relaxed conditions for stability of time varying delay systems in this paper the problem of delay dependent stability analysis of time varying delay systems is investigated firstly a new inequality which is the modified version of free matrix based integral inequality is derived and then by aid of this new inequality two novel lemmas which are relaxed conditions for some matrices in a lyapunov function are proposed based on the lemmas improved delay dependent stability criteria which guarantee the asymptotic stability of the system are presented in the form of linear matrix inequality lmi two numerical examples are given to describe the less conservatism of the proposed methods

a model for steady fluid flow in random three dimensional networks of disc shaped fractures a model for steady fluid flow in three dimensional random networks of fractures has been developed in this model the fractures are disc shaped discontinuities in an impermeable matrix the fracture discs can be arbitrarily located within the rock volume and can have any desired distribution of aperture radius orientation and density thus where the disc model is appropriate it is possible to calculate flow through fracture networks which are statistically similar to those that occur in nature after the boundary conditions and the desired fractures are specified the intersections nodes between these discs elements are identified then steady flow through the network is calculated using a mixed analytical numerical technique in each fracture analytic equations for flow into or out of each node as a function of the average head at each node are developed the equations are based on image theory and the assumption that each node is a source or sink of uniform strength a set of mass balance equations is constructed which equate flow into a node from one of its associated fractures to flow out of the node into the other associated fracture these equations are solved for the average head at each node and flux between fractures can then be calculated by substituting the average head values back into the analytical equations the model has been successfully checked against analytical results for several cases of two and three intersecting fractures we plan to use these techniques to measure the permeability of fracture networks

asynchronous l 2 l filtering for discrete time stochastic markov jump systems with randomly occurred sensor nonlinearities this paper is concerned with the problem of asynchronous l 2 l filtering for discrete time stochastic markov jump systems with sensor nonlinearity the sensor nonlinearity is assumed to occur randomly according to a stochastic variable satisfying the bernoulli distribution a sufficient condition is first given such that the resultant filtering error system which is a kind of nonhomogeneous markov jump system is stochastically stable with a guaranteed l 2 l performance index then the existence criterion of the desired asynchronous filter with piecewise homogeneous markov chain is proposed in terms of a set of linear matrix inequalities a numerical example is given to show the effectiveness and potential of the developed theoretical results

one particle subspaces in the stochastic xy model we study the spectrum of the generatorh of the glauber dynamics for a model of planar rotators on a lattice in the case of a high temperature 1 we construct two so called one particle subspacesh forh and describe the spectrum of the generator in these subspaces as a consequence we find time asymptotics of the correlations for the glauber dynamics

upscaling discrete fracture network simulations an alternative to continuum transport models 1 particle tracking through stochastically generated networks of discrete fractures provides an alternative to the conventional advection dispersion description of transport in fractured rock however discrete fracture network simulations are computationally intensive and usually limited to small scales an approach for direct upscaling of discrete fracture simulations is described trajectories for nonreacting tracer particles are first extracted from relatively small discrete fracture network simulations tracer rock interaction is represented by also calculating a cumulative reactivity parameter along each trajectory the residence time reactivity information is then used in a monte carlo simulation to construct artificial particle trajectories of any length thereby achieving the upscaling objective in its simplest form the procedure has the form of a random walk evolving in a two dimensional space tests using site specific and generic networks show that it is necessary to modify the random walk to produce sequential correlation along the trajectories we achieve this by using a discrete state markov process to direct the random walk the procedure is computationally efficient easily implemented and compares well with the network simulations

stability analysis of uncertain sampled data systems with incremental delay using looped functionals the robust stability analysis of asynchronous and uncertain sampled data systems with constant incremental input delay is addressed in the looped functional framework these functionals have been shown to be suitable for the analysis of impulsive systems as they allow one to express discrete time stability conditions in an affine way enabling then the consideration of uncertain and time varying systems the stability conditions are obtained by first reformulating the sampled data system as an impulsive system and by then considering a tailored looped functional along with wirtinger s inequality a recently introduced inequality that has been shown to be less conservative than jensen s inequality several examples are given for illustration

free matrix based integral inequality for stability analysis of systems with time varying delay the free weighting matrix and integral inequality methods are widely used to derive delay dependent criteria for the stability analysis of time varying delay systems because they avoid both the use of a model transformation and the technique of bounding cross terms this technical note presents a new integral inequality called a free matrix based integral inequality that further reduces the conservativeness in those methods it includes well known integral inequalities as special cases using it to investigate the stability of systems with time varying delays yields less conservative delay dependent stability criteria which are given in terms of linear matrix inequalities two numerical examples demonstrate the effectiveness and superiority of the method

