measuring the strangeness of strange attractors we study the correlation exponent v introduced recently as a characteristic measure of strange attractors which allows one to distinguish between deterministic chaos and random noise the exponent v is closely related to the fractal dimension and the information dimension but its computation is considerably easier its usefulness in characterizing experimental data which stem from very high dimensional systems is stressed algorithms for extracting v from the time series of a single variable are proposed the relations between the various measures of strange attractors and between them and the lyapunov exponents are discussed it is shown that the conjecture of kaplan and yorke for the dimension gives an upper bound for v various examples of finite and infinite dimensional systems are treated both numerically and analytically

countable nondeterminism and random assignment four semantics for a small programming language involving unbounded but countable nondeterminism are provided these comprise an operational semantics two state transformation semantics based on the egli milner and smyth orders respectively and a weakest precondition semantics their equivalence is proved a hoare like proof system for total correctness is also introduced and its soundness and completeness in an appropriate sense are shown finally the recursion theoretic complexity of the notions introduced is studied admission of countable nondeterminism results in a lack of continuity of various semantic functions and this is shown to be necessary for any semantics satisfying appropriate conditions in proofs of total correctness one resorts to the use of countable ordinals and it is shown that all recursive ordinals are needed

strain and stress based continuum damage models ii computational aspects abstract in part i of this work we developed continuum isotropic and anisotropic elastoplastic damage models formulated either in strain space on the basis of the effective stress concept or in stress space and employing the dual notion of effective strain in part ii we consider in detail the variational formulation and subsequent numerical implementation of these models the former relies crucially on the notions of maximum plastic and maximum damage dissipation the latter makes systematic use of the operator splitting methodology to derive unconditionally stable algorithms for the numerical integration of the elastoplastic damage equations of evolution appropriate extensions to treat the proposed rate dependent viscous damage are also presented for stress based damage models our numerical treatment relies on a new three step operator split the algorithms developed lead to simple and efficient stress update procedures suitable for large scale finite element calculations application is made to a class of inviscid and rate dependent cap models with an isotropic strain based damage mechanism remarkably good agreement with existing experimental data that includes complicated stress paths is obtained numerical examples are also presented that demonstrate the good performance of the proposed algorithms

localization and regularization behavior of mixed finite elements for 2d structural problems with damaging material abstract a class of lagrangian mixed finite elements is presented for applications to 2d structural problems based on a damage constitutive model attention is focused on localization and regularization issues as compared with the correspondent behavior of lagrangian displacement based elements a non local regularization procedure of integral type is adopted a predictor corrector technique is used to solve the evolution problem of the damage variable the proposed elements show superior performances for typical structural applications

over nonlocal gradient enhanced plastic damage model for concrete abstract classical continuum models exhibit strong mesh dependency during softening one method to regularize the problem is to introduce a length scale parameter via the nonlocal formulation however standard nonlocal enhancement either by integral or gradient formulation may serve only as a partial localization limiter for many material models the over nonlocal formulation where the weight for the nonlocal value is greater than unity and the excesses compensated by assigning a negative weight to the local value is able to fully regularize certain material models when standard nonlocal enhancement fails to do so a plastic damage model for concrete is formulated with this over nonlocal enhancement via the gradient approach and the full regularizing capabilities demonstrated

efficient modeling of localized material failure by means of a variationally consistent embedded strong discontinuity approach this paper is concerned with a novel embedded strong discontinuity approach suitable for the analysis of material failure at finite strains focus is on localized plastic deformation particularly relevant for slip bands in contrast to already existing models the proposed implementation allows to consider several interacting discontinuities in each finite element based on a proper re formulation of the kinematics an efficient parameterization of the deformation gradient is derived it permits to compute the strains explicitly that improves the performance significantly however the most important novel contribution of the present paper is the advocated variational constitutive update within this framework every aspect is naturally driven by energy minimization i e all unknown variables are jointly computed by minimizing the stress power the proposed update relies strongly on an extended principle of maximum dissipation this framework provides enough flexibility for different failure types and for a broad class of non associative evolution equations by discretizing the aforementioned continuous variational principle an efficient numerical implementation is obtained it shows in addition to its physical and mathematical elegance several practical advantages for instance the physical minimization principle itself specifies automatically and naturally the set of active strong discontinuities copyright 2011 john wiley sons ltd

