dispersion analysis and element free galerkin solutions of second and fourth order gradient enhanced damage models gradient dependent damage formulations incorporate higher order derivatives of state variables in the constitutive equations different formulations have been derived for this gradient enhancement comparison of which is difficult in a finite element context due to higher order continuity requirements for certain formulations on the other hand the higher order continuity requirements are met naturally by element free galerkin efg shape functions thus the efg method provides a suitable tool for the assessment of gradient enhanced continuum models dispersion analyses have been carried out to compare different gradient enhanced models with the non local damage model the formulation of the additional boundary conditions is addressed numerical examples show the objectivity with respect to the discretization and the differences between various gradient formulations with second and fourth order derivatives it is shown that with the same underlying internal length scale very different results can be obtained copyright 2000 john wiley sons ltd

dimer statistics of honeycomb lattices on klein bottle mobius strip and cylinder abstract dimer statistics is a central problem in statistical physics in this paper the enumerations of close packed dimers of honeycomb lattices on klein bottle mobius strip and cylinder are considered by establishing a pfaffian orientation or a crossing orientation and then computing the determinants of the skew symmetric matrices of the resulting orientation graphs we obtain explicit expressions of the number of close packed dimers of the klein bottle polyhex the mobius polyhex and the cylindrical polyhex

rotation free isogeometric thin shell analysis using pht splines this paper presents a novel approach for isogeometric analysis of thin shells using polynomial splines over hierarchical t meshes pht splines the method exploits the flexibility of t meshes for local refinement the main advantage of the pht splines in the context of thin shell theory is that it achieves c1 continuity so the kirchhoff love theory can be used in pristine form no rotational degrees of freedom are needed numerical results show the excellent performance of the present method

variable elimination in chemical reaction networks with mass action kinetics we consider chemical reaction networks taken with mass action kinetics the steady states of such a system are solutions to a system of polynomial equations even for small systems the task of finding the solutions is daunting we develop an algebraic framework and procedure for linear elimination of variables the procedure reduces the variables in the system to a set of core variables by eliminating variables corresponding to a set of noninteracting species the steady states are parameterized algebraically by the core variables and a graphical condition is given that ensures that a steady state with positive core variables necessarily takes positive values for all variables further we characterize graphically the sets of eliminated variables that are constrained by a conservation law and show that this conservation law takes a specific form

the number and degree distribution of spanning trees in the tower of hanoi graph the number of spanning trees of a graph is an important invariant related to topological and dynamic properties of the graph such as its reliability communication aspects synchronization and so on however the practical enumeration of spanning trees and the study of their properties remain a challenge particularly for large networks in this paper we study the number and degree distribution of the spanning trees in the hanoi graph we first establish recursion relations between the number of spanning trees and other spanning subgraphs of the hanoi graph from which we find an exact analytical expression for the number of spanning trees of the n disc hanoi graph this result allows the calculation of the spanning tree entropy which is then compared with those for other graphs with the same average degree then we introduce a vertex labeling which allows to find for each vertex of the graph its degree distribution among all possible spanning trees

a finite element method for the computational modelling of cohesive cracks the present contribution is concerned with the computational modelling of cohesive cracks in quasi brittle materials whereby the discontinuity is not limited to interelement boundaries but is allowed to propagate freely through the elements in the elements which are intersected by the discontinuity additional displacement degrees of freedom are introduced at the existing nodes therefore two independent copies of the standard basis functions are used one set is put to zero on one side of the discontinuity while it takes its usual values on the opposite side and vice versa for the other set to model inelastic material behaviour a discrete damage type constitutive model is applied formulated in terms of displacements and tractions at the surface some details on the numerical implementation are given concerning the failure criterion the determination of the direction of the discontinuity and the integration scheme finally numerical examples show the performance of the method