set membership identification of switched linear systems with known number of subsystems this paper addresses the problem of robust identification of a class of discrete time linear hybrid systems switched linear models in a set membership framework given a finite collection of input output data from a noisy process the objective is twofold i establish whether this data was generated by a system that switches amongst an a priori known number of subsystems and ii in that case identify a suitable set of linear models along with a switching sequence that can explain the available experimental information our main result shows that these problems are equivalent to minimizing the rank of a matrix whose entries are affine in the optimization variables subject to a convex constraint imposing that these variables are the moments of an unknown borel measure with finite support the use of well known tight convex relaxations of rank allows for further reducing the problem to a semidefinite optimization that can be efficiently solved in the second part of the paper we extend these results to handle sensor failures that result in corrupted input output measurements assuming that these failures are infrequent we show that the problem can be recast into an optimization form where the objective is to simultaneously minimize the rank of a matrix and the number of nonzero rows of a second one in both cases appealing to well known convex relaxations of rank and sparsity leads to overall semidefinite optimization problems that can be efficiently solved these results are illustrated with multiple examples showing substantially improved identification performance in the presence of noise and sensor faults

asymptotics of eigenvalues of two particle schrodinger operators on lattices with zero range interaction the hamiltonian of a system of two quantum mechanical particles moving on the d dimensional lattice z d and interacting via zero range attractive pair potentials is considered for the two particle energy operator h k k t d d thetwo particlequasi momentum theexistenceofaunique positive eigenvalue z k above the upper edge of the essential spectrum of h k is proven and asymptotics for z k are found when approaches to some 0 k and k 0

conditional simulations of fluid flow in three dimensional networks of discrete fractures how to predict flow through a network of discrete fractures in a three dimensional domain is investigated fractures are modeled as circular discs of arbitrary size orientation transmissivity and location a fracture network is characterized by the statistical distributions of these quantities fracture traces observed on a wall form the basis for estimates of mean fracture radius fracture orientation parameters and fracture density fracture trace lengths are estimated with the scanline method and from areal sampling on circular regions the traces observed on the wall can also be used to condition the network this trace conditioning is achieved by forcing the network generator to always reproduce the observed traces conditioning might be a means of decreasing the variability of the fracture networks a numerical simulation model has been developed which is capable of generating a fracture network of desired statistical properties and solving for the steady state flow on each fracture disc the flow is discretized with the boundary element method a series of hypothetical examples are analyzed these examples consist of sets of monte carlo simulations of flow through a series of networks generated from the same statistical distributions the examples lead to the following conclusions large fractures and high fracture density implies good connectivity in the networks a high fracture density implies a small variance in the flow through the network trace conditioning decreases estimation variance only when the fracture network consists of large fractures fracture statistics can be estimated reasonably well from fracture traces observed on a wall

the threshold effects for the two particle hamiltonians on lattices for a wide class of two body energy operators h k on the d dimensional lattice d d 3 k being the two particle quasi momentum we prove that if the following two assumptions i and ii are satisfied then for all nontrivial values k k 0 the discrete spectrum of h k below its threshold is non empty the assumptions are i the two particle hamiltonian h 0 corresponding to the zero value of the quasi momentum has either an eigenvalue or a virtual level at the bottom of its essential spectrum and ii the one particle free hamiltonians in the coordinate representation generate positivity preserving semi groups

the efimov effect of three body schrodinger operators abstract the author studies the efimov effect of three body schrodinger operators by use of the variational method the effect is proved under the assumptions that pair potentials fall off with order o x 2 at infinity and that all three two body subsystems have a zero resonance energy

robust extended dissipative control for sampled data markov jump systems this paper investigates the problem of the sampled data extended dissipative control for uncertain markov jump systems the systems considered are transformed into markov jump systems with polytopic uncertainties and sawtooth delays by using an input delay approach the focus is on the design of a mode independent sampled data controller such that the resulting closed loop system is mean square exponentially stable with a given decay rate and extended dissipative a novel exponential stability criterion and an extended dissipativty condition are established by proposing a new integral inequality the reduced conservatism of the criteria is demonstrated by two numerical examples furthermore a sufficient condition for the existence of a desired mode independent sampled data controller is obtained by solving a convex optimisation problem finally a resistance inductance and capacitance rlc series circuit is employed to illustrate the effectiveness of the proposed approach

