kramers like escape driven by fractional gaussian noise we investigate the escape from a potential well of a test particle driven by fractional gaussian noise with hurst exponent 0 h 1 from a numerical analysis we demonstrate the exponential distribution of escape times from the well and analyze in detail the dependence of the mean escape time on the hurst exponent h and the particle diffusivity d we observe different behavior for the subdiffusive antipersistent and superdiffusive persistent domains in particular we find that the escape becomes increasingly faster for decreasing values of h consistent with previous findings on the first passage behavior approximate analytical calculations are shown to support the numerically observed dependencies

effective edwards wilkinson equation for single file diffusion in this work we present an effective discrete edwards wilkinson equation aimed to describe the single file diffusion process the key physical properties of the system are captured defining an effective elasticity which is proportional to the single particle diffusion coefficient and to the inverse squared mean separation between particles the effective equation gives a description of single file diffusion using the global roughness of the system of particles which presents three characteristic regimes namely normal diffusion subdiffusion and saturation separated by two crossover times we show how these regimes scale with the parameters of the original system additional repulsive interaction terms are also considered and we analyze how the crossover times depend on the intensity of the additional terms finally we show that the roughness distribution can be well characterized by the edwards wilkinson universal form for the different single file diffusion processes studied here

control input separation methods for reduced order model based feedback flow control first principle based models of the dynamics of flow systems are often of limited use for model based control design not only because of their nonlinear and infinite dimensional nature but also because the control input is generally specified as a boundary condition proper orthogonal decomposition and galerkin projection are among the most effective and commonly used methods to obtain reduced order models of flow dynamics however the final form of these models may not account for the presence of a forcing or control input from a control design perspective it is desirable to obtain a reduced order model in which the control input appears explicitly in the dynamic equations in this paper two methods for control input separation are introduced and comparatively evaluated in experimentally based reduced order modeling of cavity flow both in their ability to reconstruct the forced flowfield and to provide models suitable for feedback control design the proposed methods namely 1 actuated proper orthogonal decomposition expansion and 2 l 2 optimization extend the baseline flow model through the use of innovation vectors which capture the deviation of the actuated flow from the baseline space the new methods address some of the issues associated with the subdomain separation technique employed in our previous works linear quadratic regulator controllers built using models obtained from the new methods have been tested on a cavity flow experiment although the new models perform satisfactorily and comparably to our previous models in terms of suppression of cavity tones they offer a substantial advantage in terms of the required input power to achieve a similar or better performance

single file diffusion with random diffusion constants the single file problem of n particles in one spatial dimension is analysed when each particle has a randomly distributed diffusion constant d sampled in a density d the averaged one particle distributions of the edge particles and the asymptotic n 1 behaviours of their transport coefficients anomalous velocity and diffusion constant are strongly dependent on the d distribution law broad or narrow when is exponential it is shown that the average one particle front for the edge particles does not shrink when n becomes very large in contrast to the pure non disordered case in addition when is a broad law the same occurs for the averaged front which can even have infinite mean and variance on the other hand it is shown that the central particle dynamically trapped by all others as it is follows a narrow distribution which is a gaussian with a diffusion constant scaling as n 1 when the fractional moment d 1 2 exists and is finite otherwise d d 1 this density is far from the origin a stretched exponential with an exponent in the range 0 2 then the effective diffusion constant scales as n with 1 2

on global stabilization of burgers equation by boundary control abstract although often referred to as a one dimensional cartoon of navier stokes equation because it does not exhibit turbulence the burgers equation is a natural first step towards developing methods for control of flows recent references include burns and kang nonlinear dynamics 2 1991 235 262 choi et al j fluid mech 253 1993 509 543 ito and kang siam j control optim 32 1994 831 854 ito and yan j math anal appl 227 1998 271 299 byrnes et al j dynam control systems 4 1998 457 519 and van ly et al numer funct anal optim 18 1997 143 188 while these papers have achieved tremendous progress in local stabilization and global analysis of attractors the problem of global asymptotic stabilization has remained open this problem is non trivial because for large initial conditions the quadratic convective term which is negligible in a linear local analysis dominates the dynamics we derive nonlinear boundary control laws that achieve global asymptotic stability we consider both the viscous and the inviscid burgers equation using both neumann and dirichlet boundary control we also study the case where the viscosity parameter is uncertain as well as the case of stochastic burgers equation for some of the control laws that would require the measurement in the interior of the domain we develop the observer based versions

