yang yang anomalies and coexistence diameters simulation of asymmetric fluids a general method for estimating the yang yang ratio mathcal r ensuremath mu of a model fluid via monte carlo simulations is presented on the basis of data for a hard core square well hcsw fluid and the restricted primitive model rpm electrolyte the isothermal minima of q l ensuremath equiv m 2 l 2 m 4 l are evaluated at t c in an l ifmmode times else texttimes fi l ifmmode times else texttimes fi l box where m ensuremath rho ensuremath ensuremath rho l is the density fluctuation the complete finite size scaling theory for the q mathrm min ifmmode pm else textpm fi t c l incorporates pressure mixing in the scaling fields thereby allowing for a yang yang anomaly it yields a dominant term in the asymmetry q mathrm min ensuremath q mathrm min ensuremath varying as l ensuremath ensuremath beta ensuremath nu with an amplitude proportional to the crucial pressure mixing coefficient j 2 the reliably known critical order parameter distribution for d 3 ising systems then enables one to estimate j 2 thereby yielding mathcal r ensuremath mu from the q minima together with information on the nonuniversal amplitudes for the order parameter and the susceptibility the detailed analysis needed to estimate j 2 for an hcsw fluid and the rpm is presented furthermore the q minima below t c can also provide the coexistence curve diameters ensuremath rho mathrm diam t ensuremath equiv frac 1 2 ensuremath rho ensuremath rho ensuremath very close to t c for both models here ensuremath rho ifmmode pm else textpm fi t are the densities of the coexisting liquid and gas phases the recently developed recursive scaling algorithm for ensuremath delta ensuremath rho ensuremath infty t ensuremath equiv ensuremath rho ensuremath ensuremath rho ensuremath is adapted to investigate the corresponding universal scaling functions the two extremal forms of these scaling functions are computed with the aid of the exactly soluble decorated lattice gas model the critical densities for the rpm and hcsw fluid found via this route are consistent with previous estimates obtained from the data above t c the magnitudes of the leading ensuremath mid t ensuremath t c ensuremath mid 2 ensuremath beta and ensuremath mid t ensuremath t c ensuremath mid 1 ensuremath ensuremath alpha corrections to ensuremath rho mathrm diam t are estimated

using relative entropy to find optimal approximations an application to simple fluids abstract we develop a maximum relative entropy formalism to generate optimal approximations to probability distributions the central results consist of a justifying the use of relative entropy as the uniquely natural criterion to select a preferred approximation from within a family of trial parameterized distributions and b to obtain the optimal approximation by marginalizing over parameters using the method of maximum entropy and information geometry as an illustration we apply our method to simple fluids the exact canonical distribution is approximated by that of a fluid of hard spheres the proposed method first determines the preferred value of the hard sphere diameter and then obtains an optimal hard sphere approximation by a suitably weighed average over different hard sphere diameters this leads to a considerable improvement in accounting for the soft core nature of the interatomic potential as a numerical demonstration the radial distribution function and the equation of state for a lennard jones fluid argon are compared with results from molecular dynamics simulations

stochastic stability and robust control for sampled data systems with markovian jump parameters in this paper the problems of stochastic stability and robust control for a class of uncertain sampled data systems are studied the systems consist of random jumping parameters described by finite state semi markov process sufficient conditions for stochastic stability or exponential mean square stability of the systems are presented the conditions for the existence of a sampled data feedback control and a multirate sampled data optimal control for the continuous time uncertain markovian jump systems are also obtained the design procedure for robust multirate sampled data control is formulated as linear matrix inequalities lmis which can be solved efficiently by available software toolboxes finally a numerical example is given to demonstrate the feasibility and effectiveness of the proposed techniques

stability analysis of impulsive stochastic nonlinear systems this paper studies stochastic input to state stability and stochastic global stability for impulsive stochastic nonlinear systems using fixed dwell time condition and lyapunov based approach sufficient conditions are established for the stability properties two cases are studied 1 the case that the continuous dynamics is stable and 2 the case that the impulsive effects are stable furthermore the relations among different dwell time conditions are studied finally two examples are used to illustrate the developed theory

