a time domain decomposition iterative method for the solution of distributed linear quadratic optimal control problems we study a class of time domain decomposition based methods for the numerical solution of large scale linear quadratic optimal control problems our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete time optimal control dtoc problem the optimality conditions for this dtoc problem lead to a linear block tridiagonal system the diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time subintervals this motivates the application of block gauss seidel gs type methods for the solution of the block tridiagonal systems numerical experiments show that the spectral radii of the block gs iteration matrices are larger than one for typical applications but that the eigenvalues of the iteration matrices decay to zero fast hence while the gs method is not expected to convergence for typical applications it can be effective as a preconditioner for krylov subspace methods this is confirmed by our numerical tests a byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block gs method applied to the dtoc optimality system

the velocity tracking problem for navier stokes flows with bounded distributed controls we present some systematic approaches to the mathematical analysis and numerical approximation of the time dependent optimal control problem of tracking the velocity for navier stokes flows in bounded two dimensional domains with bounded distributed controls we study the existence of optimal solutions and derive an optimality system from which optimal solutions may be determined we also define and analyze semidiscrete in time and fully space time discrete approximations of the optimality system and a gradient method for the solution of the fully discrete system the results of some computational experiments are provided

fundamental monogamy relation between contextuality and nonlocality we show that the no disturbance principle imposes a tradeoff between locally contextual correlations violating the klyachko can biniciog lu shumovski inequality and spatially separated correlations violating the clauser horne shimony holt inequality the violation of one inequality forbids the violation of the other we also obtain the corresponding monogamy relation imposed by quantum theory for a qutrit qubit system our results show the existence of fundamental monogamy relations between contextuality and nonlocality that suggest that entanglement might be a particular form of a more fundamental resource

a penalized neumann control approach for solving an optimal dirichlet control problem for the navier stokes equations we introduce a penalized neumann boundary control approach for solving an optimal dirichlet boundary control problem associated with the two or three dimensional steady state navier stokes equations we prove the convergence of the solutions of the penalized neumann control problem the suboptimality of the limit and the optimality of the limit under further restrictions on the data we describe the numerical algorithm for solving the penalized neumann control problem and report some numerical results

analysis and approximation of linear feedback control problems for the boussinesq equations the mathematical formulation and numerical solution of the linear feedback control problem associated with the boussinesq equations are presented we show that the unsteady solutions to the boussinesq equations are stabilizable by internal controllers with exponential decaying property semidiscrete in time and full space time discrete approximations are also studied some computational results are presented

a monte carlo method for solving unsteady adjoint equations traditionally solving the adjoint equation for unsteady problems involves solving a large structured linear system this paper presents a variation on this technique and uses a monte carlo linear solver the monte carlo solver yields a forward time algorithm for solving unsteady adjoint equations when applied to computing the adjoint associated with burgers equation the monte carlo approach is faster for a large class of problems while preserving sufficient accuracy

the extension problem for partial boolean structures in quantum mechanics alternative partial boolean structures implicit in the discussion of classical representability of sets of quantum mechanical predictions are characterized with definite general conclusions on the equivalence of the approaches going back to bell and kochen specker an algebraic approach is presented allowing for a discussion of partial classical extension amounting to reduction of the number of contexts classical representability arising as a special case as a result known techniques are generalized and some of the associated computational difficulties overcome the implications on the discussion of boole bell inequalities are indicated

quantum work fluctuations versus macrorealism in terms of non extensive entropies abstract fluctuations of the work performed on a driven quantum system can be characterized by the so called fluctuation theorems the jarzynski relation and the crooks theorem are famous examples of exact equalities characterizing non equilibrium dynamics such statistical theorems are typically formulated in a similar manner in both classical and quantum physics leggett garg inequalities are inspired by the two assumptions referred to as the macroscopic realism and the non invasive measurability together these assumptions are known as the macrorealism in the broad sense quantum mechanics is provably incompatible with restrictions of the leggett garg type it turned out that leggett garg inequalities can be used to distinguish quantum and classical work fluctuations we develop this issue with the use of entropic functions of the tsallis type varying the entropic parameter we are often able to reach more robust detection of violations of the corresponding leggett garg inequalities in reality all measurement devices suffer from losses within the entropic formulation detection inefficiencies can naturally be incorporated into the consideration this question also shows advantages that are provided due to the use of generalized entropies