nonlinear proper orthogonal decomposition based model of forced convection heat transfer in pulsating flow a nonlinear low order physics based model for the dynamics of forced convection wall heat transfer in pulsating flow is formulated based on the proper orthogonal decomposition technique in a multivariate approach proper orthogonal decomposition modes are constructed from computational fluid dynamics data for laminar flow and heat transfer over a flat plate in pulsating flow spanning a range of pulsation frequencies and amplitudes then the conservation equations for mass momentum and energy are projected onto the proper orthogonal decomposition modes such that a system of ordinary differential equations for the modal amplitudes is obtained the forcing at the inlet is written explicitly in the ordinary differential equations of the low order model the contribution of the nonvanishing pressure term resulting from the incompressible navier stokes equation is included with a calibration method the accuracy and stability of the low order model are evaluated by comparison with computational fluid dy

analysis and approximation for linear feedback control for tracking the velocity in navier stokes flows abstract some systematic approaches to the mathematical formulation and numerical resolution of the linear feedback control problem for tracking the velocity in navier stokes flows in a bounded two dimensional domain with bounded distributed control are presented semidiscrete in time and full space time discrete approximations are also studied some computational results are presented and compared with analogous results from optimal control theory

fuzzy γ hypernear rings the concept of c hypernear rings which is a generalization of c near rings and hypernear rings is introduced some related properties of c hypernear rings are described in particular three isomorphism theorems of c hypernear rings are established by using this new idea we consider the fuzzy hyperideals of c hypernear rings finally the fundamental relations between c hypernear rings and c near rings are discussed

optimal solution for the viscous nonlinear dispersive wave equation in this paper we study the optimal control problem for the viscous nonlinear dispersive wave equation we first prove the existence and uniqueness of a weak solution to this equation in a short interval by using the galerkin method furthermore the existence of an optimal solution to the viscous nonlinear dispersive wave equation is proved

the asymmetric simple exclusion process an integrable model for non equilibrium statistical mechanics the asymmetric simple exclusion process asep plays the role of a paradigm in non equilibrium statistical mechanics we review exact results for the asep obtained by the bethe ansatz and put emphasis on the algebraic properties of this model the bethe equations for the eigenvalues of the markov matrix of the asep are derived from the algebraic bethe ansatz using these equations we explain how to calculate the spectral gap of the model and how global spectral properties such as the existence of multiplets can be predicted an extension of the bethe ansatz leads to an analytic expression for the large deviation function of the current in the asep that satisfies the gallavotti cohen relation finally we describe some variants of the asep that are also solvable by the bethe ansatz

gain scheduled controller synthesis for a nonlinear pde linear parameter varying lpv modelling and control of a nonlinear partial differential equation pde is considered in this article the one dimensional viscous burgers equation is discretised using a finite difference scheme the boundary conditions are taken as control inputs and the velocities at two grid points are assumed to be measurable a nonlinear high order state space model is generated and proper orthogonal decomposition is used for model order reduction after assessing the accuracy of the reduced model a low order functional observer is designed to estimate the reduced states which are linear combinations of the velocities at all grid points a discrete time quasi lpv model that is affine in scheduling parameters is derived based on the reduced model a polytopic lpv controller is synthesised based on a generalised plant containing the lpv model and the functional observer more generally the proposed method can be used to design an lpv controller for a quasi lpv system with non measura

remarks on the internal exponential stabilization to a nonstationary solution for 1d burgers equations the feedback stabilization of the burgers system to a nonstationary solution using finite dimensional internal controls is considered estimates for the dimension of the controller are derived in the particular case of no constraint on the support of the control a better estimate is derived and the possibility of getting an analogous estimate for the general case is discussed some numerical examples are presented illustrating the stabilizing effect of the feedback control and suggesting that the existence of an estimate in the general case analogous to that in the particular one is plausible

