upper bounds for survival probability of the contact process a precise description of the nontrivial upper invariant measure for c is still an open problem for the basic contact process which is a self dual attractive but nonreversible markov process of an interacting particle system by its self duality to identify the invariant measure is equivalent to determining the initial state dependence of the survival probability of the process a procedure to give rigorous upper bounds for the survival probability is presented based on a lemma given by harris two new bounds are given improving the simple branching process bound in the one dimensional case the present procedure can be viewed as a trial to make approximate measures by generalized markov extensions

discontinuous displacement approximation for capturing plastic localization it is proposed to capture localized plastic deformation via the inclusion of regularized displacement discontinuities at element boundaries interfaces of the finite element subdivision the regularization is based on a kinematic assumption for an interface that resembles that which is pertinent to the classical shear band concept as a by product of the regularization an intrinsic band width is introduced as a constitutive property rather than a geometric feature of the finite element mesh in this way the spurious mesh sensitivity which is obtained when the displacement approximation is continuous can be avoided another consequence is that the interfacial relation between the elements is derived directly from the conventional constitutive properties of the continuously deforming material an interesting feature is that the acoustic tensor will not only play a role for diagnosing discontinuous bifurcation but will also serve as the tangent stiffness tensor of the interface up to within a scalar factor an analytical investigation of the behaviour of the interface is carried out and it is shown that dilatation may indeed accompany slip within a shear band for a general plasticity model the significance of proper mesh alignment is demonstrated for a simple problem in plane strain and plane stress it is shown that a unique structural post peak response in accordance with non linear fracture mechanics can be achieved when the plastic softening modulus is properly related to the bandwidth the paper concludes with a numerical simulation of the gradual development of a shear band in a soil slope

vibration analysis of liquid filled pipelines with elastic constraints abstract in this paper a transfer matrix method tmm in frequency domain considering fluid structure interaction of liquid filled pipelines with elastic constraints is proposed the time domain equations considering fluid structure interaction are transformed into frequency domain by laplace transformation and then twelve fourth order ordinary differential equations and two second order ordinary differential equations are deduced from the frequency domain equations the results of the fourteen frequency domain equations are assembled into a transfer matrix which represents the motion of a single pipe section combined with point matrices that describe specified boundary conditions an overall transfer matrix for liquid filled pipeline system can be assembled using the method all the pipeline with no and rigid constraints can be easily calculated by simply setting the stiffness of the restraining springs from zero to a large number taking into account the longitudinal vibration transverse vibration and torsional vibration the proposed method can be used to analyze the pipelines with bends several numerical examples with different constraints are presented here to illustrate the application of the proposed method the results are validated by measured and simulation data through the numerical examples it is shown that the proposed method is efficient

crabgrass measles and gypsy moths an introduction to modern probability on etudie cinq modeles qui permettent d expliquer des processus lies aux systemes de particules en interaction ainsi que d autres processus

the contact process in high dimensions on renforce le theoreme de convergence complete pour le processus de contact en grandes dimensions en elargissant l etendue du parametre d infection dans l hypothese du theoreme

an analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids abstract this paper presents an analysis of strong discontinuities in inelastic solids at finite strains solutions exhibiting this type of discontinuities characterized by a discontinuous displacement field are shown to make physical and mathematical sense in a classical multiplicative plasticity continuum model if the softening modulus is reinterpreted as a singular distribution physically the strainsoftening is localized along the discontinuity conditions for the appearance of strong discontinuities in the geometrically nonlinear range are characterized as it is the response of the material during localization in addition these analytical results are exploited in the design of a new class of finite element methods the proposed methods fall within the class of enhanced strain methods and lead to solutions independent of the mesh size and insensitive to mesh alignment without requiring any regularization of the solutions by numerical parameters like a characteristic length

asymptotic behaviors of upper invariant measures for high dimensional threshold one contact processes abstract in this paper we are concerned with the threshold one contact process on z d we give a limit theorem of the probability of the event that the origin is occupied for the upper invariant measure of the process as the dimension d grows to infinity while the infection rate is inversely proportional to d a branching process and a sir model are introduced as auxiliary processes for the proof of our main result

