fast sweeping algorithms for a class of hamilton jacobi equations we derive a godunov type numerical flux for the class of strictly convex homogeneous hamiltonians that includes h p q sqrt ap 2 bq 2 2cpq c 2 ab we combine our godunov numerical fluxes with simple gauss seidel type iterations for solving the corresponding hamilton jacobi hj equations the resulting algorithm is fast since it does not require a sorting strategy as found e g in the fast marching method in addition it providesa way to compute solutions to a class of hj equations for which the conventional fast marching method is not applicable our experiments indicate convergence after a few iterations even in rather difficult cases

existence and qualitative properties of travelling waves for an epidemiological model with mutations in this article we are interested in a non monotone system of logistic reaction diffusion equations this system of equations models an epidemics where two types of pathogens are competing and a mutation can change one type into the other with a certain rate we show the existence of minimal speed travelling waves that are usually non monotonic we then provide a description of the shape of those constructed travelling waves and relate them to some fisher kpp fronts with non minimal speed

a viscosity solutions approach to shape from shading the problem of recovering a lambertian surface from a single two dimensional image may be written as a first order nonlinear equation which presents the disadvantage of having several continuous and even smooth solutions a new approach based on hamilton jacobi bellman equations and viscosity solutions theories enables one to study non uniqueness phenomenon and thus to characterize the surface among the various solutions a consistent and monotone scheme approximating the surface is constructed thanks to the dynamic programming principle and numerical results are presented

upwind finite difference calculation of traveltimes seismic traveltimes can be computed efficiently on a regular grid by an upwind finite difference method the method solves a conservation law that describes changes in the gradient components of the traveltime field the traveltime field itself is easily obtained from the solution of the conservation law by numerical integration the conservation law derives from the eikonal equation and its solution depicts the first arrival time field the upwind finite difference scheme can be implemented in fully vectorized form in contrast to a similar scheme proposed recently by vidale the resulting traveltime field is useful both in kirchhoff migration and modeling and in seismic tomography many reliable methods exist for the numerical solution of conservation laws which appear in fluid mechanics as statements of the conservation of mass momentum etc a first order upwind finite difference scheme proves accurate enough for seismic applications upwind schemes are stable because they mimic the behavior of flu

a fast level set method for propagating interfaces a method is introduced to decrease the computational labor of the standard level set method for propagating interfaces the fast approach uses only points close to the curve at every time step we describe this new algorithm and compare its efficiency and accuracy with the standard level set approach

a new eulerian method for the computation of propagating short acoustic and electromagnetic pulses a new method is described to compute short acoustic or electromagnetic pulses that propagate according to geometrical optics the pulses are treated as zero thickness sheets that can propagate over long distances through inhomogeneous media with multiple reflections the method has many of the advantages of lagrangian ray tracing but is completely eulerian typically using a uniform cartesian grid accordingly it can treat arbitrary configurations of pulses that can reflect from surfaces and pass through each other without requiring special computational marker arrays for each pulse also information describing the pulses which are treated as continuous surfaces can be available throughout the computational grid rather than only at isolated individual markers the method uses a new type of representation which we call dynamic surface extension the basic idea is to propagate or broadcast defining fields from each pulse surface through a computational grid these fields carry information about a nearby pulse surface that is used at each node to compute the location of the pulse surfaces and other attributes such as amplitude thus the emphasis is on the dynamics of these propagating defining fields which obey only local eulerian equations at each node the dynamic surface extension representation can be thought of as dual to level set representation the defining fields involve single valued variables which are constant at each time along lines that are normal to the evolving surface whereas level set techniques involve a function which has constant values on the evolving surface and neighboring surfaces in this way the new method overcomes the inability of level set or eikonal methods to treat intersecting pulses that obey a wave equation and can pass through each other while still using only single valued variables propagating thin pulse surfaces in 1 d 2 d and 3 d that can reflect from boundaries and pass through each other are computed using the new method the method was first presented as a new general representation of surfaces filaments and particles by j steinhoff and m fan 1998 eulerian computation of evolving surfaces curves and discontinuous fields utsi preprint

