on the hull of two dimensional percolation clusters a recently proven equivalence between certain random walks with memory and the hull of percolation clusters in two dimensions is used to estimate the fractal dimension of the latter by means of monte carlo simulations the authors calculate the value dh 1 750 or 0 002 in agreement with a recent conjecture that dh 7 4 exactly

the blow up rate for a system of heat equations with nonlinear boundary conditions this paper deals with the blow up rate estimates of positive solutions for systems of heat equations with nonlinear boundary conditions the upper and lower bounds of blow up rate are obtained

blowup rate for heat equation in lipschitz domains with nonlinear heat source terms on the boundary abstract this paper establishes the blowup rate estimate near the blowup time for the heat equation ut u with the nonlinear boundary condition un up on the boundary 0 t for a bounded lipschitz domain and for the nonlinear boundary condition un exp u on the boundary for a two dimensional disc with nonradially symmetric data

parabolic evolution equations and nonlinear boundary conditions on etudie le probleme aux valeurs limites et initiales u 7b a t u f t u 7b b t u g t u 0 t t u 0 u 0 qui peut etre considere comme une contrepartie abstraite a des problemes paraboliques semilineaires

multirate lqg control of continuous time stochastic systems abstract the lqg problem for stochastic continuous time systems subject to multirate sampling of both input and output variables is considered by restating the problem as a discrete time periodic lqg problem a sufficient condition for the existence of an optimal stabilizing regulator is given in terms of the structural properties of the original system and the cost function this improves on previous contributions where optimal control schemes were proposed without addressing existence and or stability issues the possibility of incorporating an integral action within the optimal lqg regulator is also briefly discussed

transport properties of the one dimensional stochastic lorentz model i velocity autocorrelation function point scatterers are placed on the real line such that the distances between scatterers are independent identically distributed random variables stationary renewal process for a fixed configuration of scatterers a particle performs the following random walk the particle starts at the pointx with velocity 1 in between scatterers the particle moves freely at a scatterer the particle is either transmitted or reflected both with probability 1 2 for given initial conditions of the particle the velocity autocorrelation function is a random variable on the scatterer configurations if this variable is averaged over the distribution of scatterers it decays not faster thant 3 2

linear time varying h 2 optimal control of sampled data systems abstract the goal in this paper is twofold first it is shown that linear time varying control is in general superior to linear time invariant lti control for lti plants with an h 2 criterion an expression for the optimal performance using time varying control is derived and a condition under which there is no advantage in using linear time varying control over lti control is determined second the h 2 optimal control of continuous time systems is studied via dual rate sampled data controllers it is shown that such a problem can be recast via the lifting technique as a standard lti h 2 problem in discrete time a design procedure for the dual rate h 2 optimal controller is proposed

lattice lorentz gas in cellular automaton fluids where binary collision laws admit reflections the stosszahl ansatz and the boltzmann equation are no longer valid at low densities this is proven for a class of lorentz gas models defined on cubic lattices for which the diffusion coefficient is calculated from a self consistent ring kinetic equation or effective medium theory the calculated results are in excellent agreement with results from molecular dynamics simulations over the whole density interval

h and h 2 optimal controllers for periodic and multirate systems in this paper we present the solutions to the optimal l2 to l2 disturbance rejection problem h as well as to the lqg h2 problem in periodic systems using the lifting technique both problems involve a causality condition on the optimal lti compensator when viewed in the lifted domain the h problem is solved using nehari s theorem whereas in the h2 problem the solution is obtained using the projection theorem exactly the same methods of solution can be applied in the case of multirate sampled data systems finally stability robustness issues in periodic and multirate systems are analyzed

a lifting technique for linear periodic systems with applications to sampled data control abstract a lifting technique is developed for periodic linear systems and applied to the h and h 2 sampled data control problems

brief paper direct state space solution of multirate sampled data h2 optimal control in solving the multirate sampled data h 2 control problem using the lifting approach one needs to solve a constraint discrete time h 2 optimal control problem for a generalized plant with infinite dimensional input output spaces to solve this problem the existing sampled data h 2 design technique computes an equivalent finite dimensional discrete time system and then designs the optimal h 2 controller for the equivalent system in this paper we will show that this problem can be solved using state space formulas by dealing with operators directly the operator compositions are computed explicitly using discrete multirate lifting and matrix exponentials the advantages of the direct method are it is straightforward it has clear physical meanings and it is more efficient computationally a sufficient condition for the existence and uniqueness of multirate sampled data h 2 optimal controller is given in terms of the continuous time plant