a matrix methodology for spectral analysis of wave propagation in multiple connected timoshenko beams the dynamics of the timoshenko beam is recast such that the description requires information only at the end points this is then presented in the form of a dynamic stiffness relation suitable for assembling as is done analogously for conventional finite elements the analysis gives the exact frequency dependent response for the timoshenko beam irrespective of the length of the element the frequency domain response is converted to the time domain response using the fast fourier algorithm fft examples of its use in wave propagation studies are given

a note on the ising model in high dimensions we consider thed dimensional ising model with a nearest neighbor ferromagnetic interactionj d 1 4d we show that asd the phase and the phase approaches a product measure with density given by the mean field approximation in particular the spontaneous magnetization converges to its mean field value a similar result holds for the unique gibbs measure of the system subject to an external fieldh 0

coupled axial and flexural vibration of 1 d members abstract the method of characteristics is used to model vibrations of one dimensional members in the presence of coupling between axial and flexural waves only small deflections are considered and so the couple fx y is large only when the axial force fx is large alternative numerical schemes are presented for the integration of terms describing coupling and a suitable explicit scheme is identified the analysis is used to illustrate the influence of axial loads on frequencies and amplitudes of lateral oscillations of cantilever structures strong parametric behaviour is reproduced for a single storey shear structure including unstable resonance at double the linear natural frequency

generalized potlatch and smoothing processes we consider simple generalizations of the potlatch and smoothing processes which were introduced in 8 and studied in 5 these generalizations provide relatively simple examples of infinite interacting systems which exhibit phase transition the original potlatch and smoothing processes do not exhibit phase transition our results show that for the generalized processes phase transition does not usually occur in one or two dimensions but usually does occur in higher dimensions upper and lower bounds for the relevant critical values are obtained as one application of our results we obtain the limiting behavior of the critical values for the linear contact process in d dimensions as d thus answering a question we raised in 3 this is done by comparing the contact process with an appropriate generalized smoothing process

branching exclusion process on a strip we consider a model of stochastically interacting particles on an infinite strip of 2 in this model known as a branching exclusion process particles jump to each empty neighboring site with rate 4 and also can create a new particle with rate 1 4 at each one of these sites the initial configuration is assumed to have a rightmost particle and we study the process as seen from the rightmost vertical line occupied we prove that this process has exactly one invariant measure with the property thath the number of empty sites to the left of the rightmost particle has an exponential moment this refines a result presented by bramson eaet al who proved that ford 1 h is finite with probability 1

the threshold contact process a continuum limit in the threshold contact process on thed dimensional integer lattice with ranger healthy sites become infected at rate if they have at least one infectedr neighbour and recover at rate 1 we show that the critical value c r is asymptotic tor d c asr where c is the critical value of the birth rate for a continuum threshold contact process which may be described in terms of an oriented continuous percolation model driven by a poisson process of rate ind 1 dimensions we have bounds of 0 7320 c 3 ford 1

embedded localization band in undrained soil based on regularized strong discontinuity theory and fe analysis abstract the paper presents a novel approach to the analysis of a developing localization zone in undrained soil considered as a mixture of a solid skeleton and fluid filled pores where the solid phase is considered as elastic plastic the basic feature is the concept of regularized displacement and pore pressure discontinuities which are assumed to occur across an internal discontinuity surface in this respect the present developments are extensions of those suggested by simo et al 1993 comput mech 12 277 296 and more recently by larsson and runesson 1995 j engng mech asce in press a finite element formulation is proposed on the basis of a mixed variational formulation in the spirit of the enhanced strain concept by simo and rifai 1990 int j numer meth engng 29 1595 1638 in this fashion the localization zone is embedded into a base element for the ordinary analysis of the non localized mixture problem