parallel machine scheduling with a deteriorating maintenance activity and total absolute differences penalties in this paper we consider identical parallel machines scheduling problems with a deteriorating maintenance activity in this model each machine has a deteriorating maintenance activity that is delaying the maintenance increases the time required to perform it we need to make a decision on when to schedule the rate modifying activities and the sequence of jobs to minimize some objective function we concentrate on two goals separately namely minimizing the total absolute differences in completion times tadc and the total absolute differences in waiting times tadw we show that the problems remain polynomially solvable under the proposed model

computing interface motion in compressible gas dynamics a hamilton jacobi level set formulation of the equations of motion for propagating interfaces has been introduced recently by osher and sethian this formulation allows fronts to self intersect develop singularities and change topology the numerical algorithms based on this approach handle topological merging and breaking naturally work in any number of space dimensions and do not require that the moving front be written as a function instead the moving front is embedded as a particular level set in a fixed domain partial differential equation numerical techniques borrowed from hyperbolic conservation laws are then used to accurately capture the complicated surface motion that satisfies the global entropy condition for propagating fronts given by sethian in this paper we analyze the coupling of this level set formulation to a system of conservation laws for compressible gas dynamics we study both conservative and non conservative differencing of the level set function and compare the two approaches to illustrate the capability of the method we study the compressible rayleigh taylor and kelvin helmholtz instabilities for air air and air helium boundaries we perform numerical convergence studies of the method over a range of parameters and analyze the accuracy of this approach applied to these problems

high order essentially nonsocillatory schemes for hamilton jacobi equations hamilton jacobi h j equations are frequently encountered in applications e g in control theory and differential games h j equations are closely related to hyperbolic conservation laws in one space dimension the former is simply the integrated version of the latter similarity also exists for the multidimensional case and this is helpful in the design of difference approximations in this paper high order essentially nonoscillatory eno schemes for h j equations are investigated which yield uniform high order accuracy in smooth regions and sharply resolve discontinuities in the derivatives the eno scheme construction procedure is adapted from that for hyperbolic conservation laws the schemes are numerically tested on a variety of one dimensional and two dimensional problems including a problem related to control optimization and high order accuracy in smooth regions good resolution of discontinuities in the derivatives and convergence to viscosity solutions are observed

the strong np hardness of the maximum lateness minimization scheduling problem with the processing time based aging effect abstract in this paper we analyse the single machine maximum lateness minimization scheduling problem with the processing time based aging effect where the processing time of each job is described by a non decreasing function dependent on the sum of the normal processing times of preceded jobs the computational complexity of this problem was not determined however we show it is strongly np hard by proving the strong np hardness of the single machine maximum completion time minimization problem with this aging model and job deadlines furthermore we determine the boundary between polynomially solvable and np hard cases

a numerical method for solving incompressible flow problems with a surface of discontinuity a numerical method for solving problems in which a moving surface of discontinuity separates regions of incompressible flow is presented the method developed is notable in that it does not introduce any artificial smoothing of the change in fluid properties across the surface of discontinuity this results in an increase in accuracy relative to methods which introduce smoothing effects the method was also shown to be fairly versatile problems describing a free surface an immiscible fluid interface and a premixed flame discontinuity were solved there is a limitation however in that the method appears to be most suitable for application to inviscid problems the reason for this limitation and possible approaches toward resolving it are discussed

on hopf s formulas for solutions of hamilton jacobi equations soit h r n r on considere l equation de hamilton jacobi u t h du 0 dans r n 1 r n 0 on etudie les proprietes des formules de hopf pour les solutions

level set methods for the simulation of epitaxial phenomena we introduce a model for epitaxial phenomena based on the motion of island boundaries which is described by the level set method our model treats the growing film as a continuum in the lateral direction but retains atomistic discreteness in the growth direction an example of such an island dynamics model using the level set method is presented and compared with the corresponding rate equation description extensions of our methodology to more general settings are then discussed s1063 651x 98 50212 7

imaging complex structures with semirecursive kirchhoff migration i present a semirecursive kirchhoff migration algorithm that is capable of obtaining accurate images of complex structures by combining wave equation datuming and kirchhoff migration the method is successful because breaking up the complex velocity structure into small depth regions allows traveltimes to be calculated in regions where the computation is well behaved and where the computation corresponds to energetic arrivals the traveltimes computed in such a region are used first for imaging and second for downward continuation of the entire survey shots and receivers to the boundary of the next region this process results in images comparable to those obtained by shot profile migration but at reduced computational cost because traveltimes are computed for small depth domains the adverse effects of caustics headwaves and multiple arrivals do not develop in principle this method requires only the same number of traveltime calculations as a standard migration tests on the marmousi data set produce excellent results

