bayesian analysis of dichotomous quantal response models abstract qualitative response models qrm s are analyzed from the bayesian point of view using diffuse and informative prior distributions exact finite sample bayesian and large sample bayesian and non bayesian estimation results are compared in addition the paper provides 1 plots and discussion of the properties of likelihood functions for qrm s 2 posterior distributions for logit models derivatives and elasticities 3 bayesian prediction procedures for qrm s 4 new estimates for the median and other fractiles of the logistic distribution 5 posterior odds ratios for model selection problems and 6 comparisons of two alternative monte carlo numerical integration procedures it is concluded that asymptotic approximations are not accurate for small to moderate sized samples even when only a single input variable is used and that operational bayesian methods are available for providing both exact small sample and large sample approximate inferences for drm s

from linear to nonlinear mpc bridging the gap via the real time iteration linear model predictive control mpc can be currently deployed at outstanding speeds thanks to recent progress in algorithms for solving online the underlying structured quadratic programs in contrast nonlinear mpc nmpc requires the deployment of more elaborate algorithms which require longer computation times than linear mpc nonetheless computational speeds for nmpc comparable to those of mpc are now regularly reported provided that the adequate algorithms are used in this paper we aim at clarifying the similarities and differences between linear mpc and nmpc in particular we focus our analysis on nmpc based on the real time iteration rti scheme as this technique has been successfully tested and in some applications requires computational times that are only marginally larger than linear mpc the goal of the paper is to promote the understanding of rti based nmpc within the linear mpc community

adjoint based predictor corrector sequential convex programming for parametric nonlinear optimization this paper proposes an algorithmic framework for solving parametric optimization problems which we call adjoint based predictor corrector sequential convex programming after presenting the algorit

simulating the dynamics of inextensible vesicles by the penalty immersed boundary method in this paper we develop an immersed boundary ib method to simulate the dynamics of inextensible vesicles interacting with an incompressible fluid in order to take into account the inextensibility constraint of the vesicle the penalty immersed boundary pib method is used to virtually decouple the fluid and vesicle dynamics as numerical tests of our current pib method the dynamics of single and multiple inextensible vesicles under shear flows have been extensively explored and compared with the previous literature the method is also validated by a series of convergence study which confirms its consistent first order accuracy on the velocity field the vesicle configuration the vesicle area and the perimeter errors in addition the method is also applied to study a binary component vesicle problem

a parallel newton type method for nonlinear model predictive control abstract a parallel newton type method for nonlinear model predictive control is presented that exploits the particular structure of the associated discrete time euler lagrange equations obtained by utilizing an explicit discretization method in the reverse time direction these equations are approximately decoupled into single step subproblems along the prediction horizon for parallelization the coupling variable of each subproblem is approximated to its optimal value using a simple efficient and effective method at each iteration the rate of convergence of the proposed method is proved to be superlinear under mild conditions numerical simulation of using the proposed method to control a quadrotor showed that the proposed method is highly parallelizable and converges in only a few iterations even to a high accuracy comparison of the proposed method s performance with that of several state of the art methods showed that it is faster

an immersed boundary method with direct forcing for the simulation of particulate flows we present an improved method for computing incompressible viscous flow around suspended rigid particles using a fixed and uniform computational grid the main idea is to incorporate peskin s regularized delta function approach acta numerica 11 2002 1 into a direct formulation of the fluid solid interaction force in order to allow for a smooth transfer between eulerian and lagrangian representations while at the same time avoiding strong restrictions of the time step this technique was implemented in a finite difference and fractional step context a variety of two and three dimensional simulations are presented ranging from the flow around a single cylinder to the sedimentation of 1000 spherical particles the accuracy and efficiency of the current method are clearly demonstrated

three dimensional front tracking we describe a three dimensional front tracking algorithm discuss its numerical implementation and present studies to validate the correctness of this approach based on the results of the two dimensional computations we expect three dimensional front tracking to significantly improve computational efficiencies for problems dominated by discontinuities in some cases for which the interface computations display considerable numerical sensitivity we expect a greatly enhanced capability

modeling a no slip flow boundary with an external force field abstract a novel technique related to peskin s immersed boundary approach is used to introduce solid surfaces into a simulated flow field the navier stokes equations permit the presence of an externally imposed body force that may vary in space and time forces are chosen to lie along a desired surface and to have a magnitude and direction opposing the local flow such that the flow is brought to rest on an element of the surface for unsteady viscous flow the direct calculation of the needed force is facilitated by a feedback scheme in which the velocity is used to iteratively determine the desired value in particular we determine the surface body force from the relation f x 5 t t 0 u x 5 t dt u x 5 t for surface points x 5 velocity u time t and negative constants and examples are presented which include 2d flow around cylinders 3d turbulent channel flow where one boundary is simulated with a force field and turbulent channel flow over a riblet covered surface while the new method may be applied to complex geometries on a non cartesian mesh we have chosen to use a simple cartesian grid all simulations are done with a spectral code in a single computational domain without any mapping of the mesh

bayesian analysis of logit models using natural conjugate priors abstract this study provides a bayesian investigation of conditional logit and multinomial logit models based on a conjugate prior which has many appealing computational properties a one parameter neutral prior is developed which concentrates prior mass over the region corresponding to equiprobable alternatives this prior is particularly attractive in sensitivity analysis an empirical example of occupational choice illustrates the proposed techniques

the contraction number of a multigrid method for solving the poisson equation the treatment of a multigrid method in the framework of numerical analysis elucidates that regularity of the solution is not necessary for the convergence of the multigrid algorithm but only for fast convergence for the linear equations which arise from the discretization of the poisson equation a convergence factor 0 5 is established independent of the shape of the domain and of the regularity of the solution

newton type minimization via the lanczos method this paper discusses the use of the linear conjugate gradient method developed via the lanczos method in the solution of large scale unconstrained minimization problems at each iteration of a newton type method the direction of search is defined as the solution of a quadratic subproblem when the number of variables is very large this subproblem may be solved using the linear conjugate gradient method of hestenes and stiefel we show how the equivalent lanczos characterization of the linear conjugate gradient method may be exploited to define a modified newton method which can be applied to problems that do not necessarily have positive definite hessian matrices at all points of the region of interest this derivation also makes it possible to compute a negative curvature direction at a stationary point the idea of a truncated newton method is to perform only a limited number of iterations of the quadratic subproblem this effectively gives a search direction that interpolates between the steepest de