damage tensors and the crack density distribution abstract the paper presents an algorithm for the derivation of damage tensors emphasizing its relationship with the actual and approximate crack density distributions the proposed model is illustrated using scalar second and fourth order continuous tensor approximations of some typical two and three dimensional crack distributions it is also shown that the occurrence of regions with negative crack density anticrack regions is in many cases a common and as yet unexplored feature of the approximate solutions

an analysis of a new class of integration algorithms for elastoplastic constitutive relations an accuracy analysis of a new class of integration algorithms for finite deformation elastoplastic constitutive relations recently proposed by the authors is carried out in this paper for simplicity attention is confined to infinitesimal deformations the integration rules under consideration fall within the category of return mapping algorithms and follow in a straightforward manner from the theory of operator splitting applied to elastoplastic constitutive relations general rate independent and rate dependent behaviour with plastic hardening or softening associated or non associated flow rules and nonlinear elastic response can be efficiently treated within the present framework isoerror maps are presented which demonstrate the good accuracy properties of the algorithm even for strain increments much larger than the characteristic strains at yielding

gradient enhanced damage for quasi brittle materials summary conventional continuum damage descriptions of material degeneration suffer from loss of well posedness beyond a certain level of accumulated damage as a consequence numerical solutions are obtained which are unacceptable from a physical point of view the introduction of higher order deformation gradients in the constitutive model is demonstrated to be an adequate remedy to this deficiency of standard damage models a consistent numerical solution procedure of the governing partial differential equations is presented which is shown to be capable of properly simulating localization phenomena

damage and plasticity in microplane theory the paper deals with the microplane model in which the stress strain relations are defined independently on planes of all possible orientations in the microstructure and the microplane stresses or strains are then constrained kinematically or statically to the macroscopic stress or strain tensor the existing formulations of the microplane constitutive model for concrete are mainly based on the kinematic constraint they have been shown capable of reproducing satisfactorily most experimental results available for concrete specimens with the advantages of great conceptual simplicity convenient numerical explicitness intrinsic induced anisotropy and microcrack opening closure conditions etc however from the theoretical viewpoint little has been said about how these formulations relate to classical constitutive models of elasto plasticity or continuum damage mechanics in this paper a new apemu of microplane theory is achieved by systematically intro ducing damage and plasticity concepts into the microplane framework new insight is provided on the role played by the split of the normal components and on the role of the different possible types of micro macro constraint specific formulations are developed and discussed within the new theoretical framework which can be easily related to von mises plasticity and to the existing models based on the second and fourth order damage tensors 0 1997 elsevier science ltd

nonlinear dynamic research on eeg signals in hai experiment abstract according to the phase space reconstruction techniques from one dimensional time series and the quantitative criteria of chaotic system analyses and computations are conducted on electroencephalogram eeg signals of piglets resulted from hai hypoxic asphyxic injury experiments based on the comparative studies of the phase graph the power spectra the correlation dimension and the lyapunov exponent of eeg signals of piglets under normal and injury conditions the following conclusions are shown 1 the analyses of phase graph power spectra correlation dimension and lyapunov exponent of eeg signals manifest the whole dynamic characteristics of cerebrum and they may be used as new quantitative methods for early diagnosis of brain injuries 2 under normal physiological conditions eeg signals are chaotic while under pathologic conditions eeg signals approach regularity

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

a unified theory of elastic degradation and damage based on a loading surface a number of new models with stiffness degradation have been proposd in recent literature in the small strain regime however most of these works represent specific formulations each using its own terminology notation and assumptions and relatively little effort has been spent so far towards achieving a common theoretical framework similar for instance to the theory of elastoplasticity moreover most of the existing damage models are presented with intensive recourse to abstract thermodynamics concepts and they combine stiffness degradation with plasticity which though being ultimately necessary to represent the actual material behavior makes it much more difficult to isolate analyse and understand the properties of the formulation for elastic stiffness degradation as a contribution in this field this paper presents a unifying theoretical framework to describe a class of models for elastic stiffness degradation based on the concept of loading surface the derivation includes two consecutive steps first the constitutive framework for elastic degrading models with evolution laws which are expressed directly in terms of the secant stiffness or compliance tensor and second the elastic damage models in which the scant stiffness or compliance is assumed to depend on a reduced set of damage variables with clearer physical meaning and simpler evolution laws whenever possible terminology is borrowed from the classical formulation of elastoplasticity and thermodynamic concepts are introduced only as needed both stress based and strain based developments are compared throughout the paper and the concept of associativity is reanalysed and generalized within the new unified framework of elastic degradation the most significant scalar damage models found in the literature are reinterpreted in the context of this unified theory finally a general expression is obtained for the tangential stiffness operator of associated scalar models stress and strain based of the 1 d type that includes all the models considered as particular cases more general damage formulations scalar non 1 d vectorial tensorial are reviewed and discussed systematically in a sequel paper