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

minimizing the makespan with an availability constraint on a single machine under simple linear deterioration this article considers a single machine scheduling problem with an availability constraint under simple linear deterioration the non preemptive case is taken into account as well the objective is to minimize the makespan in the system the addressed problem is first described as a 0 1 integer programming model and is then solved optimally subsequently we prove that the addressed problem belongs to np hard thus some heuristic algorithms based on the bin packing concepts are provided for solving the addressed problem computational results show that the proposed algorithm h3 performs well in addition a good strategy that sets the maintenance to start epoch when half the jobs have been already processed is suggested as well

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

multicomponent flow calculations by a consistent primitive algorithm the dynamics of inviscid multicomponent fluids may be modelled by the euler equations augmented by one or more additional species equation s attempts to compute solutions for extended euler models in conservation form show strong oscillations and other computational inaccuracies near material interfaces these are due to erroneous pressure fluctuations generated by the conservative wave model this problem does not occur in single component computations and arises only in the presence of several species a nonconservative primitive euler formulation is proposed which results in complete elimination of the oscillations the numerical algorithm uses small viscous perturbations to remove leading order conservation errors and is conservative to the order of numerical approximation numerical experiments show clean monotonic solution profiles with acceptably small conservation error for shocks of weak to moderate strengths

asymptotic profile in selection mutation equations gauss versus cauchy distributions abstract in this paper we study the asymptotic large time behaviour of a selection mutation competition model for a population structured with respect to a phenotypic trait when the rate of mutation is very small we assume that the reproduction is asexual and that the mutations can be described by a linear integral operator we are interested in the interplay between the time variable t and the rate e of mutations we show that depending on 0 the limit e 0 with t e can lead to population number densities which are either gaussian like when is small or cauchy like when is large

some single machine and flowshop scheduling problems with a non linear deterioration function the deteriorating job scheduling problems have received increasing attention recently however most researchers assume that the actual job processing time is a linear function of its starting time in fact in some situations the deterioration rate might increase or decrease as time passes for example the temperature of the ingot in the rolling machine might drop at a slower pace as the surface cools down thus the drop of the ingot temperature might have a decreasing rate on the other hand the time to control a fire might go dramatically as time passes and the time to cease a fire might have an increasing rate in this paper we propose a new deteriorating model where the deterioration rate might be increasing or decreasing as time passes under the proposed model we provide the optimal solutions for some single machine problems and some flowshop problems

generalized traveling waves for time dependent reaction diffusion systems traveling wave solutions in general time dependent including time periodic reaction diffusion equations and systems of equations have attracted great attention in the last two decades the aim of this paper is to study the propagation phenomenon in a general time heterogeneous environment more specifically we investigate generalized traveling wave solutions for a two component time dependent non cooperative reaction diffusion system which has applications in epidemiology and ecology sufficient conditions on the existence and nonexistence of generalized traveling wave solutions are established in the susceptible infectious epidemic model setting generalized traveling waves describe the spatio temporal invasion of a disease into a totally susceptible population in the context of predator prey systems the generalized traveling waves describe the spatial invasion of predators introduced into a new environment where the prey population is at its carrying capacity

motion of multiple junctions a level set approach abstract a coupled level set method for the motion of multiple junctions is proposed the new method extends the hamilton jacobi level set formulation of osher and sethian it retains the feature of tracking fronts by following level sets and allows the specification of arbitrary velocities on each front the diffusion equation is shown to generate curvature dependent motion and this is used to develop an algorithm to move multiple junctions with curvature dependent speed systems of reaction diffusion equations are shown to possess inherent properties which prohibit efficient numerical solutions when applied to curvature dependent motion

user s guide to viscosity solutions of second order partial differential equations the notion of viscosity solutions of scalar fully nonlinear partial differential equations of second order provides a framework in which startling comparison and uniqueness theorems existence theorems and theorems about continuous dependence may now be proved by very efficient and striking arguments the range of important applications of these results is enormous this article is a self contained exposition of the basic theory of viscosity solutions