application of renormalization group corrected coupling parameter expansion method to square well fluids abstract in this paper we have applied the seventh order version of coupling parameter expansion cpe method combined with global renormalization group theory grgt to square well fluids of various ranges and have performed the following studies firstly the convergence of the grgt iteration scheme has been studied it is observed that the point wise convergence is non uniform and slow in the coexistence region away from the critical point however the point wise convergence improved as the critical temperature is approached secondly we have obtained the liquid vapor phase diagrams lvpds for the square well fluids the lvpds obtained using grgt corrected seventh order cpe are significantly accurate over those obtained from grgt corrected 1 order thermodynamic perturbation theory tpt also excessive flatness of lvpds close to the critical region as observed in grgt corrected 1 order tpt has not been seen in the lvpds of present method thirdly the critical exponents have been obtained using present method the exponents are seen to be of ising universality class and follow the rushbrooke and griffiths equalities qualitatively finally a study of yang yang anomaly has been done using our method it has been observed that the method predicts the existence of the anomaly but the predictions of the strength of anomaly differed from those of simulations the reasons for the differences are analyzed

on robustness of impulsive stabilization abstract the paper studies global asymptotic stability property of the trivial solution to nonlinear impulsive differential equations robustness of the global asymptotic stability with respect to the perturbations of the moments of jumps is investigated less conservative estimates on the admissible magnitude of perturbations preserving stability compared to the existing ones in the literature are proposed a relation between stability properties of the perturbed and unperturbed systems is studied finally utilizing wintner conti theorem we present two new lyapunov like theorems ensuring the global asymptotic stability of the impulsive system with unstable continuous dynamics that is being stabilized by impulsive jumps and discuss their relation to the previously known results

input to state stability for impulsive stochastic nonlinear systems with delayed impulses in this paper the problems of the stochastic input to state stability siss properties are investigated for impulsive stochastic nonlinear systems with delayed impulses by employing lyapunov method together with average impulsive interval approach the sufficient conditions are established to ensure properties for impulsive stochastic systems with all stable subsystems moreover the iss properties are also derived for the stochastic systems when the system is with both stable and unstable subsystems then we also study impulsive systems with multiple jumps i e there exist different impulses in a system by now there has been no papers to consider multiple jumps for stochastic cases finally two examples are provided to illustrate the effectiveness of our results

stability analysis for stochastic hybrid systems this survey addresses stability analysis for stochastic hybrid systems shs which are dynamical systems that combine continuous change and instantaneous change and that also include random effects we re emphasize the common features found in most of the models that have appeared in the literature which include stochastic switched systems markov jump systems impulsive stochastic systems switching diffusions stochastic impulsive systems driven by renewal processes diffusions driven by levy processes piecewise deterministic markov processes general stochastic hybrid systems and stochastic hybrid inclusions then we review many of the stability concepts that have been studied including lyapunov stability lagrange stability asymptotic stability and recurrence next we detail lyapunov based sufficient conditions for these properties and additional relaxations of lyapunov conditions many other aspects of stability theory for shs like converse lyapunov theorems and robustness theory are not fully developed hence we also formulate some open problems to serve as a partial roadmap for the development of the underdeveloped pieces

stability of networked control systems with asynchronous renewal links an impulsive systems approach we consider networked control systems in which sensors actuators and controller transmit through asynchronous communication links each introducing independent and identically distributed intervals between transmissions we model these scenarios through impulsive systems with several reset maps triggered by independent renewal processes i e the intervals between jumps associated with a given reset map are identically distributed and independent of the other jump intervals for linear dynamic and reset maps we establish that mean exponential stability is equivalent to the spectral radius of an integral operator being less than one we also prove that the origin of a non linear impulsive system is locally stable with probability one if its local linearization about the zero equilibrium is mean exponentially stable which justifies the importance of studying the linear case the applicability of the results is illustrated through an example using a linearized model of a batch reactor

