometry and described by a divergence free surface stress tensor this stress tensor can be used to express the force on a particle as a line integral along any conveniently chosen closed contour that surrounds the particle the resulting expression is exact i e free of any smallness assumptions and independent of the chosen surface parametrization additional surface degrees of freedom such as vector fields describing lipid tilt are readily included in this formalism as an illustration we derive the exact force for several important surface hamiltonians in various symmetric two particle configurations in terms of the midplane geometry its sign is evident in certain interesting limits specializing to the linear regime where the shape can be analytically determined these general expressions yield force distance relations several of which have originally been derived by using an energy based approach

spectral and condition number estimates of the acoustic single layer operator for low frequency multiple scattering in dilute media the aim of this paper is to develop an analysis of the distribution of the eigenvalues of the acoustic single layer potential for various low frequency two dimensional multiple scattering problems the obstacles are supposed to be distant dilute media in cite thierrythesis it is shown that an approach based on the gershgorin disks provides limited spectral information we therefore introduce an alternative approach by applying the power iteration method to the limit matrix associated with the zero order spatial modes which results in satisfactory estimates all these approximations are built for circular cylinders and formally extended to ellipses and rectangles for linear boundary element methods with non uniform meshes this study is completed in cite antoinethierrypart2 by spectral estimates for the case of close obstacles

how paper folds bending with local constraints a variational framework is introduced to describe how a surface bends when it is subject to local constraints on its geometry this framework is applied to describe the patterns of a folded sheet of paper the unstretchability of paper implies a constraint on the surface metric bending is penalized by an energy quadratic in mean curvature the local lagrange multipliers enforcing the constraint are identified with a conserved tangential stress that couples to the extrinsic curvature of the sheet the framework is illustrated by examining the deformation of a flat sheet into a generalized cone

spectral and condition number estimates of the acoustic single layer operator for low frequency multiple scattering in dense media the aim of this paper is to derive spectral and condition number estimates of the single layer operator for low frequency multiple scattering problems this work extends to dense media the analysis initiated in antoine and thierry in press 19 estimates are obtained first in the case of circular cylinders by fourier analysis and are next formally adapted to disks ellipses and rectangles in the framework of boundary element methods numerical simulations validating the approach are also given

generating true minima in constrained variational formulations via modified lagrange multipliers variational principles are important in the investigation of large classes of physical systems they can be used both as analytical methods as well as starting points for the formulation of powerful computational techniques such as dynamical optimization methods systems with charged objects in dielectric media and systems with magnetically active particles are important examples in these examples and other important cases the variational principles describing the system are required to obey a number of constraints these constraints are implemented within the variational formulation by means of lagrange multipliers such constrained variational formulations are in general not unique for the application of efficient simulation methods one must find specific formulations that satisfy a number of important conditions an often required condition is that the functional be positive definite in other words its extrema be actual minima in this article we present a general approach to attack the problem of finding among equivalent variational functionals those that generate true minima the method is based on the modification of the lagrange multiplier which allows us to generate large families of effective variational formulations associated with a single original constrained variational principle we demonstrate its application to different examples and in particular to the important cases of poisson and poisson boltzmann equations we show how to obtain variational formulations for these systems with extrema that are always minima

three dimensional finite element calculations in acoustic scattering using arbitrarily shaped convex artificial boundaries we report on a generalization of the bayliss gunzburger turkel non reflecting boundary conditions to arbitrarily shaped convex artificial boundaries for elongated scatterers such as submarines we show that this generalization can improve significantly the computational efficiency of finite element methods applied to the solution of three dimensional acoustic scattering problems copyright 2001 john wiley sons ltd

a comparison of techniques for overcoming non uniqueness of boundary integral equations for the collocation partition of unity method in two dimensional acoustic scattering the partition of unity method has become an attractive approach for extending the allowable frequency range for wave simulations beyond that available using piecewise polynomial elements the non uniqueness of solution obtained from the conventional boundary integral equation cbie is well known the cbie derived through green s identities suffers from a problem of non uniqueness at certain characteristic frequencies two of the standard methods of overcoming this problem are the so called combined helmholtz integral equation formulation chief method and that of burton and miller the latter method introduces a hypersingular integral which may be treated in various ways in this paper we present the collocation partition of unity boundary element method pubem for the helmholtz problem and compare the performance of chief against a burton miller formulation regularised using the approach of li and huang