scheduling deteriorating jobs subject to job or machine availability constraints we consider two problems of scheduling a set of independent non preemptable and proportionally deteriorating jobs on a single machine in the first problem the machine is not continuously available for processing but the number of non availability periods the start time and end time of each period are known in advance in the second problem the machine is available all the time but for each job a ready time and a deadline are defined in both problems the criterion of schedule optimality is the maximum completion time we show that the decision version of the first the second problem is np complete in the ordinary or in the strong sense depending on the number of non availability periods the number of ready times and deadlines

explicit solutions for replicator mutator equations extinction versus acceleration we consider a class of nonlocal reaction diffusion problems referred to as replicator mutator equations in evolutionary genetics by using explicit changes of unknown function we show that they are equivalent to the heat equation and therefore compute their solution explicitly based on this we then prove that in the case of beneficial mutations in asexual populations solutions dramatically depend on the tails of the initial data they can be global become extinct in finite time or even be defined for no positive time in the first case we prove that solutions are accelerating and in many cases converge for large times to some universal gaussian profile this sheds light on the biological relevance of such models

a fast sweeping method for eikonal equations in this paper a fast sweeping method for computing the numerical solution of eikonal equations on a rectangular grid is presented the method is an iterative method which uses upwind difference for discretization and uses gauss seidel iterations with alternating sweeping ordering to solve the discretized system the crucial idea is that each sweeping ordering follows a family of characteristics of the corresponding eikonal equation in a certain direction simultaneously the method has an optimal complexity of o n for n grid points and is extremely simple to implement in any number of dimensions monotonicity and stability properties of the fast sweeping algorithm are proven convergence and error estimates of the algorithm for computing the distance function is studied in detail it is shown that 2 n gauss seidel iterations is enough for the distance function in n dimensions an estimation of the number of iterations for general eikonal equations is also studied numerical examples are used to verify the analysis

an acoustic wave equation for anisotropic media a wave equation derived using the acoustic medium assumption for p waves in transversely isotropic ti media with a vertical symmetry axis vti media yields a good kinematic approximation to the familiar elastic wave equation for vti media the wavefield solutions obtained using this vti acoustic wave equation are free of shear waves which significantly reduces the computation time compared to the elastic wavefield solutions for exploding reflector type applications from this vti acoustic wave equation the eikonal and transport equations that describe the ray theoretical aspects of wave propagation in a ti medium are derived these equations based on the acoustic assumption shear wave velocity 0 are much simpler than their elastic counterparts yet they yield an accurate description of traveltimes and geometrical amplitudes numerical examples prove the usefulness of this acoustic equation in simulating the kinematic aspects of wave propagation in complex ti models

mathematical properties of a class of integro differential models from population genetics we propose a mathematical analysis of an integro differential model arising in population genetics the model describes the dynamics of fitness distribution in an asexual population under the effect of mutation and selection these two processes are represented by two nonlocal terms first we prove the existence and uniqueness of the solution and we derive asymptotic estimates of the distribution as the fitness tends to pm infty based on these asymptotic estimates we show that the cumulant generating function of the distribution is well defined and satisfies a linear nonlocal transport equation that we solve explicitly this explicit formula allows us to characterize the dependence of the long time behavior of the distribution with respect to the mutation kernel on the one hand if the kernel contains some beneficial mutations the distribution diverges which is reminiscent of the results of alfaro and carles siam j appl math 74 2014 pp 1919 1934 who analyzed a mutator replicator equat

a second order discontinuous galerkin fast sweeping method for eikonal equations in this paper we construct a second order fast sweeping method with a discontinuous galerkin dg local solver for computing viscosity solutions of a class of static hamilton jacobi equations namely the eikonal equations our piecewise linear dg local solver is built on a dg method developed recently y cheng c w shu a discontinuous galerkin finite element method for directly solving the hamilton jacobi equations journal of computational physics 223 2007 398 415 for the time dependent hamilton jacobi equations the causality property of eikonal equations is incorporated into the design of this solver the resulting local nonlinear system in the gauss seidel iterations is a simple quadratic system and can be solved explicitly the compactness of the dg method and the fast sweeping strategy lead to fast convergence of the new scheme for eikonal equations extensive numerical examples verify efficiency convergence and second order accuracy of the proposed method

