passivity based synchronization of a class of complex dynamical networks with time varying delay this paper proposes a complex delayed dynamical network consisting of n linearly and diffusively coupled identical reaction diffusion neural networks by utilizing some inequality techniques a sufficient condition ensuring the output strict passivity is derived for the proposed network model then we reveal the relationship between output strict passivity and synchronization of the proposed network model moreover based on the obtained passivity result and the relationship between output strict passivity and synchronization a criterion for synchronization is established finally a numerical example is provided to illustrate the correctness and effectiveness of the proposed results

a precise computation of stress intensity factor on the front of a convex planar crack in this paper we consider a general integral expression for mode i stress intensity factor along the fronts of convex planar cracks for this integral approximation we develop a simple numerical quadrature formula on every convex set which allows a precise estimation of the error this permits the use of extrapolation techniques for the accurate computation of the integral

oscillator representations of the 2d conformal algebra and superalgebra for the virasoro algebra and for the neveu schwarz ramond nsr superalgebra oscillator representations are found by localising the miura and the super miura maps from the theory of the korteweg de vries kdv and the super kdv equations respectively

edge singularities in 3 d elastic anisotropic and multi material domains abstract the solution to elasticity problems in three dimensional 3 d polyhedral multi material anisotropic domains in the vicinity of an edge is addressed it includes eigen functions similar to 2 d domains complemented by shadow functions and their associated edge stress intensity functions esifs which are functions along the edge these can be complex and are of major engineering importance in composite materials because failure theories directly or indirectly involve them the p version finite element methods presented in yosibash and omer z yosibash n omer numerical methods for extracting edge stress intensity functions in anisotropic three dimensional domains comput methods appl mech engrg 196 2007 3624 3649 are extended herein to compute complex eigen functions and shadows and applied to multi material anisotropic interfaces the quasidual function method m costabel m dauge z yosibash a quasidual function method for extracting edge stress intensity functions siam j math anal 35 5 2004 1177 1202 is also extended for extracting complex esifs from finite element solutions numerical examples for 3 d isotropic and anisotropic multi material interfaces are provided for which the complex eigen pairs and shadow functions are numerically computed and esifs extracted these examples show the efficiency and high accuracy of the numerical approximations

an accurate scheme for mixed mode fracture analysis of functionally graded materials using the interaction integral and micromechanics models summary the interaction integral is a conservation integral that relies on two admissible mechanical states for evaluating mixed mode stress intensity factors sifs the present paper extends this integral to functionally graded materials in which the material properties are determined by means of either continuum functions e g exponentially graded materials or micromechanics models e g self consistent mori tanaka or three phase model in the latter case there is no closed form expression for the material property variation and thus several quantities such as the explicit derivative of the strain energy density need to be evaluated numerically this leads to several implications in the numerical implementation the sifs are determined using conservation integrals involving known auxiliary solutions the choice of such auxil

local symplectic operators and structures related to them matrices with entries being differential operators that endow the phase space of an evolution system with a pre symplectic structure are considered special types of such structures are explicitly described links with integrability geometry of loop spaces and backlund transformations are traces

domain integral formulation for 3 d curved and non planar cracks with the extended finite element method abstract the computation of stress intensity factors sifs in curved and non planar cracks using domain integrals introduces some difficulties related to the use of curvilinear gradients several approaches exist in the literature that consider curvilinear corrections within a finite element framework but these depend on each particular crack configuration and they are not general in this work we introduce the curvilinear gradient correction within the extended finite element method framework xfem based only on the level set information used for the crack description and the local coordinate system definition our formulation depends only on the level set coordinates and therefore an explicit analytical description of the crack is not needed it is shown that this curvilinear correction improves the results and enables the study of generic cracks in addition we have introduced a simple error indicator for improving the sif computed via the interaction integral thanks to the better behavior of the j integral as it does not need auxiliary extraction fields

an evaluation of mode decomposed energy release rates for arbitrarily shaped delamination fronts using cohesive elements abstract computing mode decomposed energy release rates in arbitrarily shaped delaminations involving large fracture process zones has not been previously investigated the j integral is a suitable method for calculating this because its domain independence can be employed to reduce the integration domain to a cohesive interface and reduce it to a line integral however the existing formulations for the evaluation of the mode decomposed j integrals rely on the assumption of negligible fracture process zones in this work a method for the computation of the mode decomposed j integrals in three dimensional problems involving large fracture process zones and using the cohesive zone model approach is presented the formulation is applicable to curved fronts with non planar crack faces a growth driving direction criterion which takes into account the loading state at each point is used to render the integration paths and to decompose the j integral into loading modes this results in curved and non planar integration paths crossing the cohesive zone furthermore its implementation into the finite element framework is also addressed the formulation is validated against virtual crack closure technique vcct and linear elastic fracture mechanics lefm based analytical solutions and the significance and generality of the formulation are demonstrated with crack propagation in a three dimensional composite structure