inverted catenoid as a fluid membrane with two points pulled together under inversion in any interior point a catenoid transforms into a deflated compact geometry which touches at two points its poles the catenoid is a minimal surface and as such is an equilibrium shape of a symmetric fluid membrane the conformal symmetry of the hamiltonian implies that inverted minimal surfaces are also equilibrium shapes however they will exhibit curvature singularities at their poles such singularities are the geometrical signature of the external forces required to pull the poles together these forces will set up stresses in the inverted shapes tuning the force corresponds geometrically to the translation of the point of inversion for any fixed surface area there will be a maximum force the associated shape is a symmetric discocyte lowering the external force will induce a transition from the discocyte to a cup shaped stomatocyte

a genetic algorithm for an industrial multiprocessor flow shop scheduling problem with recirculation abstract we propose in this paper an effective heuristic algorithm to solve a scheduling problem that comes from industry the workshop is an hybrid flow shop with recirculation and the problem is to perform jobs between a release date and a due date in order to minimize the weighted number of tardy jobs firstly an integer linear programming formulation of the problem is proposed then a lower bound a greedy algorithm and a genetic algorithm are described as approximate methods to evaluate these heuristics experiences on instances like industrial ones are computed and show the efficiency of the genetic algorithm

environmental bias and elastic curves on surfaces the behavior of an elastic curve bound to a surface will reflect the geometry of its environment this may occur in an obvious way the curve may deform freely along directions tangent to the surface but not along the surface normal however even if the energy itself is symmetric in the curve s geodesic and normal curvatures which control these modes very distinct roles are played by the two if the elastic curve binds preferentially on one side or is itself assembled on the surface not only would one expect the bending moduli associated with the two modes to differ binding along specific directions reflected in spontaneous values of these curvatures may be favored the shape equations describing the equilibrium states of a surface curve described by an elastic energy accommodating environmental factors will be identified by adapting the method of lagrange multipliers to the darboux frame associated with the curve the forces transmitted to the surface along the surface normal will be determined features associated with a number of different energies both of physical relevance and of mathematical interest are described the conservation laws associated with trajectories on surface geometries exhibiting continuous symmetries are also examined

the fast multipole method we study integral methods applied to the resolution of the maxwell equations where the linear system is solved using an iterative method which requires only matrix vector products the fast multipole method fmm is one of the most efficient methods used to perform matrix vector products and accelerate the resolution of the linear system a problem involving n degrees of freedom may be solved in cniternlogn floating operations where c is a constant depending on the implementation of the method in this article several techniques allowing one to reduce the constant c are analyzed this reduction implies a lower total cpu time and a larger range of application of the fmm in particular new interpolation and anterpolation schemes are proposed which greatly improve on previous algorithms several numerical tests are also described these confirm the efficiency and the theoretical complexity of the fmm

membrane geometry with auxiliary variables and quadratic constraints consider a surface described by a hamiltonian which depends only on the metric and extrinsic curvature induced on the surface the metric and the curvature along with the basis vectors which connect them to the embedding functions defining the surface are introduced as auxiliary variables by adding appropriate constraints all of them quadratic the response of the hamiltonian to a deformation in each of the variables is determined and the relationship between the multipliers implementing the constraints and the conserved stress tensor of the theory established for the purpose of illustration a fluid membrane described by a hamiltonian quadratic in curvature is considered

on surface radiation condition for multiple scattering of waves the formulation of the on surface radiation condition osrc is extended to handle wave scattering problems in the presence of multiple obstacles the new multiple osrc simultaneously accounts for the outgoing behavior of the wave fields as well as the multiple wave reflections between the obstacles like boundary integral equations bie this method leads to a reduction in dimensionality from volume to surface of the discretization region however as opposed to bie the proposed technique leads to boundary integral equations with smooth kernels hence these fredholm integral equations can be handled accurately and robustly with standard numerical approaches without the need to remove singularities moreover under weak scattering conditions this approach renders a convergent iterative method which bypasses the need to solve single scattering problems at each iteration inherited from the original osrc the proposed multiple osrc is generally a crude approximate method if accuracy is not satisfactory this approach may serve as a good initial guess or as an inexpensive pre conditioner for krylov iterative solutions of bie