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

strain based transient gradient damage model for failure analyses a transient gradient enhanced damage model has been developed for the numerical modelling of the damage and fracture process within a continuum damage mechanics framework some deficiencies of existing gradient enhanced damage formulations for the simulation of macroscopic crack propagation are pointed out the transient gradient approach assumes a direct coupling between the material length parameter and the local strain state of the material which leads to a transient behaviour of the nonlocal effect details of the method are presented and fully elaborated in an incremental iterative solution scheme mesh objectivity and physical relevance of the method are analysed by one dimensional and two dimensional numerical examples

tutte polynomial of scale free networks the tutte polynomial of a graph or equivalently the q state potts model partition function is a two variable polynomial graph invariant of considerable importance in both statistical physics and combinatorics the computation of this invariant for a graph is np hard in general in this paper we focus on two iteratively growing scale free networks which are ubiquitous in real life systems based on their self similar structures we mainly obtain recursive formulas for the tutte polynomials of two scale free networks lattices one is fractal and large world while the other is non fractal but possess the small world property furthermore we give some exact analytical expressions of the tutte polynomial for several special points at x y plane such as the number of spanning trees the number of acyclic orientations etc

a quadratic identity for the number of perfect matchings of plane graphs we present a quadratic identity on the number of perfect matchings of plane graphs by the method of graphical condensation which generalizes the results found by propp j propp generalized domino shuffling theoret comput sci 303 2003 267 301 kuo e h kuo applications of graphical condensation for enumerating matchings and tilings theoret comput sci 319 2004 29 57 and yan yeh and zhang w g yan y n yeh f j zhang graphical condensation of plane graphs a combinatorial approach theoret comput sci 349 2005 452 461

a bridging domain method for coupling continua with molecular dynamics abstract a bridging domain method for coupling continuum models with molecular models is described in this method the continuum and molecular domains are overlapped in a bridging subdomain where the hamiltonian is taken to be a linear combination of the continuum and molecular hamiltonians we enforce the compatibility in the bridging domain by lagrange multipliers or by the augmented lagrangian method an explicit algorithm for dynamic solutions is developed results show that this multiscale method can avoid spurious wave reflections at the molecular continuum interface without any additional filtering procedures even for problems with significant nonlinearities the method is also shown to naturally handle the coupling of the continuum energy equation with the molecular subdomain a multiple time step algorithm is also developed within this framework

graphical condensation of plane graphs a combinatorial approach the method of graphical vertex condensation for enumerating perfect matchings of plane bipartite graph was found by propp generalized domino shuffling theoret comput sci 303 2003 267 301 and was generalized by kuo applications of graphical condensation for enumerating matchings and tilings theoret comput sci 319 2004 29 57 and yah and zhang graphical condensation for enumerating perfect matchings j combin theory ser a 110 2005 113 125 in this paper by a purely combinatorial method some explicit identities on graphical vertex condensation for enumerating perfect matchings of plane graphs which do not need to be bipartite are obtained as applications of our results some results on graphical edge condensation for enumerating perfect matchings are proved and we count the sum of weights of perfect matchings of weighted aztec diamond

polyhedral lyapunov functions structurally ensure global asymptotic stability of dynamical networks iff the jacobian is non singular for a vast class of dynamical networks including chemical reaction networks crns with monotonic reaction rates the existence of a polyhedral lyapunov function plf implies structural i e parameter free local stability global structural stability is ensured under the additional assumption that each of the variables chemical species concentrations in crns is subject to a spontaneous infinitesimal dissipation this paper solves the open problem of global structural stability in the absence of the infinitesimal dissipation showing that the existence of a plf structurally ensures global convergence if and only if the system jacobian passes a structural non singularity test it is also shown that if the jacobian is structurally non singular under positivity assumptions for the system partial derivatives the existence of an equilibrium is guaranteed for systems subject to positivity constraints it is shown that if the system admits a plf under structural non singularity assumptions global convergence within the positive orthant is structurally ensured while the existence of an equilibrium can be proven by means of a linear programming test and the computation of a piecewise linear in rate lyapunov function

an isogeometric analysis approach to gradient damage models continuum damage formulations are commonly used for the simulation of diffuse fracture processes implicit gradient damage models are employed to avoid the spurious mesh dependencies associated with local continuum damage models the c 0 continuity of traditional finite elements has hindered the study of higher order gradient damage approximations in this contribution we use isogeometric finite elements which allow for the construction of higher order continuous basis functions on complex domains we study the suitability of isogeometric finite elements for the discretization of higher order gradient damage approximations

