stabilization of partitioned solution procedure for pore fluid soil interaction analysis on montre que la solution decalee conventionnelle des problemes d interaction fluide sol dans les pores souffre de restrictions sur la stabilite on presente une forme stabilisee de la procedure de solution decalee de ce probleme on recommande cette procedure pour l implementation des problemes d interaction sol fluide

persistence properties of a system of coagulating and annihilating random walkers we study a d dimensional system of diffusing particles that on contact either annihilate with probability 1 q ensuremath 1 or coagulate with probability q ensuremath 2 q ensuremath 1 in one dimension the system models the zero temperature glauber dynamics of domain walls in the q state potts model we calculate overline p m t the probability that a randomly chosen lattice site contains a particle whose ancestors have undergone exactly m ensuremath 1 coagulations using perturbative renormalization group analysis for dl2 we show that if the number of coagulations m is much less than the typical number m t then overline p m t ensuremath sim m ensuremath zeta d t ensuremath ensuremath theta with ensuremath theta dq q q ensuremath 1 2 ensuremath epsilon o ensuremath epsilon 2 ensuremath zeta 2q ensuremath 1 ensuremath epsilon 2q ensuremath 1 q ensuremath 1 1 2 aq ensuremath epsilon 2 o ensuremath epsilon 3 where q q ensuremath 1 q ensuremath epsilon 2 ensuremath d and a ensuremath 0 006 dots m t is shown to scale as m t ensuremath sim t d 2 ensuremath ensuremath delta where ensuremath delta d 1 ensuremath q q ensuremath 1 q ensuremath 1 2 ensuremath epsilon o ensuremath epsilon 2 in two dimensions we show that overline p m t ensuremath sim mathrm ln t q 3 ensuremath 2q mathrm ln m 2q ensuremath 1 2 t ensuremath 2q for m ensuremath ll t 2q ensuremath 1 we also derive an exact nonperturbative relation between the exponents namely ensuremath delta q ensuremath theta 1 ensuremath q the one dimensional results corresponding to ensuremath epsilon 1 are compared with results from monte carlo simulations

standard staggered and staggered newton schemes in thermo hydro mechanical problems the aim of the paper is to compare the rates of iteration convergence of two staggered numerical schemes one using successive substitutions and the other the newton method in the case of very weakly coupled problems the newton method is one order faster but there are specific cases when it is slower than the standard staggered algorithm in both cases a convergence condition must be verified the behaviour of the investigated staggered procedures in case of thermo hydro mechanical problems are shown on examples

modeling and simulation of piezocomposites solution procedures for large scale transient analysis of piezocomposites are developed computational efficiency of unconditionally stable and conditionally stable implicit partitioned schemes as well as explicit partitioned schemes is investigated in the context of multilevel solution methods applied to separate field equations

algorithms for strong coupling procedures abstract this paper considers algorithms for computing the response of a coupled problem with a partitioned approach one important example treated here is fluid structure interaction fsi often procedures or even software exists to solve each sub problem separately and one wants to couple both this setting seems to allow only the so called weak coupling which is not sufficient for some problems the so called strong coupling is often a totally implicit formulation where the system components are evaluated at the same time level this usually requires an iterative procedure the fsi problem is cast as an abstract differential algebraic equation dae for which the coupling procedures are developed with the partitioned approach one simple and frequently used computational procedure is similar to a block gauss seidel iteration it is shown why this approach may experience difficulties and how they may be circumvented with newton like methods still staying in the partitioned framework the functional and software engineering requirements for the simulation interface are described and analysed some simple coupled example problems demonstrate how the proposed procedures work

unconditionally stable staggered solution procedure for soil pore fluid interaction problems this paper presents a simple procedure for modifying the dynamic coupled soil pore fluid equations in a manner which allows a stable and efficient staggered solution procedure to be used the solution method is simpler than an alternative suggested by park15 and has a direct physical interpretation this stabilized procedure is efficient in numerical time domain analysis of soil pore fluid occurring in earthquake and consolidation problems numerical examples of one and two dimensional saturated poroelastic media demonstrate the procedure