h sub infinity control and quadratic stabilization of systems with parameter uncertainty via output feedback the article concerns linear systems which are subject to both time varying norm bounded parameter uncertainty and exogenous disturbance it addresses the robust h sub infinity control problem of designing a linear dynamic output feedback controller such that the closed loop system is quadratically stable and achieves a prescribed level of disturbance attenuation for all admissible parameter uncertainties it is shown that such a problem is equivalent to a scaled h sub infinity control problem

robust spl hscr sub spl infin filtering for uncertain discrete time state delayed systems this paper addresses the problem of robust spl hscr sub spl infin filtering for linear discrete time systems subject to parameter uncertainties in the system state space model and with multiple time delays in the state variables the uncertain parameters are supposed to belong to a given convex bounded polyhedral domain a methodology is developed to design a stable linear filter that assures asymptotic stability and a prescribed spl hscr sub spl infin performance for the filtering error irrespective of the uncertainty and the time delays the proposed design is given in terms of linear matrix inequalities which has the advantage in that it can be implemented numerically very efficiently

generalized domain independent interaction integral for solving the stress intensity factors of nonhomogeneous materials abstract the generalized domain independent interaction integral dii integral is investigated due to its extremely promising application in solving the stress intensity factors sifs of nonhomogeneous materials with complex interfaces a recent study revealed that the dii integral which is domain independent for material interfaces can be established by defining an appropriate auxiliary field regrettably the kind of auxiliary field that can be used is not very clear this work first discusses the conditions that the auxiliary field must satisfy for establishing a dii integral and provides a framework for designing more applicable auxiliary fields in this framework a generalized auxiliary field and the corresponding generalized dii integral are derived the generalized auxiliary field contains two free constants and can be expressed as the linear combination of a widely used auxiliary field and a new auxiliary field which are referred to as the crack face traction free auxiliary field and the zero mean stress auxiliary field respectively the generalized auxiliary field is effective in establishing the dii integral for purely mechanical loading and the zero mean stress auxiliary field is also effective in the establishment of the dii integral for isotropic mismatch strain problems the generalized dii integral is the linear function of mode i and mode ii sifs and its expression does not involve the free constants in the generalized auxiliary field then a patched extended finite element method xfem is briefly introduced to remove the crack tip enrichment and instead employ a patched mesh in the modeling the patched xfem does not depend on the material constitutive relations and thus has a larger applicable scale than does the traditional xfem finally the dii integral combined with the patched xfem is employed to investigate four representative crack problems numerical examples show that the generalized dii integral exhibits good domain independence for homogeneous nonhomogeneous and discontinuous properties although the numerical values of the dii integral do not remain constant for different values of the free constants due to numerical errors good numerical precision can be achieved if the free constants do not deviate too much from those used in the crack face traction free auxiliary field in addition the dii integral using the zero mean stress auxiliary field is demonstrated to be reliable and convenient in solving the sifs of particulate composites under an initial thermal strain

inverse extraction of cohesive zone laws by field projection method using numerical auxiliary fields summary the cohesive zone law relates the cohesive tractions with the cohesive separations within the fracture process zone of a material and is used to quantify the strength and toughness of the material determining the material s cohesive zone law however is a nontrivial inverse problem of finding unknown tractions and separations from measurement data previously a field projection method was established to extract the cohesive zone laws from far field data using interaction j integrals between the physical field of interest and auxiliary analytical probing fields here we extend the universality of the field projection method and its ease of numerical implementation by using numerical auxiliary fields these numerical fields are generated by systematically imposing uniform surface tractions element by element along the crack faces in finite element models then interaction j and m integrals between these auxiliary probing fields and the measurement field are used to reconstruct the traction and separation relationship along the crack faces the effectiveness of this method in extracting the cohesive zone law from measured displacements in the far field region is demonstrated through numerical experiments copyright 2012 john wiley sons ltd

domain integral formulation for stress intensity factor computation along curved three dimensional interface cracks new domain integrals for extracting mixed mode stress intensity factors along curved three dimensional bimaterial interface cracks are derived in the derivation the asymptotic auxiliary fields for the plane problem of a bimaterial interface crack are imposed along a curved crack front the general crack tip interaction integral a contour integral surrounding a point on the crack front which is evaluated in the limit as the contour is shrunk onto the crack tip is then expressed in domain form which is more suitable for numerical computation a consequence of imposing the auxiliary fields along a curved crack front is that the auxiliary stress fields do not satisfy equilibrium and the auxiliary strain fields do not satisfy compatibility the terms which arise due to the lack of equilibrium and compatibility are not sufficiently singular to contribute to the crack tip interaction integral or to affect its path independence however these terms become important when domain integral representations are introduced because they involve fields which are not asymptotically close to the crack tip in order to compute the pointwise stress intensity factors along the crack front the domain integrals are evaluated as a post processing step in the finite element method in the numerical results it is demonstrated that it is crucial to incorporate the terms that arise due to lack of equilibrium and compatibility of the auxiliary fields especially in regions where the local crack front curvature is high in the paper we present two numerical examples as a benchmark we first consider the problem of a penny shaped interface crack embedded in a cylinder the results for the complex stress intensity factor and phase angle are found to be in excellent agreement with the analytical solution the problem of an elliptical crack embedded between two dissimilar isotropic materials is also considered and the results are discussed