a higher order phase field model for brittle fracture formulation and analysis within the isogeometric analysis framework phase field models based on the variational formulation for brittle fracture have recently been gaining popularity these models have proven capable of accurately and robustly predicting complex crack behavior in both two and three dimensions in this work we propose a fourth order model for the phase field approximation of the variational formulation for brittle fracture we derive the thermodynamically consistent governing equations for the fourth order phase field model by way of a variational principle based on energy balance assumptions the resulting model leads to higher regularity in the exact phase field solution which can be exploited by the smooth spline function spaces utilized in isogeometric analysis this increased regularity improves the convergence rate of the numerical solution and opens the door to higher order convergence rates for fracture problems we present an analysis of our proposed theory and numerical examples that support this claim we also demonstrate the robustness of the model in capturing complex three dimensional crack behavior

maximum matchings and minimum dominating sets in apollonian networks and extended tower of hanoi graphs abstract the apollonian networks display the remarkable power law and small world properties as observed in most realistic networked systems their dual graphs are extended tower of hanoi graphs which are obtained from the tower of hanoi graphs by adding a special vertex linked to all its three extreme vertices in this paper we study analytically maximum matchings and minimum dominating sets in apollonian networks and their dual graphs both of which have found vast applications in various fields e g structural controllability of complex networks for both networks we determine their matching number domination number the number of maximum matchings as well as the number of minimum dominating sets

pfaffian orientations and perfect matchings of scale free networks counting perfect matchings is of great interest in theoretical computer science mathematics among other disciplines however explicitly determining the number of perfect matchings of general graphs is a challenge in this paper we present a first analytical study of the enumeration problem of perfect matchings on scale free networks which are ubiquitous in real life systems we focus on two iteratively growing scale free networks one is fractal while the other is non fractal for each network we construct an orientation and prove that it is pfaffian then based on the connection between the number of perfect matchings and determinant of the skew adjacency matrix corresponding to a pfaffian orientation we derive the recursive expressions for the number of perfect matchings of the networks at two successive iterations furthermore using the recursive relations we show that for both scale free networks their entropy is zero which is in sharp contrast to the previously obtained results for other networks without scale free behavior but having the same average degree as the studied networks such as square lattice and honeycomb lattice whose entropies are larger than zero our results indicate from another angle that scale free networks have a distinct architecture in comparison with those lattices lacking the power law property

global asymptotic stability for a class of nonlinear chemical equations we consider a class of nonlinear differential equations that arises in the study of chemical reaction systems known to be locally asymptotically stable and prove that they are in fact globally asymptotically stable more specifically we will consider chemical reaction systems that are weakly reversible have a deficiency of zero and are equipped with mass action kinetics we show that if for each c in mathbb r 0 m the intersection of the stoichiometric compatibility class c s with the subsets on the boundary that could potentially contain equilibria l w are at most discrete then global asymptotic stability follows previous global stability results for the systems considered in this paper required c s cap l w emptyset for each c in mathbb r m 0

dimers on two types of lattices on the klein bottle the problem of enumerating close packed dimers or perfect matchings on two types of lattices the so called 8 8 4 and 8 8 6 lattices embedded on the klein bottle is considered and we obtain the explicit expression of the number of close packed dimers and entropy our results imply that 8 8 4 lattices have the same entropy under three different boundary conditions cylindrical toroidal and klein bottle and 8 8 6 lattices have the same property this article is part of lattice models and integrability a special issue of journal of physics a mathematical and theoretical in honour of f y wu s 80th birthday

the deficiency zero theorem and global asymptotic stability for a class of chemical reaction networks with arbitrary time delays abstract the deficiency zero theorem dzt is extended to be applied to chemical reaction networks crns with time delays the time evolution of concentrations of species in which networks is described by delay differential equations ddes the extended dzt provides a sufficient condition for a positive equilibrium point of ddes to exist and be locally asymptotically stable furthermore it is proven that the absence of boundary equilibria is a sufficient condition for the positive equilibrium point to be globally asymptotically stable these results are natural analogues of theorems proven for crns without time delays