evaluation of three and two field finite element methods for the dynamic response of saturated soil the three field formulation u p u is presented and is applied to solve dynamic equations for saturated porous media in order to evaluate the accuracy and the performance of this three field approximation the u u and the u w formulations are also considered and a few one and two dimensional examples are solved using the three methods problems for which both the pore fluid and the solid grains are incompressible are also considered and are solved using the u p u approximation accuracy was determined by a comparison of the finite element results with the analytical solution given by gajo and mongiovi 19 for a wide range of permeability

stability of bounded subsets of metzler sparse matrix cones abstract we study the existence of hurwitz matrices in a class of metzler sparse matrix cones where the non zero entries are constrained to be in a bounded set in particular we provide necessary and sufficient conditions for the existence of one or more hurwitz matrices in this class of sparse matrix spaces for scenarios with uniform and non uniform bounds several examples illustrate our results

exact results for vicious walker models of domain walls non intersecting or vicious random walker models in one dimension can be interpreted as models of domain walls in two dimensions three problems pertaining to vicious walker models are solved the first is the exact evaluation of the partition function for the random turns model of vicious walkers on a lattice in this model at each tick of the clock a randomly chosen walker must move one step to the left or one step to the right the second problem is the calculation of the mean spacing between walls in terms of the chemical potential for a brownian motion model of continuous domain walls in a strip while the final problem solved is the calculation of the correlation between defects which occur when two domain walls meet and end without crossing the whole system

stable element free galerkin solution procedures for the coupled soil pore fluid problem it is always difficult to solve the coupled soil pore fluid problem when the soil is saturated and impermeable because this situation often results in intensive oscillations of the solutions this topic has been discussed widely in the field of the finite element method but rarely by meshless methods the element free galerkin efg method has outstanding advantages of solving this problem based on the fact that its interpolation function can be constructed flexibly by the nodes in the compact domain in this study an efg numerical model together with a stabilization technique is proposed to obtain stable solutions especially for the saturated and impermeable soil close agreement between computational results and analytical solutions for one and two dimensional examples shows that the proposed numerical model not only provides highly accurate solutions for the saturated soil with relatively high permeability but also eliminates the oscillations of the solutions very effectively for the saturated and impermeable soil furthermore the influences of the hydraulic anisotropy a typical property of two dimensional problems on the proposed stabilization technique are discussed it is suggested that the optimal distribution of the nodes of essential variables can be designed according to the relative importance of the permeability in different directions copyright c 2010 john wiley sons ltd

fixed point convergence of modular steady state heat transfer models coupling multiple scales and phenomena for melt crystal growth a block gauss seidel iteration procedure is employed to couple two independent heat transfer codes representing different scales and phenomena in a melt crystal growth system via shared domain boundaries in general such strategies are attractive because of their simplicity for solving problems that may be represented by linking via shared boundary conditions existing codes using a modular design however these approaches often meet with limited success due to convergence difficulties associated with the overall model the mathematical framework of fixed point iterations is employed to assess convergence behaviour for steady state non linear heat transfer models analytical forms describe the convergence of one dimensional problems and provide insight to the behaviour of more complicated two dimensional models certain implementations that are physically reasonable result in algorithms that will never converge demonstrating that notions based on physical intuition may not be useful for predicting algorithm performance a mixing of flux and temperature information along the shared model boundary leads to successful iterative strategies under many conditions

alternating kinetics of annihilating random walks near a free interface the kinetics of annihilating random walks in one dimension with the half line x 0 initially filled is investigated the survival probability of the nth particle from the interface exhibits power law decay with for n 1 and all odd values of n for all n even a faster decay with is observed from consideration of the eventual survival probability in a finite cluster of particles the rigorous bound is derived while a heuristic argument gives numerically this latter value appears to be a lower bound for the average position of the first particle moves to the right approximately as with a relatively sharp and asymmetric probability distribution