a sharp interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations a method for reducing the spurious pressure oscillations observed when simulating moving boundary flow problems with sharp interface immersed boundary methods ibms is proposed by first identifying the primary cause of these oscillations to be the violation of the geometric conservation law near the immersed boundary we adopt a cut cell based approach to strictly enforce geometric conservation in order to limit the complexity associated with the cut cell method the cut cell based discretization is limited only to the pressure poisson and velocity correction equations in the fractional step method and the small cell problem tackled by introducing a virtual cell merging technique the method is shown to retain all the desirable properties of the original finite difference based ibm while at the same time reducing pressure oscillations for moving boundaries by roughly an order of magnitude

survey constrained model predictive control stability and optimality model predictive control is a form of control in which the current control action is obtained by solving at each sampling instant a finite horizon open loop optimal control problem using the current state of the plant as the initial state the optimization yields an optimal control sequence and the first control in this sequence is applied to the plant an important advantage of this type of control is its ability to cope with hard constraints on controls and states it has therefore been widely applied in petro chemical and related industries where satisfaction of constraints is particularly important because efficiency demands operating points on or close to the boundary of the set of admissible states and controls in this review we focus on model predictive control of constrained systems both linear and nonlinear and discuss only briefly model predictive control of unconstrained nonlinear and or time varying systems we concentrate our attention on research dealing with stability and optimality in these areas the subject has developed in our opinion to a stage where it has achieved sufficient maturity to warrant the active interest of researchers in nonlinear control we distill from an extensive literature essential principles that ensure stability and use these to present a concise characterization of most of the model predictive controllers that have been proposed in the literature in some cases the finite horizon optimal control problem solved on line is exactly equivalent to the same problem with an infinite horizon in other cases it is equivalent to a modified infinite horizon optimal control problem in both situations known advantages of infinite horizon optimal control accrue

a real time iteration scheme for nonlinear optimization in optimal feedback control an efficient newton type scheme for the approximate on line solution of optimization problems as they occur in optimal feedback control is presented the scheme allows a fast reaction to disturbances by delivering approximations of the exact optimal feedback control which are iteratively refined during the runtime of the controlled process the contractivity of this real time iteration scheme is proven and a bound on the loss of optimality compared with the theoretical optimal solution is given the robustness and excellent real time performance of the method is demonstrated in a numerical experiment the control of an unstable system namely an airborne kite that shall fly loops

a note on a albert and j a anderson s conditions for the existence of maximum likelihood estimates in logistic regression models summary this note expands the paper by albert anderson 1984 on the existence and uniqueness of maximum likelihood estimates in logistic regression models their three possible mutually exclusive data pattems i overlap ii complete separation and iii quasiseparation are considered the maximum likelihood estimate exists only in i modifications of the statement and proofs of albert anderson s results are given for ii and iii the identifiability for a more general model arising in the study of iii is discussed together with the maximization of the corresponding likelihood a linear program is presented which determines whether data is of type i ii or iii and in the case of iii identifies albert anderson s minimal set qm

a grid based particle method for solving partial differential equations on evolving surfaces and modeling high order geometrical motion we develop numerical methods for solving partial differential equations pde defined on an evolving interface represented by the grid based particle method gbpm recently proposed in s leung h k zhao a grid based particle method for moving interface problems j comput phys 228 2009 7706 7728 in particular we develop implicit time discretization methods for the advection diffusion equation where the time step is restricted solely by the advection part of the equation we also generalize the gbpm to solve high order geometrical flows including surface diffusion and willmore type flows the resulting algorithm can be easily implemented since the method is based on meshless particles quasi uniformly sampled on the interface furthermore without any computational mesh or triangulation defined on the interface we do not require remeshing or reparametrization in the case of highly distorted motion or when there are topological changes as an interesting application we study locally inextensible flows governed by energy minimization we introduce tension force via a lagrange multiplier determined by the solution to a helmholtz equation defined on the evolving interface extensive numerical examples are also given to demonstrate the efficiency of the proposed approach

minimal curvature trajectories riemannian geometry concepts for slow manifold computation in chemical kinetics in dissipative ordinary differential equation systems different time scales cause anisotropic phase volume contraction along solution trajectories model reduction methods exploit this for simplifying chemical kinetics via a time scale separation into fast and slow modes the aim is to approximate the system dynamics with a dimension reduced model after eliminating the fast modes by enslaving them to the slow ones via computation of a slow attracting manifold we present a novel method for computing approximations of such manifolds using trajectory based optimization we discuss riemannian geometry concepts as a basis for suitable optimization criteria characterizing trajectories near slow attracting manifolds and thus provide insight into fundamental geometric properties of multiple time scale chemical kinetics the optimization criteria correspond to a suitable mathematical formulation of minimal relaxation of chemical forces along reaction trajectories under given constraints we present various geometrically motivated criteria and the results of their application to four test case reaction mechanisms serving as examples we demonstrate that accurate numerical approximations of slow invariant manifolds can be obtained

efficient robust optimization for robust control with constraints this paper proposes an efficient computational technique for the optimal control of linear discrete time systems subject to bounded disturbances with mixed linear constraints on the states and inputs the problem of computing an optimal state feedback control policy given the current state is non convex a recent breakthrough has been the application of robust optimization techniques to reparameterize this problem as a convex program while the reparameterized problem is theoretically tractable the number of variables is quadratic in the number of stages or horizon length n and has no apparent exploitable structure leading to computational time of mathcal o n 6 per iteration of an interior point method we focus on the case when the disturbance set is norm bounded or the linear map of a hypercube and the cost function involves the minimization of a quadratic cost here we make use of state variables to regain a sparse problem structure that is related to the structure of the original problem that is the policy optimization problem may be decomposed into a set of coupled finite horizon control problems this decomposition can then be formulated as a highly structured quadratic program solvable by primal dual interior point methods in which each iteration requires mathcal o n 3 time this cubic iteration time can be guaranteed using a riccati based block factorization technique which is standard in discrete time optimal control numerical results are presented using a standard sparse primal dual interior point solver that illustrate the efficiency of this approach

a computational approach to modeling cellular scale blood flow in complex geometry we present a computational methodology for modeling cellular scale blood flow in arbitrary and highly complex geometry our approach is based on immersed boundary methods which allow modeling flows in arbitrary geometry while resolving the large deformation and dynamics of every blood cell with high fidelity the present methodology seamlessly integrates different modeling components dealing with stationary rigid boundaries of complex shape moving rigid bodies and highly deformable interfaces governed by nonlinear elasticity thus it enables us to simulate whole blood suspensions flowing through physiologically realistic microvascular networks that are characterized by multiple bifurcating and merging vessels as well as geometrically complex lab on chip devices the focus of the present work is on the development of a versatile numerical technique that is able to consider deformable cells and rigid bodies flowing in three dimensional arbitrarily complex geometries over a diverse range of scenarios after describing the methodology a series of validation studies are presented against analytical theory experimental data and previous numerical results then the capability of the methodology is demonstrated by simulating flows of deformable blood cells and heterogeneous cell suspensions in both physiologically realistic microvascular networks and geometrically intricate microfluidic devices it is shown that the methodology can predict several complex microhemodynamic phenomena observed in vascular networks and microfluidic devices the present methodology is robust and versatile and has the potential to scale up to very large microvascular networks at organ levels