robust passivity and passification of stochastic fuzzy time delay systems in this paper the passivity and passification problems are investigated for a class of uncertain stochastic fuzzy systems with time varying delays the fuzzy system is based on the takagi sugeno t s model that is often used to represent the complex nonlinear systems in terms of fuzzy sets and fuzzy reasoning to reflect more realistic dynamical behaviors of the system both the parameter uncertainties and the stochastic disturbances are considered where the parameter uncertainties enter into all the system matrices and the stochastic disturbances are given in the form of a brownian motion we first propose the definition of robust passivity in the sense of expectation then by utilizing the lyapunov functional method the ito differential rule and the matrix analysis techniques we establish several sufficient criteria such that for all admissible parameter uncertainties and stochastic disturbances the closed loop stochastic fuzzy time delay system is robustly passive in the sense of expectation the derived criteria which are either delay independent or delay dependent are expressed in terms of linear matrix inequalities lmis that can be easily checked by using the standard numerical software illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results

hamiltonian theory over noncommutative rings and integrability in multidimensions a generalization of the adler gel fand dikii scheme is used to generate bi hamiltonian structures in two spatial dimensions in order to implement this scheme a hamiltonian theory is built over a noncommutative ring namely the ring of formal pseudodifferential operators bi hamiltonian structures generated in this way can be used for the kadomtsev petviashvili equation as well as other integrable equations in 2 1

passivity analysis and passification for uncertain signal processing systems the problem of passivity analysis finds important applications in many signal processing systems such as digital quantizers decision feedback equalizers and digital and analog filters equally important is the problem of passification where a compensator needs to be designed for a given system to become passive this paper considers these two problems for a large class of systems that involve uncertain parameters time delays quantization errors and unmodeled high order dynamics by characterizing these and many other types of uncertainty using a general tool called integral quadratic constraints iqcs we present solutions to the problems of robust passivity analysis and robust passification more specifically for the analysis problem we determine if a given uncertain system is passive for all admissible uncertainty satisfying the iqcs similarly for the problem of robust passification we are concerned with finding a loop transformation such that a particular part of the uncertain signal processing system becomes passive for all admissible uncertainty the solutions are given in terms of the feasibility of one or more linear matrix inequalities lmis which can be solved efficiently

brief paper passivity based sliding mode control of uncertain singular time delay systems in this paper the problem of sliding mode control smc with passivity of a class of uncertain nonlinear singular time delay systems is studied an integral type switching surface function is designed by taking the singular matrix into account thus the resulting sliding mode dynamics is a full order uncertain singular time delay system by introducing some slack matrices a delay dependent sufficient condition is proposed in terms of linear matrix inequality lmi which guarantees the sliding mode dynamics to be generalized quadratically stable and robustly passive the passification solvability condition is then established moreover a smc law and an adaptive smc law are synthesized to drive the system trajectories onto the predefined switching surface in a finite time finally a numerical example is provided to illustrate the effectiveness of the proposed theory

passivity and stability analysis of reaction diffusion neural networks with dirichlet boundary conditions this paper is concerned with the passivity and stability problems of reaction diffusion neural networks rdnns in which the input and output variables are varied with the time and space variables by utilizing the lyapunov functional method combined with the inequality techniques some sufficient conditions ensuring the passivity and global exponential stability are derived furthermore when the parameter uncertainties appear in rdnns several criteria for robust passivity and robust global exponential stability are also presented finally a numerical example is provided to illustrate the effectiveness of the proposed criteria

boundary element analysis of three dimensional mixed mode thermoelastic crack problems using the interaction and energy domain integrals a three dimensional boundary element method bem implementation of the interaction integral methodology for the numerical analysis of mixed mode three dimensional thermoelastic crack problems is presented in this paper the interaction integral is evaluated from a domain representation naturally compatible with the bem since stresses strains temperatures and derivatives of displacements and temperatures at internal points can be evaluated using the appropriate boundary integral equations several examples are analysed and the results compared with those available in the literature to demonstrate the efficiency and accuracy of the implementation to solve straight and curved crack front problems copyright 2007 john wiley sons ltd

investigation of mixed mode stress intensity factors for nonhomogeneous materials using an interaction integral method abstract an interaction energy integral is derived for the computation of mixed mode stress intensity factors sifs in nonhomogeneous materials with continuous or discontinuous properties this method is based on a conservation integral that relies on two admissible mechanical states actual and auxiliary fields in general the interaction energy contour integral is converted into an equivalent domain integral in numerical computations it can be seen from the equivalent domain integral the integrand does not involve any derivatives of material properties moreover the formulation can be proved valid even when the integral domain contains material interfaces therefore it is not necessary to limit the material properties to be continuous for the present method due to these advantages the application range of the interaction integral method can be greatly enlarged the numerical implementation of the derived expression is combined with the extended finite element method xfem using this method the influences of material properties on the mixed mode sifs are investigated for four types of material properties selected in this work numerical results show that the mechanical properties and their first order derivatives can affect mode i and ii sifs greatly while the higher order derivatives affect the sifs very slightly