the mathematics of infectious diseases many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases threshold theorems involving the basic reproduction number r 0 the contact number sigma and the replacement number r are reviewed for the classic sir epidemic and endemic models similar results with new expressions for r 0 are obtained for mseir and seir endemic models with either continuous age or age groups values of r 0 and sigma are estimated for various diseases including measles in niger and pertussis in the united states previous models with age structure heterogeneity and spatial structure are surveyed

fractional step methods for index 1 differential algebraic equations in the numerical solution of ordinary differential systems the method of fractional steps also known as operator splitting yields high order accurate schemes based on separate computationally convenient treatments of distinct physical effects such schemes are equally desirable but much less accurate for semi explicit index 1 differential algebraic equations daes in the first half of this note it is shown that email protected ve application to daes of standard splitting schemes suffers from order reduction both first and second order schemes are only first order accurate for daes in the second half of this note a new family of higher order splitting schemes for semi explicit index 1 daes is developed the new schemes are based on a deferred correction paradigm in which an error equation is solved numerically and therefore inherit a simple computationally convenient structure higher order convergence of the new schemes is proved and numerical results confirm the expected order of accuracy in addition to establishing efficiency

stability analysis of finite difference schemes revisited a study of decoupled solution strategies for coupled multifield problems summary many problems in engineering physics or other disciplines require an integrated treatment of coupled heterogeneous fields the mathematical models of such problems commonly consist of a coupled pde system considerable progress has been made in the development of schemes to solve such systems resulting in a wide spectrum of monolithic and decoupled numerical solution approaches in particular the flexibility offered by the decoupled strategies in choosing appropriate solution methods and adjustable time step sizes has motivated the elaboration of these schemes however the way of decoupling can influence the stability of the resulting solution algorithm and hence urges a comprehensive stability analysis the purpose of this contribution is to elucidate the salient points in the stability analysis of the numerical solution schemes to this end we introduce a general framework for the stability analysis of solution strategies and provide an easy to use procedure to find the necessary stability condition the procedure is tested against decoupled solution strategies for volume and surface coupled problems namely thermoelastodynamics porous media dynamics and fluid and structure structure interaction in this context the influence of explicit and implicit predictors and the sequence of the time integration on the stability condition is carefully examined copyright 2013 john wiley sons ltd

unconditionally stable sequential schemes for all way coupled thermoporomechanics undrained adiabatic and extended fixed stress splits abstract we propose two sequential methods for the all way coupled thermoporomechanical problems the undrained adiabatic split that combines together the undrained and adiabatic methods of poromechanics and thermomechanics respectively and the extended fixed stress split we perform nonlinear stability analysis for the two sequential methods introducing a new extended norm that can encompass the all way coupled thermoporomechanical problems we find that the two sequential methods are unconditionally stable if 0 5 where is the parameter of time discretization for the generalized midpoint rule at t n we also perform the spectral analysis in order to further investigate stability and convergence of the two methods the spectral analysis shows unconditional stability of the two sequential methods which yields the magnitudes of the amplification factor less than unity we then show numerical examples which support the a priori stability and convergence estimates

sparse stable systems abstract in the design of decentralized networked systems it is important to know whether a given network topology can sustain stable dynamics we consider a basic version of this problem here given a vector space of sparse real matrices does it contain a stable hurwitz matrix said differently is a feedback channel corresponding to a non zero entry necessary for stabilization or can it be done without we provide in this paper a set of necessary conditions and a set of sufficient conditions for the existence of stable matrices in a vector space of sparse matrices we further prove some properties of the set of sparse matrix spaces that contain hurwitz matrices the conditions we exhibit are most easily stated in the language of graph theory which we thus adopt in this paper

on convergence conditions of partitioned solution procedures for consolidation problems abstract a systematic approach to determine conditions for convergence of partitioned staggered procedures for consolidation problems is presented consistency convergence and stability is investigated for linear and nonlinear problems and a comparison of the partitioned and direct method is made conclusions based also on numerical evidence are drawn the significance of the ratio of the time step length to the square of the finite element mesh length is shown