blow up analysis for a system of heat equations with nonlinear flux which obey different laws abstract we consider a system of heat equations u t u and v t v in 0 t completely coupled by nonlinear boundary conditions u e p v u v u q e v on 0 t we prove that the solutions always blow up in finite time for non zero and non negative initial values also the blow up only occurs on with c 1 t t p 2 p q max u x t c 2 t t p 2 p q log c 3 t t q 1 2 p q max v x t log c 4 t t q 1 2 p q for p q 0 0 1 and 0 p

mas consensus and delay limits under delayed output feedback in this technical note we study the consensus problem for discrete time multi agent systems over an undirected fixed network communication graph focusing on the robustness of consensus with respect to communication delay we assume that the agents input is subject to a constant albeit possibly unknown time delay and is generated by a distributed dynamic output feedback control protocol drawing upon concepts and techniques from robust control notably those concerning gain margin optimization and analytic interpolation we derive explicit closed form conditions for general linear agents to achieve consensus our results display an explicit dependence of the consensus condition on the delay value as well as on the agent s unstable poles and non minimum phase zeros showing that delayed communication between agents will generally hinder consensus and impose restrictions on the network topology we also show that a lower bound on the maximal delay allowable for consensus can be computed by a simple line search method

the blow up behavior of the heat equation with neumann boundary conditions abstract we establish the blow up rate for the solution of the heat equation u t u xx 0 x t 0 subject to neumann boundary conditions u x 0 t 0 u x 1 t e u 1 t with convex initial data

systematic density expansion for random resistor networks the authors present a systematic density expansion for calculating transport properties return probabilities and spectral densities for lattice hopping models with diluted randomness the method is applied to a disordered square lattice where the bonds carry conductances sigma 1 and sigma 2 in concentrations c and 1 c respectively and they calculate explicitly the o c and o c2 contributions to the static conductivity diffusion coefficient and to the coefficient beta c of the long time tail in the velocity autocorrelation function vacf upsilon x 0 upsilon x t approximately beta c t 2 to o c the vacf is calculated for all times and shows negative correlation cage effect for all times

lattice lorentz gas kinetic theory standard approximation schemes in kinetic theory are compared with the effective medium approximation ema that was developed earlier for the stochastic lorentz gas on cubic lattices in models with reflecting collisions the low density results are in strong disagreement with molecular chaos and in excellent agreement with the simulation data the analysis identifies the diagrams that are taken into account in the different approximations the ema accounts in a self consistent way for all nested ring diagrams

model validation of multirate systems from time domain experimental data the model validation problem using time domain experimental data is studied for multirate linear fractional uncertain models in this note as a technical tool the caratheodory fejer cf interpolation problem with a nest operator constraint is first investigated this problem is itself of interest mathematically and has potential applications in addressing other problems in control signal processing and circuit theory a necessary and sufficient solvability condition for this interpolation problem is given the validation tests are then presented based on this condition and the lifting technique tractable convex optimization methods can be used to solve the validation problems

survey invariant representations of discrete time periodic systems the correspondence between periodic and time invariant systems can take a variety of forms the purpose of this survey paper is to present a complete and clear picture on time invariant representations for discrete time periodic systems the core of the treatment evolves around the concept of periodic transfer function

novel phenomena in lorentz lattice gases abstract in lorentz lattice gases a point particle moves along the bonds of a lattice whose lattice sites are occupied by randomly placed scatterers which scatter the particle according to certain a priori given scattering rules we consider here mainly the simplest case of a square lattice fully or partly covered with two kinds of scatterers which scatter the particle to its right or its left respectively either according to probabilistic or strictly deterministic scattering rules although the global probability of the particle to be scattered to its right or left is equal for the two scattering rules the local probability is very different leading to a completely different diffusive behavior for the two cases while the probabilistic scattering rules lead to gaussian diffusion the deterministic rules lead either to anomalous or no diffusion depending on the concentrations of the scatterers on the lattice in the first case the mean square displacement is still proportional to the time so that a diffusion coefficient can be defined but the diffusion is non gaussian while in the second case the mean square displacement is bounded and all particles are trapped in a finite time in both cases this behavior is due to the existence of closed periodic orbits which in the first case can be of infinite extent extended closed orbits while in the second case they can only be of finite extent the lengths of the extended closed orbits show for a lattice fully occupied equally by right and left scatterers a scaling behavior identical to that of percolation clusters at the bond percolation threshold of a related bond percolation problem for special concentrations on a not fully occupied lattice the same scaling behavior is found leading to two critical lines but no known related percolation like problem exists in this case this critical behavior of the closed orbits in anomalous diffusion appears to obtain for all two dimensional lattices studied so far a number of extensions of the above results are indicated