solving optimal control problems for the unsteady burgers equation in comsol multiphysics the optimal control of unsteady burgers equation without constraints and with control constraints are solved using the high level modelling and simulation package comsol multiphysics using the first order optimality conditions projection and semi smooth newton methods are applied for solving the optimality system the optimality system is solved numerically using the classical iterative approach by integrating the state equation forward in time and the adjoint equation backward in time using the gradient method and considering the optimality system in the space time cylinder as an elliptic equation and solving it adaptively the equivalence of the optimality system to the elliptic partial differential equation pde is shown by transforming the burgers equation by the cole hopf transformation to a linear diffusion type equation numerical results obtained with adaptive and nonadaptive elliptic solvers of comsol multiphysics are presented both for the unconstrained and the control constrained case

topological hypergroupoids hypergroups are generalizations of groups if this binary operation is taken to be multivalued then we arrive at a hypergroup the motivation for generalization of the notion of group resulted naturally from various problems in non commutative algebra another motivation for such an investigation came from geometry in various branches of mathematics we encounter important examples of topologico algebraical structures like topological groupoids groups rings fields etc in this contribution various kinds of continuity of hyperoperations will be introduced namely pseudocontinuous strongly pseudocontinuous and continuous hyperoperations further the relationship between them is studied our aim is to generalize the concept of topological groupoid to topological hypergroupoid

feedback induced oscillations in one dimensional colloidal transport we investigate a driven one dimensional system of colloidal particles in a periodically corrugated narrow channel subject to a time delayed feedback control our goal is to identify conditions under which the control induces oscillatory time periodic states the investigations are based on the fokker planck equation involving the density distribution of the system first by using the numerical continuation technique we determine the linear stability of a stationary density second the nonlinear regimes are analyzed by studying numerically the temporal evolution of the first moment of the density distribution in this way we construct a bifurcation diagram revealing the nature of the instability apart from the case of a system with periodic boundary conditions we also consider a microchannel of finite length finally we study the influence of repulsive particle interactions based on dynamical density functional theory

analysis and design of unconstrained nonlinear mpc schemes for finite and infinite dimensional systems we present a technique for computing stability and performance bounds for unconstrained nonlinear model predictive control mpc schemes the technique relies on controllability properties of the system under consideration and the computation can be formulated as an optimization problem whose complexity is independent of the state space dimension based on the insight obtained from the numerical solution of this problem we derive design guidelines for nonlinear mpc schemes which guarantee stability of the closed loop for small optimization horizons these guidelines are illustrated by a finite and an infinite dimensional example

transposition hypergroups noncommutative join spaces the study of various kinds of algebraic hypergroups is unified in the theory of transposition hypergroups the hyperoperation in any hypergroup has two inverses given bya b x a xb andb a x a bx a transposition hypergroup is a hypergroup where transposition b a c d impliesad bc holds the algebra of transposition hypergroups is developed closed subhypergroupsnthat are reflexive a n n a have distinguished structural significance the quotient space of a transposition hypergroup modulo a reflexive closed subhypergroup forms a transposition hypergroup that is a polygroup then generalizations of the isomorphism theorems and the jordan holder theorem of group theory are obtained

backstepping boundary control of burgers equation with actuator dynamics in this paper we propose a backstepping boundary control law for burgers equation with actuator dynamics while the control law without actuator dynamics depends only on the signals u 0 t and u 1 t the backstepping control also depends on ux 0 t ux 1 t uxx 0 t and uxx 1 t making the regularity of the control inputs the key technical issue of the paper with elaborate lyapunov analysis we prove that all these signals are suciently regular and the closed loop system including the boundary dynamics is globally h 3 stable and well posed c 2000 elsevier science b v all rights reserved

control input separation by actuation mode expansion for flow control problems a control input separation method is proposed for reduced order modelling in boundary control problems the dynamics of flow systems are typically described by partial differential equations where the input affects the system through boundary conditions from a control design perspective it is most desirable and natural to employ finite dimensional representations in which the input enters the dynamics directly the method proposed here to resolve the input from the boundary conditions is based on obtaining a proper orthogonal decomposition of the unforced flow of the system and then augmenting this decomposition by optimally computed actuation modes built using snapshots of the actuated flow a reduced order galerkin model is then derived for this expansion in which the input appears as an explicit term in the system dynamics the model reduces exactly to the original baseline case under zero input conditions the proposed method is then compared to an existing input separation technique namely the s