variationally derived 3 field finite element formulations for quasistatic poroelastic analysis of hydrated biological tissues hydrated biological tissues are often modeled mechanically as poroelastic media with intrinsically incompressible solid and fluid constituents unlike many engineering materials these tissues may typically experience finite deformations during normal physiological activities accurate and efficient finite element formulations are required to solve large problems of experimental and clinical relevance this manuscript describes two new 3 field u p w mixed finite element formulations based on lagrange multiplier and augmented lagrangian representations of the saturation incompressibility constraint as a precursor the continuum mixture theory for finite deformation quasistatic poroelasticity with constituent incompressibility is first reformulated within the variational framework of the principal of virtual power in doing so the equivalence of the continuum mixture theory and biot formulations for this problem is established the improved performance of the mixed formulations over an analogous 2 field u w penalty formulation is demonstrated using axisymmetric numerical examples

unbinding transition in a many string system a 1 1 dimensional model of n nonintersecting strings with short range attractive interactions on a lattice is solved exactly for arbitrary finite n 2 there is a second order binding unbinding transition with the same critical exponents as for n 2 in the limit n to infinity the transition becomes first order

the reunions of three dissimilar vicious walkers we study the behavior of three vicious random walkers which diffuse freely in one dimension witharbitrary diffusivitiesb 1 2 b 2 2 b 3 2 except that their paths may not cross the full distribution function is calculated exactly in the continuum limit the exponent 3 governing the decay of the probability r n 3 sim 1 n psi 3 of a simultaneousreunion of all three walkers aftern steps is found to varycontinuously according to psi 3 1 pi cos 1 left b 2 2 left b 1 2 b 2 2 b 2 2 b 3 2 right 1 2 right this variation has consequences for various interfacial wetting transitions in 1 1 dimensions it may also be related heuristically to the marginality of direct interface wall interactions decaying asw0 l2 in the intermediate fluctuation regime of 1 1 dimensional wetting where exponents varying continuously withw0 have recently been found

a unified set of single step algorithms part 1 general formulation and applications a general algorithm for a single step time marching scheme for use in dynamic or diffusion equations is presented this algorithm is easily programmed in its universal form for all orders of approximation and covers most of the currently used schemes as well as presenting many new possibilities in many cases it presents a computationally advantageous form over conventional procedures this is particularly so when compared with the newmark algorighm and its variants

a further look at newmark houbolt etc time stepping formulae this paper looks at some well known methods for the numerical integration of the vibration equation from the point of view of various groupings of the independent equations involved new forms are given of the general three parameter method introduced by zienkiewicz 1 some new one step methods are introduced these are of great practical importance because of the ease with which the size of time step can be changed

sign properties of metzler matrices with applications abstract several results about sign properties of metzler matrices are obtained it is first established that checking the sign stability of a metzler sign matrix can be either characterized in terms of the hurwitz stability of the unit sign matrix in the corresponding qualitative class or in terms the negativity of the diagonal elements of the metzler sign matrix and the acyclicity of the associated directed graph similar results are obtained for the case of metzler block matrices and metzler mixed matrices the latter being a class of metzler matrices containing both sign and real type entries the problem of assessing the sign stability of the convex hull of a finite and summable family of metzler matrices is also solved and a necessary and sufficient condition for the existence of common lyapunov functions for all the matrices in the convex hull is obtained the concept of sign stability is then generalized to the concept of ker b sign stability a problem that arises in the analysis of certain jump markov processes a sufficient condition for the ker b sign stability of metzler sign matrices is obtained and formulated using inverses of sign matrices and the concept of l matrices several applications of the results are discussed in the last section

synchronous vs asynchronous dynamics of diffusion controlled reactions abstract an analytical method based on the classical ruin problem is developed to compute the mean reaction time between two walkers undergoing a generalized random walk on a 1d lattice at each time step either both walkers diffuse simultaneously with probability p synchronous event or one of them diffuses while the other remains immobile with complementary probability asynchronous event reaction takes place through same site occupation or position exchange we study the influence of the degree of synchronicity p of the walkers and the lattice size n on the global reaction s efficiency for odd n the purely synchronous case p 1 is always the most effective one while for even n the encounter time is minimized by a combination of synchronous and asynchronous events this new parity effect is fully confirmed by monte carlo simulations on 1d lattices as well as for 2d and 3d lattices in contrast the 1d continuum approximation valid for sufficiently large lattices predicts a monotonic increase of the efficiency as a function of p the relevance of the model for several research areas is briefly discussed