comparing and choosing between two models with a third model in the background abstract this study discusses from the bayesian standpoint whether the comparison or choice between two competing models depends on the characteristics of a third model lurking in the background in the qualitative choice literature an obvious analog is the independence of irrelevant alternatives property usually bayesian posterior odds analysis satisfies a similar property but standard bayesian model selection does not the analysis also considers a random utility model in which the utility function of the reader is only partially known to the statistician the implications of this framework for estimation and prediction are explored

a parametric nonconvex decomposition algorithm for real time and distributed nmpc a novel decomposition scheme to solve parametric nonconvex programs as they arise in nonlinear model predictive control nmpc is presented it consists of a fixed number of alternating proximal gradient steps and a dual update per time step hence the proposed approach is attractive in a real time distributed context assuming that the nonlinear program nlp is semi algebraic and that its critical points are strongly regular contraction of the sequence of primal dual iterates is proven implying stability of the sub optimality error under some mild assumptions moreover it is shown that the performance of the optimality tracking scheme can be enhanced via a continuation technique the efficacy of the proposed decomposition method is demonstrated by solving a centralized nmpc problem to control a dc motor and a distributed nmpc program for collaborative tracking of unicycles both within a real time framework furthermore an analysis of the sub optimality error as a function of the sampling period is proposed given a fixed computational power

an immersed boundary finite volume method for simulations of flow in complex geometries abstract a new immersed boundary method for simulating flows over or inside complex geometries is developed by introducing a mass source sink as well as a momentum forcing the present method is based on a finite volume approach on a staggered mesh together with a fractional step method both momentum forcing and mass source are applied on the body surface or inside the body to satisfy the no slip boundary condition on the immersed boundary and also to satisfy the continuity for the cell containing the immersed boundary in the immersed boundary method the choice of an accurate interpolation scheme satisfying the no slip condition on the immersed boundary is important because the grid lines generally do not coincide with the immersed boundary therefore a stable second order interpolation scheme for evaluating the momentum forcing on the body surface or inside the body is proposed three different flow problems decaying vortices and flows over a cylinder and a sphere are simulated using the immersed boundary method proposed in this study and the results agree very well with previous numerical and experimental results verifying the accuracy of the present method

a continuation gmres method for fast computation of nonlinear receding horizon control in this paper a fast numerical algorithm for nonlinear receding horizon control is proposed the control input is updated by a differential equation to trace the solution of an associated state dependent two point boundary value problem a linear equation involved in the differential equation is solved by the generalized minimum residual method one of the krylov subspace methods with jacobians approximated by forward differences the error in the entire algorithm is analyzed and is shown to be bounded under some conditions the proposed algorithm is applied to a two link arm whose dynamics is highly nonlinear simulation results show that the proposed algorithm is faster than the conventional algorithms

numerical algebraic geometry for optimal control applications a new technique for solving polynomial nonlinear constrained optimal control problems is presented the problem is reformulated into a parametric optimization problem which in turn is solved in a two step procedure first in a precomputation step the equation part of the corresponding first order optimality conditions is solved for a generic value of the parameter relying on the underlying algebraic geometry this first solution makes it possible to solve efficiently and in real time the corresponding optimal control problem at the measured parameter value for each subsequent time step this approach has a probability one guarantee of finding the global optimal solution at each step controller synthesis for two applications from the area of power electronics featuring a dc ac converter and a dc dc converter are discussed to motivate the proposed approach

sources of spurious force oscillations from an immersed boundary method for moving body problems when a discrete forcing immersed boundary method is applied to moving body problems it produces spurious force oscillations on a solid body in the present study we identify two sources of these force oscillations one source is from the spatial discontinuity in the pressure across the immersed boundary when a grid point located inside a solid body becomes that of fluid with a body motion the addition of mass source sink together with momentum forcing proposed by kim et al j kim d kim h choi an immersed boundary finite volume method for simulations of flow in complex geometries journal of computational physics 171 2001 132 150 reduces the spurious force oscillations by alleviating this pressure discontinuity the other source is from the temporal discontinuity in the velocity at the grid points where fluid becomes solid with a body motion the magnitude of velocity discontinuity decreases with decreasing the grid spacing near the immersed boundary four moving body problems are simulated by varying the grid spacing at a fixed computational time step and at a constant cfl number respectively it is found that the spurious force oscillations decrease with decreasing the grid spacing and increasing the computational time step size but they depend more on the grid spacing than on the computational time step size

a moving least squares immersed boundary method for simulating the fluid structure interaction of elastic bodies with arbitrary thickness a versatile numerical method is presented to predict the fluid structure interaction of bodies with arbitrary thickness immersed in an incompressible fluid with the aim of simulating different biological engineering applications a direct forcing immersed boundary method is adopted based on a moving least squares approach to reconstruct the solution in the vicinity of the immersed surface a simple spring network model is considered for describing the dynamics of deformable structures so as to easily model and simulate different biological systems that not always may be described by simple continuum models without affecting the computational time and simplicity of the overall method the fluid and structures are coupled in a strong way in order to avoid instabilities related to large accelerations of the bodies the effectiveness of the method is validated by means of several test cases involving rigid bodies either falling in a quiescent fluid fluttering or tumbling or transported by a shear flow infinitely thin elastic structures with mass such as a two dimensional flexible filament and concerning three dimensional cases a flapping flag and an inverted flag in a free stream finally a three dimensional model of a bio prosthetic aortic valve opening and closing under a pulsatile flowrate a very good agreement is obtained in all the cases comparing with available experimental data and numerical results obtained by different methods in particular the method is shown to be second order accurate by means of a mesh refinement study moreover it is able to provide results comparable with those of sharp direct forcing approaches and can manage high pressure differences across the surface still obtaining very smooth hydrodynamic forces