on the essential spectrum of schrodinger operators with spherically symmetric potentials on determine le spectre essentiel des operateurs de schrodinger avec un potentiel a symetrie spherique v x q x

ensuring well posedness by analogy stokes problem and boundary control for the wave equation abstract in this article we give a comparative discussion of the finite element approximation of two partial differential equation problems these two problems which are apparantly quite unrelated are the stokes problem for incompressible viscous flow and an exact boundary controllability problem for the wave equation we show that straightforward discrete approximations to these problems yield approximate problems which are ill posed the analysis of the ill posedness of the above problems shows an identical cause namely the strong damping of the high frequency modes beyond a critical wave number from this analogy a well known cure for the discrete stokes problem i e using more accurate approximations for velocity than for pressure provides a simple way to eliminate the ill posedness of the discrete exact boundary controllability problem numerical examples concerning the control problem testify about the soundness of the new approach to conclude this paper one takes advantage of the previous analysis to give a brief discussion of the wavelet approximation of the stokes problem for dirichlet boundary conditions

optimal controls of navier stokes equations this paper studies optimal control problems of the fluid flow governed by the navier stokes equations two control problems are formulated in the case of the driven cavity and flow through a channel with sudden expansion and solved successfully using a numerical optimization algorithm based on the augmented lagrangian method existence and the first order optimality condition of the optimal control are established a convergence result on the augmented lagrangian method for nonsmooth cost functional is obtained

adjoint optimization of one dimensional hyperbolic equations with constrained periodic boundary conditions abstract this paper presents a continuous adjoint based optimization theory for a general closed loop transport hyperbolic model controlled via a periodic boundary control to minimize a cost functional the periodic boundary control is subject to a nonlinear differential equation constraint thus resulting in a coupling between the hyperbolic equation and the ordinary differential equation variational principles are used to derive the pontryagin s minimum principle for optimality that results in a dual adjoint system a numerical optimization method is implemented using the adjoint based second order gradient method to solve for the optimal trajectory of the control numerical methods for solving the hyperbolic equation using an explicit scheme wave splitting method and for solving the adjoint equation using an implicit scheme and a quasi steady state method are described

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

on the optimal control problem for the novikov equation with strong viscosity abstract in this paper we consider an optimal control problem for the novikov equation with strong viscosity using the faedo galerkin method we derive the existence of a unique weak solution to this equation applying lions theory we obtain the existence of an optimal solution to the control problem for this equation we also deduce the first order necessary optimality condition moreover we establish two second order sufficient optimality conditions which require coercivity of the augmented lagrangian functional on the whole space or on a suitable subspace

entropic tests of multipartite nonlocality and state independent contextuality we introduce a multipartite extension of an information theoretic distance introduced by zurek nature london 341 119 1989 we use it to develop a new tool for studying quantum correlations from an information theoretic perspective in particular we derive entropic tests of multipartite nonlocality for three qubits and for an arbitrary even number of qubits as well as a test of state independent contextuality in addition we rederive the tripartite mermin inequality and a state independent noncontextuality inequality by cabello phys rev lett 101 210401 2008 this suggests that the information theoretic distance approach to multipartite nonlocality and state independent contextuality can provide a more general treatment of nonclassical correlations than the orthodox approach based on correlation functions

pointwise control of burgers equation a numerical approach abstract we describe a methodology for numerically solving pointwise control problems for the viscous burger s equation in one space dimension the solution methods are based on a combination of finite difference and finite element techniques for the time and space discretizations with iterative algorithms such as quasi newton methods and gmres numerical experiments validate the methods

information theoretic bell inequalities we formulate information theoretic bell inequalities which apply to any pair of widely separated physical systems if local realism holds the two systems must carry information consistent with the inequalities two spin s particles in a state of zero total spin violate these information bell inequalities