input to state stability of nonlinear impulsive systems we prove that impulsive systems which possess an input to state stable iss lyapunov function are iss for time sequences satisfying the fixed dwell time condition if an iss lyapunov function is the exponential one we provide a stronger result which guarantees uniform iss of the whole system over sequences satisfying the generalized average dwell time condition then we prove two small gain theorems that provide a construction of an iss lyapunov function for an interconnection of impulsive systems if the iss lyapunov functions for subsystems are known the construction of local iss lyapunov functions via the linearization method is provided relations between small gain and dwell time conditions as well as between different types of dwell time conditions are also investigated although our results are novel already in the context of finite dimensional systems we prove them for systems based on differential equations in banach spaces that makes obtained results considerably more general

fifth order thermodynamic perturbation theory of uniform and nonuniform fluids a recently proposed numerical third order thermodynamic perturbation theory tpt is extended to its fifth order counterpart extensive performance evaluation based on several model potentials indicates that the fifth order version is generally superior to both the third order version and a well known second order macroscopic compressibility approximation tpt and is at least comparable to an accurate self consistent ornstein zernike integral equation approximation scoza with regard to predictions of varying bulk thermodynamic properties a bulk second order direct correlation function dcf free of numerical solution of a bulk oz integral equation is proposed which in combination with the framework of classical density functional theory dft and a thermodynamic consistency condition extends the uniform fifth order tpt to nonuniform case grand canonical ensemble monte carlo simulation is carried out to produce density profile of a core softened fluid confined in a hard spherical cavity the resultant density profile is employed to evaluate the performance of the present nonuniform fifth order tpt and a recently proposed third second order perturbation dft it is found that the present nonuniform fifth order tpt is generally more accurate than the third second order perturbation dft additional advantages of the present nonuniform fifth order tpt over the third second order perturbation dft is discussed

brief paper reachability and observability of linear impulsive systems linear impulsive systems constitute a class of hybrid systems in which the state propagates according to linear continuous time dynamics except for a countable set of times at which the state can change instantaneously while in general these impulsive effects can be time driven and or event driven here we focus our attention on the time driven case for this class of systems we address the fundamental concepts of reachability and observability in particular we present a geometric characterization of the reachable and unobservable sets in terms of invariant subspaces and provide algorithms for their construction

the cost of the control in the case of a minimal time of control the example of the one dimensional heat equation in this article we consider the controllability of the one dimensional heat equation with an internal control depending only on the time variable and an imposed profile depending on the space variable it is well known that in this context there might exist a minimal time of null controllability t0 depending on the behavior of the fourier coefficients of the profile we prove two different results the first one which is surprising is that the cost of the controllability in time t t0 close to t0 may explode in an arbitrary way on the other hand we prove as a second result that for a large class of profiles the cost of controllability at time t t0 is bounded from above by exp c t0 t t0 for some constant c t0 0 depending on t0 the main method used here is the moment method and some tools coming from complex analysis

brief paper input to state stability and integral input to state stability of nonlinear impulsive systems with delays this paper is concerned with analyzing input to state stability iss and integral iss iiss for nonlinear impulsive systems with delays razumikhin type theorems are established which guarantee iss iiss for delayed impulsive systems with external input affecting both the continuous dynamics and the discrete dynamics it is shown that when the delayed continuous dynamics are iss iiss but the discrete dynamics governing the impulses are not the iss iiss property of the impulsive system can be retained if the length of the impulsive interval is large enough conversely when the delayed continuous dynamics are not iss iiss but the discrete dynamics governing the impulses are the impulsive system can achieve iss iiss if the sum of the length of the impulsive interval and the time delay is small enough in particular when one of the delayed continuous dynamics and the discrete dynamics are iss iiss and the others are stable for the zero input the impulsive system can keep iss iiss no matter how often the impulses occur our proposed results are evaluated using two illustrative examples to show their effectiveness

vector lyapunov function based input to state stability of stochastic impulsive switched time delay systems in this paper the input to state stability is studied for stochastic impulsive switched time delay systems using the vector lyapunov function average dwell time and the properties of m matrix different types of sufficient conditions are established both the case that the continuous dynamics is stable and the case that the discrete dynamics is stable are addressed and the stability conditions are obtained in the obtained stability conditions different components of the vector lyapunov function are allowed to be coupled the information in consecutive impulsive switching intervals is also allowed to be coupled therefore the magnification on the corresponding coupling items is avoided and the obtained results are more general and less conservative than the existing results furthermore we investigate the relationships among the vector lyapunov function approach the approach based on the comparison principle and the scalar lyapunov function approach according to the vector lyapunov function the comparison system is constructed and the scalar lyapunov function based stability conditions are established finally the applicability of our results is illustrated through two examples from neural systems and the synchronization problem of chaos based secure communication systems