on strategies for enforcing interfacial constraints and evaluating jump conditions with the extended finite element method we consider a problem stemming from recent models of phase transitions in stimulus responsive hydrogels wherein a sharp interface separates swelled and collapsed phases extended finite element methods that approximate the local solution with an enriched basis such that the mesh need not explicitly fit the interface geometry are emphasized attention is focused on the weak enforcement of the normal configurational force balance and various options for evaluating the jump in the normal component of the solute flux at the interface we show that as the reciprocal interfacial mobility vanishes it plays the role of a penalty parameter enforcing a pure dirichlet constraint eventually triggering oscillations in the interfacial velocity we also examine alternative formulations employing a lagrange multiplier to enforce this constraint it is shown that the most convenient choice of basis for the lagrange multiplier results in oscillations in the multiplier field and a decrease in accuracy and rate of convergence in local error norms suggesting a lack of stability in the discrete formulation under such conditions neither the direct evaluation of the gradient of the approximation at the phase interface nor the interpretation of the lagrange multiplier field provide a robust means to obtain the jump in the normal component of solute flux fortunately the adaptation and use of local domain integral methodologies considerably improves the flux evaluations several example problems are presented to compare and contrast the various techniques and methods

passivity of delayed reaction diffusion networks with application to a food web model this paper is concerned with the passivity problem of a class of delayed reaction diffusion networks in which the input and output variables are varied with the time and space variables firstly two new passivity definitions are proposed which are totally different from some existing concepts of passivity then we establish several criteria for the passivity input strict passivity and output strict passivity by using the lyapunov functional method combined with the inequality techniques and also reveal the relationship between passivity and stability of the reaction diffusion networks moreover these results are applied to investigate the asymptotic stability and control design of a food web model with time delay and reaction diffusion terms numerical simulations are presented finally to demonstrate the effectiveness of the proposed results

finite time non fragile passivity control for neural networks with time varying delay abstract in this paper the problem of finite time non fragile passivity control for neural networks with time varying delay is studied we construct a new lyapunov krasovskii function with triple and four integral terms and then utilizing wirtinger type inequality technique the sufficient conditions for finite time boundedness and finite time passivity are derived furthermore a non fragile state feedback controller is designed such that the closed loop system is finite time passive moreover the proposed sufficient conditions can be simplified into the form of linear matrix inequalities lmis using matlab lmi toolbox finally three numerical examples are presented to illustrate the effectiveness of the proposed criteria

mode decomposition of three dimensional mixed mode cracks via two state integrals a numerical scheme is proposed to obtain the individual stress intensity factors in an axisymmetric crack and in a three dimensional mixed mode crack the procedures presented here are based on the path independence of j and m integrals and mutual or two state conservation integrals which involve two elastic fields a useful method to decompose the stress intensity factors along curved three dimensional cracks under mixed mode is derived by using appropriate auxiliary fields for the plane problems the choice of the auxiliary fields available is critical to success of the present scheme and in this study it is made of not only the asymptotic plane strain solution which requires some remedy in application of the two state integral due to the lack of equilibrium and compatibility but a numerical solution with a given stress intensity as well some numerical examples of penny shaped cracks are presented to investigate the applicability and effectiveness of the method for problems of axisymmetric and three dimensional cracks

a linear matrix inequality approach to robust h sub spl infin filtering we consider the robust h sub spl infin filtering problem for a general class of uncertain linear systems described by the so called integral quadratic constraints iqcs this problem is important in many signal processing applications where noise nonlinearity quantization errors time delays and unmodeled dynamics can be naturally described by iqcs the main contribution of this paper is to show that the robust h spl infin filtering problem can be solved using linear matrix inequality lmi techniques which are numerically efficient owing to recent advances in convex optimization the paper deals with both continuous and discrete time uncertain linear systems

an interaction integral method for 3d curved cracks in nonhomogeneous materials with complex interfaces this work derives an interaction integral for the computation of mixed mode stress intensity factors sifs in three dimensional 3d nonhomogeneous materials with continuous or discontinuous properties the present method is based on a two state integral by the superposition of actual and auxiliary fields in 3d domain formulation of the interaction integral derived here the integrand does not involve any derivatives of material properties furthermore the formulation can be proved to be still valid even when the integral domain contains material interfaces therefore it is not necessary to limit the material properties to be continuous for the present formulation on account of these advantages the application range of the interaction integral can be greatly enlarged this method in conjunction with the finite element method fem is employed to solve several representative fracture problems according to the comparison between the results and those from the published lectures good agreement demonstrates the validation of the interaction integral the results show that the present interaction integral is domain independent for nonhomogeneous materials with interfaces