on the limited memory bfgs method for large scale optimization we study the numerical performance of a limited memory quasi newton method for large scale optimization which we call the l bfgs method we compare its performance with that of the method developed by buckley and lenir 1985 which combines cycles of bfgs steps and conjugate direction steps our numerical tests indicate that the l bfgs method is faster than the method of buckley and lenir and is better able to use additional storage to accelerate convergence we show that the l bfgs method can be greatly accelerated by means of a simple scaling we then compare the l bfgs method with the partitioned quasi newton method of griewank and toint 1982a the results show that for some problems the partitioned quasi newton method is clearly superior to the l bfgs method however we find that for other problems the l bfgs method is very competitive due to its low iteration cost we also study the convergence properties of the l bfgs method and prove global convergence on uniformly convex problems

a general framework to design stabilizing nonlinear model predictive controllers abstract we propose a new model predictive control mpc framework to generate feedback controls for time varying nonlinear systems with input constraints we provide a set of conditions on the design parameters that permits to verify a priori the stabilizing properties of the control strategies considered the supplied sufficient conditions for stability can also be used to analyse the stability of most previous mpc schemes the class of nonlinear systems addressed is significantly enlarged by removing the traditional assumptions on the continuity of the optimal controls and on the stabilizability of the linearized system some important classes of nonlinear systems including some nonholonomic systems can now be stabilized by mpc in addition we can exploit increased flexibility in the choice of design parameters to reduce the constraints of the optimal control problem and thereby reduce the computational effort in the optimization algorithms used to implement mpc

immersed finite element method abstract in this paper the immersed finite element method ifem is proposed for the solution of complex fluid and deformable structure interaction problems encountered in many physical models in ifem a lagrangian solid mesh moves on top of a background eulerian fluid mesh which spans over the entire computational domain hence the mesh generation is greatly simplified moreover both fluid and solid domains are modeled with the finite element methods and the continuity between the fluid and solid sub domains are enforced via the interpolation of the velocities and the distribution of the forces with the reproducing kernel particle method rkpm delta function in comparison with the immersed boundary ib method the higher ordered rkpm delta function enables the fluid domain to have nonuniform spatial meshes with arbitrary geometries and boundary conditions the use of such kernel functions may eventually open doors to multi scale and multi resolution modelings of complex fluid structure interaction problems rigid and deformable spheres dropping in channels are simulated to demonstrate the unique capabilities of the proposed method the results compare well with the experimental data to the authors knowledge these are the first solutions that deal with particulate flows with very flexible solids

a second order projection method for the incompressible navier stokes equations in this paper we describe a second order projection method for the time dependent incom pressible navier stokes equations as in the original projection method developed by chorin we first solve diffusion convection equations to predict intermediate velocities which are then projected onto the space of divergence free vector fields by introducing more coupling between the diffusion onvection step and the projection step we obtain a temporal discretiza tion that is second order accurate our treatment of the diffusion convection step uses a specialized higher order godunov method for differencing the nonlinear convective terms that provides a robust treatment of these terms at high reynolds number the godunov procedure is second order accurate for smooth flow and remains stable for discontinuous initial data even in the zero viscosity limit we approximate the projection directly using a galerkin procedure that uses a local basis for discretely divergence free vector fields numerical results are presented validating the convergence properties of the method we also apply the method to doubly periodic shear layers to assess the performance of the method on more difficult

fluid structure interaction in blood flow capturing non zero longitudinal structure displacement we present a new model and a novel loosely coupled partitioned numerical scheme modeling fluid structure interaction fsi in blood flow allowing non zero longitudinal displacement arterial walls are modeled by a linearly viscoelastic cylindrical koiter shell model capturing both radial and longitudinal displacement fluid flow is modeled by the navier stokes equations for an incompressible viscous fluid the two are fully coupled via kinematic and dynamic coupling conditions our numerical scheme is based on a new modified lie operator splitting that decouples the fluid and structure sub problems in a way that leads to a loosely coupled scheme which is unconditionally stable this was achieved by a clever use of the kinematic coupling condition at the fluid and structure sub problems leading to an implicit coupling between the fluid and structure velocities the proposed scheme is a modification of the recently introduced kinematically coupled scheme for which the newly proposed modified lie splitting significantly increases the accuracy the performance and accuracy of the scheme were studied on a couple of instructive examples including a comparison with a monolithic scheme it was shown that the accuracy of our scheme was comparable to that of the monolithic scheme while our scheme retains all the main advantages of partitioned schemes such as modularity simple implementation and low computational costs

relaxed logarithmic barrier function based model predictive control of linear systems in this paper we investigate the use of relaxed logarithmic barrier functions in the context of linear model predictive control we present results that allow to guarantee asymptotic stability of the corresponding closed loop system and discuss further properties like performance and constraint satisfaction in dependence of the underlying relaxation the proposed stabilizing mpc schemes are not necessarily based on an explicit terminal set or state constraint and allow to characterize the stabilizing control input sequence as the minimizer of a globally defined continuously differentiable and strongly convex function the results are illustrated by means of a numerical example

solutions to the hamilton jacobi equation with algebraic gradients in this paper the hamilton jacobi equation hje with coefficients consisting of rational functions is considered and its solutions with algebraic gradients are characterized in terms of commutative algebra it is shown that there exists a solution with an algebraic gradient if and only if an involutive maximal ideal containing the hamiltonian exists in a polynomial ring over the rational function field if such an ideal is found the gradient of the solution is defined implicitly by a set of algebraic equations then the gradient is determined by solving the set of algebraic equations pointwise without storing the solution over a domain in the state space thus the so called curse of dimensionality can be removed when a solution to the hje with an algebraic gradient exists new classes of explicit solutions for a nonlinear optimal regulator problem are given as applications of the present approach

bayesian analysis of long memory and persistence using arfima models abstract this paper provides a bayesian analysis of autoregressive fractionally integrated moving average arfima models we discuss in detail inference on impulse responsens and show how bayesian methods can be used to i test arfima models against arima alternatives and ii take model uncertainty into account when making inferences on quantities of interest our methods are then used to investigate the persistence properties of real u s gnp

receding horizon control with numerical solution for nonlinear parabolic partial differential equations the optimal control of nonlinear partial differential equations pdes is an open problem with applications that include fluid thermal biological and chemical systems receding horizon control is a kind of optimal feedback control and its performance index has a moving initial time and a moving terminal time in this study we develop a design method of receding horizon control for systems described by nonlinear parabolic pdes the objective of this study is to develop a novel algorithm for numerically solving the receding horizon control problem for nonlinear parabolic pdes the effectiveness of the proposed method is verified by numerical simulations