multirate sampled data systems all h sub spl infin suboptimal controllers and the minimum entropy controller for a general multirate sampled data sd system the authors characterize explicitly the set of all causal stabilizing controllers that achieve a certain h sub spl infin norm bound moreover they give explicitly a particular controller that further minimizes an entropy function for the sd system the characterization lays the groundwork for synthesizing multirate control systems with multiple mixed control specifications

percolation and motion in a simple random environment the authors present a particularly simple model of deterministic classical motion in a two dimensional random environment as the parameters of the model are varied a transition occurs from all trajectories being localised to some being extended they construct a mean field theory for this transition and relate the model exactly to percolation models in particular parameter ranges they point out that it is a member of a new class of site percolation analogues of direct bond percolation

blow up properties for heat equations coupled via different nonlinearities this paper deals with heat equations coupled via exponential and power nonlinearities subject to null dirichlet boundary conditions the complete and optimal classification on non simultaneous and simultaneous blow ups is proposed by four sufficient and necessary conditions we find out that in some exponent region the blow up properties of the solutions depend much on the choosing of initial data moreover all kinds of non simultaneous and simultaneous blow up rates are obtained

blow up phenomena for a system of semilinear heat equations with nonlinear boundary flux abstract this paper deals with the blow up for a system of semilinear r laplace heat equations with nonlinear boundary flux it is shown that under certain conditions on the nonlinearities and data blow up will occur at some finite time and when blow up does occur upper and lower bounds for the blow up time are obtained

deterministic lattice lorentz gas i chiral model the author studies diffusion by using a specific type of cellular automaton where particles move in an environment of scatterers the deterministic collision rules used in the model give rise to certain difficulties related to nonergodicity the class of models introduced by gunn and ortuno 1985 also contains the model studied by gates 1972 previously developed theory including the boltzmann approximation the ring and repeated ring approximations and the effective medium approximation ema is generalized for this model the validity is further investigated using computer simulations in the presence of reflecting scatterers ema yields low density results that show the breakdown of the boltzmann equation while they agree quantitatively with the low density simulations ema also agrees with a phase transition that occurs for some parameter choices

multirate control a new approach abstract a new multirate digital control of linear periodic and time invariant systems is proposed an explicit multirate law is given which transforms the overall control design into that of a relatively small dimensional discrete time invariant system for which standard design techniques can be used it is shown that the proposed multirate scheme is in general more effective as a design tool than current multirate designs the controllability properties of the multirate system are studied consequently necessary and sufficient conditions for pole placement and stabilizability of the multirate system are given in terms of the continuous plant matrices moreover the multirate lqr problem is solved in this case the solution is obtained by solving an algebraic discrete riccati equation here necessary and sufficient conditions for the existence of a unique nonnegative definite solution of the riccati equation and the asymptotic stability of the corresponding closed loop multirate system are obtained these conditions are given in terms of the continuous time parameters

a parametrization of stabilizing controllers for multirate sampled data systems all linear multirate controllers for a given multirate sampled data system plant are parameterized in terms of a single parameter q z that is allowed to be any stable transfer matrix provided that certain causality conditions are met the result parallels a well known parameterization result for single rate sampled data plants the parameterization suggests architectures for multirate controllers

sampled data and discrete time h_2 optimal control this paper deals with the sampled data h 2 optimal control problem given a linear time invariant continuous time system the problem of minimizing the h 2 performance over all sampled data controllers with a fixed sampling period can be reduced to a pure discrete time h 2 optimal control problem this discrete time h 2 problem is always singular motivated by this in this paper we give a treatment of the discrete time h 2 optimal control problem in its full generality the results we obtain are then applied to the singular discrete time h 2 problem arising from the sampled data h 2 problem in particular we give conditions for the existence of optimal sampled data controllers we also show that the h 2 performance of a continuous time controller can always be recovered asymptotically by choosing the sampling period sufficiently small finally we show that the optimal sampled data h 2 performance converges to the continuous time optimal h 2 performance as the sampling period converges to zero