two dimensional polymers and conformal invariance abstract the critical properties of self avoiding walks percolation clusters and critical exponents associated with the planar brownian motion are reviewed in two dimensions 2d the conformal spectrum of these geometrical critical systems is made of an infinite descrete series of scaling dimensions the latter are calculated in the framework of coulomb gas methods and conformal invariance the statistical mechanics of the same critical models on a random 2d lattice i e on a random surface namely in presence of a critically fluctuating metric in the so called 2d quantum gravity is also addressed and the above critical geometrical systems are exactly solvable in this case the new gravitational conformal spectrum is related to the standard conformal spectrum in the plane as predicted recently

nonlinear transient phenomena in saturated porous media abstract in this report the transient static and dynamic response of saturated porous medium is analyzed the saturated porous medium viewed as a two phase system whose state is described by the stresses displacements velocities and accelerations within each phase the coupled field and constitutive equations based on mixture s theories are presented and solved numerically by the use of the finite element method time integration is achieved by using an implicit explicit predictor multicorrector scheme developed by hughes and co workers the procedure allows for a convenient selection of implicit and explicit elements and for an implicit explicit split of the various operators appearing in the differential equations accuracy and versatility of the proposed procedure are demonstrated by applying it to obtain solution to various dynamic and pseudo static one and two dimensional initial value problems

laser induced heating of dynamic particulate depositions in additive manufacturing abstract many applications in additive manufacturing involve the dynamic deposition of powders and the in flight heating of such material by a laser in order to characterize such systems the discrete element method dem is employed specifically this paper focuses on the initial stages of this process by developing a modular discrete element type multiphysics simulation method for the particle dynamics and heating by a laser and detailed thermal behavior the objective is to provide researchers with a framework to construct computational tools for this growing industry in order to achieve this from a simulation standpoint the overall particle mixture system is constructed by coupling submodels for each primary physical process dynamics and heating together an iterative staggering scheme is developed whereby within every time step each individual particle is solved freezing the state of the remaining multiparticle system the state of the particle is then updated and the algorithm moves to the next particle in the system and the process is repeated the overall process sweeps through the entire system repeatedly until convergence is achieved in an appropriate norm as the system evolves an error estimate dictates the time step size that is needed to induce convergence to below an appropriate error level thus the process can be considered as an implicit time stepping scheme which is combined with an internal iterative staggering process in order to control rates of convergence within a time step the algorithm adjusts the time step size if the iterative process does not converge within a desired number of iterations below an error tolerance the time step is reduced the degree of time step reduction is determined by utilizing an estimate of the spectral radius of the coupled system since the construction of model and solution process is modular one can easily replace physical submodels with other choices making it easy to numerically experiment with a variety of models qualitative and quantitative analyses are provided as well as three dimensional numerical examples this paper addresses the first of two overall macrostages of a complex manufacturing process with dem the first stage addressed in this paper concentrates on dry powder materials which are of a discrete particulate character using dem to characterize the deposition and in flight particle heating other papers of the author zohdi 2010 2013 2014 2015 81 82 2008 have addressed stage two namely phase transformations curing cooling and stress analysis using more appropriate continuum and hybrid dem continuum approaches