a lattice boltzmann dynamic immersed boundary scheme for the transport of deformable inertial capsules in low re flows abstract in this work a dynamic immersed boundary method combined with a bgk lattice boltzmann technique is developed and critically discussed the fluid evolution is obtained on a three dimensional lattice with 19 reticular velocities d3q19 computational molecule while the immersed body surface is modeled as a collection of lagrangian points responding to an elastic potential and a bending resistance a moving least squares reconstruction is used to accurately interpolate flow quantities and the forcing field needed to enforce the boundary condition on immersed bodies the proposed model is widely validated against well known benchmark data for rigid and deformable objects rigid transport is validated by computing the settling of a sphere under gravity for five different conditions then the tumbling of inertial particles with different shape is considered recovering the jefferey orbit for a prolate spheroid moreover the revolution period for an oblate spheroid and for a disk like particle is obtained as a function of the reynolds number the existence of a critical reynolds number is demonstrated for both cases above which revolution is inhibited the transport of deformable objects is also considered the steady deformation of a membrane under shear for three different values of the mechanical stiffness is assessed then the tumbling of a weakly deformable spheroid under shear is systematically analyzed as a function strain stiffness bending resistance and membrane mass

differential dynamic programming and newton s method a modified version of the original differential dynamic programming ddp algorithm for unconstrained discrete optimal control problems is described this version which differs from the original b

a dlm fd method for fluid flexible body interactions in this study we extended the distributed lagrange multiplier fictitious domain dlm fd formulation of glowinski et al int j multiphase flow 25 1999 755 for the fluid rigid body interactions to deal with the fluid flexible body interactions by replacing newton s equations of motion for the rigid body with the continuum equations for the general solid material similar to the rigid body case where the dlm is introduced as a pseudo body force to enforce the constraint of rigid body motion of the fictitious fluid in the solid domain the lagrange multiplier in our formulation is to enforce the fictitious fluid to move at the same velocity as the solid for our computational scheme a first order accurate fractional step scheme is employed to decouple the entire system into three sub systems a fluid problem a solid problem and a lagrange multiplier problem the flow problem is solved with the projection method on half staggered grids the solid problem is solved with the lagrangian finite element method and the newton iterative method and the incompressibility of the material is implemented with the penalty function method the proposed method is applied to two typical fluid structure interaction problems the flow driven oscillation of a flexible plate along the flow direction and the self sustained oscillation across the flow direction both results compare favorably with previously reported numerical and experimental results and show that our method is suited to the simulation of the motion of an incompressible non linear elastic material in a fluid

an embedded boundary formulation for large eddy simulation of turbulent flows interacting with moving boundaries a non boundary conforming formulation for simulating complex turbulent flows with dynamically moving boundaries on fixed cartesian grids is proposed the underlying finite difference solver for the filtered incompressible navier stokes equations is based on a second order fractional step method on a staggered grid to satisfy the boundary conditions on an arbitrary immersed interface the velocity field at the grid points near the interface is reconstructed using momentum forcing without smearing the sharp interface the concept of field extension is also introduced to treat the points emerging from a moving solid body to the fluid laminar flow cases and large eddy simulations les are presented to demonstrate the formal accuracy and range of applicability of the method in particular simulations of laminar flow induced by the harmonic in line oscillation of a circular cylinder in quiescent fluid and from a transversely oscillating cylinder in a free stream are presented and compared to reference simulations and experiments les of turbulent flow over a traveling wavy wall and transitional flow through a bileaflet prosthetic heart valve are also shown all results are in very good agreement with reference results in the literature

systematic coarse graining of spectrin level red blood cell models we present a rigorous procedure to derive coarse grained red blood cell rbc models which yield accurate mechanical response based on a semi analytic theory the linear and nonlinear elastic properties of healthy and infected rbcs in malaria can be matched with those obtained in optical tweezers stretching experiments the present analysis predicts correctly the membrane young s modulus in contrast to about 50 error in predictions by previous models in addition we develop a stress free model which avoids a number of pitfalls of existing rbc models such as non smooth or poorly controlled equilibrium shape and dependence of the mechanical properties on the initial triangulation quality here we employ dissipative particle dynamics for the implementation but the proposed model is general and suitable for use in many existing continuum and particle based numerical methods

a numerical approach for simulating fluid structure interaction of flexible thin shells undergoing arbitrarily large deformations in complex domains we present a new numerical methodology for simulating fluid structure interaction fsi problems involving thin flexible bodies in an incompressible fluid the fsi algorithm uses the dirichlet neumann partitioning technique the curvilinear immersed boundary method curvib is coupled with a rotation free finite element fe model for thin shells enabling the efficient simulation of fsi problems with arbitrarily large deformation turbulent flow problems are handled using large eddy simulation with the dynamic smagorinsky model in conjunction with a wall model to reconstruct boundary conditions near immersed boundaries the curvib and fe solvers are coupled together on the flexible solid fluid interfaces where the structural nodal positions displacements velocities and loads are calculated and exchanged between the two solvers loose and strong coupling fsi schemes are employed enhanced by the aitken acceleration technique to ensure robust coupling and fast convergence especially for low mass ratio problems the coupled curvib fe fsi method is validated by applying it to simulate two fsi problems involving thin flexible structures 1 vortex induced vibrations of a cantilever mounted in the wake of a square cylinder at different mass ratios and at low reynolds number and 2 the more challenging high reynolds number problem involving the oscillation of an inverted elastic flag for both cases the computed results are in excellent agreement with previous numerical simulations and or experiential measurements grid convergence tests studies are carried out for both the cantilever and inverted flag problems which show that the curvib fe fsi method provides their convergence finally the capability of the new methodology in simulations of complex cardiovascular flows is demonstrated by applying it to simulate the fsi of a tri leaflet prosthetic heart valve in an anatomic aorta and under physiologic pulsatile conditions

tree based trajectory optimization based on local linearity of continuous non linear dynamics this technical note addresses a tradeoff in the tree based trajectory optimization algorithms for open loop optimal control problem of rigid body system in this technical note linear prediction based uniform state sampling method lpuss which relaxes the tradeoff between solutions quality and computational efficiency is proposed on the basis of the local linearity of motion equations lpuss has a lower calculation order than randomized kinodynamic planning rkp and rapid semi optimal motion planning rasmo in the validation using multi degree of freedom dof under actuated manipulator models the solutions quality and the computational efficiency of lpuss were better than those of rkp and rasmo lpuss finished the optimization for the 6 dof model within 40 minutes this was the world s first success of the optimization of the swing up motion of a 6 dof under actuated manipulator model

specifying and testing econometric models for rank ordered data abstract the rank ordered logit model is used as the basic specification for rank ordered consumer choice data two specification tests are proposed for this specification the first is a hausman specification test for the independence from irrelevant alternatives hypothesis the second test examines the possibility that the estimates of equivalent prices are consistent two alternative estimators are also proposed one generalizes the rank ordered logit specification to allow for a form of heteroscedasticity that permits top ranked choices to be more precisely ranked than bottom ranked choices the other estimator is an application of a weighted m estimator that yields consistent equivalent price estimators despite any misspecification of the distribution in the rank ordered logit model

