symbolic model checking for real time systems abstract we describe finite state programs over real numbered time in a guarded command language with real valued clocks or equivalently as finite automata with real valued clocks model checking answers the question which states of a real time program satisfy a branching time specification given in an extension of ctl with clock variables we develop an algorithm that computes this set of states symbolically as a fixpoint of a functional on state predicates without constructing the state space for this purpose we introduce a calculus on computation trees over real numbered time unfortunately many standard program properties such as response for all nonzeno execution sequences during which time diverges cannot be characterized by fixpoints we show that the expressiveness of the timed calculus is incomparable to the expressiveness of timed ctl fortunately this result does not impair the symbolic verification of implementable real time programs those whose safety constraints are machine closed with respect to diverging time and whose fairness constraints are restricted to finite upper bounds on clock values all timed ctl properties of such programs are shown to be computable as finitely approximable fixpoints in a simple decidable theory

the jackknife and the bootstrap for general stationary observations we extend the jackknife and the bootstrap method of estimating standard errors to the case where the observations form a general stationary sequence we do not attempt a reduction to i i d values the jackknife calculates the sample variance of replicates of the statistic obtained by omitting each block of l consecutive data once in the case of the arithmetic mean this is shown to be equivalent to a weighted covariance estimate of the spectral density of the observations at zero under appropriate conditions consistency is obtained if l l n rightarrow infty and l n n rightarrow 0 general statistics are approximated by an arithmetic mean in regular cases this approximation determines the asymptotic behavior bootstrap replicates are constructed by selecting blocks of length l randomly with replacement among the blocks of observations the procedures are illustrated by using the sunspot numbers and some simulated data

a cartesian parametrization for the numerical analysis of material instability summary we examine four parametrizations of the unit sphere in the context of material stability analysis by means of the singularity of the acoustic tensor we then propose a cartesian parametrization for vectors that lie a cube of side length two and use these vectors in lieu of unit normals to test for the loss of the ellipticity condition this parametrization is then used to construct a tensor akin to the acoustic tensor it is shown that both of these tensors become singular at the same time and in the same planes in the presence of a material instability the performance of the cartesian parametrization is compared against the other parametrizations with the results of these comparisons showing that in general the cartesian parametrization is more robust and more numerically efficient than the others copyright 2016 john wiley sons ltd

numerical solutions of strain localization with nonlocal softening plasticity abstract softening plasticity when it is deprived of a characteristic length often leads to boundary value problems that are ill posed and produce unreliable numerical solutions as meshes are refined plastic strains localize into bands that become narrower and narrower and generate load displacement responses with excessive softening which may even degenerate into unrealistic snapbacks in the case of discrete systems the underlying reasons for this poor numerical performance can be examined using a spectral analysis of the tangential stiffness matrix derived from incremental equilibrium equations in one dimensional boundary valued problems the introduction of a weak softening element into a mesh of elasto plastic elements produces a dominant eigenvector that clearly exhibits a strain localization width directly related to the weak element size the dominant eigenvector that controls the incremental solution varies spuriously when the mesh is refined which results in mesh dependency over nonlocal softening plasticity introduces a length scale forces more elements to become plastic and preserves the width of the plastic zone when the mesh is refined when one dimensional meshes are refined spectral analysis shows that the dominant eigenvector does not vary erratically and that its deformation patterns are smooth and display a constant localization width this explains why the spatial distribution of plastic strains and the global load displacement responses converge to analytical solutions in one dimension the generalization to higher dimensions will be the object of future studies

a k nearest neighbor simulator for daily precipitation and other weather variables a multivariate nonparametric time series simulation method is provided to generate random sequences of daily weather variables that honor the statistical properties of the historical data of the same weather variables at the site a vector of weather variables solar radiation maximum temperature minimum temperature average dew point temperature average wind speed and precipitation on a day of interest is resampled from the historical data by conditioning on the vector of the same variables feature vector on the preceding day the resampling is done from the k nearest neighbors in state space of the feature vector using a weight function this approach is equivalent to a nonparametric approximation of a multivariate lag 1 markov process it does not require prior assumptions as to the form of the joint probability density function of the variables an application of the resampling scheme with 30 years of daily weather data at salt lake city utah is provided results are compared with those from the application of a multivariate autoregressive model similar to that of richardson 1981