dissipativity based sampled data control for fuzzy markovian jump systems abstract in this paper the problems of dissipativity analysis and sampled data control are considered for fuzzy markovian jump systems firstly by constructing a mode dependent lyapunov function consisting of the two sided closed loop function where the information of both intervals x tk to x t and x t to x t k 1 are fully utilized the stochastically stable criteria and strictly q s r dissipative criteria are proposed in the form of linear matrix inequalities lmis then on the basis of the strictly dissipativity criteria a controller with state feedback is designed for the studied systems at last a truck trailer model is shown to demonstrate the efficiency of the presented method

on the spectrum of an hamiltonian in fock space discrete spectrum asymptotics a model operator h associated with the energy operator of a system describing three particles in interaction without conservation of the number of particles is considered the location of the essential spectrum of h is described the existence of infinitely many eigenvalues resp the finiteness of eigenvalues below the bottom ess h of the essential spectrum of h is proved for the case where the associated friedrichs model has a threshold energy resonance resp a threshold eigenvalue for the number n z of eigenvalues of h lying below z ess h the following asymptotics is found lim limits z to tau rm ess h 0 frac n z log z tau rm ess h u 0 0 u 0 infty

large time behavior of the lp norm of schrodinger semigroups abstract letv 0 v c0 rv with v 3 be such that h 1 2 v 0 but for any e 0 1 2 1 e v is not positive we determine the exact rate of divergence of the norm of e th as a map from l to l a number of related problems are discussed

energy momentum spectrum of some two particle lattice schrodinger hamiltonians we determine the excitation spectrum of some one and two particle z d lattice schrodinger hamiltonians they occur as approximate hamiltonians for the low lying energy momentum spectrum of diverse infinite lattice nonlinear quantum systems a unitary staggering transformation relates the low energy momentum spectrum to the high energy momentum spectrum of the transformed operators a feature for the one particle repulsive delta function hamiltonian is that in addition to the continuous band spectrum there is a bound state above the band and the repulsive case spectrum and scattering can be obtained from the attractive potential case by staggering for the two particle pair potential hamiltonian there are commuting self adjoint energy momentum operators and we determine the joint spectrum for the case of a lambda delta pair potential and equal particle masses for arbitrarily small lambda lambda or 3 there is no bound state for small system momentum but a bound state exists below the band if the momentum is large we find that the binding energy is an increasing function of the system momentum the existence of this bound state is in contrast with the continuum case where the birman schwinger bound excludes negative energy bound states for small couplings this bound state is absent if the two masses are different other spectral results are also obtained for the large coupling case an eigenfunction expansion that uses products of plane waves in the sum and difference coordinates is used to obtain the spectral results

the threshold effects for a family of friedrichs models under rank one perturbations a family of friedrichs models under rank one perturbations h p p 3 0 associated to a system of two particles on the three dimensional lattice z3 is considered we prove the existence of a unique eigenvalue below the bottom of the essential spectrum of h p for all non trivial values of p under the assumption that h 0 has either a threshold energy resonance virtual level or a threshold eigenvalue the threshold energy expansion for the fredholm determinant associated to a family of friedrichs models is also obtained

on the spectrum of the generator of an infinite system of interacting diffusions we study the spectrum of the operator generating an infinite dimensional diffusion process t in space here is a natural t invariant measure on which is a gibbs distribution corresponding to a formal hamiltonian h of an anharmonic crystal with a value of the inverse temperature 0 for small enough we establish the existence of an l invariant subspace such that has a distinctive character related to a quasi particle picture in particular has a lebesgue spectrum separated from the rest of the spectrum of l and concentrated near a point 1 0 giving the smallest non zero eigenvalue of a limiting problem associated with 0

on the number of eigenvalues of a model operator related to a system of three particles on lattices a model operator h associated to a system of three particles on the threedimensional lattice 3 that interact via nonlocal pair potentials is studied the following results are established i the operator h has infinitely many eigenvalues lying below the bottom of the essential spectrum and accumulating at this point if both the friedrichs model operators h mu alpha 0 1 2 have threshold resonances ii the operator h has finitely many eigenvalues lying outside the essential spectrum if at least one of the operators h mu alpha 0 1 2 has a threshold eigenvalue