preconditioning based on calderon s formulae for periodic fast multipole methods for helmholtz equation solution of periodic boundary value problems is of interest in various branches of science and engineering such as optics electromagnetics and mechanics in our previous studies we have developed a periodic fast multipole method fmm as a fast solver of wave problems in periodic domains it has been found however that the convergence of the iterative solvers for linear equations slows down when the solutions show anomalies related to the periodicity of the problems in this paper we propose preconditioning schemes based on calderon s formulae to accelerate convergence of iterative solvers in the periodic fmm for helmholtz equations the proposed preconditioners can be implemented more easily than conventional ones we present several numerical examples to test the performance of the proposed preconditioners we show that the effectiveness of these preconditioners is definite even near anomalies

fluid membrane tethers minimal surfaces and elastic boundary layers thin cylindrical tethers are common lipid bilayer membrane structures arising in situations ranging from micromanipulation experiments on artificial vesicles to the dynamic structure of the golgi apparatus we study the shape and formation of a tether in terms of the classical soap film problem which is applied to the case of a membrane disk under tension subject to a point force a tether forms from the elastic boundary layer near the point of application of the force for sufficiently large displacement analytic results for various aspects of the membrane shape are given

formulation and accuracy of on surface radiation conditions for acoustic multiple scattering problems the aim of this paper is 1 to address an extension of the on surface radiation condition osrc method to multiple scattering by a cluster of convex obstacles and 2 to analyze the numerical accuracy of the formulation for some model problems first the acoustic scattering problem is considered and materials about integral equations and osrcs are recalled then an osrc integral equation formulation is developed for the dirichlet multiple scattering problems finally an extensive numerical study of the method is proposed in the special case of the scattering by circular cylinders even if this situation is not completely general it provides an assessment of the accuracy of the approximation with respect to various parameters including thanks to the choice of the osrc operators

spinor representation of surfaces and complex stresses on membranes and interfaces variational principles are developed within the framework of a spinor representation of the surface geometry to examine the equilibrium properties of a membrane or interface this is a far reaching generalization of the weierstrass enneper representation for minimal surfaces introduced by mathematicians in the 1990s permitting the relaxation of the vanishing mean curvature constraint in this representation the surface geometry is described by a spinor field satisfying a two dimensional dirac equation coupled through a potential associated with the mean curvature as an application the mesoscopic model for a fluid membrane as a surface described by the canham helfrich energy quadratic in the mean curvature is examined an explicit construction is provided of the conserved complex valued stress tensor characterizing this surface

dirichlet to neumann boundary conditions for multiple scattering problems a dirichlet to neumann dtn condition is derived for the numerical solution of time harmonic multiple scattering problems where the scatterer consists of several disjoint components it is obtained by combining contributions from multiple purely outgoing wave fields the dtn condition yields an exact non reflecting boundary condition for the situation where the computational domain and its exterior artificial boundary consist of several disjoint components because each sub scatterer can be enclosed by a separate artificial boundary the computational effort is greatly reduced and becomes independent of the relative distances between the different sub domains the dtn condition naturally fits into a variational formulation of the boundary value problem for use with the finite element method moreover it immediately yields as a by product an exact formula for the far field pattern of the scattered field numerical examples show that the dtn condition for multiple scattering is as accurate as the well known dtn condition for single scattering problems j comput phys 82 1989 172 numerical methods for problems in infinite domains elsevier amsterdam 1992 while being more efficient due to the reduced size of the computational domain

hamilton s equations for a fluid membrane axial symmetry consider a homogeneous fluid membrane or vesicle described by the helfrich canham energy quadratic in the mean curvature when the membrane is axially symmetric this energy can be viewed as an action describing the motion of a particle the contours of equilibrium geometries are identified with particle trajectories a novel hamiltonian formulation of the problem is presented which exhibits the following two features i the second derivatives appearing in the action through the mean curvature are accommodated in a natural phase space and ii the intrinsic freedom associated with the choice of evolution parameter along the contour is preserved as a result the phase space involves momenta conjugate not only to the particle position but also to its velocity and there are constraints on the phase space variables this formulation provides the groundwork for a field theoretical generalization to arbitrary configurations with the particle replaced by a loop in space

flowshop scheduling with identical jobs and uniform parallel machines the single stage scheduling problem to minimize the makespan of identical jobs on uniform parallel machines is known to be solvable in polynomial time we extend this work to consider multi stage systems with flowshop configuration we show that the 2 stage problem may also be solved in polynomial time and for the number of stages greater than two the problem is shown to be np hard we present a branch and bound procedure which provides an optimal solution to the 3 stage problem and a fast heuristic procedure that is shown to provide good approximate solutions on sample problems this heuristic is a natural extension of the 2 stage polynomial time procedure we develop theoretical bounds showing that the maximum deviation between the solution derived by the heuristic procedure and the optimal solution is bounded by the maximum processing time of a machine at the second stage independent of the number of jobs and the processing times at the first and third stages we also show that the heuristic provides an approximate solution bounded by a ratio of 1 75 to the optimal solution

