condition for intracellular adaptive dynamics for chemotaxis chemotaxis is ubiquitously performed by bacteria they sense and move toward a region with a higher concentration of an attractive chemical by changing the rate of tumbling for random walk we numerically studied several models with internal adaptive dynamics to examine the validity of the condition for chemotaxis proposed by oosawa and nakaoka j theor biol 66 747 1977 which states that the time scale of tumbling frequency must be smaller than that of adaptation and greater than that of sensing suitable renormalization of the time scales showed that the condition holds for a variety of environments and for both short and long term behavior

feedback control for linear time invariant systems with state and control bounds in the presence of disturbances the problem of the stabilizing linear control synthesis in the presence of state and input bounds for systems with additive unknown disturbances is considered the only information required about the disturbances is a finite convex polyhedral bound discrete and continuous time systems are considered the property of positive d invariance of a region is introduced and it is proved that a solution of the problem is achieved by the selection of a polyhedral set s and the computation of a feedback matrix k such that s is positively d invariant for the closed loop system it is shown that if polyhedral sets are considered the solution involves simple linear programming algorithms however the procedure suggested requires a great amount of computational work offline if the state space dimension is large because the feedback matrix k is obtained as a solution of a large set of linear inequalities all of the vertices of s are required

adaptive mesh and algorithm refinement using direct simulation monte carlo adaptive mesh and algorithm refinement amar embeds a particle method within a continuum method at the finest level of an adaptive mesh refinement amr hierarchy the coupling between the particle region and the overlaying continuum grid is algorithmically equivalent to that between the fine and coarse levels of amr direct simulation monte carlo dsmc is used as the particle algorithm embedded within a godunov type compressible navier stokes solver several examples are presented and compared with purely continuum calculations

free vibrations of beams with a single edge crack abstract the equation of motion and associated boundary conditions are derived for a uniform bernoulli euler beam containing one single edge crack the generalized variational principle used allows for modified stress strain and displacement fields that satisfy the compatibility requirements in the vicinity of the crack the concentration in stress is represented by introducing a crack function into the beam s compatibility relations a displacement function is also introduced to modify the in plane displacement and its slope near the crack both functions are chosen to have their maximum value at the cracked section and to decay exponentially along the beam s longitudinal direction the rate of exponential decay is evaluated from finite element calculations the resulting equation of motion is solved for simply supported and cantilevered beams with single edge cracks by a galerkin and a local ritz procedure respectively these theoretical natural frequencies and mode shapes match closely with experimental and finite element results the possibility of determining the damage properties of cracked beams from changes in dynamic behavior is discussed

an equation free computational approach for extracting population level behavior from individual based models of biological dispersal abstract the movement of many organisms can be described as a random walk at either or both the individual and population level the rules for this random walk are based on complex biological processes and it may be difficult to develop a tractable quantitatively accurate individual level model however important problems in areas ranging from ecology to medicine involve large collections of individuals and a further intellectual challenge is to model population level behavior based on a detailed individual level model because of the large number of interacting individuals and because the individual level model is complex classical direct monte carlo simulations can be very slow and often of little practical use in this case an equation free approach i g kevrekidis c w gear j m hyman p kevrekidis o runborg k theodoropoulos equation free coarse grained multiscale computation enabling microscopic simulators to perform system level analysis commun math sci 1 4 2003 715 762 may provide effective methods for the analysis and simulation of individual based models in this paper we analyze equation free coarse projective integration for analytical purposes we start with known partial differential equations describing biological random walks and we study the projective integration of these equations in particular we illustrate how to accelerate explicit numerical methods for solving these equations then we present illustrative kinetic monte carlo simulations of these random walks and show that a decrease in computational time by as much as a factor of a thousand can be obtained by exploiting the ideas developed by analysis of the closed form pdes the illustrative biological example here is chemotaxis but it could be any random walker that biases its movement in response to environmental cues