a symmetric nonlocal damage theory abstract the paper presents a thermodynamically consistent formulation for nonlocal damage models nonlocal models have been recognized as a theoretically clean and computationally efficient approach to overcome the shortcomings arising in continuum media with softening the main features of the presented formulation are i relations derived by the free energy potential fully complying with nonlocal thermodynamic principles ii nonlocal integral operator which is self adjoint at every point of the solid including zones near to the solid s boundary iii capacity of regularizing the softening ill posed continuum problem restoring a meaningful nonlocal boundary value problem in the present approach the nonlocal integral operator is applied consistently to the damage variable and to its thermodynamic conjugate force i e nonlocality is restricted to internal variables only the present model when associative nonlocal damage flow rules are assumed allows the derivation of the continuum tangent moduli tensor and the consistent tangent stiffness matrix which are symmetric the formulation has been compared with other available nonlocal damage theories finally the theory has been implemented in a finite element program and the numerical results obtained for 1 d and 2 d problems show its capability to reproduce in every circumstance a physical meaningful solution and fully mesh independent results

numerical technique in plasticity including solution advancement control numerical techniques applied to the consistent formulation of plasticity which is based on convex analysis are investigated for each time step the stress is found as the projection in complementary energy of the elastic stress onto the set of plastically admissible stresses while the velocity field is the extremal of a non quadratic functional explicit formulas for von mises yield criterion with mixed hardening are developed and the nonlinear equations arising from finite element discretization are solved for comparison by a number of newton type iteration procedures with line search and are length control a few numerical examples with proportional and non proportional loading are analyzed

the infinite number of generalized dimensions of fractals and strange attractors abstract we show that fractals in general and strange attractors in particular are characterized by an infinite number of generalized dimensions dq q 0 to this aim we develop a rescaling transformation group which yields analytic expressions for all the quantities dq we prove that lim q 0 dq fractal dimension d limq 1dq information dimension and dq 2 correlation exponent v dq with other integer q s correspond to exponents associated with ternary quaternary and higher correlation functions we prove that generally dq dq for any q q for homogeneous fractals dq dq a particularly interesting dimension is dq for two examples feigenbaum attractor generalized baker s transformation we calculate the generalized dimensions and find that d is a non trivial number all the other generalized dimensions are bounded between the fractal dimension and d

multifractality of complex networks we demonstrate analytically and numerically the possibility that the fractal property of a scale free network cannot be characterized by a unique fractal dimension and the network takes a multifractal structure it is found that the mass exponents q for several deterministic stochastic and real world fractal scale free networks are nonlinear functions of q which implies that structural measures of these networks obey the multifractal scaling in addition we give a general expression of q for some class of fractal scale free networks by a mean field approximation the multifractal property of network structures is a consequence of large fluctuations of local node density in scale free networks

adaptive technique for discrete models of fracture abstract static discrete models are advantageously used for the simulation of fracture in quasibrittle heterogeneous materials in order to correctly capture strain localization during the fracture process it is often necessary to represent material heterogeneity in the model directly via its discrete geometry depending on the specimen size and the size of the heterogeneities these simulations are typically extremely computationally demanding the contribution aims to reduce this computational cost via the implementation of adaptivity in the construction of the discrete model geometry the simulation starts with coarse discretization which provides correct elastic behavior and is then adaptively refined during the simulation in regions that suffer high stresses that induce cracking and strain localization the technique is applied in deterministic and probabilistic simulations and demonstrated on several examples

elastic properties of isotropic discrete systems connections between geometric structure and poisson s ratio abstract the use of discrete material representation in numerical models is advantageous due to the straightforward way it takes into account material heterogeneity and randomness and the discrete and orientated nature of cracks unfortunately it also restricts the macroscopic poisson s ratio and therefore narrows its applicability the paper studies the poisson s ratio of a discrete model analytically it derives theoretical limits for cases where the geometry of the model is completely arbitrary but isotropic in the statistical sense it is shown that the widest limits are obtained for models where normal directions of contacts between discrete units are parallel with the vectors connecting these units any deviation from parallelism causes the poisson s ratio limits to shrink a comparison of the derived equations to the results of the actual numerical model is presented it shows relatively large deviations from the theory because the fundamental assumptions behind the theoretical derivations are largely violated in systems with complex geometry the real shrinking of the poisson s ratio limit is less severe compared to that which is theoretically derived