non equilibrium behaviour of a many particle process density profile and local equilibria one considers a simple exclusion particle jump process on where the underlying one particle motion is a degenerate random walk that moves only to the right one starts with the configuration in which the left halfline is completely occupied and the right one free it is shown that the number of particles at time t between site u t and v t divided by t converges a s to int limits u nu f w dw where f might be called the density profile it is explicitely determined and shown to be an affine function secondly we prove that the distribution of the process looked at by an observer travelling at constant speed u converges weakly to the bernoulli measure with density f u as the time tends to infinity

the survival of the large dimensional basic contact process we consider the d dimensional basic contact process obtaining the limit value of the probability of survival when d and showing that the finite dimensional distributions of the upper invariant measure become of the product form as d

stochastic spatial models in the models we will consider space is represented by a grid of sites that can be in one of a finite number of states and that change at rates that depend on the states of a finite number of sites our main aim here is to explain an idea of durrett and levin 1994 the behavior of these models can be predicted from the properties of the mean field ode i e the equations for the densities of the various types that result from pretending that all sites are always independent we will illustrate this picture through a discussion of eight families of examples from statistical mechanics genetics population biology epidemiology and ecology some of our findings are only conjectures based on simulation but in a number of cases we are able to prove results for systems with fast stirring by exploiting connections between the spatial model and an associated reaction diffusion equation

on the localization properties of multiplicative hyperelasto plastic continua with strong discontinuities abstract the objective of this work is to examine the large strain localization properties of hyperelasto plastic materials which are based on the multiplicative decomposition of the deformation gradient thereby the case of strong discontinuities is investigated to this end first an explicit expression for the spatial tangent operator is given taking into account anisotropic as well as nonassociated material behaviour then the structure of a regularized discontinuous velocity gradient is elaborated and discussed in detail based on these two results the localization condition is derived with special emphasis on the loading conditions inside and outside an anticipated localization band thereby the intriguingly simple structure of the tangent operator which resembles the structure of the geometrically linear theory is extensively exploited this similarity carries over to the general representation for the critical hardening modulus which is exemplified for isotropic materials as a result analytical solutions are available under the assumption of small elastic strains which is justified for metals finally examples are given for the special case of the associated von mises flow rule to this end the critical localization direction and the critical hardening modulus are investigated with respect to the amount of finite elastic strain within different modes of homogeneous elasto plastic deformations

fsi analysis of liquid filled pipes most reported work on transient fluid structure interaction fsi in liquid filled pipes has been carried out in the time domain when needed information in the frequency domain e g frequency responses has been deduced by discrete fourier transforms in this paper the analysis is undertaken directly in the frequency domain and has the advantage of enabling linear dispersive terms to be included in a fully coupled manner in principle time domain results e g pressure histories can be obtained by numerical inverse laplace transforms in both domains the mathematical model has one pair of equations for each mode of wave propagation e g pressure waves in the liquid flexural waves in the pipe axial fsi coupling exists in the equations and also in boundary conditions the development used herein highlights common features between analysis in the frequency domain and analysis by the method of characteristics moc in the time domain a general formulation not restricted to pipe systems is presented the method is validated by comparison with an alternative exact analytical solution with results obtained by discrete fourier transform from an moc analysis and by comparison with measured data from a laboratory apparatus

on the stability of a population growth model with sexual reproduction on z d d geq 2 we continue our study on the stability properties of a population growth model with sexual reproduction on z d d 2 in the author s previous work it was proved that in the type iv process the two dimensional symmetric model on z 2 the vacant state o is stable under perturbation of the initial state the first kind of perturbation and it is unstable under perturbation of the birth rate the second kind of perturbation in this paper we prove that in the type iii process on z 2 the vacant state o is stable under the second kind of perturbation and in three or higher dimensional symmetric models the vacant state o is unstable under the first kind of perturbation these results combined with the results obtained earlier provide a fairly complete picture concerning the stability properties of these models