controlled invariance and feedback laws we consider controlled invariance for cones translated cones polyhedra and various special polyhedral structures for any polyhedron if controlled invariance occurs then all and nothing but the admissible controls can be obtained by an inequative feedback controller for each special polyhedral structure we compare this feedback controller against piecewise affine linear and affine feedback controllers

on the use of reverse brownian motion to accelerate hybrid simulations multiscale and multiphysics simulations are two rapidly developing fields of scientific computing efficient coupling of continuum deterministic or stochastic constitutive solvers with their discrete stochastic particle based counterparts is a common challenge in both kinds of simulations we focus on interfacial tightly coupled simulations of diffusion that combine continuum and particle based solvers the latter employs the reverse brownian motion rbm a monte carlo approach that allows one to enforce inhomogeneous dirichlet neumann or robin boundary conditions and is trivially parallelizable we discuss numerical approaches for improving the accuracy of rbm in the presence of inhomogeneous neumann boundary conditions and alternative strategies for coupling the rbm solver with its continuum counterpart numerical experiments are used to investigate the convergence stability and computational efficiency of the proposed hybrid algorithm

kinetic solvers with adaptive mesh in phase space an adaptive mesh in phase space amps methodology has been developed for solving multidimensional kinetic equations by the discrete velocity method a cartesian mesh for both configuration r and velocity v spaces is produced using a tree of trees tot data structure the r mesh is automatically generated around embedded boundaries and is dynamically adapted to local solution properties the v mesh is created on the fly in each r cell mappings between neighboring v space trees is implemented for the advection operator in r space we have developed algorithms for solving the full boltzmann and linear boltzmann equations with amps several recent innovations were used to calculate the discrete boltzmann collision integral with dynamically adaptive v mesh the importance sampling multipoint projection and variance reduction methods we have developed an efficient algorithm for calculating the linear boltzmann collision integral for elastic and inelastic collisions of hot light particles in a lorentz gas our amps technique has been demonstrated for simulations of hypersonic rarefied gas flows ion and electron kinetics in weakly ionized plasma radiation and light particle transport through thin films and electron streaming in semiconductors we have shown that amps allows minimizing the number of cells in phase space to reduce the computational cost and memory usage for solving challenging kinetic problems

model adaptivity for goal oriented inference using adjoints abstract an inverse problem seeks to infer unknown model parameters using observed data we consider a goal oriented inverse problem where the goal of inferring parameters is to use them in predicting a quantity of interest qoi recognizing that multiple models of varying fidelity and computational cost may be available to describe the physical system we formulate a goal oriented model adaptivity approach that leverages multiple models while controlling the error in the qoi prediction in particular we adaptively form a mixed fidelity model by using models of different levels of fidelity in different subregions of the domain taking the solution of the inverse problem with the highest fidelity model as our reference qoi prediction we derive an adjoint based third order estimate for the qoi error from using a lower fidelity model localization of this error then guides the formation of mixed fidelity models we demonstrate the method for example problems described by convection diffusion reaction models for these examples our mixed fidelity models use the high fidelity model over only a small portion of the domain but result in qoi estimates with small relative errors we also demonstrate that the mixed fidelity inverse problems can be cheaper to solve and less sensitive to the initial guess than the high fidelity inverse problems

computing the maximum robust controlled invariant subspace abstract an algorithm is presented to compute the maximum robust controlled invariant subspace contained in a given subspace it is based on a special computational scheme to derive the intersection of a family of subspaces which is particularly convenient when the system coefficients depend polynomially on the uncertain parameter an example is presented to illustrate the algorithm