a numerical procedure for interaction integrals developed for curved cracks of general shape in 3 d this study presents a numerical procedure for the evaluation of interaction energy integrals used to extract mixed mode stress intensity factors the interaction energy integral is expressed as a domain integral and the proposed numerical procedure delivers accurate results for three dimensional cracks with curved crack fronts and curved crack surfaces for a rather general set of integration domains it is clearly shown that when the curvature of the crack surface becomes sufficiently large special care must be taken in the evaluation of both the volume and the area integrals involved to improve the accuracy in the evaluation of the former a composite rule for the gaussian quadrature scheme is employed four benchmark geometries with available analytical solutions are considered firstly mesh design parameters for planar cracks with straight and curved crack fronts are established secondly non planar cracks with straight and curved crack fronts are employed to examine the accuracy of the numerical procedure

antisymmetrical 3 d stress field near the crack front of a thin elastic plate abstract based on detailed three dimensional finite clement analysis the near tip field of a thin elastic plate remotely subjected to mode ii antisymmctrical loading is investigated the computed results show the transition to a three dimensional state to occur near the radial distance from the crack tip of 1 5 times the plate thickness in the close vicinity of the crack front the asymptotic stress field is characterized by a combination of plane strain mode ii and anti plane mode iii singular 1 r fields the domain of such fields extends approximately 0 5 of the thickness in the radial direction the mixed mode stress intensity factors along the crack front are determined from 3 d conservation integrals and unlike the case of symmetrical loading their magnitudes are greater towards the free surface near the intersection of the crack front and free surface the stress field converges to the antisymmetrical corner singularity solution the asymptotic form of stress near the intersection under general loading conditions is presented along with the corner stress intensity factors

extended finite element method for three dimensional crack modelling an extended finite element method x fem for three dimensional crack modelling is described a discontinuous function and the two dimensional asymptotic crack tip displacement fields are added to the finite element approximation to account for the crack using the notion of partition of unity this enables the domain to be modelled by finite elements with no explicit meshing of the crack surfaces computational geometry issues associated with the representation of the crack and the enrichment of the finite element approximation are discussed stress intensity factors sifs for planar three dimensional cracks are presented which are found to be in good agreement with benchmark solutions copyright 2000 john wiley sons ltd

passivity and passification of memristor based recurrent neural networks with additive time varying delays this paper presents a new design scheme for the passivity and passification of a class of memristor based recurrent neural networks mrnns with additive time varying delays the predictable assumptions on the boundedness and lipschitz continuity of activation functions are formulated the systems considered here are based on a different time delay model suggested recently which includes additive time varying delay components in the state the connection between the time varying delay and its upper bound is considered when estimating the upper bound of the derivative of lyapunov functional it is recognized that the passivity condition can be expressed in a linear matrix inequality lmi format and by using characteristic function method for state feedback passification it is verified that it is apathetic to use immediate or delayed state feedback by constructing a lyapunov krasovskii functional and employing jensen s inequality and reciprocal convex combination technique together with a tighter estimation of the upper bound of the cross product terms derived from the derivatives of the lyapunov functional less conventional delay dependent passivity criteria are established in terms of lmis moreover second order reciprocally convex approach is employed for deriving the upper bound for terms with inverses of squared convex parameters the model based on the memristor with additive time varying delays widens the application scope for the design of neural networks finally pertinent examples are given to show the advantages of the derived passivity criteria and the significant improvement of the theoretical approaches

positive real control problem for uncertain linear time invariant systems abstract this paper focuses on positive real control of linear time invariant systems which are subjected to norm bounded uncertainties in the state equation we address the problem of designing a linear dynamic output feedback controller that robustly stabilizes the uncertain system and achieves the extended strict positive realness property for a given closed loop transfer function it is shown that a solution to the above problem can be obtained by solving a scaled strict positive real control problem for which no parameter uncertainty occurs

an explicit dynamics extended finite element method part 1 mass lumping for arbitrary enrichment functions this paper presents a general mass lumping technique for explicit dynamics simulations using the extended finite element method with arbitrary enrichment functions the proposed mass lumping technique is a generalization of previously published results for cracks and holes time step estimates are studied for crack singular enrichment functions and for hole enrichment in both cases we show that the critical time step does not tend to zero and is of the same order as that of the same unenriched element the performance of the method is demonstrated on several numerical examples that compare well with classical finite elements and previously published x fem results

generalized kalman yakubovich popov lemma for 2 d fm lss model this paper is concerned with the generalized kalman yakubovich popov kyp lemma for 2 d fornasini marchesini local state space fm lss systems by carefully analyzing the feature of the states in 2 d fm lss models a linear matrix inequality lmi characterization for a rectangular finite frequency region is constructed and then by combining this characterization with s procedure a generalized kyp lemma is proposed for 2 d fm lss models as applications of the developed kyp lemma new conditions are further derived for designing controllers guaranteeing finite frequency positive realness of the closed loop systems where both state feedback and dynamic output feedback control laws are considered finally two illustrative examples clearly show the effectiveness of the proposed results the main contribution of the paper is trifold 1 a novel characterization for a finite frequency region has been developed 2 a generalized kyp lemma has been proposed including the existing bounded realness and positive realness results as special cases and 3 systematic methods for finite frequency positive real control of 2 d systems have been presented