spanning trees in a fractal scale free lattice spanning trees provide crucial insight into the origin of fractality in fractal scale free networks in this paper we present the number of spanning trees in a particular fractal scale free lattice network we first study analytically the topological characteristics of the lattice and show that it is simultaneously scale free highly clustered large world fractal and disassortative any previous model does not have all the properties as the studied one then by using the renormalization group technique we derive analytically the number of spanning trees in the network under consideration based on which we also determine the entropy for the spanning trees of the network these results shed light on understanding the structural characteristics of and dynamical processes on scale free networks with fractality moreover our method and process for employing the decimation technique to enumerate spanning trees are general and can be easily extended to other deterministic media with self similarity

nc algorithms for computing the number of perfect matchings in k 3 3 free graph and related problems abstract we show that the problem of computing the number of perfect matchings in k3 3 free graphs is in nc this contrasts with the p completeness of counting the number of perfect matchings in arbitrary graphs as corollaries we obtain nc algorithms for checking if a given k3 3 free graph has a perfect matching and if it has an exact matching our result also opens up the possibility of obtaining an nc algorithm for finding a perfect matching in k3 3 free graphs

isogeometric analysis of the cahn hilliard phase field model abstract the cahn hilliard equation involves fourth order spatial derivatives finite element solutions are not common because primal variational formulations of fourth order operators are only well defined and integrable if the finite element basis functions are piecewise smooth and globally c 1 continuous there are a very limited number of two dimensional finite elements possessing c 1 continuity applicable to complex geometries but none in three dimensions we propose isogeometric analysis as a technology that possesses a unique combination of attributes for complex problems involving higher order differential operators namely higher order accuracy robustness two and three dimensional geometric flexibility compact support and most importantly the possibility of c 1 and higher order continuity a nurbs based variational formulation for the cahn hilliard equation was tested on two and three dimensional problems we present steady state solutions in two dimensions and for the first time in three dimensions to achieve these results an adaptive time stepping method is introduced we also present a technique for desensitizing calculations to dependence on mesh refinement this enables the calculation of topologically correct solutions on coarse meshes opening the way to practical engineering applications of phase field methodology

applications of graphical condensation for enumerating matchings and tilings a technique called graphical condensation is used to prove various combinatorial identities among numbers of perfect matchings of planar bipartite graphs and tilings of regions graphical condensation involves superimposing matchings of a graph onto matchings of a smaller subgraph and then re partitioning the united matching actually a multigraph into matchings of two other subgraphs in one of two possible ways this technique can be used to enumerate perfect matchings of a wide variety of planar bipartite graphs applications include domino tilings of aztec diamonds and rectangles diabolo tilings of fortresses plane partitions and transpose complement plane partitions

stress based nonlocal damage model abstract progressive microcracking in brittle or quasi brittle materials as described by damage models presents a softening behavior that in turn requires the use of regularization methods in order to maintain objective results such regularization methods which describe interactions between points provide some general properties including objectivity and the non alteration of a uniform field as well as drawbacks damage initiation free boundary a modification of the nonlocal integral regularization method that takes the stress state into account is proposed in this contribution the orientation and intensity of nonlocal interactions are modified in accordance with the stress state the fundamental framework of the original nonlocal method has been retained making it possible to maintain the method s advantages the modification is introduced through the weight function which in this modified version depends not only on the distance between two points as for the original model but also on the stress state at the remote point the efficiency of this novel approach is illustrated using several examples the proposed modification improves the numerical solution of problems observed in numerical simulations involving regularization techniques damage initiation and propagation in mode i as well as shear band formation are analyzed herein

piecewise linear lyapunov functions for structural stability of biochemical networks we consider the problem of assessing structural stability of biochemical reaction networks with monotone reaction rates namely of establishing if all the networks with a certain structure are stable regardless of specific parameter values we investigate stability by absorbing the network equations in a linear differential inclusion and seeking for a polyhedral lyapunov function proper to the considered network structure a numerical recursive procedure is devised to test stability for a wide class of mono and bimolecular reaction networks which we name unitary the procedure is shown to be very efficient since due to the particular structure of the problem it requires iterations in the space of integer valued matrices we also consider a similar less conservative procedure that allows us to test even when the lyapunov function cannot be found whether the system evolution is structurally bounded in this case we absorb the equations in a positive linear differential inclusion to show the effectiveness of the proposed procedure we report the outcomes of both a stability and a boundedness test for many non trivial biochemical reaction networks and we analyze well established models in the literature