hybrid continuum molecular simulations of transient gas flows with rarefaction an adaptively coupled continuum molecular approach for compressible viscous flows in transient calculations is presented the continuum domain is described by the unsteady compressible navier stokes equations and the molecular domain is solved by direct simulation monte carlo a strategy is described to extend the overlapped schwarz method with dirichlet dirichlet boundary condition coupling procedure to transient simulations the method has been successfully validated against full direct simulation monte carlo results for transient simulations of a one dimensional shock tube and a two dimensional pressure driven slit flow a sensitivity analysis showed that the used overlapped schwarz coupling method with dirichlet dirichlet boundary conditions is only weakly sensitive to various parameters e g the exact position of the continuum molecular interface the size of the overlap region and the scatter in the molecular solution which is a clear advantage over the more commonly used flux based coupling technique another advantage of the chosen coupling method is that the continuum and molecular time steps can be decoupled and that in general a coupling time step can be used that is much larger than the molecular time step the study performed also highlighted a limit of the method it was found to be necessary to keep the courant number based on the coupling time step the cell size in the continuum region and the molecular most probable velocity below 1 to avoid instabilities

hybrid block amr in cartesian and curvilinear coordinates mhd applications abstract we present a novel hybrid block adaptive scheme for use in solving sets of near conservation laws in general orthogonal coordinate systems the adaptive mesh refinement amr scheme is block based i e individual grids have a pre fixed number of grid cells and is implemented for any dimensionality d its hybrid character relaxes the common approach where a block that needs refinement triggers 2 d subblocks when grids are refined by a factor of 2 this introduces incomplete families in the grid hierarchy but approaches the optimal fit to developing flow features inherent in the original patch based amr strategy our hybrid block amr approach is compared with a patch based amr one both exploiting openmp parallelism the implementation is able to handle general curvilinear coordinates for which restriction and prolongation formulae are presented along with boundary treatments at singular boundaries demonstrative examples cover hydro and magnetohydrodynamic mhd applications including tests on a 2d polar grid a 2 5d spherical and a 3d cylindrical configuration the applications cover classical up to relativistic mhd simulations of particular relevance for astrophysical magnetized jet and stellar wind studies

generation of the chapman enskog distribution a pair of simple efficient and robust algorithms for generating random velocities sampled from the chapman enskog distribution is presented

development and verification of a coupled dsmc ns scheme using unstructured mesh an efficient and accurate parallel coupled dsmc ns method using three dimensional unstructured grid topology is proposed and verified for the simulation of high speed gas flows involving continuum and rarefied regimes a domain overlapping strategy taking advantage of unstructured data format with dirichlet dirichlet type boundary conditions based on two breakdown parameters is used iteratively to determine the choice of solvers in the spatial domain the selected breakdown parameters for this study include 1 a local maximum knudsen number defined as the ratio of the local mean free path and local characteristic length based on property gradient and 2 a thermal non equilibrium indicator defined as the ratio of the difference between translational and rotational temperatures to the translational temperature a supersonic flow m 4 over a quasi 2 d 25 wedge is employed as the first step in verifying the present coupled method the results of simulation using the coupled method are in excellent agreement with those of the pure dsmc method which is taken as the benchmark solution effects of the size of overlapping regions and the choice of breakdown parameters on the convergence history are discussed results show that the proposed iteratively coupled method predicts the results more accurately as compared to the one shot coupled method which has been often used in practice further a realistic 3 d nitrogen flow which two near continuum parallel orifice jets underexpand into a near vacuum environment is simulated using the present coupled method to demonstrate its capability finally developments in extending the present method are also outlined in this paper

coupling boltzmann and navier stokes equations by friction the aim of this paper is to introduce and validate a coupled navier stokes boltzman approach for the calculation of hypersonic rarefied flows around manoeuvering vehicles the proposed strategy uses locally a kinetic model in the boundary layer coupled through wall friction forces to a global navier stokes solver dif ferent numerical experiments illustrate the potentialities of the method

reduction of simulation cost and error for particle simulations of rarefied flows abstract the computational cost in simulating a steady rarefied gas flow by use of a particle method is shown to be greatly reduced if the simulation employs an average number of particles per cell that is greater than a certain approximate minimum the minimum value depends on the rms level of statistical fluctuations judged acceptable in the resultant data and is found to be significantly greater than values often used in practice when two and three dimensional flows are simulated the computational cost is found to remain fixed for values greater than the minimum showing that the ensemble and time averaging operations become interchangeable for the problem studied it is shown that a regime exists for which computational cost may be reduced by a factor of 10 by merely increasing the size of the simulation by a factor of five when holding the rms level of statistical fluctuations fixed