effect of deviatoric nonassociativity on the failure prediction for elastic plastic materials abstract this paper presents a theoretical study of the effect of nonassociativity of the plastic flow rule on the critical plastic modulus for discontinuous bifurcation in an elastic plastic material nonassociativity in both the spherical and the deviatoric spaces are considered with an emphasis on the effect of nonassociativity in the deviatoric space a particular form of nonassociativity in the deviatoric space is introduced where the projections of the plastic flow direction and the normal to the yield surface are assumed to have the same length but the projection of plastic flow direction is allowed to lag that of the normal by an angle it is shown that even for the simple yield surface of von mises nonassociativity in the deviatoric space can lead to a bifurcation for a load parameter significantly lower than the value predicted with an associated flow rule

streamflow simulation a nonparametric approach in this paper kernel estimates of the joint and conditional probability density functions are used to generate synthetic streamflow sequences streamflow is assumed to be a markov process with time dependence characterized by a multivariate probability density function kernel methods are used to estimate this multivariate density function simulation proceeds by sequentially resampling from the conditional density function derived from the kernel estimate of the underlying multivariate probability density function this is a nonparametric method for the synthesis of streamflow that is data driven and avoids prior assumptions as to the form of dependence e g linear or nonlinear and the form of the probability density functions e g gaussian we show using synthetic examples with known underlying models that the nonparametric method presented is more flexible than the conventional models used in stochastic hydrology and is capable of reproducing both linear and nonlinear dependence the effectiveness of this model is illustrated through its application to simulation of monthly streamflow from the beaver river in utah

a nearest neighbor bootstrap for resampling hydrologic time series a nonparametric method for resampling scalar or vector valued time series is introduced multivariate nearest neighbor probability density estimation provides the basis for the resampling scheme developed the motivation for this work comes from a desire to preserve the dependence structure of the time series while bootstrapping resampling it with replacement the method is data driven and is preferred where the investigator is uncomfortable with prior assumptions as to the form e g linear or nonlinear of dependence and the form of the probability density function e g gaussian such prior assumptions are often made in an ad hoc manner for analyzing hydrologic data connections of the nearest neighbor bootstrap to markov processes as well as its utility in a general monte carlo setting are discussed applications to resampling monthly streamflow and some synthetic data are presented the method is shown to be effective with time series generated by linear and nonlinear autoregressive models the utility of the method for resampling monthly streamflow sequences with asymmetric and bimodal marginal probability densities is also demonstrated

when are timed automata weakly timed bisimilar to time petri nets in this paper we compare timed automata ta and time petri nets tpn with respect to weak timed bisimilarity it is already known that the class of bounded tpns is strictly included in the class of ta it is thus natural to try and identify the subclass ta w t b of ta equivalent to some tpn for the weak timed bisimulation relation we give a characterization of this subclass and we show that the membership problem and the reachability problem for ta w t b are pspace complete furthermore we show that for a ta in ta w t b with integer constants an equivalent tpn can be built with integer bounds but with a size exponential w r t the original model surprisingly using rational bounds yields a tpn whose size is linear

event clock automata a determinizable class of timed automata we introduce event recording automata an event recording automaton is a timed automaton that contains for every event a a clock that records the time of the last occurrence of a the class of event recording automata is on one hand expressive enough to model finite timed transition systems and on the other hand determinizable and closed under all boolean operations as a result the language inclusion problem is decidable for event recording automata we present a translation from timed transition systems to event recording automata which leads to an algorithm for checking if two timed transition systems have the same set of timed behaviors we also consider event predicting automata which contain clocks that predict the time of the next occurrence of an event the class of event clock automata which contain both event recording and event predicting clocks is a suitable specification language for real time properties we provide an algorithm for checking if a timed automaton meets a specification that is given as an event clock automaton