uniform and strict persistence in monotone skew product semiflows with applications to non autonomous nicholson systems abstract we determine sufficient conditions for uniform and strict persistence in the case of skew product semiflows generated by solutions of non autonomous families of cooperative systems of odes or delay fdes in terms of the principal spectrums of some associated linear skew product semiflows which admit a continuous separation our conditions are also necessary in the linear case we apply our results to a noncooperative almost periodic nicholson system with a patch structure whose persistence turns out to be equivalent to the persistence of the linearized system along the null solution

bridging domain methods for coupled atomistic continuum models with l2 or h1 couplings a bridging domain method for coupled atomistic continuum models is proposed that enables to compare various coupling terms the approach does not require the finite element mesh to match the lattice spacing of the atomic model it is based on an overlapping domain decomposition method that makes use of lagrange multipliers and weight functions in the coupling zone in order to distribute the energy between the two competing models two couplings are investigated the l 2 coupling enforces the continuity of displacements between the two models directly the h 1 coupling involves the definition of a strain measure for this purpose a moving least square interpolant of the atomic displacement is defined the choice of the weight functions is studied patch tests and a graphene sheet with a crack are studied it is shown that both continuous and discontinuous weight functions can be used with the h 1 coupling whereas the l 2 coupling requires continuous weight functions for the examples developed herein the l 2 coupling produces less error in the zone of interest the flexibility of the h 1 coupling with constant weight function may be beneficial but the results may be affected depending on the topology of the bridging zone

topologically robust zero sum games and pfaffian orientation how network topology determines the long time dynamics of the antisymmetric lotka volterra equation to explore how the topology of interaction networks determines the robustness of dynamical systems we study the antisymmetric lotka volterra equation alve the alve is the replicator equation of zero sum games in evolutionary game theory in which the strengths of pairwise interactions between strategies are defined by an antisymmetric matrix such that typically some strategies go extinct over time here we show that there also exist topologically robust zero sum games such as the rock paper scissors game for which all strategies coexist for all choices of interaction strengths we refer to such zero sum games as coexistence networks and construct coexistence networks with an arbitrary number of strategies by mapping the long time dynamics of the alve to the algebra of antisymmetric matrices we identify simple graph theoretical rules by which coexistence networks are constructed examples are triangulations of cycles characterized by the golden ratio phi 1 6180 cycles with complete subnetworks and non hamiltonian networks in graph theoretical terms we extend the concept of a pfaffian orientation from even sized to odd sized networks our results show that the topology of interaction networks alone can determine the long time behavior of nonlinear dynamical systems and may help to identify robust network motifs arising for example in ecology

weak dynamical nonemptiability and persistence of chemical kinetics systems a frequently desirable characteristic of chemical kinetics systems is that of persistence the property that if all the species are initially present then none of them may tend toward extinction it is known that solutions of deterministically modeled mass action systems may approach only portions of the boundary of the positive orthant which correspond to semilocking sets alternatively called siphons consequently most recent work on persistence of these systems has been focused on these sets in this paper we focus on a result which states that for a conservative mass action system persistence holds if every critical semilocking set is dynamically nonemptiable and the system contains no nested locking sets we will generalize this result by introducing the notion of a weakly dynamically nonemptiable semilocking set and making novel use of the well known farkas lemma we will also connect this result to known results regarding complex balanced systems and systems with facets