approximate calculation of the fundamental frequency for bending vibrations of cracked beams abstract a simplified method of evaluating the fundamental frequency for the bending vibrations of cracked euler bernouilli beams is presented the method is based on the well known approach of representing the crack in a beam through a hinge and an elastic spring but here the transverse deflection of the cracked beam is constructed by adding polynomial functions to that of the uncracked beam with this new admissible function which satisfies the boundary and the kinematic conditions and by using the rayleigh method the fundamental frequency is obtained this approach is applied to simply supported beams with a cracked section in any location of the span for this case the method provides closed form expressions for the fundamental frequency its validity is confirmed by comparison with numerical simulation results

deciding the nature of the coarse equation through microscopic simulations the baby bathwater scheme recent developments in multiscale computation allow the solution of coarse equations for the expected macroscopic behavior of microscopically evolving particles without ever obtaining these coarse equations in closed form the closure is obtained on demand through appropriately initialized bursts of microscopic simulation the effective coupling of microscopic simulators with macroscopic behavior requires certain decisions about the nature of the unavailable coarse equation such decisions include a the highest spatial derivative active in the coarse equation b whether the equation satisfies certain conservation laws or c whether the coarse dynamics is hamiltonian or dissipative these decisions affect the number and type of boundary conditions as well as the algorithms employed in the absence of an explicit formula for the temporal derivative we propose implement and validate a simple scheme for deciding these and other similar questions about the coarse equation using only the microscopic simulator simulations under periodic boundary conditions are carried out for appropriately chosen families of random initial conditions evaluating the sample variance of certain statistics over the simulation ensemble allows us to infer the highest order of spatial derivatives active in the coarse equation in the same spirit we show how to determine whether a certain coarse conservation law exists or not and we discuss plausibility tests for the existence of a coarse hamiltonian or integrability we believe that such schemes constitute an important part of the equation free approach to multiscale computation

from individual to collective behavior in bacterial chemotaxis bacterial chemotaxis is widely studied from both the microscopic cell and macroscopic population points of view and here we connect these very different levels of description by deriving the classical macroscopic description for chemotaxis from a microscopic model of the behavior of individual cells the analysis is based on the velocity jump process for describing the motion of individuals such as bacteria wherein each individual carries an internal state that evolves according to a system of ordinary differential equations forced by a time and or space dependent external signal in the problem treated here the turning rate of individuals is a functional of the internal state which in turn depends on the external signal using moment closure techniques in one space dimension we derive and analyze a macroscopic system of hyperbolic differential equations describing this velocity jump process using a hyperbolic scaling of space and time we obtain a single second order hyperbolic equation for the

wave motion analysis in arch structures via wavelet finite element method abstract the application of b spline wavelet on interval bswi finite element method for wave motion analysis in arch structures is presented in this paper instead of traditional polynomial interpolation scaling functions at certain scales have been adopted to form the shape functions and construct wavelet based elements different from other wavelet numerical methods adding wavelets directly the element displacement field represented by the coefficients of wavelets expansions is transformed from wavelet space to physical space via the corresponding transformation matrix the energy functional of the arch is obtained by the generalized shell theory and the finite element model for wave motion analysis is constructed according to hamilton s principle and the central difference method in time domain taking the practical application into account damaged arch waveguides are also investigated proper analysis of the responses from structure damages allows one to indicate the location very precisely this paper mainly focuses on the crack in structures based on castigliano s theorem and the pairs equation the local flexibility of crack is formulated for bswi element numerical experiments are performed to study the effect of wave propagations in arch waveguides that is frequency dispersion and mode spilt in the arch the responses of the arch with cracks are simulated under the broad band narrow band and chirp excitations in order to estimate the spatial time and frequency concentrations of responses the reciprocal length time frequency transform and correlation coefficient are introduced in this investigation