input to state stability of impulsive and switching hybrid systems with time delay this paper investigates input to state stability iss and integral input to state stability iiss of impulsive and switching hybrid systems with time delay using the method of multiple lyapunov krasovskii functionals it is shown that even if all the subsystems governing the continuous dynamics in the absence of impulses are not iss iiss impulses can successfully stabilize the system in the iss iiss sense provided that there are no overly long intervals between impulses i e the impulsive and switching signal satisfies a dwell time upper bound condition moreover these impulsive iss iiss stabilization results can be applied to systems with arbitrarily large time delays conversely in the case when all the subsystems governing the continuous dynamics are iss iiss in the absence of impulses the iss iiss properties can be retained if the impulses and switching do not occur too frequently i e the impulsive and switching signal satisfies a dwell time lower bound condition several illustrative examples are presented with their numerical simulations to demonstrate the main results

towards a unification of the hierarchical reference theory and the self consistent ornstein zernike approximation the hierarchical reference theory and the self consistent ornstein zernike approximation are two liquid state theories that both furnish a largely satisfactory description of the critical region as well as phase coexistence and the equation of state in general furthermore there are a number of similarities that suggest the possibility of a unification of both theories as a first step towards this goal we consider the problem of combining the lowest order gamma expansion result for the incorporation of a fourier component of the interaction with the requirement of consistency between internal and free energies leaving aside the compressibility relation for simplicity we restrict ourselves to a simplified lattice gas that is expected to display the same qualitative behavior as more elaborate models it turns out that the analytically tractable mean spherical approximation is a solution to this problem as are several of its generalizations analysis of the characteristic equations shows the potential for a practical scheme and yields necessary conditions that any closure to the ornstein zernike relation must fulfill for the consistency problem to be well posed and to have a unique differentiable solution these criteria are expected to remain valid for more general discrete and continuous systems even if consistency with the compressibility route is also enforced where possible explicit solutions will require numerical evaluations

brief paper a unified synchronization criterion for impulsive dynamical networks this paper focuses on the problem of globally exponential synchronization of impulsive dynamical networks two types of impulses are considered synchronizing impulses and desynchronizing impulses in previous literature all of the results are devoted to investigating these two kinds of impulses separately thus a natural question arises is there any unified synchronization criterion which is simultaneously effective for synchronizing impulses and desynchronizing impulses in this paper a unified synchronization criterion is derived for directed impulsive dynamical networks by proposing a concept named average impulsive interval the derived criterion is theoretically and numerically proved to be less conservative than existing results numerical examples including scale free and small world structures are given to show that our results are applicable to large scale networks

new phenomena for the null controllability of parabolic systems minimal time and geometrical dependence abstract we consider the null controllability problem for two coupled parabolic equations with a space depending coupling term we analyze both boundary and distributed null controllability in each case we exhibit a minimal time of control that is to say a time t 0 0 such that the corresponding system is null controllable at any time t t 0 and is not if t t 0 in the distributed case this minimal time depends on the relative position of the control interval and the support of the coupling term we also prove that for a fixed control interval and a time 0 0 there exist coupling terms such that the associated minimal time is 0

exponentially incremental dissipativity for nonlinear stochastic switched systems in this paper we investigate the exponentially incremental dissipativity for nonlinear stochastic switched systems by using the designed state dependent switching law and multiple lyapunov functio

sharp estimates of the one dimensional boundary control cost for parabolic systems and application to the n dimensional boundary null controllability in cylindrical domains in this paper we consider the boundary null controllability of a system of n parabolic equations on domains of the form omega 0 pi times omega 2 with omega 2 a smooth domain of mathbb r n 1 n 1 when the control is exerted on 0 times omega 2 with omega 2 subset omega 2 we obtain a necessary and sufficient condition that completely characterizes the null controllability this result is obtained through the lebeau robbiano strategy and requires an upper bound of the cost of the one dimensional boundary null control on 0 pi the latter is obtained using the moment method and it is shown to be bounded by ce c t when t goes to 0