drag reduction in transitional linearized channelow using distributed control this work focuses on feedback control of incompressible transitional newtonian channel flow described by the twodimensional linearized navier stokes equations the control objective is to use distributed feedback to achieve stabilization of the parabolic velocity profile for values of the reynolds number for which this profile is unstable and therefore to reduce the frictional drag exerted on the lower channel wall compared to the open loop values the control system uses measurements of shear stresses on the lower channel wall and the control actuation is assumed to be in the form of electromagnetic lorentz forces applied to the flow near the bottom wall galerkin s method is initially used to derive a high order discretization of the linearized flow field that captures the flow instability and accounts for the effect of control actuation on all the modes then a low order approximation of the linearized flow field is derived and used for the synthesis of a linear output feedback controller that enfor

domain imbedding methods for the stokes equations we study direct and iterative domain imbedding methods for the stokes equations on certain non rectangular domains in two space dimensions we analyze a continuous analog of numerical domain imbedding for bounded smooth domains and give an example of a simple numerical algorithm suggested by the continuous analysis this algorithms is applicable for simply connected domains which can be covered by rectangular grids with uniformly spaced grid lines in at least one coordinate direction we also discuss a related fft based fast solver for stokes problems with physical boundary conditions on rectangles and present some numerical results

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

existence of optimal controls for viscous flow problems a class of optimal control problems in viscous flow is studied main result is the existence theorem for optimal control three typical flow control problems are formulated within this general class

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

adjoint based optimization of particle trajectories in laminar flows we present a performant numerical algorithm for the optimal control of particle controls in low reynolds number flows in particular circular particles with mass are considered an optimal control problem for the particle trajectories is presented which is solved by means of a steepest descent algorithm here the derivative information is obtained using adjoint calculus finally numerical results are presented underlining the feasibility of our approach

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

dynamics and approximations of a velocity tracking problem for the navier stokes flows with piecewise distributed controls we study the dynamics of a piecewise in time distributed optimal control problem for the navier stokes equations which models velocity tracking over time we also study the dynamics of semidiscrete and fully discrete approximations of this velocity tracking problem we prove that the rates of velocity tracking are exponential some computational results are presented which reinforces the theoretical results derived

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

analysis and finite element approximation of optimal control problems for the stationary navier stokes equations with distributed and neumann controls we examine certain analytic and numerical aspects of optimal control problems for the stationary navier stokes equations the controls considered may be of either the distributed or neumann type the functionals minimized are either the viscous dissipation or the l4 distance of candidate flows to some desired flow we show the existence of optimal solutions and justify the use of lagrange multiplier techniques to derive a system of partial differential equations from which optimal solutions may be deduced we study the regularity of solutions of this system then we consider the approximation by finite element methods of solutions of the optimality system and derive optimal error estimates

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

instantaneous closed loop control of the navier stokes system instantaneous control is applied to the control of the instationary navier stokes system this control technique is closely related to receding horizon control and allows for an interpretation as suboptimal closed loop controller whose parameters may be adjusted so as to stabilize the nonlinear equation under consideration besides stability analysis for the distributed control case numerical examples for the continuous and discrete in time control laws are presented

necessary and sufficient conditions for optimal controls in viscous flow problems a class of optimal control problems in viscous flow is studied main results are the pontryagin maximum principle and the verification theorem for the hamilton jacobi bellman equation characterising the feedback problem the maximum principle is established by two quite different methods

optimal control of the viscous weakly dispersive degasperis procesi equation abstract in this paper we study the optimal control problem for the viscous weakly dispersive degasperis procesi equation we deduce the existence and uniqueness of a weak solution to this equation in a short interval by using the galerkin method then according to optimal control theories and distributed parameter system control theories the optimal control of the viscous weakly dispersive degasperis procesi equation under boundary conditions is given and the existence of an optimal solution to the viscous weakly dispersive degasperis procesi equation is proved

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

a reduced order method for simulation and control of fluid flows this article presents a reduced order modeling approach for simulation and control of viscous incompressible flows the reduced order models suitable for control and which capture the essential physics are developed using the reduced basis method the so called lagrange approach is used to define reduced bases and the basis functions in this approach are obtained from the numerical solutions the feasibility of this method for flow control is demonstrated on boundary control problems in closed cavity and in wall bounded channel flows control action is effected through boundary surface movement on a part of the solid wall our formulation of the reduced order method applied to flow control problems leads to a constrained minimization problem and is solved by applying newton like methods to the necessary conditions of optimality through our computational experiments we demonstrate the feasibility and applicability of the reduced order method for simulation and control of fluid flows