fractional langevin equation we investigate fractional brownian motion with a microscopic random matrix model and introduce a fractional langevin equation we use the latter to study both subdiffusion and superdiffusion of a free particle coupled to a fractal heat bath we further compare fractional brownian motion with the fractal time process the respective mean square displacements of these two forms of anomalous diffusion exhibit the same power law behavior here we show that their lowest moments are actually all identical except the second moment of the velocity this provides a simple criterion that enable us to distinguish these two non markovian processes

scaling limits of a tagged particle in the exclusion process with variable diffusion coefficient we prove a law of large numbers and a central limit theorem for a tagged particle in a symmetric simple exclusion process in z with variable diffusion coefficient the scaling limits are obtained from a similar result for the current through 1 2 for a zero range process with bond disorder for the clt we prove convergence to a fractional brownian motion of hurst exponent 1 4

low dimensional modelling and dirichlet boundary controller design for burgers equation modelling and boundary control for the burgers equation is studied in this paper modelling has been done via processing of numerical observations through proper orthogonal decomposition pod with galerkin projection this results in a set of spatial basis functions together with a set of ordinary differential equations odes describing the temporal evolution since the dynamics described by the burgers equation are non linear the corresponding reduced order dynamics turn out to be non linear the presented analysis explains how the free boundary condition appears as a control input in the odes and how controller design can be accomplished the issues of control system synthesis are discussed from the point of practicality performance and robustness the numerical results obtained are in good compliance with the theoretical claims a comparison of various different approaches is presented

asymptotic properties of receding horizon optimal control problems the asymptotic behavior of receding horizon optimal control problems with terminal cost chosen as a control liapunov function is analyzed for regulator as well as disturbance attenuation problems both the continuous as well as the discrete time cases are treated further the approximation of the continuous time optimal control problem by the discrete time receding horizon problems is studied

propagator and mean square displacement in single file systems it is shown that the propagator in single file systems may quite generally be deduced from the propagator in the corresponding unrestricted case irrespective of its structure in the unrestricted case the propagator of single file systems in the long time limit approaches a gaussian distribution it is found that the exponent of the time dependence of the mean square displacement is reduced by a factor of two compared with the unrestricted case examples for different models of particle propagation are considered and compared with literature data for one model the theoretical result is compared with a molecular dynamics simulation

infinite dimensional and reduced order observers for burgers equation obtaining a representative model in feedback control system design problems is a key step and is generally a challenge for spatially continuous systems it becomes more difficult as the dynamics is infinite dimensional and the well known techniques of systems and control engineering are difficult to apply directly in this paper observer design is reported for one dimensional burgers equation which is a non linear partial differential equation an infinite dimensional form of the observer is demonstrated to converge asymptotically to the target dynamics and proper orthogonal decomposition is used to obtain the reduced order observer when this is done the corresponding observer is shown to be successful under certain circumstances the paper unfolds the connections between target dynamics observer and their finite dimensional counterparts a set of simulation results has been presented to justify the theoretical claims of the paper

diffusion of finite sized hard core interacting particles in a one dimensional box tagged particle dynamics we solve a nonequilibrium statistical mechanics problem exactly namely the single file dynamics of n hard core interacting particles the particles cannot pass each other of size delta diffusing in a one dimensional system of finite length l with reflecting boundaries at the ends we obtain an exact expression for the conditional probability density function rho t yt t vertical bar yt 0 that a tagged particle t t 1 n is at position yt at time t given that it at time t 0 was at position yt 0 using a bethe ansatz we obtain the n particle probability density function and by integrating out the coordinates and averaging over initial positions of all particles but particle t we arrive at an exact expression for rho t yt t vertical bar yt 0 in terms of jacobi polynomials or hypergeometric functions going beyond previous studies we consider the asymptotic limit of large n maintaining l finite using a nonstandard asymptotic technique we derive an exact expression for rho t yt t vertical bar yt 0 for a tagged particle located roughly in the middle of the system from which we find that there are three time regimes of interest for finite sized systems a for times much smaller than the collision time t tau coll 1 rho d 2 where rho n l is the particle concentration and d is the diffusion constant for each particle the tagged particle undergoes a normal diffusion b for times much larger than the collision time t tau coll but times smaller than the equilibrium time t tau eq l 2 d we find a single file regime where rho t yt t vertical bar yt 0 is a gaussian with a mean square displacement scaling as t 1 2 and c for times longer than the equilibrium time t tau eq rho t yt t vertical bar yt 0 approaches a polynomial type equilibrium probability density function notably only regimes a and b are found in the previously considered infinite systems