on the spectrum of the electric field integral equation and the convergence of the moment method existing convergence estimates for numerical scattering methods based on boundary integral equations are asymptotic in the limit of vanishing discretization length and break down as the electrical size of the problem grows in order to analyse the efficiency and accuracy of numerical methods for the large scattering problems of interest in computational electromagnetics we study the spectrum of the electric field integral equation efie for an infinite conducting strip for both the tm weakly singular kernel and te polarizations hypersingular kernel due to the self coupling of surface wave modes the condition number of the discretized integral equation increases as the square root of the electrical size of the strip for both polarizations from the spectrum of the efie the solution error introduced by discretization of the integral equation can also be estimated away from the edge singularities of the solution the error is second order in the discretization length for low order bases with exact integration of matrix elements and is first order if an approximate quadrature rule is employed comparison with numerical results demonstrates the validity of these condition number and solution error estimates the spectral theory offers insights into the behaviour of numerical methods commonly observed in computational electromagnetics copyright 2001 john wiley sons ltd

scheduling a two stage hybrid flowshop with separable setup and removal times abstract this paper considers the two stage flowshop scheduling problem where each stage consists of several identical parallel machines and the setup and removal times of each job at each stage are separated from the processing times a polynomial optimization algorithm is developed for the special case where the first stage contains only one machine and the number of identical parallel machines at the second stage is equal to or greater than the total number of jobs in view of the np completeness of this problem four heuristic algorithms are developed for the case where there is one machine at stage 1 and the number of identical parallel machines at the second stage is less than the total number of jobs the proposed heuristic algorithms are empirically tested to determine their effectiveness in finding an optimal schedule

branch and bound algorithm for the flow shop with multiple processors abstract the sequencing of a flow shop with multiple processors at each stage is a general case of the flow shop problem it involves sequencing n jobs in a flow shop where for at least one stage the facility has one or more identical machines the purpose of this paper is to present a branch and bound algorithm to solve scheduling problems of such facilities for optimizing the maximum completion time the lower bounds and elimination rules developed in this research are based upon the generalization of the flow shop problem furthermore a computational algorithm along with results is also presented the branch and bound algorithm can also be used to optimize other measures of performance in a flow shop with multiple processors

a flexible flowshop problem with total flow time minimization abstract in this study we consider total flow time problem in a flexible flowshop environment we develop a branch and bound algorithm to find the optimal schedule the efficiency of the algorithm is enhanced by upper and lower bounds and a dominance criterion computational experience reveals that the algorithm solves moderate sized problems in reasonable solution times

a trefftz based numerical modelling framework for helmholtz problems with complex multiple scatterer configurations the aim of the work presented in this paper is the numerical solution of low and mid frequency time harmonic acoustic multiple scattering problem a novel so called multi level modelling approach is proposed which is applicable to the study of a configuration of well separated obstacles of arbitrary shape on which any type of acoustic boundary condition can be applied the generic character of the method is obtained by embedding the superposition principle for the multiple scattering influence in a state of the art acoustic modelling technique the so called wave based method the resulting approach successfully alleviates the geometrical limitations of the underlying trefftz based method and preserves the method s computational efficiency resulting in a generic multiple scattering modelling framework with a superior computational efficiency in the low as well as the mid frequency range several numerical validation examples show that the proposed approach is as accurate as the classical single scattering wave based method and illustrate the computational efficiency as compared to boundary element methods

area constrained planar elastica we determine the equilibria of a rigid loop in the plane subject to the constraints of fixed length and fixed enclosed area rigidity is characterized by an energy functional quadratic in the curvature of the loop we find that the area constraint gives rise to equilibria with remarkable geometrical properties not only can the euler lagrange equation be integrated to provide a quadrature for the curvature but in addition the embedding itself can be expressed as a local function of the curvature the configuration space is shown to be essentially one dimensional with surprisingly rich structure distinct branches of integer indexed equilibria exhibit self intersections and bifurcations a gallery of plots is provided to highlight these findings perturbations connecting equilibria are shown to satisfy a first order ode which is readily solved we also obtain analytical expressions for the energy as a function of the area in some limiting regimes