a set induced norm approach to the robust control of constrained systems most realistic control problems involve both some type of time domain constraints and model uncertainty however the majority of controller design procedures currently available focus only on one aspect of the problem with only a handful of methods capable of simultaneously addressing both issues recently it has been proposed to address this class of problems by using a constrained robustness measure generated by a constraint set induced operator norm to assess the stability properties of a family of systems in this paper the properties of this constrained robustness measure are explored and the theoretical framework is extended to include control as well as state constraints these results are applied to the problem of designing fixed order stabilizing feedback controllers for systems subject to structured parametric model uncertainty and time domain constraints

positively invariant sets for constrained continuous time systems with cone properties this note deals with some properties of particular bounded sets w r t linear continuous time systems described by x spl dot t a 0 x t c t where c t spl isin spl omega spl sub r sup n spl omega a compact set and matrix e sup ta 0 has the property of leaving a proper cone k positively invariant that is e sup ta 0 k spl sub k the considered bounded sets spl dscr k a b are described as the intersection of shifted cones necessary and sufficient conditions are given they guarantee that such sets are positively invariant w r t the considered system the trajectories starting from x sub 0 spl isin r sup n spl dscr k a b respectively to x sub 0 spl isin r sup n are studied in terms of attractivity and contractivity of the set spl dscr k a b the results are applied to the study of the constrained state feedback regulator problem

a hybrid method for hydrodynamic kinetic flow part i a particle grid method for reducing stochastic noise in kinetic regimes in this work we present a hybrid particle grid monte carlo method for the boltzmann equation which is characterized by a significant reduction of the stochastic noise in the kinetic regime the hybrid method is based on a first order splitting in time to separate the transport from the relaxation step the transport step is solved by a deterministic scheme while a hybrid dsmc based method is used to solve the collision step such a hybrid scheme is based on splitting the solution in a collisional and a non collisional part at the beginning of the collision step and the dsmc method is used to solve the relaxation step for the collisional part of the solution only this is accomplished by sampling only the fraction of particles candidate for collisions from the collisional part of the solution performing collisions as in a standard dsmc method and then projecting the particles back onto a velocity grid to compute a piecewise constant reconstruction for the collisional part of the solution the latter is added to a piecewise constant reconstruction of the non collisional part of the solution which in fact remains unchanged during the relaxation step numerical results show that the stochastic noise is significantly reduced at large knudsen numbers with respect to the standard dsmc method indeed in this algorithm the particle scheme is applied only on the collisional part of the solution so only this fraction of the solution is affected by stochastic fluctuations but since the collisional part of the solution reduces as the knudsen number increases stochastic noise reduces as well at large knudsen numbers

on invariant sets for constrained discrete time linear systems with disturbances and parametric uncertainties we consider discrete time linear systems with disturbances and parametric uncertainties in the matrix a with constraints on both control and state variables we give the explicit expression of maximal sets of disturbances and or parameters such that it is possible to control the state trajectory of the system to the given constraining set the case of static linear state feedback control is analyzed

coupling of the boltzmann and euler equations with automatic domain decomposition a criterion for automatic domain decomposition has been introduced for the coupling of the boltzmann and euler equations this criterion is obtained by using the grad s 13 moments expansion method the boltzmann and euler equations have been solved by the particle method this criterion has been further tested for the spatial homogeneous relaxation case and the coupling of the boltzmann and euler equations in two dimensional physical space some numerical results obtained from the particle code of the full boltzmann equation are compared with those of coupling of the boltzmann and euler equations