receding horizon control with incomplete observations to overcome the difficulties related to the computational requirements for solving the optimality systems for optimal control problems on long time horizons receding horizon techniques provide an important alternative rather than finding the optimal solution a suboptimal control is obtained which achieves the design objective with significantly less computational effort moreover the obtained control can be interpreted as a state feedback control in this work we continue our analysis of receding horizon strategies considering the situation when only partial state observations are available the receding horizon strategy is combined with a state estimator framework a linear quadratic gaussian design based on a linearization procedure is proposed and its asymptotic performance is analyzed for systems with nonlinear dynamics numerical examples validate the proposed methodology

exact solution of the master equation for the asymmetric exclusion process using the bethe ansatz we obtain the exact solution of the master equation for the totally asymmetric exclusion process on an infinite one dimensional lattice we derive explicit expressions for the conditional probabilitiesp x1 xn t y1 yn 0 of findingn particles on lattices sitesx1 xn at timet with initial occupationy1 yn at timet 0

excluded volume effects in the diffusion of hard spheres excluded volume effects can play an important role in determining transport properties in diffusion of particles here the diffusion of finite sized hard core interacting particles in two or three dimensions is considered systematically using the method of matched asymptotic expansions the result is a nonlinear diffusion equation for the one particle distribution function with excluded volume effects enhancing the overall collective diffusion rate an expression for the effective collective diffusion coefficient is obtained stochastic simulations of the full particle system are shown to compare well with the solution of this equation for two examples

dynamics for controlled navier stokes systems with distributed controls the long time behavior of solutions for an optimal distributed control problem associated with the navier stokes equations is studied first a linear feedback solution for the navier stokes equations is constructed this feedback solution possesses decay in time properties then some preliminary estimates for the long time behavior of all solutions of the navier stokes equations are derived next the existence of a solution for the optimal control problem is proved finally the long time decay properties for the optimal solutions are established

numerical solution of a flow control problem vorticity reduction by dynamic boundary action in order to laminarize an unsteady internal flow the vorticity field is minimized in a least squares sense using an optimal control approach the flow model is the navier stokes equation for a viscous incompressible fluid and the flow is controlled by suction and blowing on a part of the boundary a quasi newton method is used for the minimization of a quadratic objective function involving a measure of the vorticity and a regularization term the navier stokes equations are approximated using a finite difference scheme in time and finite element approximations in space accurate expressions for the gradient of the discrete objective function are needed to obtain a satisfactory convergence rate of the minimization algorithm therefore first order necessary conditions for a minimizer of the objective function are derived in the fully discrete case a memory saving device is discussed without which problems of any realistic size especially in three space dimensions would remain computationally intractable the feasibility of the optimal control approach for flow control problems is demonstrated by numerical experiments for a two dimensional flow in a rectangular cavity at a reynolds number high enough for nonlinear effects to be important

the restaurant at the end of the random walk recent developments in the description of anomalous transport by fractional dynamics fractional dynamics has experienced a firm upswing during the past few years having been forged into a mature framework in the theory of stochastic processes a large number of research papers developing fractional dynamics further or applying it to various systems have appeared since our first review article on the fractional fokker planck equation metzler r and klafter j 2000a phys rep 339 1 77 it therefore appears timely to put these new works in a cohesive perspective in this review we cover both the theoretical modelling of sub and superdiffusive processes placing emphasis on superdiffusion and the discussion of applications such as the correct formulation of boundary value problems to obtain the first passage time density function we also discuss extensively the occurrence of anomalous dynamics in various fields ranging from nanoscale over biological to geophysical and environmental systems

analysis and approximation of the velocity tracking problem for navier stokes flows with distributed control we consider the mathematical formulation analysis and the numerical solution of a time dependent optimal control problem associated with the tracking of the velocity of a navier stokes flow in a bounded two dimensional domain through the adjustment of a distributed control the existence of optimal solutions is proved and the first order necessary conditions for optimality are used to derive an optimality system of partial differential equations whose solutions provide optimal states and controls semidiscrete in time and fully discrete space time approximations are defined and their convergence to the exact optimal solutions is shown a gradient method for the solution of the fully discrete equations is examined as are its convergence properties finally the results of some illustrative computational experiments are presented