explicit lower bounds for the cost of fast controls for some 1 d parabolic or dispersive equations and a new lower bound concerning the uniform controllability of the 1 d transport diffusion equation in this paper we prove explicit lower bounds for the cost of fast boundary controls for a class of linear equations of parabolic or dispersive type involving the spectral fractional laplace operator we notably deduce the following striking result in the case of the heat equation controlled on the boundary the miller s conjecture formulated in geometric bounds on the growth rate of null controllability cost for the heat equation in small time j differential equations 204 2004 pp 202 226 is not verified moreover we also give a new lower bound for the minimal time needed to ensure the uniform controllability of the one dimensional convection diffusion equation with negative speed controlled on the left boundary proving that the conjecture formulated in j m coron and s guerrero singular optimal control a linear 1 d parabolic hyperbolic example asymptot anal 44 2005 pp 237 257 concerning this problem is also not verified at least for negative speeds the proof is based on complex analysis and more precisely on a representation formula for entire functions of exponential type and is quite related to the moment method of fattorini and russell

input to state stability of impulsive stochastic delayed systems under linear assumptions in this paper the input to state stability iss integral iss iiss and stochastic iss siss are investigated for impulsive stochastic delayed systems by means of the lyapunov krasovskii function and the average impulsive interval approach the conditions for iss type properties are derived under linear assumptions respectively for destabilizing and stabilizing impulses it is shown that if the continuous stochastic delayed system is iss and the impulsive effects are destabilizing then the hybrid system is iss with respect to a lower bound of the average impulsive interval moreover it is unveiled that if the continuous stochastic delayed system is not iss the impulsive effects can successfully stabilize the system for a given upper bound of the average impulsive interval an improved comparison principle is developed for impulsive stochastic delayed systems which facilitates the derivations of our results for iss iiss siss an example of networked control systems is provided to illustrate the effectiveness of the proposed results

local controllability to stationary trajectories of a burgers equation with nonlocal viscosity abstract this article studies the local controllability to trajectories of a burgers equation with nonlocal viscosity by linearization we are led to an equation with a non local term whose controllability properties are analyzed by using fourier decomposition and biorthogonal techniques once the existence of controls is proved and the dependence of their norms with respect to the time is established for the linearized model a fixed point method allows us to deduce the result for the nonlinear initial problem

input to state stability for nonlinear systems with stochastic impulses abstract in this study the problem of input to state stability iss is systematically investigated for nonlinear systems with stochastic impulses first the iss problem is considered for systems where impulsive strengths are assumed to be stochastic and impulsive intervals are confined by the average impulsive interval then the iss problem is analyzed for nonlinear systems with both stochastic impulsive intensity and density several different cases are considered i e cases where the impulsive instants are satisfied by a renewal process poisson process semi markov chain and markov chain an example of coordination of multi agent systems is provided to illustrate the effectiveness of the proposed new stability criteria

stochastic input to state stability of switched stochastic nonlinear systems in this paper global asymptotic stability in probability gasip and stochastic input to state stability siss for nonswitched stochastic nonlinear nssnl systems and switched stochastic nonlinear ssnl systems are investigated for the study of gasip the definition which we considered is not the usual notion of asymptotic stability in probability stability in probability plus attractivity in probability it can depict the properties of the system quantitatively correspondingly based on this definition some sufficient conditions are provided for nssnl systems and ssnl systems furthermore the definition of siss is introduced and corresponding criteria are provided for nssnl systems and ssnl systems in the proof of the above results to overcome the difficulties coming with the appearance of switching and the stochastic property at the same time we generalize the past comparison principle and fully use the properties of the functions which we constructed in terms of the average dwell time of the switching laws a sufficient siss condition is obtained for ssnl systems finally some examples are provided to demonstrate the applicability of our results