complexity and approximability of scheduling resumable proportionally deteriorating jobs abstract a set of independent resumable and proportionally deteriorating jobs is to be executed on a single machine the machine is not continuously available for processing but the number of non availability periods the start time and end time of each period are known in advance the criterion of schedule optimality is the maximum completion time it is proved that the decision version of the problem with a single non availability period is ordinarily np complete it is also proved that for the problem with a single non availability period there exists a fully polynomial time approximation scheme finally it is proved that for the problem with two or more non availability periods there does not exist a polynomial time approximation algorithm with a constant worst case ratio unless p np

fast marching methods fast marching methods are numerical schemes for computing solutions to the nonlinear eikonal equation and related static hamilton jacobi equations based on entropy satisfying upwind schemes and fast sorting techniques they yield consistent accurate and highly efficient algorithms they are optimal in the sense that the computational complexity of the algorithms is o n log n where n is the total number of points in the domain the schemes are of use in a variety of applications including problems in shape offsetting computing distances from complex curves and surfaces shape from shading photolithographic development computing first arrivals in seismic travel times construction of shortest geodesics on surfaces optimal path planning around obstacles and visibility and reflection calculations in this paper we review the development of these techniques including the theoretical and numerical underpinnings provide details of the computational schemes including higher order versions and demonstrate the techniques in a collection of different areas

phase transitions and generalized motion by mean curvature we study the limiting behavior of solutions to appropriately rescaled versions of the allen cahn equation a simplified model for dynamic phase transitions we rigorously establish the existence in the limit of a phase antiphase interface evolving according to mean curvature motion this assertion is valid for all positive time the motion interpreted in the generalized sense of evans spruck and chen giga goto after the onset of geometric singularities

3 d traveltime computation using huygens wavefront tracing traveltime computation is widely used in seismic modeling imaging and velocity analysis the two most commonly used methods are ray tracing and numerical solutions to the eikonal equation eikonal solvers are fast and robust but are limited to computing only the first arrival traveltimes ray tracing can compute multiple arrivals but lacks the robustness of eikonal solvers we propose a robust and complete method of traveltime computation it is based on a system of partial differential equations which is equivalent to the eikonal equation but formulated in the ray coordinates system we use a first order discretization scheme that is interpreted very simply in terms of the huygens s principle our explicit finite difference solution to the eikonal equation solved in the ray coordinates system delivers both computational speed and stability since we use more than one point on the current wavefront at every time step the finite difference method has proven to be a robust alternative to conventional ray tracing while being faster and having a better ability to handle rough velocity media and penetrate shadow zones

travelling wave solutions for an infection age structured model with diffusion in this article we study the existence of travelling waves for a class of epidemic models structured in space and with respect to the age of infection we obtain a necessary and sufficient condition for the existence of travelling waves for such a class of problems as a consequence of our main result we also derive the existence of travelling waves of a class of functional partial derivative equations

concentration estimates in a multi host epidemiological model structured by phenotypic traits in this work we consider an epidemic system modelling the evolution of a spore producing pathogen within a multi host population of plants here we focus our analysis on the study of the stationary states we first discuss the existence of such nontrivial states by using the theory of global attractors then we introduce a small parameter epsilon that characterises the width of the mutation kernel and we describe the asymptotic shape of steady states with respect to epsilon in particular we show that the distribution of spores converges to the singular measure concentrated on the maxima of fitness of the pathogen in each plant population this asymptotic description allows us to show the local stability of each of the positive steady states in the regime of narrow mutations from which we deduce a uniqueness result for the nontrivial stationary states by means of a topological degree argument these analyses rely on a careful investigation of the spectral properties of some non local operators