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

entropic test of quantum contextuality we study the contextuality of a three level quantum system using classical conditional entropy of measurement outcomes first we analytically construct the minimal configuration of measurements required to reveal contextuality next an entropic contextual inequality is formulated analogous to the entropic bell inequalities derived by braunstein and caves phys rev lett 61 662 1988 that must be satisfied by all noncontextual theories we find optimal measurements for violation of this inequality the approach is easily extendable to higher dimensional quantum systems and more measurements our theoretical findings can be verified in the laboratory with current technology

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

optimal control of the viscous degasperis procesi equation this paper studies the problem for optimal control of the viscous degasperis procesi equation the existence and uniqueness of weak solution to the equation are proved in a short interval the optimal control of the viscous degasperis procesi equation under boundary condition is given and the existence of optimal solution to the equation is proved

eigenvalues in gaps of perturbed periodic dirac operators numerical evidence this paper presents a method for the numerical investigation of the distribution of the eigenvalues introduced into a spectral gap of a periodic dirac system by a perturbation of the type of the angular momentum term a number of examples illustrate the effectiveness of the method and show the remarkable accuracy of the strong coupling asymptotic formula even for small values of the perturbation coupling constant furthermore the results shed some light on the spectrum in the exceptional gap of radially periodic three dimensional dirac operators

state independent proof of kochen specker theorem with 13 rays quantum contextuality as proved by kochen and specker and also by bell should manifest itself in any state in any system with more than two distinguishable states and recently has been experimentally verified however for the simplest system capable of exhibiting contextuality a qutrit the quantum contextuality is verified only state dependently in experiment because too many at least 31 observables are involved in all the known state independent tests here we report an experimentally testable inequality involving only 13 observables that is satisfied by all noncontextual realistic models while being violated by all qutrit states thus our inequality facilitates a state independent test of the quantum contextuality for an indivisible quantum system we also provide a record breaking state independent proof of the kochen specker theorem with 13 directions determined by 26 points on the surface of a magic cube

the velocity tracking problem for navier stokes flows with boundary control we present some systematic approaches to the mathematical formulation and numerical approximation of the time dependent optimal control problem of tracking the velocity for navier stokes flows in a bounded two dimensional domain with boundary control we study the existence of optimal solutions and derive an optimality system from which optimal solutions may be determined we also define and analyze semidiscrete in time and full space time discrete approximations of the optimality system and a gradient method for the solution of the fully discrete system the results of some computational experiments are provided

a self contained automated methodology for optimal flow control this paper describes a self contained automated methodology for active flow control which couples the time dependent navier stokes system with an adjoint navier stokes system and optimality conditions from which optimal states i e unsteady flow fields and controls e g actuators may be determined the problem of boundary layer instability suppression through wave cancellation is used as the intital validation case to test the methodology here the objective of control is to match the stress vector along a portion of the boundary to a steady base flow control is effected through the injection or suction of fluid through a single orifice on the boundary the results demonstrate that instability suppression can be achieved without any a priori knowledge of the flow unsteadiness such as frequencies instability type etc the present methodology has been extended to three dimensions and may potentially be applied to separation control relaminarization and turbulence control applications using one to many sensors and actuators

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

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

optimal control of a nonlinear parabolic elliptic system abstract in this paper we shall study the problem of optimal control of the parabolic elliptic system u t f t x u x g t x u p x a t x u x x f 0 b and p x x p h t x u u x k t x u with initial data u t 0 u 0 the existence and uniqueness of weak solution to the parabolic elliptic system are given in a short interval according to the variational method optimal control theories and distributed parameter system control theories we can deduce that the norm of the solution is related to the control item and initial value in the special hilbert space the optimal control of the parabolic elliptic system with the initial data is given and the existence of an optimal solution to the parabolic elliptic system is proved

optimal control of thermally convected fluid flows we examine the optimal control of stationary thermally convected fluid flows from the theoretical and numerical point of view we use thermal convection as control mechanism that is control is effected through the temperature on part of the boundary control problems are formulated as constrained minimization problems existence of optimal control is given and a first order necessary condition of optimality from which optimal solutions can be obtained is established we develop numerical methods to solve the necessary condition of optimality and present computational results for control of cavity and channel type flows showing the feasibility of the proposed approach