stability and convergence of sequential methods for coupled flow and geomechanics fixed stress and fixed strain splits abstract we analyze stability and convergence of sequential implicit methods for coupled flow and geomechanics in which the flow problem is solved first we employ the von neumann and energy methods for linear and nonlinear problems respectively we consider two sequential methods with the generalized midpoint rule for tn where is the parameter of time discretization namely the fixed strain and fixed stress splits the von neumann method indicates that the fixed strain split is only conditionally stable and that its stability limit is a coupling strength less than unity if 0 5 on the other hand the fixed stress split is unconditionally stable when 0 5 the amplification factors of the fixed stress split are different from those of the undrained split and are identical to the fully coupled method unconditional stability of the fixed stress split is also obtained from the energy method for poroelastoplasticity we show that the fixed stress split is contractive and b stable when 0 5 we also estimate the convergence behaviors for the two sequential methods by the matrix based and spectral analyses for the backward euler method in time from the estimates the fixed strain split may not be convergent with a fixed number of iterations particularly around the stability limit even though it is stable the fixed stress split however is convergent for a fixed number of iterations showing better accuracy than the undrained split even when we cannot obtain the exact local bulk modulus or exact rock compressibility at the flow step a priori due to complex boundary conditions or the nonlinearity of the materials the fixed stress split can still provide stability and convergence by an appropriate estimation of the local bulk modulus such as the dimension based estimation by which the employed local bulk modulus is less stiff than the exact local bulk modulus we provide numerical examples supporting all the estimates of stability and convergence for the fixed strain and fixed stress splits

fdm solutions to linear dynamics of porous media efficiency stability and parallel solution strategy summary this paper presents a strategy to improve the efficiency of simulations involving porous materials with linear behaviour and full saturation the method is named parallel lines finite difference and uses a method to decouple a discretised version of the governing equations allowing parallel computations as a result the complexity and the bandwidth of the global matrix are significantly reduced and hence the efficiency is improved the other advantage of the scheme is the fulfilment of the inf sup stability condition the scheme is developed to solve porous media formulations derived from the theory of porous media both the u p and u v p formulations are considered u displacement of solid p pressure of liquid and v velocity of liquid several simulations are performed to demonstrate the capabilities of the method

unconditionally convergent partitioned solution procedure for dynamic coupled mechanical systems a new partitioned solution procedure for the direct time integration of second order coupled field systems is presented and it is applied to the problem of soil pore fluid interaction the necessary convergence analysis for the iterative method is carried out and the fulfilment of the convergence condition is achieved with the introduction of two suitable auxiliary matrices in the basic equations governing the dynamic phenomena numerical examples are presented to demonstrate the effectiveness and the versatility of the proposed solution procedure

an iterative stabilized fractional step algorithm for finite element analysis in saturated soil dynamics abstract the discretization of the u p model for saturated porous media results in the semi discrete system of mixed type in displacements and pressures the babuska brezzi condition or the simpler patch test proposed by zienkiewicz and taylor precludes the use of elements with the equal low order of interpolation for u and p unless special stabilization techniques such as the fractional step algorithms are used the purpose of this paper is to present a modified version of the fractional step algorithm which allows much larger time step sizes than those for the existing ones the method is based on introducing an iteration algorithm the numerical experiments demonstrate the effectiveness and improved performance of the proposed modified version of the fractional step algorithm

a new numerically stable sequential algorithm for coupled finite strain elastoplastic geomechanics and flow abstract we propose a new numerically stable sequential implicit method for coupled flow and finite strain multiplicative elastoplastic geomechanics we find from stability analysis that the sequential method that solves the flow problem first by fixing the first piola kirchhoff total stress solving the geomechanics solid deformation problem at the next step is unconditionally stable contractive and b stable in this sense this method named the fixed first piola kirchhoff stress method is an extension of the fixed stress method in coupled flow and infinitesimal geomechanics we also study the fixed second piola kirchhoff stress method comparing it with the fixed first piola kirchhoff stress method because the constitutive relations are formulated by the second piola kirchhoff total stress although fixing the second piola kirchhoff total stress field does not provide theoretical unconditional stability in space discretization we use the finite element method for the geomechanics problem with the total lagrangian approach while employing the finite volume method for the flow problem geometrical nonlinearity from the total lagrangian approach results in full tensor permeability even if the initial permeability is isotropic to consider the full tensor permeability accurately we employ the multipoint flux approximation in solving the flow problem in time discretization the backward euler method is used then we perform numerical experiments of the two fixed stress sequential methods with various scenarios and find superiority of their numerical stability specifically the two fixed stress sequential methods provide almost identical results for elasticity for j 2 plasticity the two sequential methods yield slightly different numerical results although the trends of the results are similar for the drucker prager plasticity we find that the results from the two methods are almost identical for all the test cases the two sequential methods are numerically stable