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

ordered upwind methods for static hamilton jacobi equations theory and algorithms we develop a family of fast methods for approximating the solutions to a wide class of static hamilton jacobi pdes these fast methods include both semi lagrangian and fully eulerian versions numerical solutions to these problems are typically obtained by solving large systems of coupled nonlinear discretized equations our techniques which we refer to as ordered upwind methods oums use partial information about the characteristic directions to decouple these nonlinear systems greatly reducing the computational labor our techniques are considered in the context of control theoretic and front propagation problems we begin by discussing existing oums focusing on those designed for isotropic problems we then introduce a new class of oums which decouple systems for general anisotropic problems we prove convergence of one such scheme to the viscosity solution of the corresponding hamilton jacobi pde next we introduce a set of finite differences methods based on an analysis of the role played by anisotropy in the context of front propagation and optimal trajectory problems the performance of the methods is analyzed and computational experiments are performed using test problems from computational geometry and seismology

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

travelling wave solutions for a non local evolutionary epidemic system abstract in this work we study the travelling wave solutions for a spatially distributed system of equations modelling the evolutionary epidemiology of plant pathogen interaction here the mutation process is described using a non local convolution operator in the phenotype space using dynamical system ideas coupled with refined estimates on the asymptotic behaviour of the profiles we prove that the wave solutions have a rather simple structure this analysis allows us to reduce the infinite dimensional travelling wave profile system of equations to a four dimensional ode system the latter is used to prove the existence of travelling wave solutions for any wave speed larger than a minimal wave speed c provided some parameters condition expressed using the principle eigenvalue of some integral operator it is also used to prove that any travelling wave solution connects two determined stationary states

scanning anisotropy parameters in complex media parameter estimation in an inhomogeneous anisotropic medium offers many challenges chief among them is the trade off between inhomogeneity and anisotropy it is especially hard to estimate the anisotropy anellipticity parameter in complex media using perturbation theory and taylor s series i have expanded the solutions of the anisotropic eikonal equation for transversely isotropic ti media with a vertical symmetry axis vti in terms of the independent parameter from a generally inhomogeneous elliptically anisotropic medium background this new vti traveltime solution is based on a set of precomputed perturbations extracted from solving linear partial differential equations the traveltimes obtained from these equations serve as the coefficients of a taylor type expansion of the total traveltime in terms of shanks transform is used to predict the transient behavior of the expansion and improve its accuracy using fewer terms a homogeneous medium simplification of the expansion provides classic

minimizing the total completion time in single machine scheduling with aging deteriorating effects and deteriorating maintenance activities in a real manufacturing system a machine may need multiple maintenance activities to improve its production efficiency due to the effects of aging or deteriorating this paper considers scheduling with aging or deteriorating effects and deteriorating maintenance activities simultaneously on a single machine we assume that the machine may be subject to several maintenance activities during the planning horizon however due to the restriction of budget of maintenance the upper bound of the maintenance frequency on the machine is assumed to be known in advance moreover we assume that the duration of each maintenance activity depends on the running time of the machine the objective is to find jointly the optimal maintenance frequencies the optimal maintenance positions and the optimal job sequence for minimizing the total completion time we show that all the problems studied are polynomially solvable

the computational complexity analysis of the two processor flowshop problems with position dependent job processing times the two processor flowshop makespan scheduling with piecewise linear position learning aging effects is strongly np hard the two processor flowshop makespan scheduling with common linear position learning aging effects is polynomially solvable the boundary between polynomially solvable and np hard has been is compressed the strong np hardness proof supporting method is described in this paper we analyse the makespan minimization problem in the two processor flowshop environment where the processing time of each job depends on its position in a sequence a position dependent job processing time that is equivalent to the number of previously processed jobs namely if processing times of jobs increase with the number of processed jobs then the aging fatigue deterioration effect is modelled whereas the non increasing dependency describes the learning effect we prove that the considered problem becomes strongly np hard if the processing time of each job is described by a piecewise linear function dependent on its position in a sequence we analyse two types of functions non decreasing aging and non increasing learning furthermore we describe the strong np hardness proof supporting method and elucidate correctness of our other strong np hardness proofs additionally we provide a modification of the johnson s algorithm and prove that it optimally solves the considered problem in the two processor flowshop environment if job processing times are characterized by a common linear non increasing or non decreasing dependency on a job position