high order surface radiation conditions for time harmonic waves in exterior domains abstract we formulate a new family of high order on surface radiation conditions to approximate the outgoing solution to the helmholtz equation in exterior domains motivated by the pseudo differential expansion of the dirichlet to neumann operator developed by antoine et al 1999 we design a systematic procedure to apply pseudo differential symbols of arbitrarily high order numerical results are presented to illustrate the performance of the proposed method for solving both the dirichlet and the neumann boundary value problems possible improvements and extensions are also discussed

axially symmetric membranes with polar tethers axially symmetric equilibrium configurations of the conformally invariant willmore energy are shown to satisfy an equation that is two orders lower in derivatives of the embedding functions than the equilibrium shape equation not one as would be expected on the basis of axial symmetry modulo a translation along the axis this equation involves a single free parameter c if c 0 a geometry with spherical topology will possess curvature singularities at its poles the physical origin of the singularity is identified by examining the noether charge associated with the translational invariance of the energy it is consistent with an external axial force acting at the poles a one parameter family of exact solutions displaying a discocyte to stomatocyte transition is described

bayliss turkel like radiation conditions on surfaces of arbitrary shape this paper addresses the extension of the bayliss turkel second order radiation condition to an arbitrarily shaped surface the derivation is based mainly on the pseudo differential calculus as well as on the introduction of a criterion providing a precise handling of the approximation process involved in the derivation of the radiation condition the radiation condition then ranges among the most accurate of those of order two as a by product of the derivation almost all known radiation conditions of order less than or equal to two are recovered and their respective accuracies are compared

calderon s preconditioning for periodic fast multipole method for elastodynamics in 3d summary preconditioning methods based on calderon s formulae for the periodic fast multipole method for elastodynamics in 3d are investigated three different types of formulations are proposed the first type is a preconditioning just by appropriately ordering the coefficient matrix without multiplying preconditioners the other two types utilise preconditioners constructed using matrices needed in the main fast multipole method algorithms we make several numerical experiments with proposed preconditioners to confirm the efficiency of these proposed methods we also conclude that the preconditioning of the first type is faster with respect to the computational time than other preconditioning methods discussed in this article copyright 2012 john wiley sons ltd

stresses in lipid membranes the stresses in a closed lipid membrane described by the helfrich hamiltonian quadratic in th ee xtrinsic curvature are identified using noether s theorem three equations describe the conservation of the stress tensor the norma lp rojection is identified as the shape equation describing equilibrium configurations the tangential projections are consistency conditions on the stresses which capture the fluid character of such membranes the corresponding torque tensor is also identified the use of the stress tensor as a basis for perturbation theory is discussed the conservation laws are cast in terms of the forces and torques on closed curves as an application the first integral of the shape equation for axially symmetric configurations is derived by examining the forces which are balanced along the circles of constant latitude

rapid solution of integral equations of scattering theory in two dimensions abstract the present paper describes an algorithm for rapid solution of boundary value problems for the helmholtz equation in two dimensions based on iteratively solving integral equations of scattering theory cpu time requirements of previously published algorithms of this type are of the order n 2 where n is the number of nodes in the discretization of the boundary of the scatterer the cpu time requirements of the algorithm of the present paper are n 4 3 and can be further reduced making it considerably more practical for large scale problems

spherical vesicles distorted by a grafted latex bead an exact solution we present an exact solution to the problem of the global shape description of a spherical vesicle distorted by a grafted latex bead this solution is derived by treating the nonlinearity in bending elasticity through the topological bogomol nyi decomposition technique and elastic compatibility we recover the hat model approximation in the limit of a small latex bead and find that the region antipodal to the grafted latex bead flattens we also derive the appropriate shape equation using the variational principle and relevant constraints

acoustic scattering for 3d multi directional periodic structures using the boundary element method an efficient boundary element formulation is proposed to solve three dimensional exterior acoustic scattering problems with multi directional periodicity the multi directional periodic acoustic problem is represented as a multilevel block toeplitz matrix by exploiting the toeplitz structure the computational time and storage requirements to construct and to solve the linear system of equations arising from the boundary element formulation are significantly reduced the generalized minimal residual method is implemented to solve the linear system of equations to efficiently calculate the matrix vector product in the iterative algorithm the original matrix is embedded into a multilevel block circulant matrix a multi dimensional discrete fourier transform is then employed to accelerate the matrix vector product the proposed approach is applicable to a periodic acoustic problem for any arbitrary shape of the structure in both full space and half space two case studies involving sonic crystal barriers