solution to the positive real control problem for linear time invariant systems in this paper we study the problem of synthesizing an internally stabilizing linear time invariant controller for a linear time invariant plant such that a given closed loop transfer function is extended strictly positive real necessary and sufficient conditions for the existence of a controller are obtained state space formulas for the controller design are given in terms of solutions to algebraic riccati equations or inequalities the order of the constructed controller does not exceed that of the plant

strictly positive real transfer functions revisited the two most commonly used definitions of strictly positive real spr transfer functions are reviewed contrary to what has been suggested in the literature it is proven that the least restrictive weak definition of the two is clearly related to the yacubovich kalman lemma the relationship between time and frequency domain conditions pertaining to the weak definition of spr systems is established

an improved secure communication scheme based passive synchronization of hyperchaotic complex nonlinear system in this paper an improved secure communication scheme is proposed based on passive synchronization of hyperchaotic complex nonlinear system the hyperchaotic complex lu system is employed to encrypt the emitted signal comparing with the existing approaches the useful information in our work can be unbounded in the transmitter the original information signal is modulated into one parameter of hyperchaotic complex lu system and it is assumed that the parameter of the receiver system is unknown in the receiver based on the passivity theory the controllers and corresponding parameter update rule are designed to make two identical hyperchaotic complex lu systems asymptotically synchronized and identify the unknown parameter simultaneously the information signal can be recovered accurately by the estimated parameter corresponding theoretical proofs and numerical simulations demonstrate the feasibility and effectiveness of the proposed method it is also shown that the presented secure communication scheme is robust against different channel noise

on the computation of mixed mode stress intensity factors in functionally graded materials a new interaction energy integral method for the computation of mixed mode stress intensity factors at the tips of arbitrarily oriented cracks in functionally graded materials is described in the method interaction energy contour integrals are defined and expressed in equivalent domain form the interaction energy integrals involve products of the actual fields that arise from solution to the boundary value problem with known auxiliary fields the auxiliary stress and displacement fields are chosen to be the asymptotic near tip fields for a crack in a homogeneous material having the same elastic constants as those found at the crack tip in the functionally graded material the auxiliary strain fields are obtained from the auxiliary stress fields using the constitutive relation for the functionally graded material a consequence of our choice for the auxiliary strain field is lack of compatibility which leads to extra terms in the domain integrals that need to be evaluated for the sake of accuracy the mixed mode stress intensity factors are obtained from the domain integrals as a post processing step in the extended finite element method to assess the accuracy of the method we consider the benchmark problems of an edge cracked plate and an angled center crack for specimens with a functional gradient in material properties excellent agreement is obtained between the numerical results and the analytical solutions for both stress intensity factors in all cases all numerical results for the stress intensity factors also exhibit domain independence the pertinent post processing routines are provided for download via the world wide web

a disk shaped domain integral method for the computation of stress intensity factors using tetrahedral meshes a novel domain integral approach is introduced for the accurate computation of pointwise j integral and stress intensity factors sifs of 3d planar cracks using tetrahedral elements this method is efficient and easy to implement and does not require a structured mesh around the crack front the method relies on the construction of virtual disk shaped integral domains at points along the crack front and the computation of domain integrals using a series of virtual triangular and line elements the accuracy of the numerical results computed for through the thickness penny shaped and elliptical crack configurations has been validated by using the available analytical formulations the average error of computed sifs remains below 1 for fine meshes and 2 3 for coarse ones the results of an extensive parametric study suggest that there exists an optimum mesh dependent domain radius at which the computed sifs are the most accurate furthermore the results provide evidence that tetrahedral elements are efficient reliable and robust instruments for accurate linear elastic fracture mechanics calculations

boundary element analysis of three dimensional mixed mode cracks via the interaction integral a three dimensional boundary element method bem implementation of the interaction integral methodology for the numerical analysis of mixed mode three dimensional cracks is presented in this paper the interaction integral is evaluated from a domain representation naturally compatible with the bem since stresses strains and derivatives of displacements at internal points can be evaluated using their appropriate boundary integral equations special emphasis is put in the selection of the auxiliary function that represents the virtual crack advance in the domain integral this is found to be a key feature to obtain reliable results at the intersection of crack fronts with free surfaces several examples are analysed to demonstrate the efficiency and accuracy of the implementation

a numerical strategy for investigating the kinetic response of stimulus responsive hydrogels we present a strategy for obtaining numerical solutions to a system of non linear coupled evolution equations describing volume transitions in stimulus responsive hydrogels srhs the theory underlying our sharp interface model of phase transitions in srhs is provided along with the assumptions leading to the specialized formulation that is the starting point for the numerical method the discrete formulation is then developed with a hybrid extended finite element level set method xfe lsm domain integral methodologies are used consistently to extract interfacial quantities such as the mechanical driving traction the jump in the normal component of the solute flux and requisite geometric information several benchmark studies are provided to demonstrate the accuracy and robustness of the numerical strategy we then investigate various features of srh kinetics including the regimes of unstable and stable phase transitions surface pattern formation and bulk phase separation