spectral analysis of localization in nonlocal and over nonlocal materials with softening plasticity or damage the paper shows that spectral wave propagation analysis reveals in a simple and clear manner the effectiveness of various regularization techniques for softening materials i e materials for which the yield limits soften as a function of the total strain both plasticity and damage models are considered it is verified analytically in a simple way that the nonlocal integral type model with degrading yield limit depending on the total strain works correctly if and only one adopts an unconventional nonlocal formulation introduced in 1994 by vermeer and brinkgreve and in 1996 by planas and by stromberg and ristinmaa which is here called for the sake of brevity over nonlocal because it uses a linear combination of local and nonlocal variables in which a negative weight imposed on the local variable is com pensated by assigning to the nonlocal variable weight greater than 1 this is equivalent to a nonlocal variable with a smooth positive weight function of total weight greater than 1 normalized by superposing a negative delta function spike at the center the spectral approach readily confirms that the nonlocal integral type generalization of softening plasticity with an additive format gives correct localization properties only if an over nonlocal formulation is adopted by contrast the nonlocal integral type generalization of softening plasticity with a multiplicative format provides real istic localization behavior just like the nonlocal integral type damage model and thus does not necessitate an over non local formulation the localization behavior of explicit and implicit gradient type models is also analyzed a simple analysis shows that plasticity and damage models with gradient type localization limiter whether explicit or implicit have very different localization behaviors 2005 elsevier ltd all rights reserved

analytical and numerical tests for loss of material stability material instability occurs when ellipticity is lost for symmetric constitutive equations prior to loss of ellipticity it is possible that the second order work of hill or drucker becomes negative there are implications in the literature that numerical solutions cease to be meaningful when a material strain softens and the second order work is not positive the instant that the second order work is zero or negative simultaneously with the additional restriction that the strain increments satisfy compatibility is equivalent to the loss of the ellipticity criterion for symmetric constitutive relations the loss of ellipticity criterion is the appropriate one for identifying when numerical solutions cease to show convergence and may also be a suitable criterion for identifying the instant at which material failure is initiated an analytical development is provided for loss of ellipticity together with an explicit expression for the normal to the bifurcation plane numerical solutions are given for several sample problems for all cases the numerical solutions based on the finite element method conform to the theoretical expectations that unique numerical solutions exist prior to the point at which ellipticity is lost

bifurcations in elastic plastic materials abstract when strain softening elastic plastic materials are loaded into the plastic regime they often exhibit deformations that are localized into small regions at some point in the loading process this intense localized deformation limits the formability of materials and will often quickly lead to failure with continued loading localized deformation is often associated with satisfaction of the classical discontinuous bifurcation criterion here we propose that the loss of strong ellipticity criterion should be used in place of the classical discontinuous bifurcation criterion as a necessary condition for localization the application of the strong ellipticity criterion implies that a bifurcation mode associated with loss of positive definiteness of the symmetric part of the acoustic tensor must be identified rather than a mode associated with the first zero eigenvalue of the acoustic tensor itself the eigensystem for the symmetric part of the tangent modulus tensor is obtained for several different plasticity models this eigensystem provides information about deformation modes associated with both diffuse and discontinuous bifurcations material properties boundary conditions and body geometry are all shown to affect the diffuse and localized deformation modes that are generated numerous experimental observations of necking and localization in metal specimens subject to various boundary conditions are explained with the proposed approach

acceleration waves in elasto plasticity a spectral analysis of the acceleration wave problem in general elasto plastic materials is carried out whereby explicit expressions for the eigenvalues and eigenvectors are obtained in case of nonassociated plasticity all eigenvectors become nonorthogonal and one eigenvalue always remains unchanged and equal to the shear modulus for a very broad class of nonassociated plasticity models it is shown that the eigenvalues are always real implying that so called divergence instability can occur while flutter instability can never occur it is found that a certain value of the hardening modulus exists for which specific propagation directions will always imply that all wave speeds are identical and equal to the elastic distortion wave speed moreover in this situation the eigenvectors are arbitrary corresponding to a state of diffuse wave modes the criteria of von mises and rankine are used to illustrate some of the findings

non local yield limit degradation presented is a new type of a non local continuum model which avoids problems of convergence at mesh refinement and spurious mesh sensitivity in a softening continuum characterized by degradation of the yield limit the key idea which has recently been proposed in a general context and has already been applied to softening damage due to stiffness degradation is to apply the non local concept only to those parameters which cause the degradation while keeping the definition of the strains local compared to the previously advanced fully non local continuum formulation the new approach has the advantage that the stresses are subjected to the standard differential equations of equilibrium and standard boundary or interface conditions the new formulation exhibits no zero energy periodic modes imbrication of finite elements is unnecessary and finite elements with standard continuity requirements are sufficient two dimensional finite element solutions with up to 3248 degrees of freedom are presented to document convergence and efficacy the formulation is applied to tunnel excavation in a soil stabilized by cement grouting with the objective of preventing cave in burst of the tunnel sides due to compression softening