stability and convergence of sequential methods for coupled flow and geomechanics drained and undrained splits abstract we perform a stability and convergence analysis of sequential methods for coupled flow and geomechanics in which the mechanics sub problem is solved first we consider slow deformations so that inertia is negligible and the mechanical problem is governed by an elliptic equation we use biot s self consistent theory to obtain the classical parabolic type flow problem we use a generalized midpoint rule parameter between 0 and 1 time discretization and consider two classical sequential methods the drained and undrained splits the von neumann method provides sharp stability estimates for the linear poroelasticity problem the drained split with backward euler time discretization 1 is conditionally stable and its stability depends only on the coupling strength and it is independent of time step size the drained split with the midpoint rule 0 5 is unconditionally unstable the mixed time discretization with 1 0 for mechanics and 0 5 for flow has the same stability properties as the backward euler scheme the von neumann method indicates that the undrained split is unconditionally stable when 0 5 we extend the stability analysis to the nonlinear regime poro elastoplasticity via the energy method it is well known that the drained split does not inherit the contractivity property of the continuum problem thereby precluding unconditional stability for the undrained split we show that it is b stable therefore unconditionally stable at the algorithmic level when 0 5 we also analyze convergence of the drained and undrained splits and derive the a priori error estimates from matrix algebra and spectral analysis we show that the drained split with a fixed number of iterations is not convergent even when it is stable the undrained split with a fixed number of iterations is convergent for a compressible system i e finite biot modulus for a nearly incompressible system i e very large biot modulus the undrained split loses first order accuracy and becomes non convergent in time we also study the rate of convergence of both splits when they are used in a fully iterated sequential scheme when the medium permeability is high or the time step size is large which corresponds to a high diffusion of pressure the error amplification of the drained split is lower and therefore converges faster than the undrained split the situation is reversed in the case of low permeability and small time step size we provide numerical experiments supporting all the stability and convergence estimates of the drained and undrained splits in the linear and nonlinear regimes we also show that our spatial discretization finite volumes for flow and finite elements for mechanics removes the well documented spurious instability in consolidation problems at early times

ordering of random walks the leader and the laggard we investigate two complementary problems related to maintaining the relative positions of n random walks on the line i the leader problem that is the probability n t that the leftmost particle remains the leftmost as a function of time and ii the laggard problem the probability n t that the rightmost particle never becomes the leftmost we map these ordering problems onto an equivalent n 1 dimensional electrostatic problem from this construction we obtain a very accurate estimate for n t for n 4 the first case that is not exactly solvable 4 t t 4 with 4 0 91342 8 the probability of being the laggard also decays algebraically n t t n we derive 2 1 2 3 3 8 and argue that n n 1 ln n as n

fractals in two dimensions and conformal invariance abstract the exact fractal properties of critical geometrical systems in two dimensions are briefly reviewed they are generically described by an infinite discrete spectrum of scaling dimensions associated with underlying conformal operators applications involve polymers percolation brownian motion and ising clusters a seemingly essential distinction between critical phenomena spectra and multifractal ones is given

error propagation of staggered solution procedures for transient problems abstract closed formulas for the error of staggered and simultaneous procedures are derived and compared conditions of global convergence are determined it is shown that in some cases a complicated condition for stability of the staggered scheme can be replaced by a simpler one the simultaneous stability condition for one iteration step a counterexample for global convergence of the staggered method with a constant number of iterations is presented

mixed finite element methods reduced and selective integration techniques a unification of concepts the equivalence of certain classes of mixed finite element methods with displacement methods which employ reduced and selective integration techniques is established this enables one to obtain the accuracy of the mixed formulation without incurring the additional computational expense engendered by the auxiliary field of the mixed method applications and numerical examples are presented for problems with constraints which can be difficult to enforce in finite element approximations and have often dictated the use of mixed principles these include thin beams and plates and linear and nonlinear incompressible and nearly incompressible continuum problems in solid and fluid mechanics