finite element methods for the analysis of strong discontinuities in coupled poro plastic media this paper presents the formulation of finite element methods for the numerical resolution of strong discontinuities in poro plastic solids fully coupled infinitesimal conditions are considered these solutions are characterized by a discontinuous displacement field with the associated singular strains and a singular distribution of the fluid content here singular distributions refer to dirac delta functions the singular component of the fluid content distribution models the fluid accumulated per unit area of the discontinuity surface and it is directly related with the dilatancy characterizing singular inelastic strains localized along such a surface it further accounts for a discontinuous fluid flow vector given by darcy s law in terms of a continuous pore pressure field all these considerations are incorporated in the proposed finite element methods through a local enhancement of the finite element interpolations as these discontinuities appear the local character of these interpolations lead after the static condensation of the enhanced fields to a large scale problem exhibiting the same structure as common finite element models of the global poro plastic problem but incorporating now crucially the localized dissipative effects characteristic of the localized failures several numerical simulations are presented to evaluate the performance of the proposed methods

on multidimensional branching random walks in random environment we study branching random walks in random i i d environment in z d d geq 1 for this model the population size cannot decrease and a natural definition of recurrence is introduced we prove a dichotomy for recurrence transience depending only on the support of the environmental law we give sufficient conditions for recurrence and for transience in the recurrent case we study the asymptotics of the tail of the distribution of the hitting times and prove a shape theorem for the set of lattice sites which are visited up to a large time

mesh refinement strategies without mapping of nonlinear solutions for the generalized and standard fem analysis of 3 d cohesive fractures summary a robust and efficient strategy is proposed to simulate mechanical problems involving cohesive fractures this class of problems is characterized by a global structural behavior that is strongly affected by localized nonlinearities at relatively small sized critical regions the proposed approach is based on the division of a simulation into a suitable number of sub simulations where adaptive mesh refinement is performed only once based on refinement window s around crack front process zone s the initialization of newton raphson nonlinear iterations at the start of each sub simulation is accomplished by solving a linear problem based on a secant stiffness rather than a volume mapping of nonlinear solutions between meshes the secant stiffness is evaluated using material state information stored read on crack surface facets which are employed to explicitly represent the geometry of the discontinuity surface independently of the volume mesh within the generalized finite element method framework moreover a simplified version of the algorithm is proposed for its straightforward implementation into existing commercial software data transfer between sub simulations is not required in the simplified strategy the computational efficiency accuracy and robustness of the proposed strategies are demonstrated by an application to cohesive fracture simulations in 3 d copyright 2016 john wiley sons ltd

modeling strong discontinuities at finite strains a novel numerical implementation abstract in this paper a finite element formulation suitable for the modeling of locally embedded strong discontinuities at finite strains is presented following the enhanced assumed strain concept eas the proposed numerical model is based on an additive decomposition of the displacement gradient into a conforming and an enhanced part the enhanced part is associated with the final failure kinematics of solids which are approximated by means of a discontinuous displacement field strong discontinuities referring to the displacement jump no special assumption such as purely mode i or mode ii failure is made the same holds for the class of interface laws considered which govern the evolution of the displacement discontinuity in terms of the traction vector acting at the surface of strong discontinuities consequently the suggested numerical framework can be applied to a broad range of different interface laws including damage based models in contrast to previous works the presented finite element formulation does not require the static condensation technique to be employed more precisely instead of computing the conforming part of deformation and the displacement jump simultaneously from the weak form of equilibrium and the weak form of traction continuity the different parts of the local deformation are decomposed according to a predictor corrector algorithm the proposed predictor and the corrector step are formally identical to that of classical computational plasticity models hence subroutines designed for standard models continuous deformation can be applied with only minor modifications necessary the applicability as well as the performance of the resulting finite element formulation are demonstrated by means of a fully three dimensional analysis of shear band formation in a bar made of a ductile material

a localization capturing fe interface based on regularized strong discontinuities at large inelastic strains the objective of this work is the development of a finite element interface formulation tailored to capture localization within geometrically nonlinear solid mechanics in this context strong discontinuities are considered as the final failure mechanism within localization problems the failure kinematics are governed by a jump in the nonlinear deformation map across a discontinuity surface in the finite element discretization the interface element is endowed with these kinematics as a consequence the interface stiffness is dominated by the weighted spatial localization tensor based on these developments a localization capturing procedure is advocated and is computationally highlighted