gradient plasticity theory with a variable length scale parameter the definition and magnitude of the intrinsic length scale are keys to the development of the gradient plasticity theory that incorporates size effects however a fixed value of the material length scale is not always realistic and different problems could require different values moreover a linear coupling between the local and nonlocal terms in the gradient plasticity theory is not always realistic and that different problems could require different couplings this work addresses the proper modifications required for the full utility of the current gradient plasticity theories in solving the size effect problem it is shown that the current gradient plasticity theories do not give sound interpretations of the size effects in micro bending and micro torsion tests if a definite and fixed length scale parameter is used a generalized gradient plasticity model with a non fixed length scale parameter is proposed based on dislocation mechanics this model assesses the sensitivity of predictions to the way in which the local and nonlocal parts are coupled or to the way in which the statically stored and geometrically necessary dislocations are coupled in addition a physically based relation for the length scale parameter as a function of the course of deformation and the material microstructural features is proposed the proposed model gives good predictions of the size effect in micro bending tests of thin films and micro torsion tests of thin wires

studies in anisotropic plasticity with reference to the hill criterion algorithms based upon the notion of return mapping have been developed for the hill yield function of anisotropic plasticity the relative accuracy of two algorithms is assessed by means of iso error maps the choice of the algorithm turns out to be much more critical for the orthotropic hill criterion than for the underlying isotropic von mises plasticity model a tangent operator that is consistent with the developed integration algorithm is formulated and its efficiency is assessed compared with the classical continuum tangent operator the model has been applied to three shell plate structures

multiscale computational analysis in mechanics using finite calculus an introduction abstract the paper introduces a general procedure for computational analysis of a wide class of multiscale problems in mechanics using a finite calculus fic formulation the fic approach is based in expressing the governing equations in mechanics accepting that the domain where the standard balance laws are established has a finite size this introduces naturally additional terms into the classical equations of infinitesimal theory in mechanics which are useful for the numerical solution of problems involving different scales in the physical parameters the discrete nodal values obtained with the fic formulation and the finite element method fem can be effectively used as the starting point for obtaining a more refined solution in zones where high gradients of the relevant variables occur using hierarchical or enriched fem typical multiscale problems in mechanics which can be solved with the fic method include convection diffusion reaction problems with high localized gradients incompressible problems in solid and fluid mechanics localization problems such as prediction of shear bands in solids and shock waves in compressible fluids turbulence etc the paper presents an introduction of the treatment of multiscale problems using the fic approach in conjunction with the fem examples of application of the fic fem formulation to the solution of simple multiscale convection diffusion problems are given

an anisotropic gradient damage model for quasi brittle materials an anisotropic continuum damage model based on the microplane concept is elaborated scalar damage laws are formulated on several individual microplanes representing the planes of potential failure these uniaxial constitutive laws can be cast into a fourthorder damage formulation such that anisotropy of the overall constitutive law is introduced in a natural fashion strain gradients are incorporated in the constitutive equations in order to account for microstructural interaction consequently the underlying boundary value problem remains well posed even in the softening regime the gradient continuum enhancement results in a set of additional partial diaerential equations which are satisfied in a weak form additional nodal degrees of freedom are introduced which leads to a modified element formulation the governing equations can be linearized consistently and solved within an incremental iterative newton raphson solution procedure the capability of the present model to properly simulate the localized failure of quasi brittle materials will be demonstrated by means of several examples 2000 elsevier science s a all rights reserved

a proof rule for fair termination of guarded commands we present a proof rule for fairly terminating guarded commands based on a well foundedness argument the rule is applied to several examples and proved to be sound and semantically complete w r t an operational semantics of computation trees the rule is related to another rule suggested by lehmann pnueli and stavi in proc internat colloq automata lang and programming 81 acre july 1981 by showing that the semantic completeness of the lps rule follows from the completeness or ours