a boundary condition capturing method for poisson s equation on irregular domains interfaces have a variety of boundary conditions or jump conditions that need to be enforced the ghost fluid method gfm was developed to capture the boundary conditions at a contact discontinuity in the inviscid euler equations and has been extended to treat more general discontinuities such as shocks detonations and deflagrations and compressible viscous flows in this paper a similar boundary condition capturing approach is used to develop a new numerical method for the variable coefficient poisson equation in the presence of interfaces where both the variable coefficients and the solution itself may be discontinuous this new method is robust and easy to implement even in three spatial dimensions furthermore the coefficient matrix of the associated linear system is the standard symmetric matrix for the variable coefficient poisson equation in the absence of interfaces allowing for straightforward application of standard black box solvers

capturing the behavior of bubbles and drops using the variational level set approach we reproduce the general behavior of complicated bubble and droplet motions using the variational level set formulation introduced by the authors earlier our approach here ignores inertial effects thus the motion is only correct as an approximation for very viscous problems however the steady states are true equilibrium solutions inertial forces will be added in future work the problems include soap bubbles colliding and merging drops falling or remaining attached to a generally irregular ceiling and liquid penetrating through a funnel in both two and three dimensions each phase is identified with a particular level set function the zero level set of this function is that particular phase boundary the level set functions all evolve in time through a constrained gradient descent procedure so as to minimize an energy functional the functions are coupled through physical constraints and through the requirements that different phases do not overlap and vacuum regions do not develop both boundary conditions and inequality constraints are cast in terms of either local or global equality constraints the gradient projection method leads to a system of perturbed by curvature if surface tension is involved hamilton jacobi equations coupled through a constraint the coupling is enforced using the lagrange multiplier associated with this constraint the numerical implementation requires much of the modern level set technology in particular we achieve a significant speed up by using the fast localization algorithm of h k zhao m kang b merriman d peng and s osher

scheduling linear deteriorating jobs with an availability constraint on a single machine we consider a single machine scheduling problem in which the processing time of a job is a simple linear increasing function of its starting time and the machine is subject to an availability constraint we consider the non resumable case the objectives are to minimize the makespan and the total completion time we show that both problems are np hard and present pseudopolynomial time optimal algorithms to solve them furthermore for the makespan problem we present an optimal approximation algorithm for the on line case and a fully polynomial time approximation scheme for the off line case for the total completion time problem we provide a heuristic and evaluate its efficiency by computational experiments

a boundary condition capturing method for incompressible flame discontinuities abstract in this paper we propose a new numerical method for treating two phase incompressible flow where one phase is being converted into the other e g the vaporization of liquid water we consider this numerical method in the context of treating discontinuously thin flame fronts for incompressible flow this method was designed as an extension of the ghost fluid method 1999 j comput phys 152 457 and relies heavily on the boundary condition capturing technology developed in liu et al 2000 j comput phys 154 15 for the variable coefficient poisson equation and in kang et al in press j comput phys for multiphase incompressible flow our new numerical method admits a sharp interface representation similar to the method proposed in helenbrook et al 1999 j comput phys 148 366 since the interface boundary conditions are handled in a simple and straightforward fashion the code is very robust e g no special treatment is required to treat the merging of flame fronts the method is presented in three spatial dimensions with numerical examples in one two and three spatial dimensions

3 d traveltime computation using the fast marching method we present a fast algorithm for solving the eikonal equation in three dimensions based on the fast marching method the algorithm is of the order o n log n where n is the total number of grid points in the computational domain the algorithm can be used in any orthogonal coordinate system and globally constructs the solution to the eikonal equation for each point in the coordinate domain the method is unconditionally stable and constructs solutions consistent with the exact solution for arbitrarily large gradient jumps in velocity in addition the method resolves any overturning propagation wavefronts we begin with the mathematical foundation for solving the eikonal equation using the fast marching method and follow with the numerical details we then show examples of traveltime propagation through the seg eage salt model using point source and planewave initial conditions and analyze the error in constant velocity media the algorithm allows for any shape of the initial wavefront while a point source is the most commonly used initial condition initial plane waves can be used for controlled illumination or for downward continuation of the traveltime field from one depth to another or from a topographic depth surface to another the algorithm presented here is designed for computing first arrival traveltimes nonetheless since it exploits the fast marching method for solving the eikonal equation we believe it is the fastest of all possible consistent schemes to compute first arrivals