puiseux series expansion for an eigenvalue of the generalized friedrichs model with perturbation of rank 1 a family h p 0 of the generalized friedrichs model with perturbation of rank 1 associated with a system of two particles moving on the one dimensional lattice is considered the existence of a unique eigenvalue e p of the operator h p lying below the essential spectrum is proved for any p from a neighborhood of the origin the puiseux series expansion for eigenvalue e p at the point p 0 is found moreover the asymptotics for e p is established as

a stochastic analysis of macroscopic dispersion in fractured media a stochastic modeling technique has been developed to investigate mass transport in a network of discrete fractures the model is based on the repetitive generation of realizations of a fracture network from probability distributions describing the fracture geometry and on a solution for mass transport within each network using a particle tracking technique the system we work with consists of two orthogonal fracture sets of finite length oriented at various angles with respect to the direction of the mean hydraulic gradient emphasis is placed on describing the character of dispersion which develops as a consequence of fracture interconnectivity and on testing the validity of the conventional diffusion based model of dispersion in describing transport in fractured media results show that mass distributions have a complex form marked longitudinal dispersion can develop even a short distance from a source the distribution of mass in the direction of flow has a consistent negative skew this pattern of dispersion arises from the limited number of pathways for mass to migrate through the network controlling factors in the transport process are the orientation of the fracture sets with respect to the mean hydraulic gradient the difference in the mean flow velocity in the two fracture sets and the standard deviation in velocity for fracture set 1 transport patterns can change greatly as the orientation of the hydraulic gradient changes with respect to the two fracture sets a conventional diffusion based model of dispersion cannot characterize transport in these fracture networks a skewed spatial distribution of mass is observed much more frequently than a gaussian distribution when the mean velocities in the two fracture sets are not equal the form of mass spreading is described by a more general skewed distribution that accounts for the bias in the probability of mass moving along one fracture set over another there is a tendency for mass to form a more symmetric distribution as the orientation of the two fracture sets is rotated toward a 45 angle with respect to the direction of the mean hydraulic gradient furthermore constant dispersivity values or simple dispersivity functions are not definable because of the sensitivity of transport to the local velocity field in the fracture network

random neighborhood graphs as models of fracture networks on rocks structural and dynamical analysis abstract we propose a new model to account for the main structural characteristics of rock fracture networks rfns the model is based on a generalization of the random neighborhood graphs to consider fractures embedded into rectangular spaces we study a series of 29 real world rfns and find the best fit with the random rectangular neighborhood graphs rrngs proposed here we show that this model captures most of the structural characteristics of the rfns and allows a distinction between small and more spherical rocks and large and more elongated ones we use a diffusion equation on the graphs in order to model diffusive processes taking place through the channels of the rfns we find a small set of structural parameters that highly correlates with the average diffusion time in the rfns we found analytically some bounds for the diameter and the algebraic connectivity of these graphs that allow to bound the diffusion time in these networks we also show that the rrngs can be used as a suitable model to replace the rfns in the study of diffusion like processes indeed the diffusion time in rfns can be predicted by using structural and dynamical parameters of the rrngs finally we also explore some potential extensions of our model to include variable fracture apertures the possibility of long range hops of the diffusive particles as a way to account for heterogeneities in the medium and possible superdiffusive processes and the extension of the model to 3 dimensional space

dissipativity based sampled data fuzzy control design and its application to truck trailer system this paper is concerned with the problem of dissipative control for takagi sugeno fuzzy systems under time varying sampling with a known upper bound on the sampling intervals based on the time dependent lyapunov krasovskii functional approach which makes full use of the available information about the actual sampling pattern a sufficient condition is established to guarantee the sampled data systems to be exponentially stable and strictly mathcal q mathcal s mathcal r gamma dissipative based on the criterion a design algorithm for the desired sampled data controller is proposed the effectiveness and benefits of the results developed in this paper is demonstrated by a controller design for a truck trailer system

two particle spectrum of the generator for stochastic model of planar rotators at high temperatures we study two particle spectrum branches of the generator in the stochastic model of planar rotators using the construction of a special basis in two particle invariant subspaces we prove that the branches of the spectrum are in a small neighborhood of the point 2 we prove the existence of two bound states in addition to the continuous part of the spectrum in the one dimensional case

geometry and topology of fracture systems random three dimensional fracture networks are generated according to various rules geometrical and topological features such as the number of three dimensional blocks the percolation thresholds and the cyclomatic numbers are studied with respect to fracture shapes and densities all the results could be successfully interpreted by means of the excluded volume