density expansion of transport properties on 2d site disordered lattices i general theory a systematic kinetic theory is developed for calculating transport properties on 2d lattices with random site impurities in concentration c which can be modelled by hopping models the authors main results are expressions in terms of lattice sums for the static and frequency dependent conductivity and for the velocity autocorrelation function

deterministic lattice lorentz gas ii mirror model for pt i see ibid vol 24 p 787 806 1991 as a model for diffusion a lattice version of the lorentz gas is studied using specular collision rules a previously developed theory containing the molecular chaos approximation several ring approximations and the effective medium approximation ema is applied and compared with simulations the correction to the boltzmann equation result resulting from effective medium approximation ema is opposite to the simulation results this indicates that other diagrams than ring diagrams should be considered which is peculiar if one considers the successes of the ema for other models this is investigated by using variants of the model the diffusion tensor is in general nonisotropic the corresponding features are qualitatively described by theory

a generalized entropy criterion for nevanlinna pick interpolation with degree constraint we present a generalized entropy criterion for solving the rational nevanlinna pick problem for n 1 interpolating conditions and the degree of interpolants bounded by n the primal problem of maximizing this entropy gain has a very well behaved dual problem this dual is a convex optimization problem in a finite dimensional space and gives rise to an algorithm for finding all interpolants which are positive real and rational of degree at most n the criterion requires a selection of a monic schur polynomial of degree n it follows that this class of monic polynomials completely parameterizes all such rational interpolants and it therefore provides a set of design parameters for specifying such interpolants the algorithm is implemented in a state space form and applied to several illustrative problems in systems and control namely sensitivity minimization maximal power transfer and spectral estimation

extensions of band matrices with band inverses abstract let r ij be a given set of i j matrices for i j 1 n and i j m where 0 m n 1 necessary and sufficient conditions are established for the existence and uniqueness of an invertible block matrix f ij i j 1 n such that f ij r ij for i j m f admits either a left or right block triangular factorization and f 1 ij 0 for i j m the well known conditions for an invertible block matrix to admit a block triangular factorization emerge for the particular choice m n 1 the special case in which the given r ij are positive definite in an appropriate sense is explored in detail and an inequality which corresponds to burg s maximal entropy inequality in the theory of covariance extension is deduced the block toeplitz case is also studied

a time domain approach to model validation in this paper we offer a novel approach to control oriented model validation problems the problem is to decide whether a postulated nominal model with bounded uncertainty is consistent with measured input output data our approach directly uses time domain input output data to validate uncertainty models the algorithms we develop are computationally tractable and reduce to generally nondifferentiable convex feasibility problems or to linear programming problems in special cases we give analytical solutions to these problems

strictly contractive and positive completions for block matrices abstract this paper deals with the following two problems of completion of block matrices 1 let a ij i j q be given matrices find additional matrices a ij such that the block matrix a a ij n i 1 m j 1 has norm less than one 2 let b ij j i q be given matrices find additional b ij such that the completion b b ij n i j 1 is positive definite the analysis is based on a study of certain linear fractional maps this approach leads to an explicit description of all solutions by linear fractional maps of which the coefficients are given directly in terms of the given data the maximum entropy principle appears as a corollary of a general formula for the determinant of a completion special attention is paid to the toeplitz case

unitary dilation approach to contractive matrix completion in this paper a new method to construct all contractive matrix completion to a block triangular matrix is given this new method uses only elementary matrix operations and has the advantages of better numerical reliability and ease in implementation on computers