markov chain approximations for deterministic control problems with affine dynamics and quadratic cost in the control we consider the construction of markov chain approximations for an important class of deterministic control problems the emphasis is on the construction of schemes that can be easily implemented and which possess a number of highly desirable qualitative properties the class of problems covered is that for which the control is affine in the dynamics and with quadratic running cost this class covers a number of interesting areas of application including problems that arise in large deviations risk sensitive and robust control robust filtering and certain problems in computer vision examples are given as well as a proof of convergence

a front tracking method for viscous incompressible multi fluid flows abstract a method to simulate unsteady multi fluid flows in which a sharp interface or a front separates incompressible fluids of different density and viscosity is described the flow field is discretized by a conservative finite difference approximation on a stationary grid and the interface is explicitly represented by a separate unstructured grid that moves through the stationary grid since the interface deforms continuously it is necessary to restructure its grid as the calculations proceed in addition to keeping the density and viscosity stratification sharp the tracked interface provides a natural way to include surface tension effects both two and three dimensional full numerical simulations of bubble motion are presented

efficient traveltime solutions of the acoustic ti eikonal equation numerical solutions of the eikonal hamilton jacobi equation for transversely isotropic ti media are essential for imaging and traveltime tomography applications such solutions however suffer from the inherent higher order nonlinearity of the ti eikonal equation which requires solving a quartic polynomial for every grid point analytical solutions of the quartic polynomial yield numerically unstable formulations thus it requires a numerical root finding algorithm adding significantly to the computational load using perturbation theory we approximate in a first order discretized form the ti eikonal equation with a series of simpler equations for the coefficients of a polynomial expansion of the eikonal solution in terms of the anellipticity anisotropy parameter such perturbation applied to the discretized form of the eikonal equation does not impose any restrictions on the complexity of the perturbed parameter field therefore it provides accurate traveltime solutions even for models with complex distribution of velocity and anisotropic anellipticity parameter such as that for the complicated marmousi model the formulation allows for large cost reduction compared to using the direct ti eikonal solver furthermore comparative tests with previously developed approximations illustrate remarkable gain in accuracy in the proposed algorithm without any addition to the computational cost

global analysis of new malaria intrahost models with a competitive exclusion principle in this paper we propose a malaria within host model with k classes of age for the parasitized red blood cells and n strains for the parasite we provide a global analysis for this model a competitive exclusion principle holds if mathcal r 0 the basic reproduction number satisfies mathcal r 0 leq 1 then the disease free equilibrium is globally asymptotically stable on the contrary if mathcal r 0 1 then generically there is a unique endemic equilibrium which corresponds to the endemic stabilization of the most virulent parasite strain and to the extinction of all the other parasites strains we prove that this equilibrium is globally asymptotically stable on the positive orthant if a mild sufficient condition is satisfied

hybrid multifluid algorithms extensions of many successful single component schemes to compute multicomponent gas dynamics suffer from oscillations and other computational inaccuracies near material interfaces that are caused by the failure of the schemes to maintain pressure equilibrium between the fluid components a new algorithm based on the compressible euler equations for multicomponent fluids augmented by the pressure evolution equation is presented the extended set of equations offers two alternative ways to update the pressure field i using the equation of state or ii using the pressure evolution equation in a numerical implementation these two procedures generally yield different answers the former is a standard conservative update but may produce oscillations near material interfaces the latter is nonconservative but becomes exact near interfaces and automatically maintains pressure equilibrium a hybrid scheme which selects from the two pressure update procedures is presented the scheme perfectly conserves total mass and momentum and conserves total energy everywhere except at a finite very small number of grid cells computed solutions exhibit oscillation free interfaces and have em negligible relative conservation errors in total energy even for very strong shocks the proposed hybrid approach and switching strategies are independent of the numerical implementation and may provide a simple framework within which to extend one s favourite scheme to solve multifluid dynamics

motion of curves in three spatial dimensions using a level set approach the level set method was originally designed for problems dealing with codimension one objects where it has been extremely succesful especially when topological changes in the interface i e merging and breaking occur attempts have been made to modify it to handle objects of higher codimension such as vortex filaments while preserving the merging and breaking property we present numerical simulations of a level set based method for moving curves in r3 the model problem for higher codimension that allows for topological changes a vector valued level set function is used with the zero level set representing the curve our results show that this method can handle many types of curves moving under all types of geometrically based flows while automatically enforcing merging and breaking