a plastic nonlocal damage model abstract in the present paper a plastic nonlocal damage model is proposed for studying the mechanical response of structural elements made of cementitious materials a new isotropic damage model which is able to describe the behavior of a wide class of cementitious materials is presented a regularization technique based on the introduction of the damage laplacian in the damage limit function is adopted to overcome the analytical and computational problems induced by the softening constitutive law a drucker prager type of plastic limit function is proposed considering isotropic hardening a numerical procedure based on an implicit backward euler technique for the time integration of the plastic and damage evolution equations is presented to solve each nonlinear step a predictor corrector iterative method is developed within the splitting method in particular the damage evolution is determined solving a constrained minimization problem of a convex functional the proposed algorithm is implemented in a finite element code and it is used to study the structural behavior of elements made of masonry materials

a thermodynamically consistent approach to microplane theory part i free energy and consistent microplane stresses microplane models are based on the assumption that the constitutive laws of the material may be established between normal and shear components of stress and strain on planes of generic orientation so called microplanes rather than between tensor components or their invariants in the kinematically constrained version of the model it is assumed that the microplane strains are projections of the strain tensor and the stress tensor is obtained by integrating stresses on microplanes of all orientations at a point traditionally microplane variables were defined intuitively and the integral relation for stresses was derived by application of the principle of virtual work in this paper a new thermodynamic framework is proposed a free energy potential is defined at the microplane level such that its integral over all orientations gives the standard macroscopic free energy from this simple assumption it is possible to introduce consistent microplane stresses and their corresponding integral relation to the macroscopic stress tensor based on this it is shown that in spite of the excellent data fits achieved many existing formulations of microplane model were not guaranteed to be fully thermodynamically compliant a consequence is the lack of work conjugacy between some of the microplane stress and strain variables used and the danger of spurious energy dissipation generation under certain load cycles the possibilities open by the new theoretical framework are developed further in part ii companion paper

damage gradient of damage and principle of virtual power a theory of continuum damage mechanics is developed within the framework of the principle of virtual power because the damage in a solid results from microscopic movements we decided to include the power of these microscopic movements in the power of the internal forces the microscopic velocities are related to the damage rate the power of the internal forces we choose depends on the damage velocity and its gradient to take into account the interactions models issued from this theory are presented they are coherent from the mechanical and mathematical points of view the numerical computations show no mesh sensitivity they describe with good agreement the main experimental properties concrete is chosen as an example to illustrate the theory a model using two damage quantities is also presented it yields the correct description of the unilateral phenomenon observed in concrete finally an extension of the existing models is proposed to describe the fatigue damage behaviour

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

hoare s logic for nondeterministic regular programs a nonstandard approach abstract this paper studies hoare s logic for nondeterministic regular programs with unbounded nondeterminism from the point of view of nonstandard dynamic logic we define a so called continuous semantics which allows certain infinitely long computations and compare it with usual semantics proving among other things the equivalence of both over reasonable data types we also establish a completeness theorem for hoare s calculus relative to continuous semantics thereby generalizing a previous result of csirmaz the proof makes use of a normal form for regular programs which is perhaps interesting in its own right

a thermodynamically consistent microplane model for shape memory alloys in microplane theory it is assumed that a macroscopic stress tensor is projected to the microplane stresses it is also assumed that 1d constitutive laws are defined for associated stress and strain components on all microplanes passing through a material point the macroscopic strain tensor is obtained by strain integration on microplanes of all orientations at a point by using a homogenization process traditionally microplane formulation has been based on the volumetric deviatoric tangential split and macroscopic strain tensor was derived using the principle of complementary virtual work it has been shown that this formulation could violate the second law of thermodynamics in some loading conditions the present paper focuses on modeling of shape memory alloys using microplane formulation in a thermodynamically consistent framework to this end a free energy potential is defined at the microplane level integrating this potential over all orientations provides the macroscopic free energy based on this free energy a new formulation based on volumetric deviatoric split is proposed this formulation in a thermodynamic consistent framework captures the behavior of shape memory alloys using experimental results for various loading conditions the validity of the model has been verified