thermal avalanche for blowup solutions of semilinear heat equations we consider the semilinear heat equation ut u up both in n and in a bounded domain with homogeneous dirichlet boundary conditions with 1 t we consider a natural approximation by reaction problems with global solution and pass to the limit as is well known the limit solution undergoes complete blowup after it blows up at t t the continuation is identically infinite for all t t we perform here a deeper analysis of how complete blowup occurs actually the singularity set of a solution that blows up as t t propagates instantaneously at time t t to cover the whole space producing a catastrophic discontinuity between t t and t t this is called the avalanche we describe its formation as a layer appearing in the limit of the natural approximate problems after a suitable scaling the initial structure of the layer is given by the solution of a limit problem described by a simple ordinary differential equation as t proceeds past t the solutions of the approximate problems have a traveling wave behavior with a speed that we compute the situation in the inner region depends on the type of approximation a conical pattern is formed with time when we approximate the power up by a flat truncation at level n while for tangent truncations we get an exponential increase in time and a diffusive spatial pattern 2003 wiley periodicals inc

optimal h and h 2 control of hybrid multirate systems the problem of using a synchronous multirate digital controller for a continuous time plant is considered the performance objectives considered are the h and the h2 norms of the periodically time varying continuous time input output behavior of the closed loop system a continuous time lifting technique is used to solve these hybrid sampled data problems this approach yields equivalent purely discrete time problems while preserving the multirate causality of the systems the later problems can then be solved using known techniques

multirate periodic systems and constrained analytic function interpolation problems multirate periodic systems and some related constrained analytic function interpolation problems are studied in this paper after showing how to convert a general multirate periodic system to an equivalent linear time invariant lti system with a structural constraint we formulate some analytic function interpolation problems with such a constraint that can find various applications in the study of multirate and periodic systems both the solvability conditions and characterization of all solutions are presented to these constrained interpolation problems

the h 2 problem for sampled data systems m for sampled data systems in this paper we pose and give a complete solution to an analog of the h2 problem for sampled data system we motivate and develop a natural generalization of the h2 cost to periodic systems which is then applied to the continuous time closed loop mapping in a sampled data control system it is shown that the cost criterion developed is actually a norm in an space of hilbert schmidt operator valued functions we give state space solutions to the optimal and suboptimal controllers synthesis problems in this new norm by establishing an equivalent standard h2 problem

blow up estimates for system of heat equations coupled via nonlinear boundary flux abstract this paper deals with a system of heat equations coupled via nonlinear boundary flux the precise blow up rate estimates are established together with the blow up set it is observed that there is some quantitative relationship regarding the blow up properties between the heat system with coupled nonlinear boundary flux terms and the corresponding reaction diffusion system with the same nonlinear terms as the source

blow up estimates of the positive solution of a parabolic system this paper establishes the blow up estimates for the systems ut u 0 vt v 0 in br 0 t br rn with the nonlinear boundary conditions u um1vn1 and v um2vn2 on sr 0 t where 0 m1 1 m2 and 0 n2 1 n1 we prove that c t t 2 max u x t c t t 2 and c t t 2 max v x t c t t 2 under some monotonicity assumptions on the initial values where n1 n2 1 m2 m1 1 and n1m2 1 m1 1 n2

state space approach to discrete time h 2 optimal control with a causality constraint abstract controller design with a causality constraint arises in periodic or multirate control systems in this paper complete state space solutions to the optimal and suboptimal h 2 control problems are developed with a causality constraint on controller feedthrough terms explicit formulas for the controllers are given in terms of solutions of two riccati equations the results are more implementable than existing frequency domain solutions

optimal two sided diagonal scaling for filter bank frames two sided diagonal scaling for transfer matrices is formulated an efficient algorithm is proposed to compute globally optimal solutions using the iterated bi section and linear matrix inequality lmi solver it is shown that the two sided scaling of filter bank fb frames can be implemented by the adjustment of channel gains and the periodic precoding of source signal and that the frame bound ratio of fb frames can be effectively improved by such scaling explicit formulas are established for both uniform and nonuniform fb frames including detail formulas for discrete weyl heisenberg frames and tree structured fbs discrete wavelets different examples show the effectiveness of the obtained results

cellular automaton fluids 1 basic theory continuum equations are derived for the large scale behavior of a class of cellular automaton models for fluids the cellular automata are discrete analogues of molecular dynamics in which particles with discrete velocities populate the links of a fixed array of sites kinetic equations for microscopic particle distributions are constructed hydrodynamic equations are then derived using the chapman enskog expansion slightly modified navier stokes equations are obtained in two and three dimensions with certain lattices viscosities and other transport coefficients are calculated using the boltzmann transport equation approximation some corrections to the equations of motion for cellular automaton fluids beyond the navier stokes order are given