nonlinear control of incompressible fluid flow application to burgers equation and 2d channel flow abstract this paper proposes a methodology for the synthesis of nonlinear finite dimensional feedback controllers for incompressible newtonian fluid flows described by two dimensional navier stokes equations combination of galerkin s method with approximate inertial manifolds is employed for the derivation of low order ordinary differential equation ode systems that accurately describe the dominant dynamics of the flow these ode systems are subsequently used as the basis for the synthesis of nonlinear output feedback controllers that guarantee stability and enforce the output of the closed loop system to follow the reference input asymptotically the method is successfully used to synthesize nonlinear finite dimensional output feedback controllers for the burgers equation and the two dimensional channel flow that enhance the convergence rate to the spatially uniform steady state and the parabolic velocity profile respectively the performance of the proposed controllers is successfully tested through simulations and is shown to be superior to the one of linear controllers

dynamic programming of the navier stokes equations a class of optimal control problems in viscous flow is studied main results are the pontryagin maximum principle and the verification theorem for the hamilton jacobi bellman equation

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

dynamics for controlled 2 d boussinesq systems with distributed controls the long time behavior of solutions for an optimal distributed control problem associated with the boussinesq equations is studied first a quasi optimal solution for the boussinesq equations is constructed this quasi optimal solution possesses the decay in time properties then some preliminary estimates for the long time behavior of all solutions of the boussinesq 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 is 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

generalized monogamy of contextual inequalities from the no disturbance principle in this letter we demonstrate that the property of monogamy of bell violations seen for no signaling correlations in composite systems can be generalized to the monogamy of contextuality in single systems obeying the gleason property of no disturbance we show how one can construct monogamies for contextual inequalities by using the graph theoretic technique of vertex decomposition of a graph representing a set of measurements into subgraphs of suitable independence numbers that themselves admit a joint probability distribution after establishing that all the subgraphs that are chordal graphs admit a joint probability distribution we formulate a precise graph theoretic condition that gives rise to the monogamy of contextuality we also show how such monogamies arise within quantum theory for a single four dimensional system and interpret violation of these relations in terms of a violation of causality these monogamies can be tested with current experimental techniques

stability enhancement by boundary control in 2 d channel flow in this paper we stabilize the parabolic equilibrium profile in a two dimensional 2 d channel flow using actuators and sensors only at the wall the control of channel flow was previously considered by speyer and coworkers and bewley and coworkers who derived feedback laws based on linear optimal control and implemented by wall normal actuation with an objective to achieve global lyapunov stabilization we arrive at a feedback law using tangential actuation using teamed pairs of synthetic jets or rotating disks and only local measurements of wall shear stress allowing to embed the feedback in microelectromechanical systems mems hardware without need for wiring this feedback is shown to guarantee global stability in at least h sup 2 norm which by sobolev s embedding theorem implies continuity in space and time of both the flow field and the control as well as their convergence to the desired steady state the theoretical results are limited to low values of reynolds number however we present simulations that demonstrate the effectiveness of the proposed feedback for values five order of magnitude higher

does ignorance of the whole imply ignorance of the parts large violations of noncontextuality in quantum theory a central question in our understanding of the physical world is how our knowledge of the whole relates to our knowledge of the individual parts one aspect of this question is the following to what extent does ignorance about a whole preclude knowledge of at least one of its parts relying purely on classical intuition one would certainly be inclined to conjecture that a strong ignorance of the whole cannot come without significant ignorance of at least one of its parts indeed we show that this reasoning holds in any noncontextual nc hidden variable model hv curiously however such a conjecture is false in quantum theory we provide an explicit example where a large ignorance about the whole can coexist with an almost perfect knowledge of each of its parts more specifically we provide a simple information theoretic inequality satisfied in any nc hv but which can be arbitrarily violated by quantum mechanics

hidden variables joint probability and the bell inequalities it is shown that the following statements about a quantum correlation experiment are mutually equivalent 1 there is a deterministic hidden variables model for the experiment 2 there is a factorizable stochastic model 3 there is one joint distribution for all observables of the experiment returning the experimental probabilities 4 there are well defined compatible joint distributions for all pairs and triples of commuting and noncommuting observables 5 the bell inequalities hold