brief solutions of nonlinear optimal and robust control problems via a mixed collocation dae s based algorithm a new algorithm for computing the solutions of nonlinear optimal and robust h control problems is proposed the algorithm is based on the use of the collocation method to transform the pde s into ode s some convergence results are given and several examples are presented

a class of prediction correction methods for time varying convex optimization this paper considers unconstrained convex optimization problems with time varying objective functions we propose algorithms with a discrete time sampling scheme to find and track the solution trajectory based on prediction and correction steps while sampling the problem data at a constant rate of 1 h where h is the sampling period the prediction step is derived by analyzing the iso residual dynamics of the optimality conditions the correction step adjusts for the distance between the current prediction and the optimizer at each time step and consists either of one or multiple gradient steps or newton steps which respectively correspond to the gradient trajectory tracking gtt or newton trajectory tracking ntt algorithms under suitable conditions we establish that the asymptotic error incurred by both proposed methods behaves as o h 2 and in some cases as o h 4 which outperforms the state of the art error bound of o h for correction only methods in the gradient correction step moreover when the characteristics of the objective function variation are not available we propose approximate gradient and newton tracking algorithms agt and ant respectively that still attain these asymptotical error bounds numerical simulations demonstrate the practical utility of the proposed methods and that they improve upon existing techniques by several orders of magnitude

simulation of flexible filaments in a uniform flow by the immersed boundary method an improved version of the immersed boundary ib method is developed for simulating flexible filaments in a uniform flow the proposed ib method is based on an efficient navier stokes solver adopting the fractional step method and a staggered cartesian grid system the fluid motion defined on an eulerian grid and the filament motion defined on a lagrangian grid are independently solved and their interaction force is explicitly calculated using a feedback law a direct numerical method is developed to calculate the filament motion under the constraint of inextensibility when applied to the case of a swinging filament analogous to a rope pendulum the proposed method gave results very similar to those of the analytical solution derived using the perturbation method for a flexible filament flapping in a uniform flow the mechanism by which small vortex processions are produced was investigated the bistable property of the system was observed by altering the filament length and the effects of the boundary condition at the fixed end simply supported or clamped were studied for two side by side filaments in a uniform flow both in phase flapping and out of phase flapping were reproduced in the present simulations a repulsive force was included in the formulation to handle collisions between the free ends of side by side filaments undergoing out of phase flapping

a fixed point iteration scheme for real time model predictive control a simple model predictive control mpc concept for nonlinear systems under input constraints is considered the presented algorithm takes advantage of an mpc formulation without terminal constraints in order to solve the optimality conditions by a fixed point iteration scheme that is easy to implement and of algorithmic simplicity sufficient conditions for the contraction of the fixed point iterations are derived to allow for a real time implementation within an mpc scheme a constant number of fixed point iterations is used in each sampling step and sufficient conditions for asymptotic stability and incremental reduction of the suboptimality are presented

the advanced step nmpc controller optimality stability and robustness widespread application of dynamic optimization with fast optimization solvers leads to increased consideration of first principles models for nonlinear model predictive control nmpc however significant barriers to this optimization based control strategy are feedback delays and consequent loss of performance and stability due to on line computation to overcome these barriers recently proposed nmpc controllers based on nonlinear programming nlp sensitivity have reduced on line computational costs and can lead to significantly improved performance in this study we extend this concept through a simple reformulation of the nmpc problem and propose the advanced step nmpc controller the main result of this extension is that the proposed controller enjoys the same nominal stability properties of the conventional nmpc controller without computational delay in addition we establish further robustness properties in a straightforward manner through input to state stability concepts a case study example is presented to demonstrate the concepts

a fictitious domain method for external incompressible viscous flow modeled by navier stokes equations abstract in this article we discuss a fictitious domain method for the numerical solutions of three dimensional elliptic problems with dirichlet boundary conditions and also of the navier stokes equations modeling incompressible viscous flow the methodology for the navier stokes equations described here takes a systematic advantage of time discretization by operator splitting in order to treat separately advection imbedding and incompressibility due to the decoupling fast elliptic solvers can be used to treat the incompressibility condition even if the original problem is taking place on a nonregular geometry the resulting methodology is applied to two dimensional unsteady external incompressible viscous flow problems and three dimensional stokes problems

inexact newton kantorovich methods for constrained nonlinear model predictive control in this paper we consider newton kantorovich type methods for solving control constrained optimal control problems that appear in model predictive control conditions for convergence are established for an inexact version of the newton kantorovich method applied to variational inequalities based on these results two groups of algorithms are proposed to solve the optimality system the first group includes exact and inexact newton and newton kantorovich implementations of the sequential quadratic programming in the second group exact and inexact newton and newton kantorovich methods are developed for solving a nonsmooth normal map equation equivalent to the optimality system numerical simulations featuring examples from the aerospace and automotive domain are presented which show that inexact newton kantorovich type methods can achieve significant reduction of the computational time

a real time framework for model predictive control of continuous time nonlinear systems a new formulation of model predictive control mpc for continuous time nonlinear systems is developed which allows for the use of ldquoreal timerdquo rt optimization techniques in which the solution to the finite horizon optimal control problem opc evolves within the same timescale as the process dynamics the computational savings of the rt solver are enhanced by the unique framework within which the opc is posed enabling significant reduction in the dimensionality of the search for situations where computational speed takes priority over optimality of the solutions this framework and its associated proof of stability encompasses results on sampled data sd nonlinear model predictive control nmpc implementation as a special case

efficient non linear model based predictive control for a large number of degrees of freedom and or large dimension systems non linear model based predictive control algorithms based on dual mode control can become intractable this paper proposes an alternative which deploys the closed loop paradigm that has proved to be very effective for the case of linear time varying or uncertain systems the various attributes and computational advantages of the approach are shown to carry over to the non linear case

continuation methods theory and applications this paper surveys in a tutorial fashion theoretical and applications aspects of the confirmation method for the solution of large scale system engineering problems the continuation method is motivated and defined the existence of the method is formulated in terms of degree theory a la algebraic topology examples are given throughout the paper and applications to engineering and economic problems are cited and described

bayesian inference in econometric models using monte carlo integration methods for the systematic application of monte carlo integration with importance sampling to bayesian inference in econometric models are developed conditions under which the numerical approximation of a posterior moment converges almost surely to the true value as the number of monte carlo replications increases and the numerical accuracy of this approximation may be assessed reliably are set forth methods for the analytical verification of these conditions are discussed