passivity analysis and passive control of fuzzy systems with time varying delays this paper is concerned with the passive controller design problem for a class of continuous time takagi sugeno t s fuzzy systems with both state and input delays the delays are assumed to be time varying and differentiable a notion of very strict passivity is adopted the purpose is to design a state feedback fuzzy controller such that the resulting closed loop system is very strictly passive vsp delay dependent conditions for the solvability of the addressed problem are obtained by applying recently developed techniques for time delay systems and fuzzy systems these conditions are expressed by means of strict linear matrix inequalities lmis that can be easily solved a numerical example and simulation results are provided to demonstrate the effectiveness of the proposed method

bi hamiltonian structure in 2 d field theory we exhibit the bi hamiltonian structure of the equations of associativity witten dijkgraaf verlinde verlinde dubrovin equations in 2 d topological field theory which reduce to a single equation of monge ampere type f ttt f xxt 2 f xxx f xtt in the case of three primary fields the first hamiltonian structure of this equation is based on its representation as a 3 component system of hydrodynamic type and the second hamiltonian structure follows from its formulation in terms of a variational principle with a degenerate lagrangian

hamiltonian structure of dubrovin s equation of associativity in 2 d topological field theory a third order monge ampere type equation of associativity that dubrovin has obtained in 2 d topological field theory is formulated in terms of a variational principle subject to second class constraints using dirac s theory of constraints this degenerate lagrangian system is cast into hamiltonian form and the hamiltonian operator is obtained from the dirac bracket there is a new type of kac moody algebra that corresponds to this hamiltonian operator in particular it is not a w algebra

non planar 3d crack growth by the extended finite element and level sets part i mechanical model a methodology for solving three dimensional crack problems with geometries that are independent of the mesh is described the method is based on the extended finite element method in which the crack discontinuity is introduced as a heaviside step function via a partition of unity in addition branch functions are introduced for all elements containing the crack front the branch functions include asymptotic near tip fields that improve the accuracy of the method the crack geometry is described by two signed distance functions which in turn can be defined by nodal values consequently no explicit representation of the crack is needed examples for three dimensional elastostatic problems are given and compared to analytic and benchmark solutions the method is readily extendable to inelastic fracture problems copyright 2002 john wiley sons ltd

alternative bi hamiltonian structures for wdvv equations of associativity the wdvv equations of associativity in two dimensional topological field theory are completely integrable third order monge ampere equations which admit bi hamiltonian structure the time variable plays a distinguished role in the discussion of hamiltonian structure whereas in the theory of wdvv equations none of the independent variables merits such a distinction wdvv equations admit very different alternative hamiltonian structures under different possible choices of the time variable but all these various hamiltonian formulations can be brought together in the framework of the covariant theory of symplectic structure they can be identified as different components of the covariant witten zuckerman symplectic 2 form current density where a variational formulation of the wdvv equation that leads to the hamiltonian operator through the dirac bracket is available

integral quadratic constraint approach vs multiplier approach integral quadratic constraints iqc arise in many optimal and or robust control problems the iqc approach can be viewed as a generalization of the classical multiplier approach in the absolute stability theory in this paper we study the relationship between the two approaches for robust stability analysis using a slightly modified multiplier approach we show that the existence of an iqc is equivalent to the existence of a multiplier in most known cases it is hoped that this result provides some new insight into both approaches and makes them more useful in robust control applications

on the jx1 integral and the out of plane constraint in a 3d elastic cracked plate loaded in tension abstract in this study the behaviour of the j x 1 integral and its components j p integral and j a integral is numerically investigated for 3d linear elastic cracked plates of different thicknesses loaded in tension unlike the path independent j x 1 integral the components j p and j a are shown to be path dependent in a region that coincides with the out of plane constrained zone due to the thickness effect enabling the characterization of this zone with such integrals the distribution of the out of plane components 33 and e 33 in the vicinity of the crack front is also analyzed for different thicknesses and confronted to 2d solutions in addition a novel tensor concept of the stress intensity k ij is introduced showing a unique structure depending on k i irrespective of the specimen thickness it is confirmed that a pure plane strain condition close and far from the crack front is only asymptotically reached when the specimen thickness is very large when compared to the in plane dimensions for thin plates it is confirmed that the 2d plane stress condition is meaningless in the neighborhood of a 3d crack front under elastic behaviour

time domain and frequency domain conditions for strict positive realness the author states various time domain and frequency domain conditions pertaining to multivariate strict positive real systems and establishes the relationship between these conditions their relationship is clarified by means of a three tier diagram each tier represents a set of equivalent conditions successively stronger than the lower tier the main theorem in the present study can be considered as the positive realness lemma for strictly positive real systems

robust fir filter design with envelope constraints and channel uncertainty in this note a finite impulse response fir filter design problem is considered the signals to be filtered are assumed to be corrupted by the channel noise in addition the channel characteristics are assumed to contain uncertainties the linear matrix inequalities approach is adopted to provide two optimization procedures for designing h sub spl infin optimal filters and robust h sub spl infin filters subject to filter output envelope constraints a numerical example is presented to illustrate the proposed filter design methods