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

correction to structure and stability of certain chemical networks and applications to the kinetic proofreading model of t cell receptor signal transduction deals with the theory of structure stability robustness and stabilization for an appealing class of nonlinear systems which arises in the analysis of chemical networks the results given here extend but are also heavily based upon certain previous work by feinberg 1977 1979 1987 1995 and horn and jackson 1972 of which a self contained and streamlined exposition is included the theoretical conclusions are illustrated through an application to the kinetic proofreading model proposed by mckeithan 1995 for t cell receptor signal transduction

a higher order stress based gradient enhanced damage model based on isogeometric analysis abstract the micro damage associated with diffuse fracture processes in quasi brittle materials can be described by continuum damage mechanics in order to overcome the mesh dependence of local damage formulations non local and gradient enhanced approaches are often employed in this manuscript a higher order stress based gradient enhanced formulation is proposed which exploits the higher order continuity of b spline functions in isogeometric analysis iga the proposed formulation does not require the decomposition of the fourth order model into two second order models two numerical examples are presented to demonstrate the performance of the formulation and to compare the obtained solutions with results from conventional gradient enhanced damage formulation

planar unclustered scale free graphs as models for technological and biological networks many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law often these networks have also a modular and self similar structure and in some cases usually associated with topological restrictions their clustering is low and they are almost planar in this paper we introduce a family of graphs which share all these properties and are defined by two parameters as their construction is deterministic we obtain exact analytic expressions for relevant properties of the graphs including the degree distribution degree correlation diameter and average distance as a function of the two defining parameters thus the graphs are useful to model some complex networks in particular several families of technological and biological networks and in the design of new practical communication algorithms in relation to their dynamical processes they can also help understanding the underlying mechanisms that have produced their particular structure

the dynamics of weakly reversible population processes near facets this paper concerns the dynamical behavior of weakly reversible deterministically modeled population processes near the facets codimension one faces of their invariant manifolds and proves that the facets of such systems are repelling it has been conjectured that any population process whose network graph is weakly reversible has strongly connected components is persistent we prove this conjecture to be true for the subclass of weakly reversible systems for which only facets of the invariant manifold are associated with semilocking sets or siphons an important application of this work pertains to chemical reaction systems that are complex balancing for these systems it is known that within the interior of each invariant manifold there is a unique equilibrium the global attractor conjecture states that each of these equilibria is globally asymptotically stable relative to the interior of the invariant manifold in which it lies our results pertaining to weakly reversible systems imply that thi

concurrently coupled atomistic and xfem models for dislocations and cracks a method for the modeling of dislocations and cracks by atomistic continuum models is described the methodology combines the extended finite element method with the bridging domain method bdm the former is used to model crack surfaces and slip planes in the continuum whereas the bdm is used to link the atomistic models with the continuum the bdm is an overlapping domain decomposition method in which the atomistic and continuum energies are blended so that their contributions decay to their boundaries on the overlapping subdomain compatibility between the continua and atomistic domains is enforced by a continuous lagrange multiplier field the methodology allows for simulations with atomistic resolution near crack fronts and dislocation cores while retaining a continuum model in the remaining part of the domain and so a large reduction in the number of atoms is possible it is applied to the modeling of cracks and dislocations in graphene sheets energies and energy distributions compare very well with direct numerical simulations by strictly atomistic models copyright 2008 john wiley sons ltd

persistence in dynamical systems soit un espace metrique localement compact de metrique d et soit e un sous ensemble clos de a frontiere e et interieur e on suppose que l on a un flot continu 7b f defini sur e tel que e est invariant par 7b f on considere la notion de persistance et on donne un critere de persistance

permanents pfaffian orientations and even directed circuits given a 0 1 square matrix a when can some of the 1 s be changed toi1 s in such a way that the permanent of a equals the determinant of the modifled matrix when does a real square matrix have the property that every real matrix with the same sign pattern that is the corresponding entries either have the same sign or are both zero is nonsingular when is a hypergraph with n vertices and n hyperedges minimally nonbipartite when does a bipartite graph have a pfa an orientation given a digraph does it have no directed circuit of even length given a digraph does it have a subdivision with no even directed circuit it is known that all of the above problems are equivalent we prove a structural characterization of the feasible instances which implies a polynomial time algorithm to solve all of the above problems the structural characterization says roughly speaking that a bipartite graph has a pfa an orientation if and only if it can be obtained by piecing together in a specifled way planar bipartite graphs and one sporadic nonplanar bipartite graph