on positively invariant sets for discrete time linear systems with disturbance an application of maximal disturbance sets this note concerns the investigation of maximal sets with respect to which a set is positively invariant and given a set a some properties of spl delta p i sets are analyzed the approach uses one step of the backward recursion introduced in d alessandro and de santis 1991 where feasibility and optimality conditions for linear dynamical input and or state constrained systems were analyzed in section ii the author gives the main definitions and some basic results in the subsequent section iii some properties of spl delta p i sets are investigated the particular case of polyhedral sets is analyzed in section iv in section v the author shows an application to linear systems with parametric uncertainties in the dynamic matrix a the author develops a technique to determine a set in the parameters space such that for any value of the parameter in the set a given set in the state space is positively invariant in the last section a numerical example is developed

projective methods for stiff differential equations problems with gaps in their eigenvalue spectrum we show that there exist classes of explicit numerical integration methods that can handle very stiff problems if the eigenvalues are separated into two clusters one containing the stiff or fast components and one containing the slow components these methods have large average step sizes relative to the fast components conventional implicit methods involve the solution of nonlinear equations at each step which for large problems requires significant communication between processors on a multiprocessor machine for such problems the methods proposed here have significant potential for speed improvement

free vibration and lateral buckling of a cantilever slender beam with an edge crack experimental and numerical studies the effects of crack ratios and positions on the fundamental frequencies and buckling loads of slender cantilever euler beams with a single edge crack are investigated both experimentally and numerically using the finite element method based on energy approach the governing matrix equations are derived from the standard and cracked beam elements combined with the local flexibility concept the experiments are conducted using specimens having edge cracks of different depths at different positions to validate the numerical results obtained the numerical results are shown to be in good agreement with the experimental results for the considered crack ratios

an unsplit 3d upwind method for hyperbolic conservation laws abstract an unsplit upwind method for solving hyperbolic conservation laws in three dimensions is developed this paper derives the algorithm by generalizing a two dimensional advection algorithm of van leer and colella to three dimensions and then making appropriate modifications the method is implemented using the equations of gas dynamics several test problems are computed to both verify and display the behavior of the method these test problems include a 1d blast wave a 2d shock reflection off a 30 ramp and a 3d astrophysical jet

an adaptive domain decomposition procedure for boltzmann and euler equations in this paper we present a domain decomposition approach for the coupling of boltzmann and euler equations particle methods are used for both equations this leads to a simple implementation of the coupling procedure and to natural interface conditions between the two domains adaptive time and space discretizations and a direct coupling procedure lead to considerable gains in cpu time compared to a solution of the full boltzmann equation several test cases involving a large range of knudsen numbers are numerically investigated

algorithm refinement for stochastic partial differential equations ii correlated systems we analyze a hybrid particle continuum algorithm for a hydrodynamic system with long ranged correlations specifically we consider the so called train model for viscous transport in gases which is based on a generalization of the random walk process for the diffusion of momentum this discrete model is coupled with its continuous counterpart given by a pair of stochastic partial differential equations at the interface between the particle and continuum computations the coupling is by flux matching giving exact mass and momentum conservation this methodology is an extension of our stochastic algorithm refinement ar hybrid for simple diffusion f alexander a garcia d tartakovsky algorithm refinement for stochastic partial differential equations i linear diffusion j comput phys 182 2002 47 66 results from a variety of numerical experiments are presented for steady state scenarios in all cases the mean and variance of density and velocity are captured correctly by the stochastic hybrid algorithm for a non stochastic version i e using only deterministic continuum fluxes the long range correlations of velocity fluctuations are qualitatively preserved but at reduced magnitude

projective and coarse projective integration for problems with continuous symmetries temporal integration of equations possessing continuous symmetries e g systems with translational invariance associated with traveling solutions and scale invariance associated with self similar solutions in a co evolving frame i e a frame which is co traveling co collapsing or co exploding with the evolving solution leads to improved accuracy because of the smaller time derivative in the new spatial frame the slower time behavior permits the use of projective and coarse projective integration with longer projective steps in the computation of the time evolution of partial differential equations and multiscale systems respectively these methods are also demonstrated to be effective for systems which only approximately or asymptotically possess continuous symmetries the ideas of projective integration in a co evolving frame are illustrated on the one dimensional translationally invariant nagumo partial differential equation pde a corresponding kinetic monte carlo model motivated from the nagumo kinetics is used to illustrate the coarse grained method a simple one dimensional diffusion problem is used to illustrate the scale invariant case the efficiency of projective integration in the co evolving frame for both the macroscopic diffusion pde and for a random walker particle based model is again demonstrated