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

the central limit theorem for supercritical oriented percolation in two dimensions we consider the cardinality of supercritical oriented bond percolation in two dimensions we show that whenever the the origin is conditioned to percolate the process appropriately normalized converges asymptotically in distribution to the standard normal law this resolves a longstanding open problem pointed out to in several instances in the literature the result applies also to the continuous time analog of the process viz the basic one dimensional contact process we also derive general random indices central limit theorems for associated random variables as byproducts of our proof

a class of mixed assumed strain methods and the method of incompatible modes a three field mixed formulation in terms of displacements stresses and an enhanced strain field is presented which encompasses as a particular case the classical method of incompatible modes within this frame work incompatible elements arise as particular compatible mixed approximations of the enhanced strain field the conditions that the stress interpolation contain piece wise constant functions and be l2 ortho gonal to the enhanced strain interpolation ensure satisfaction of the patch test and allow the elimination of the stress field from the formulation the preceding conditions are formulated in a form particularly convenient for element design as an illustration of the methodology three new elements are developed and shown to exhibit good performance a plane 3d elastic plastic quad an axisymmetric element and a thick plate bending quad the formulation described herein is suitable for non linear analysis

contact processes in several dimensions this paper deals primarily with the basic contact processes introduced and studied by harris 12t4 these are random evolutions on the state space s a l l subsets of z a zd the d dimensional integer lattice with extremely simple local dynamics namely if we think of the contact process as representing the spread of an infection t es denoting the set of infected sites at time t then x e it becomes healthy at exponential rate 1 while x z a t is infected at a rate proport ional to the number of sites neighboring x where infection is present the proportionali ty constant 2 is called the infection parameter contact processes are perhaps the simplest s valued markov processes which exhibit a critical phenomenon infection emanating from a single site dies out with probabili ty one for small positive 2 but has positive probability of surviving for all time when is large there is a critical value 2 d where the transition occurs principal objectives of analysis are the precise formulation of the critical phenomenon and detailed description of the ergodic behavior both below and above a c our recent survey articles 10 and i 6 provide introductions to contact processes and to the general field of interacting s valued systems respectively we will make constant use of notation and techniques from the surveys assuming that the reader is familiar with thern the article 10 describes in some detail the current state of knowledge concerning one dimensional contact processes the theory for d 1 is now fairly complete with two major exceptions 1 is not even determined to one decimal place 1 18 2 e there is an

green s functions for uniform timoshenko beams abstract the vibration and control of distributed parameter systems is a topic of ongoing interest the availability of closed form expressions for the green s functions or equivalently transfer functions of individual elements facilitates the analysis of these systems in this paper a concise formulation is given for the green s functions of uniform timoshenko beams it is shown that green s functions for uniform euler bernoulli beams both with and without constant axial loads can be expressed in the same form

vibration analysis of pipelines with arbitrary branches by absorbing transfer matrix method abstract branched pipes of arbitrary shapes are prevalent in pipe systems considering fluid structure interaction fsi an absorbing transfer matrix method in frequency domain for fluid filled pipelines with any branched pipes is proposed in this paper a dominant chain of pipeline would be selected and the point transfer matrix of each junction on the dominant chain would be determined here the point transfer matrix representing the influence of branched pipes at the junction on the dominant pipeline was absorbed by the dominant chain based on these with transfer matrixes of other elements the fluid and structure dynamics problem could be solved following the chain transfer matrix method process several numerical examples with different constraints are presented to illustrate the application of the proposed method moreover the experiment of cross shaped pipes with various boundary conditions was carried out and results from the present approach were validated by measured and numerical data then the forced vibrations of branched pipes were analyzed by considering the effects of various parameters which shows the fluid pressure and vibrations can be optimized by changing the branch angles and positions through these examples it is shown that the proposed method is efficient and can be used to calculate branched pipes of any shape