lyapunov conditions for input to state stability of hybrid systems with memory this paper studies input to state stability for hybrid systems with memory which models hybrid dynamics affected by time delays using both lyapunov razumikhin functions and lyapunov krasovskii functionals lyapunov based sufficient conditions are established for input to state stability in addition further extensions and relaxations are proposed for special cases such as the stable flow jump cases and the cases that lyapunov functions do not decrease strictly during flow jumps finally two examples are used to illustrate the developed results

p moment stability of stochastic differential equations with impulsive jump and markovian switching this paper introduces some new concepts of p moment stability for stochastic differential equations with impulsive jump and markovian switching some stability criteria of p moment stability for stochastic differential equations with impulsive jump and markovian switching are obtained by using liapunov function method an example is also discussed to illustrate the efficiency of the obtained results

algebraic perturbation theory for dense liquids with discrete potentials a simple theory for the leading order correction g 1 r to the structure of a hard sphere liquid with discrete e g square well potential perturbations is proposed the theory makes use of a general approximation that effectively eliminates four particle correlations from g 1 r with good accuracy at high densities for the particular case of discrete perturbations the remaining three particle correlations can be modeled with a simple volume exclusion argument resulting in an algebraic and surprisingly accurate expression for g 1 r the structure of a discrete core softened model for liquids with anomalous thermodynamic properties is reproduced as an application

stability analysis of impulsive switched time delay systems with state dependent impulses this paper studies the stability for impulsive switched time delay systems with state dependent impulses since the impulses and the switches are not necessarily synchronous we start from a stability analysis of impulsive switched time delay systems with time dependent impulses sufficient conditions are derived to guarantee the stability property which extends the previous results for the synchronous switch and impulse case for the state dependent impulse case using the b equivalent method impulsive switched time delay systems with state dependent impulses are transformed into impulsive switched time delay systems with time dependent impulses the equivalence between the original system and the transformed system is established and stability conditions are obtained for impulsive switched time delay systems with state dependent impulses finally a numerical example is given to demonstrate the obtained results

lyapunov conditions for input to state stability of impulsive systems this paper introduces appropriate concepts of input to state stability iss and integral iss for impulsive systems i e dynamical systems that evolve according to ordinary differential equations most of the time but occasionally exhibit discontinuities or impulses we provide a set of lyapunov based sufficient conditions for establishing these iss properties when the continuous dynamics are iss but the discrete dynamics that govern the impulses are not the impulses should not occur too frequently which is formalized in terms of an average dwell time adt condition conversely when the impulse dynamics are iss but the continuous dynamics are not there must not be overly long intervals between impulses which is formalized in terms of a novel reverse adt condition we also investigate the cases where i both the continuous and discrete dynamics are iss and ii one of these is iss and the other only marginally stable for the zero input while sharing a common lyapunov function in the former case we obtain a stronger notion of iss for which a necessary and sufficient lyapunov characterization is available the use of the tools developed herein is illustrated through examples from a micro electro mechanical system mems oscillator and a problem of remote estimation over a communication network

stability analysis of deterministic and stochastic switched systems via a comparison principle and multiple lyapunov functions this paper presents a general framework for analyzing stability of nonlinear switched systems by combining the method of multiple lyapunov functions with a suitably adapted comparison principle in the context of stability in terms of two measures for deterministic switched systems this leads to a unification of representative existing results and an improvement upon the current scope of the method of multiple lyapunov functions for switched systems perturbed by white noise we develop new results which may be viewed as natural stochastic counterparts of the deterministic ones in particular we study stability of deterministic and stochastic switched systems under average dwell time switching

boundary controllability of a one dimensional phase field system with one control force abstract in this paper we present some controllability results for linear and nonlinear phase field systems of caginalp type considered in a bounded interval of r when the scalar control force acts on the temperature equation of the system by means of the dirichlet condition on one of the endpoints of the interval in order to prove the linear result we use the moment method providing an estimate of the cost of fast controls using this estimate and following the methodology developed in 19 we prove a local exact boundary controllability result to constant trajectories of the nonlinear phase field system to the authors knowledge this is the first nonlinear boundary controllability result in the framework of non scalar parabolic systems framework in which some hyperbolic behaviors could arise