an analysis of equivalent operator preconditioning for equation free newton krylov methods we consider the computation of a fixed point of a time stepper using newton krylov methods and propose and analyze equivalent operator preconditioning for the resulting linear systems for a linear scalar advection reaction diffusion equation we investigate in detail how the convergence rate depends upon the choice of preconditioner parameters and upon the time discretization the results are especially valuable when computing fixed points of a coarse time stepper in the equation free multiscale framework in which one simulates an unavailable coarse scale model by wrapping a set of computational routines around appropriately initialized fine scale simulations both analytical results and numerical experiments are presented showing that one can speed up the convergence of iterative methods significantly for a wide range of parameter values in the preconditioner

three dimensional adaptive mesh refinement for hyperbolic conservation laws a local adaptive mesh refinement algorithm for solving hyperbolic systems of conservation laws in three space dimensions is described the method is based on the use of local grid patches superimpo

on the robust controlled invariant abstract the robust controlled invariant is defined as a tool to characterize systems subject to parameter changes and to set up a geometric approach to robustness in the large in multi variable control problems as a typical application the robust disturbance decoupling problem an extended version of the well known disturbance decoupling is presented and a necessary and sufficient condition for it to have a solution is derived

brief a polytopic game we consider a discrete time linear dynamic game in state space form where the actions of two players are confined to belong to prescribed convex polytopes at all times each player has a home set a polyhedral domain in state space and should devise a cooperative or a non cooperative strategy contingent on the known initial state to reach her own home set in a finite number of steps and stay there irrespective of the action taken by the opponent players act independently on the basis of the state at each time using feedback strategies purpose of the analysis is to classify the set of initial states into winning sets and draw sets for each player and prescribe strategies able to implement the kind of invariance home sets should enjoy in the paper necessary and sufficient conditions for the existence of invariant sets with the above properties are derived these conditions and the relative strategies are characterized in terms of linear programming problems that provide a straightforward algorithmic solution to the game

scalar hyperbolic pde simulations and coupling strategies we report on grid adaptive multi dimensional simulations for hyperbolic pdes with a deliberate focus on the analytically tractable scalar case motivated by recent efforts towards multi physics simulation strategies we investigate a variety of coupling strategies for numerically solving hyperbolic partial differential equations pdes we use adaptive mesh refinement in combination with shock capturing spatio temporal discretizations and first present accuracy and validation tests on both smooth and shock dominated evolutions to investigate the feasibility of coupling means for multi physics simulations we then introduce new reference tests where spatially different flux prescriptions require coupling strategies across the domains where local advection burgers or nonconvex behavior is imposed for these nonlinear single scalar equations we can illustrate and analytically explain the evolutions obtained when handling cases where fluxes differ in spatially non overlapping regions we discuss both conservative and non conservative ways of coupling across the region boundaries when coupling scalar conservation laws where the characteristic speeds change discontinuously across the regional boundaries these two strategies yield differing but mathematically sound solution behaviors their relevance for multi physics simulations where one couples systems of hyperbolic pdes is discussed

hybrid atomistic continuum method for the simulation of dense fluid flows we present a hybrid atomistic continuum method for multiscale simulations of dense fluids in this method the atomistic part is described using a molecular dynamics description while the continuum flow is described by a finite volume discretization of the incompressible navier stokes equations the two descriptions are combined in a domain decomposition formulation using the schwarz alternating method a novel method has been proposed in order to impose non periodic velocity boundary conditions from the continuum to the atomistic domain based on an effective boundary potential consistent body forces a particle insertion algorithm and specular walls the extraction of velocity boundary conditions for the continuum from the atomistic domain is formulated by taking into account the associated statistical errors the advantages and drawbacks of the proposed schwarz decomposition method as compared to related flux based schemes are discussed the efficiency and applicability of the method is demonstrated by considering hybrid and full molecular dynamics simulations of the flow of a lennard jones fluid past a carbon nanotube