a finite difference scheme for three dimensional incompressible flows in cylindrical coordinates a finite difference scheme for the direct simulation of the incompressible time dependent three dimensional navier stokes equations in cylindrical coordinates is presented the equations in primitive variables vr v vzandp are solved by a fractional step method together with an approximate factorization technique cylindrical coordinates are singular at the axis the introduction of the radial fluxqr r vron a staggered grid simplifies the treatment of the region atr 0 the method is tested by comparing the evolution of a free vortex ring and its collision with a wall with the theory experiments and other numerical results the formation of a tripolar vortex where the highest vorticity is atr 0 is also considered finally to emphasize the accurate treatment near the axis the motion of a lamb dipole crossing the origin is simulated

the explicit linear quadratic regulator for constrained systems we present a technique to compute the explicit state feedback solution to both the finite and infinite horizon linear quadratic optimal control problem subject to state and input constraints we show that this closed form solution is piecewise linear and continuous as a practical consequence of the result constrained linear quadratic regulation becomes attractive also for systems with high sampling rates as on line quadratic programming solvers are no more required for the implementation

red blood cell motion and deformation in a curved microvessel abstract the flow of cells through curved vessels is often encountered in various biomedical and bioengineering applications such as red blood cells rbcs passing through the curved arteries in circulation and cells sorting through a shear induced migration in a curved channels most of past numerical studies focused on the cell deformation in small straight microvessels or on the flow pattern in large curved vessels without considering the cell deformation however there have been few attempts to study the cell deformation and the associated flow pattern in a curved microvessel in this work a particle based method smoothed dissipative particle dynamics sdpd is used to simulate the motion and deformation of a rbc in a curved microvessel of diameter comparable to the rbc diameter the emphasis is on the effects of the curvature the type and the size of the curved microvessel on the rbc deformation and the flow pattern the simulation results show that a small curved shape of the microvessel has negligible effect on the rbc behavior and the flow pattern which are similar to those in a straight microvessel when the microvessel is high in curvature the secondary flow comes into being with a pair of dean vortices and the velocity profile of the primary flow is skewed toward the inner wall of the microvessel the rbc also loses the axisymmetric deformation and it is stretched first and then shrinks when passing through the curved part of the microvessel with the large curvature it is also found that a pair of dean vortices arise only under the condition of de 1 de is the dean number a ratio of centrifugal to viscous competition the dean vortices are more easily observed in the larger or more curved microvessels finally it is observed that the velocity profile of primary flow is skewed toward the inner wall of curved microvessel i e the fluid close to the inner wall flows faster than that close to the outer wall this is contrary to the common sense in large curved vessels this velocity skewness was found to depend on the curvature of the microvessel as well as the viscous and inertial forces

real time optimization algorithm for nonlinear receding horizon control abstract a real time optimization technique is discussed concerning state feedback control of general nonlinear systems an optimal state feedback law is determined so that a receding horizon performance index with a moving terminal time is minimized it is shown that the receding horizon control problem can be converted to an initial value problem for an ordinary differential equation that can be solved numerically without recourse to iterative methods the proposed solution technique is applied to a control experiment on a simplified space vehicle model the penalty function approach is employed in the performance index so that the space vehicle model attains the objective state avoiding an obstacle the model is controlled successfully at the sampling frequency of 30 hz in the hardware experiment

a hamiltonian approach to compute an energy efficient trajectory for a servomotor system this paper considers a nonlinear constrained optimal control problem ncocp originated from energy optimal trajectory planning of servomotor systems solving the exact optimal solution is challenging because of the nonlinear and switching cost function and various constraints this paper proposes a method to manage the switching cost function to establish a set of necessary conditions of an ncocp specifically a concept sub trajectory is introduced to match multiple hamiltonian due to switches in the cost function necessary conditions on the optimal trajectory are established as a union of conditions for all sub trajectories and weierstrass erdmann corner conditions between sub trajectories the set of feasible structures of optimal trajectories is further identified and represented by various state transition diagrams for the servomotor application a decomposition based shooting method is proposed to compute an optimal trajectory by solving multi point boundary value problems simulations and experiments validate the effectiveness of the methodology and the energy saving benefit

accurate approximations for posterior moments and marginal densities abstract this article describes approximations to the posterior means and variances of positive functions of a real or vector valued parameter and to the marginal posterior densities of arbitrary i e not necessarily positive parameters these approximations can also be used to compute approximate predictive densities to apply the proposed method one only needs to be able to maximize slightly modified likelihood functions and to evaluate the observed information at the maxima nevertheless the resulting approximations are generally as accurate and in some cases more accurate than approximations based on third order expansions of the likelihood and requiring the evaluation of third derivatives the approximate marginal posterior densities behave very much like saddle point approximations for sampling distributions the principal regularity condition required is that the likelihood times prior be unimodal

a fictitious domain method with a hybrid cell model for simulating motion of cells in fluid flow in this study we develop a hybrid model to represent membranes of biological cells and use the distributed lagrange multiplier fictitious domain dlm fd formulation for simulating the fluid cell interactions the hybrid model representing the cellular structure consists of a continuum representation of the lipid bilayer from which the bending force is calculated through energetic variational approach a discrete cytoskeleton model utilizing the worm like chain to represent network filament and area volume constraints for our computational scheme a formally second order accurate fractional step scheme is employed to decouple the entire system into three sub systems a fluid problem a solid problem and a lagrange multiplier problem the flow problem is solved by the projection method the solid problem based on the cell model is solved by a combination of level set method eno reconstruction and the newton method and the lagrange multiplier problem is solved by immerse boundary interpolation the incompressibility of the material is implemented with the penalty function method numerical results compare favorably with previously reported numerical and experimental results and show that our method is suited to the simulation of the cell motion in flow

suboptimal model predictive control feasibility implies stability practical difficulties involved in implementing stabilizing model predictive control laws for nonlinear systems are well known stabilizing formulations of the method normally rely on the assumption that global and exact solutions of nonconvex nonlinear optimization problems are possible in limited computational time in the paper we first establish conditions under which suboptimal model predictive control mpc controllers are stabilizing the conditions are mild holding out the hope that many existing controllers remain stabilizing even if optimality is lost second we present and analyze two suboptimal mpc schemes that are guaranteed to be stabilizing provided an initial feasible solution is available and for which the computational requirements are more reasonable