unified analysis of enriched finite elements for modeling cohesive cracks abstract aiming to provide a justified theoretical ground based on which different enriched finite elements can be systematically compared we developed in this work a unified framework for modeling cohesive cracks using the variational multiscale method the kinematics i e coarse and fine scale displacement and strain fields and statics i e coarse and fine scale equilibrium equations are thoroughly investigated in both continuum and discrete settings with respect to the fine scale kinematics and statics adopted in the embedded finite element method efem and the extended finite element method xfem we mainly discuss four groups of enriched finite elements with non uniform discontinuity modes i e the kinematically optimal symmetric efem and xfem as well as the kinematically and statically optimal non symmetric efem and xfem in all these methods the enrichment parameters can be regarded either as element wise local or continuous global variables the enriched finite elements with material element node enrichments are then exemplified in an increasing order of their respective capabilities in representing the fine scale kinematics and the interrelations between them are also discussed owing to this unified framework we are able to clarify some existing points of view related to efem and xfem it is found that if the same fine scale statics is used and the same local global property is assumed for the involved enrichment parameters xfem can be regarded as a kinematically enhanced efem since it accounts for a more general fine scale kinematics than that i e relative rigid body motions and self stretching considered in efem finally several simple but sufficiently representative numerical examples are presented to show the significance in appropriately reflecting the fine scale kinematics and statics in an enriched finite element for modeling cohesive cracks

a variational principle for gradient plasticity abstract we elaborate on a generalized plasticity model which belongs to the class of gradient models suggested earlier by aifantis and co workers the generalization of the conventional theory of plasticity has been accomplished by the inclusion of higher order spatial gradients of the equivalent plastic strain in the yield condition first it is shown how these gradients affect the critical condition for the onset of localization and allow for a wavelength selection analysis leading to estimates for the width and or spacing of shear bands due to the presence of higher order gradients additional boundary conditions for the equivalent plastic strain are required this question and also the associated problem of the formulation and solution of general boundary value problems were left open in the previous work we demonstrate here that upon assuming a certain type of additional boundary conditions the structural symmetries of the gradient dependent constitutive model are such that there exists a variational principle for the displacement rates and the rate of the equivalent plastic strain the variational principle can serve as a basis for the numerical solution of boundary value problems in the sense of the finite element method explicit expressions for the tangent stillness matrix and the generalized nodal point forces are given

process expressions and hoare s logic showing an irreconcilability of context free recursion with scott s induction rule abstract in this paper processes specifiable over a non uniform language are considered the language contains constants for a set of atomic actions and constructs for alternative and sequential composition furthermore it provides a mechanism for specifying processes recursively including nested recursion we consider processes as having a state atomic actions are to be specified in terms of observable behaviour relative to initial states and state transformations any process having some initial state can be associated with a transition system representing all possible courses of execution this leads to an operational semantics in the style of plotkin the partial correctness assertion p expresses that for any transition system associated with the process p and having some initial state satisfying its final states representing successful execution satisfy a logic in the style of hoare containing a proof system for deriving partial correctness assertions is presented this proof system is sound and relatively complete so any partial correctness assertion can be evaluated by investigating its derivability included is a short discussion about the extension of the process language with guarded recursion it appears that such an extension violates the completeness of the hoare logic this reveals a remarkable property of scott s induction rule in the context of non determinism only regular recursion allows a completeness result

a fractal growth model exploring the connection pattern of hubs in complex networks abstract fractal is ubiquitous in many real world networks previous researches showed that the strong disassortativity between the hub nodes on all length scales was the key principle that gave rise to the fractal architecture of networks although fractal property emerged in some models there were few researches about the fractal growth model and quantitative analyses about the strength of the disassortativity for fractal model in this paper we proposed a novel inverse renormalization method named box based preferential attachment bpa to build the fractal growth models in which the preferential attachment was performed at box level the proposed models provided a new framework that demonstrated small world fractal transition also we firstly demonstrated the statistical characteristic of connection patterns of the hubs in fractal networks the experimental results showed that given proper growing scale and added edges the proposed models could clearly show pure small world or pure fractal or both of them it also showed that the hub connection ratio showed normal distribution in many real world networks at last the comparisons of connection pattern between the proposed models and the biological and technical networks were performed the results gave useful reference for exploring the growth principle and for modeling the connection patterns for real world networks