robust stabilization of uncertain linear systems quadratic stabilizability and h sup infinity control theory the problem of robustly stabilizing a linear uncertain system is considered with emphasis on the interplay between the time domain results on the quadratic stabilization of uncertain systems and the frequency domain results on h sup infinity optimization a complete solution to a certain quadratic stabilization problem in which uncertainty enters both the state and the input matrices of the system is given relations between these robust stabilization problems and h sup infinity control theory are explored it is also shown that in a number of cases if a robust stabilization problem can be solved via lyapunov methods then it can be also be solved via h sup infinity control theory based methods

domain integrals for axisymmetric interface crack problems new domain integrals for axisymmetric interface crack problems are derived special attention is given to the specification and subsequent treatment of auxiliary fields for the extraction of mixed mode stress intensity factors using interaction energy integrals the effect of crack front curvature is shown to play an important role in the derivation of the integrals numerical examples include an interface penny shaped crack and a longitudinal interface crack fiber pull out problem and yield very accurate and consistent results when compared with analytical solutions from the literature the method is particularly suited for the analysis of fiber pull out experiments and the accurate determination of fracture parameters such as energy release rate g mixed mode stressintensity factors ki and kii and phase angle

hamiltonian structure of real monge ampere equations the variational principle for the real homogeneous monge ampere equation in two dimensions is shown to contain three arbitrary functions of four variables there exist two different specializations of this variational principle where the lagrangian is degenerate and furthermore contains an arbitrary function of two variables the hamiltonian formulation of these degenerate lagrangian systems requires the use of dirac s theory of constraints as in the case of most completely integrable systems the constraints are second class and dirac brackets directly yield the hamiltonian operators thus the real homogeneous monge ampere equation in two dimensions admits two classes of infinitely many hamiltonian operators namely a family of local as well as another family non local hamiltonian operators and symplectic 2 forms which depend on arbitrary functions of two variables the simplest non local hamiltonian operator corresponds to the kac moody algebra of vector fields and functions on the unit circle hamiltonian operators that belong to either class are compatible with each other but between classes there is only one compatible pair in the case of real monge ampere equations with constant right hand side this compatible pair is the only pair of hamiltonian operators that survives then the complete integrability of all these real monge ampere equations follows by magri s theorem some of the remarkable properties we have obtained for the hamiltonian structure of the real homogeneous monge ampere equation in two dimensions turn out to be generic to the real homogeneous monge ampere equation and the geodesic flow for the complex homogeneous monge ampere equation in arbitrary number of dimensions hence among all integrable nonlinear evolution equations in one space and one time dimension the real homogeneous monge ampere equation is distinguished as one that retains its character as an integrable system in multiple dimensions

passivity and passification of memristor based recurrent neural networks with time varying delays this paper presents new theoretical results on the passivity and passification of a class of memristor based recurrent neural networks mrnns with time varying delays the casual assumptions on the boundedness and lipschitz continuity of neuronal activation functions are relaxed by constructing appropriate lyapunov krasovskii functionals and using the characteristic function technique passivity conditions are cast in the form of linear matrix inequalities lmis which can be checked numerically using an lmi toolbox based on these conditions two procedures for designing passification controllers are proposed which guarantee that mrnns with time varying delays are passive finally two illustrative examples are presented to show the characteristics of the main results in detail

robust reduced order unbiased filtering for uncertain systems this paper presents a simple solution to the robust unbiased functional reduced order filtering problem in the case of uncertain systems described by integral quadratic constraint iqc the existence condition of the unbiased filter is expressed through a rank relation then the filter is designed via linear matrix inequalities coupled with an equality constraint the results obtained in this paper are applicable to unstable systems the approach is illustrated by a numerical example

calculation of fracture mechanics parameters for an arbitrary three dimensional crack by the equivalent domain integral method summary in this paper an equivalent domain integral edi method and the attendant numerical algorithms arc presented for the computation of a near crack tip field parameter the vector je integral and its variation along the front of an arbitrary three dimensional crack in a structural component account is taken of possible non elastic strains present in the structure in this case the near tip je values may be significantly different from the far field values jf especially under non proportional loading

convergence of domain integrals for stress intensity factor extraction in 2 d curved cracks problems with the extended finite element method summary the aim of this study is the analysis of the convergence rates achieved with domain energy integrals for the computation of the stress intensity factors sif when solving 2 d curved crack problems with the extended fem xfem domain integrals specially the j integral and the interaction integral are widely used for sif extraction and provide high accurate estimations with fems the crack description in xfem is usually realized using level sets this allows to define a local basis associated with the crack geometry in this work the effect of the level set local basis definition on the domain integral has been studied the usual definition of the interaction integral involves hypotheses that are not fulfilled in generic curved crack problems and we introduce some modifications to improve the behavior in curved crack analyses despite the good accuracy of domain integrals convergence rates are not always optimal and convergence to the exact solution cannot be assured for curved cracks the lack of convergence is associated with the effect of the curvature on the definition of the auxiliary extraction fields with our modified integral proposal the optimal convergence rate is achieved by controlling the q function and the size of the extraction domain copyright 2013 john wiley sons ltd