an extension of newton type algorithms for nonlinear process control this study extends the multistep newton type formulation li and biegler 1989 chem eng res des 67 562 577 for nonlinear constrained process control the computation of the control law is based on an augmented performance index which improves the performance of the method over the original formulation a number of modifications are also introduced in the computational algorithm to extend the range of problems eliminate steady state offsets and extend the output predictive horizon to infinity we show that the global stability properties of the original newton controller are preserved by the present modifications moreover in the absence of active constraints the method behaves as an extension of the linear quadratic regulator for exhibiting therefore excellent stability properties for a large range of tuning parameters the capabilities of the method are illustrated by application to various process examples

robust tubes in nonlinear model predictive control nonlinear model predictive control nmpc strategies based on linearization about predicted system trajectories enable the online nmpc optimization to be performed by a sequence of convex optimization problems the approach relies on bounds on linearization errors in order to ensure constraint satisfaction and convergence of the performance index both during the optimization at each sampling instant and along closed loop system trajectories this technical note proposes bounds based on robust tubes constructed around predicted trajectories to ensure local optimality the bounds are non conservative for the case of zero linearization error which requires the tube cross sections to vary along predicted trajectories the feasibility stability and convergence properties of the algorithm are established without the need for predictions to satisfy local optimality criteria the strategy is illustrated by numerical examples

a discrete forcing immersed boundary method for the fluid structure interaction of an elastic slender body we present an immersed boundary ib method for the simulation of flow around an elastic slender body the present method is based on the discrete forcing ib method for a stationary rigid body proposed by kim kim and choi 2001 25 the discrete forcing approach is used to relieve the limitation on the computational time step size the incompressible navier stokes equations are implicitly coupled with the dynamic equation for an elastic slender body motion the first is solved in the eulerian coordinate and the latter is described in the lagrangian coordinate the elastic slender body is modeled as a thin and flexible solid and is segmented by finite number of thin blocks each block is moved by external and internal forces such as the hydrodynamic elastic and buoyancy forces where the hydrodynamic force is obtained directly from the discrete forcing used in the ib method all the spatial derivative terms are discretized with the second order central difference scheme the present method is applied to three different fluid structure interaction problems flows around a flexible filament a flapping flag in a free stream and a flexible flapping wing in normal hovering respectively computations are performed at maximum cfl numbers of 0 75 1 the results obtained agree very well with those from previous studies

directional input adaptation in parametric optimal control problems this paper deals with input adaptation in dynamic processes in order to guarantee feasible and optimal operation despite the presence of uncertainty for those optimal control problems having terminal and mixed control state path constraints two orthogonal sets of adaptation directions can be distinguished in the input space the sensitivity seeking directions along which a small variation from an optimal nominal solution will not affect the respective active constraints and the complementary constraint seeking directions along which a variation will affect the respective constraints it follows that selective input adaptation strategies can be defined namely adaptation in the sensitivity and constraint seeking directions this paper proves the important result that for small parametric perturbations the cost variation resulting from adaptation in the sensitivity seeking directions over no input adaptation is typically smaller than the cost variation due to adaptation in the constraint seeking

combined immersed boundary finite difference methods for three dimensional complex flow simulations a second order accurate highly efficient method is developed for simulating unsteady three dimensional incompressible flows in complex geometries this is achieved by using boundary body forces that allow the imposition of the boundary conditions on a given surface not coinciding with the computational grid the governing equations therefore can be discretized and solved on a regular mesh thus retaining the advantages and the efficiency of the standard solution procedures two different forcings are tested showing that while the quality of the results is essentially the same in both cases the efficiency of the calculation strongly depends on the particular expression a major issue is the interpolation of the forcing over the grid that determines the accuracy of the scheme this ranges from zeroth order for the most commonly used interpolations up to second order for an ad hoc velocity interpolation the present scheme has been used to simulate several flows whose results have been validated by experiments and other results available in the literature finally in the last example we show the flow inside an ic piston cylinder assembly at high reynolds number to our knowledge this is the first example in which the immersed boundary technique is applied to a full three dimensional complex flow with moving boundaries and with a reynolds number high enough to require a subgrid scale turbulence model

jeffreys prior for logit models abstract this paper investigates jeffreys prior for logit models with covariates in conditional logit models it is not recommended and in multinomial logit models it has properties similar to a neutral natural conjugate prior but none of the computational advantages

a bayesian analysis of the multinomial probit model with fully identified parameters we present a new prior and corresponding algorithm for bayesian analysis of the multinomial probit model our new approach places a prior directly on the identified parameter space the key is the specification of a prior on the covariance matrix so that the 1 1 element if fixed at 1 and it is possible to draw from the posterior using standard distributions analytical results are derived which can be used to aid in assessment of the prior

stable loosely coupled type algorithm for fluid structure interaction in blood flow we introduce a novel loosely coupled type algorithm for fluid structure interaction between blood flow and thin vascular walls this algorithm successfully deals with the difficulties associated with the added mass effect which is known to be the cause of numerical instabilities in fluid structure interaction problems involving fluid and structure of comparable densities our algorithm is based on a time discretization via operator splitting which is applied in a novel way to separate the fluid sub problem from the structure elastodynamics sub problem in contrast with traditional loosely coupled schemes no iterations are necessary between the fluid and structure sub problems this is due to the fact that our novel splitting strategy uses the added mass effect to stabilize rather than to destabilize the numerical algorithm this stabilizing effect is obtained by employing the kinematic lateral boundary condition to establish a tight link between the velocities of the fluid and of the structure in each sub problem the stability of the scheme is discussed on a simplified benchmark problem and we use energy arguments to show that the proposed scheme is unconditionally stable due to the crucial role played by the kinematic lateral boundary condition the proposed algorithm is named the kinematically coupled scheme

modeling low reynolds number incompressible flows using sph the method of smoothed particle hydrodynamics sph is extended to model incompressible flows of low reynolds number for such flows modification of the standard sph formalism is required to minimize errors associated with the use of a quasi incompressible equation of state treatment of viscosity state equation kernel interpolation and boundary conditions are described simulations using the method show close agreement with series solutions for couette and poiseuille flows furthermore comparison with finite element solutions for flow past a regular lattice of cylinders shows close agreement for the velocity and pressure fields the sph results exhibit small pressure fluctuations near curved boundaries further improvements to the boundary conditions may be possible which will reduce these errors a similar method to that used here may permit the simulation of other flows at low reynolds numbers using sph further development will be needed for cases involving free surfaces or substantially different equations of state

forces nlp an efficient implementation of interior point methods for multistage nonlinear nonconvex programs abstractreal time implementation of optimisation based control and trajectory planning can be very challenging for nonlinear systems as a result if an implementation based on a fixed linearisatio