a new unconditionally stable fractional step method for non linear coupled thermomechanical problems a new class of time stepping algorithms for strongly coupled thermomechanical problems is presented which retains the computational convenience of traditional staggered algorithms without upsetting the unconditional stability property characteristic of fully implicit monolithic schemes 11 the proposed schemes are fractional step methods associated with a two phase operator split of the full non linear system of thermoelasticity into an adiabatic elastodynamics phase followed by a heat conduction phase at fixed configuration this operator split is shown to inherit the contractivity property of the full problem of evolution thus leading to unconditionally b stable product formula algorithms in sharp contrast with this stability result traditional staggered algorithms based on an isothermal mechanical phase followed by a heat conduction phase with an effective heat source are shown to lead at best to conditionally stable schemes it is further shown that the actual implementation of these two classes of schemes is essentially identical the numerical simulations presented include both dynamic and quasi static problems and are shown to closely replicate the stability estimates and non linear stability results derived for these two classes of staggered schemes

survival probability of a brownian motion in a planar wedge of arbitrary angle we study the survival probability and the first passage time distribution for a brownian motion in a planar wedge with infinite absorbing edges we generalize existing results obtained for wedge angles of the form ensuremath pi n with n a positive integer to arbitrary angles which in particular cover the case of obtuse angles we give explicit and simple expressions of the survival probability and the first passage time distribution in which the difference between an arbitrary angle and a submultiple of ensuremath pi is contained in three additional terms as an application we obtain the short time development of the survival probability in a wedge of arbitrary angle

field theory of branching and annihilating random walks we develop a systematic analytic approach to the problem of branching and annihilating random walks equivalent to the diffusion limited reaction processes 2a and a m 1 a where m 1 starting from the master equation a field theoretic representation of the problem is derived and fluctuation effects are taken into account via diagrammatic and renormalization group methods for d 2 the mean field rate equation which predicts an active phase as soon as the branching process is switched on applies qualitatively for both even and odd m but the behavior in lower dimensions is shown to be quite different for these two cases for even m and d near 2 the active phase still appears immediately but with nontrivial crossover exponents which we compute in an expansion in 2 d and with logarithmic corrections in d 2 however there exists a second critical dimension d c 4 3 below which a nontrivial inactive phase emerges with asymptotic behavior characteristic of the pure annihilation process this is confirmed by an exact calculation in d 1 the subsequent transition to the active phase which represents a new nontrivial dynamic universality class is then investigated within a truncated loop expansion which appears to give a correct qualitative picture the model with m 2 is also generalized to n species of particles which provides yet another universality class and which is exactly solvable in the limit n for odd m we show that the fluctuations of the annihilation process are strong enough to create a nontrivial inactive phase for all d 2 in this case the transition to the active phase is in the directed percolation universality class finally we study the modification when the annihilation reaction is 3a when m 0 mod 3 the system is always in its active phase but with logarithmic crossover corrections for d 1 while the other cases should exhibit a directed percolation transition out of a fluctuation driven inactive phase

formulation and finite element implementation of a multiplicative model of coupled poro plasticity at finite strains under fully saturated conditions in this paper we present the formulation and numerical analysis of a finite deformation model of coupled poro plasticity fully saturated conditions are assumed the model is based on a multiplicative decomposition of the deformation gradient in elastic and plastic parts together with an additive elastoplastic decomposition of the fluid content the final relations describing the evolution of the different fields are then obtained in the thermodynamic framework furnished by the principle of maximum plastic dissipation the particular case of an associated drucker prager model in effective stresses is considered as a model example a complete characterization of the dissipative structure of the problem of evolution is described through the derivation of an a priori stability estimate we describe in detail the finite element implementation of the model in the context of staggered algorithms for the solution of the physically coupled problem finally we present representative numerical simulations to illustrate the features of the proposed models in particular the case of strain localization in globally undrained conditions is studied in the proposed framework