new explicit microplane model for concrete theoretical aspects and numerical implementation abstract the microplane model is a powerful approach for the representation of the complex triaxial behavior of concrete and other similar materials however most efforts in previous formulations were devoted to the development of the model itself and to the experimental data fitting rather than to a comprehensive theoretical description or to attainment of a modular and computationally efficient implementation in a computer code in this paper these objectives are pursued the formulation of the model has been modified to rationalise the structure of the basic hypotheses simplify the equations and generalise the concepts whenever possible the result is a new formulation which while retaining the favorable properties achieved previously is also easier to understand and convenient for computer implementation and large scale calculations a computational scheme is presented with the unified structure of a general code serving the double purpose of lest specimen analysis and finite element analysis in practice this structure includes two different main programs which call the same set of constitutive subroutines a salient feature of the new version of the model is that the compulation of the stress corresponding to a prescribed strain increment of finite si e is fully explicit step by step numerical integration usually necessary for the practical use of constitutive models can be avoided consequently the complexity of the code and the cost of computations can be dramatically reduced some examples of applications used to verify the previous version of the model are also presented they demonstrate that this new formulation gives a much better numerical efficiency for code implementation while keeping the same desirable features and accuracy in experimental data fitting

an improved multifractal formalism and self similar measures abstract to characterize the geometry of a measure its generalized dimensions dq have been introduced recently the mathematically precise definition given by falconer fractal geometry 1990 turns out to be unsatisfactory for reasons of convergence as well as of undesired sensitivity to the particular choice of coordinates in the negative q range a new definition is introduced which is also based on box counting but which carries relevant information about for negative q also in particular the legendre connection between generalized dimensions and the multifractal spectrum is established using large deviations and rigorous proofs are provided for the implicit formula giving the generalized dimensions of selfsimilar measures which was until now known only for positive q

a review of fractality and self similarity in complex networks we review recent findings of self similarity in complex networks using the box covering technique it was shown that many networks present a fractal behavior which is seemingly in contrast to their small world property moreover even non fractal networks have been shown to present a self similar picture under renormalization of the length scale these results have an important effect in our understanding of the evolution and behavior of such systems a large number of network properties can now be described through a set of simple scaling exponents in analogy with traditional fractal theory

a gibbs energy barrier based computational micro sphere model for the simulation of martensitic phase transformations summary we introduce a material model for the simulation of polycrystalline materials undergoing solid to solid phase transformations as a basis we present a scalar valued phase transformation model where a helmholtz free energy function depending on volumetric and deviatoric strain measures is assigned to each phase the analysis of the related overall gibbs energy density allows for the calculation of energy barriers with these quantities at hand we use a statistical physics based approach to determine the resulting evolution of volume fractions though the model facilitates to take into account an arbitrary number of solid phases of the underlying material we restrict this work to the simulation of phase transformations between an austenitic parent phase and a martensitic tension and compression phase the scalar model is embedded into a computational micro sphere formulation in view of the simulation of three dimensional boundary value problems the final modelling approach necessary for macroscopic simulations is accomplished by a finite element formulation where the local material behaviour at each integration point is governed by the response of the micro sphere model copyright 2014 john wiley sons ltd

aggregation by attractive particle cluster interaction a quasideterministic irreversible growth model is studied where aggregates are generated by attractive cluster particle forces proportional ro r alpha it is shown that fractal dimensions and growth site probability measures of the resulting fractal structures strongly depend on the parameter alpha comparison with experimental results indicates that this model represents a further step towards realistic simulations of growth processes

ten years of hoare s logic a survey part ii nondeterminism a survey of various results concerning the use of hoare s logic in proving correctness of nondeterministic programs is presented various proof systems together with the example proofs are given and the corresponding soundness and completeness proofs of the systems are discussed programs allowing bounded and countable nondeterminism are studied proof systems deal with partial and total correctness freedom of failure and the issue of fairness the paper is a continuation of part i by apt 1981 where various results concerning hoare s approach to proving correctness of sequential programs are presented

a regularized force based beam element with a damage plastic section constitutive law a new beam finite element is presented with a generalized section constitutive law based on damage mechanics and plasticity to analyse the cyclic structural response of plane frames both displacement based and force based fb approaches are used and compared to demonstrate the significant advantages of the fb formulation in the presence of material non linearity in order to overcome the analytical problems and the pathological mesh dependency of the numerical response in the presence of strain softening post peak behaviour a classical non local regularization procedure is adopted first based on the integral definition of the associated variable governing the damaging evolution process subsequently for the fb element a new simple regularization technique is proposed based on a selected integration procedure along the element length which predefines the location of the gauss points in the beam region where the localization phenomena take place as for the other computational aspects an iterative element state determination is adopted for the fb formulation and a local predictor corrector algorithm is used to solve the incremental evolution problems of the damage and plastic internal variables finally some examples are shown on simple beams and frames subjected to monotonically increasing and cyclic loading conditions copyright 2006 john wiley sons ltd