a combined continuum dsmc technique for multiscale analysis of microfluidic filters a multiscale method that combines continuum fluid models with the direct simulation monte carlo dsmc method is presented the continuum regions are treated by stokes equations and a scattered point based finite cloud method is employed to solve the stokes equations the continuum and dsmc regions are combined by an overlapped schwarz alternating method with dirichlet dirichlet type boundary conditions a scattered point interpolation scheme is developed to interpolate the solution between subdomains the convergence characteristics of the multiscale approach are investigated in detail specifically the dependence of convergence on the overlap size the dsmc noise and the number of time steps employed in the dsmc algorithm are studied while the convergence depends weakly on the dsmc noise and the overlap size the number of dsmc time steps simulated in each coupling iteration should be selected so that the total time steps simulated until convergence of the coupled process is close to the time constant of the dsmc subsystem steady state analysis of microfluidic filters is studied in detail using the multiscale approach the multiscale approach is also applied for the simulation of a membrane with an array of microfluidic filters and a dual stage microfluidic device with an array of microfluidic filters for particle trapping and sorting

a conservative adaptive projection method for the variable density incompressible navier stokes equations in this paper we present a method for solving the equations governing time dependent variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids the method is based on a projection formulation in which we first solve advection diffusion equations to predict intermediate velocities and then project these velocities onto a space of approximately divergence free vector fields our treatment of the first step uses a specialized second order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high reynolds number flow density and other scalars are advected in such a way as to maintain conservation if appropriate and free stream preservation our approach to adaptive refinement uses a nested hierarchy of logically rectangular girds with simultaneous refinement of the girds in both space and time the integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized the single grid algorithm is described briefly but the emphasis here is on the time stepping procedure for the adaptive hierarchy numerical examples are presented to demonstrate the algorithms s accuracy and convergence properties and illustrate the behavior of the method an additional example demonstrates the performance of the method on a more realistic problem namely a three dimensional variable density shear layer

lateral torsional buckling of cantilevered elastically coupled composite strip and i beams the lateral torsional buckling of composite strip and i beams is considered the geometrically exact governing equations are simplified by consistently regarding certain configuration parameters as small the assumption that these parameters are indeed small is equivalent to the assumption that the square of the maximum prebuckling cross sectional rotation due to bending is small compared to unity the analysis takes into account various refinements of previously published results including the vlasov eaect elastic coupling the oaset of the load from the centroid and of course prebuckling deflections the analysis is thereby reduced to a single fourth order diaerential equation and boundary conditions all of which are derivable from a corresponding energy expression from the form of matched asymptotic expansions of the buckling mode when small parameters are ignored altogether a single comparison function is found which gives the correct buckling load to within 1 for a wide range of the warping rigidity using this comparison function a formula for the buckling load as a function of the small parameters of the problem is found and validated with certain exceptions regarding the load oaset parameter the formula provides results which agree quite well with the numerical solution of the exact equations as long as all the small parameters remain small however the load oaset parameter always appears in the governing equations as multiplied by a ratio of stianesses which can become large especially for composite i beams for this case a special treatment is required 2001 elsevier science ltd all rights reserved

anomalous flow profile due to the curvature effect on slip length einzel panzer and liu phys rev lett 64 2269 1990 suggest that the slip boundary condition for a fluid moving near a wall is modified by the radius of curvature of the surface using particle simulations of a microscopic flow between concentric cylinders we qualitatively confirm their prediction and point out that the effect is seen in a limiting case derived by maxwell nature london 16 244 1877