gradient dependent plasticity formulation and algorithmic aspects a plasticity theory is proposed in which the yield strength not only depends on an equivalent plastic strain measure hardening parameter but also on the laplacian thereof the consistency condition now results in a differential equation instead of an algebraic equation as in conventional plasticity to properly solve the set of non linear differential equations the plastic multiplier is discretized in addition to the usual discretization of the displacements for appropriate boundary conditions this formulation can also be derived from a variational principle accordingly the theory is complete

properties of discontinuous bifurcation solutions in elasto plasticity explicit expressions for the spectral properties of the bifurcation problem involving discontinuities for general elastic plastic materials are presented it then follows that the classical value of the critical hardening modulus derived by rice 1976 proc 14th iutam congr delft the netherlands pp 207 220 north holland amsterdam is in fact the only possible one furthermore from the spectral analysis it follows in a very straightforward fashion that bifurcation displaying elastic unloading on one side of the singular surface can never precede bifurcation with plastic loading on both sides of this surface explicit analytical results for the critical bifurcation directions and the corresponding hardening modulus are derived for non associated volumetric flow rules while the devialoric portion is associated the considered yield and potential functions may depend on all three stress invariants and may involve mixed isotropic and kinematic hardening the result obtained by rudnicki and rice 1975 j mech phys solids 23 371 394 for a drucker pruger material appear as a special case other criteria that are investigated arc those of coulomb and rankine less

a hybrid stochastic model for multiseason streamflow simulation a hybrid model is presented for stochastic simulation of multiseason streamflows this involves partial prewhitening of the streamflows using a parsimonious linear periodic parametric model followed by resampling the resulting residuals using moving block bootstrap to obtain innovations and subsequently postblackening these innovations to generate synthetic replicates this model is simple and is efficient in reproducing both linear and nonlinear dependence inherent in the observed streamflows the first part of this paper demonstrates the hybrid character of the model through stochastic simulations performed using monthly streamflows of weber river utah that exhibit a complex dependence structure in the latter part of the paper the hybrid model is shown to be efficient in simulating multiseason streamflows through an example of the san juan river new mexico this model ensures annual to monthly consistency without the need for any adjustment procedures furthermore the hybrid model is able to preserve both within year and cross year monthly serial correlations for multiple lags also it is seen to be consistent in predicting the reservoir storage validation statistic at low as well as high demand levels

fe formulation of a nonlocal plasticity theory a nonlocal continuum plasticity theory is presented the nonlocal field introduced here is defined as a certain weighted average of the corresponding local field taken over all the material points in the body hereby a quantity with the dimension of length occurs as a material parameter when this so called internal length is equal to zero the local classical plasticity theory is regained in the present model the yield function will depend on a nonlocal field the consistency condition and the integration algorithm result in integral equations for determination of the field of plastic multipliers the integral equations are classified as fredholm equations of the second kind and the existence of a solution will be commented upon after discretization a matrix equation is obtained and an algorithm for finding the solution is proposed for a generalized von mises material a plane boundary value problem is solved with a fe method since the nonlocal quantities are integrals c0 continuous elements are sufficient the solution strategy is split into a displacement estimate for equilibrium and the integration of constitutive equations in the numerical simulations shear band formation is analysed and the results display mesh insensitivity

the expressive power of time petri nets we investigate expressiveness questions for time petri nets tpns and some of their most useful extensions we first introduce generalised time petri nets gtpns as an abstract model that encompasses variants of tpns such as self modifications and read reset and inhibitor arcs we give a syntactical translation from bounded gtpns to timed automata ta that generates isomorphic transition systems we prove that the class of bounded gtpns is strictly less expressive than ta w r t weak timed bisimilarity we prove that bounded gtpns bounded tpns and ta are equally expressive w r t timed language acceptance finally we characterise a syntactical subclass of ta that is equally expressive to bounded gtpns a la merlin w r t weak timed bisimilarity these results provide a unified comparison of the expressiveness of many variants of timed models often used in practice it leads to new important results for tpns among them are 1 safe tpns and bounded tpns are equally expressive e transitions strictly increase the expressive power of tpns self modifying nets as well as read inhibitor and reset arcs do not add expressiveness to bounded tpns