queueing process with excluded volume effect we introduce an extension of the m m 1 queueing process with a spatial structure and excluded volume effect the rule of particle hopping is the same as for the totally asymmetric simple exclusion process tasep a stationary state solution is constructed in a slightly arranged matrix product form of the open tasep we obtain the critical line that separates the parameter space depending on whether the model has the stationary state we calculate the average length of the model and the number of particles and show the monotonicity of the probability of the length in the stationary state we also consider a generalization of the model with backward hopping of particles allowed and an alternate joined system of the m m 1 queueing process and the open tasep

scaling of avalanche queues in directed dissipative sandpiles using numerical simulations and analytical methods we study a two dimensional directed sandpile automaton with nonconservative random defects concentration c and varying driving rate r the automaton is driven only at the top row and driving rate is measured by the number of added particles per time step of avalanche evolution the probability distribution of duration of elementary avalanches at zero driving rate is exactly given by p 1 t c t ensuremath 3 2 mathrm exp t mathrm ln 1 ensuremath c for driving rates in the interval 0lrl 1 the avalanches are queuing one after another increasing the periods of noninterrupted activity of the automaton recognizing the probability p 1 as a distribution of service time of jobs arriving at a server with frequency r the model represents an example of the class e 1 gi ensuremath infty 1 server queue in the queue theory we study scaling properties of the busy period and dissipated energy of sequences of noninterrupted activity in the limit stackrel ensuremath rightarrow c 0 and varying linear system size l ensuremath ll 1 c we find that at driving rates rl l ensuremath 1 2 the distributions of duration and energy of the avalanche queues are characterized by a multifractal scaling and we determine the corresponding spectral functions for l ensuremath gg 1 c increasing the driving rate somewhat compensates for the energy losses at defects above the line r ensuremath sim sqrt c the scaling exponents of the distributions in this region of phase diagram vary approximately linearly with the driving rate using properties of recurrent states and the probability theory we determine analytically the exact upper bound of the probability distribution of busy periods in the case of conservative dynamics c 0 the probability of a continuous flow increases as f ensuremath infty ensuremath sim r 2 for small driving rates

efficient modification scheme of stress strain tensor for wrinkled membranes a new modification scheme of the stress strain tensor for wrinkled membranes is presented on the basis of the tension field theory the scheme is applicable to finite element analysis of partly wrinkled membranes with arbitrary shapes derivation of the modification scheme rests on an introduction of the so called wrinkle strain and a simplification of the virtual work equation of wrinkled membranes because all of the modifications required to account for wrinkling are totally confined within the stress strain relations of membranes the scheme can be easily implemented with existing finite element codes furthermore the modified stress strain tensor automatically leads to the consistent tangent stiffness matrix where changes in both the wrinkling direction and the amount of wrinkliness are taken into account three numerical examples are treated to show the accuracy and effectiveness of the proposed modification scheme

a note on the stirling matrix of the second kind in this article a new algorithm for generating the elements of the n 1 by n 1 stirling matrix of the second kind is presented based on this algorithm a computational maple procedure is written and a sample output of this procedure is also given for some values of n

on level set regularization for highly ill posed distributed parameter estimation problems the recovery of a distributed parameter function with discontinuities from inverse problems with elliptic forward pdes is fraught with theoretical and practical difficulties better results are obtained for problems where the solution may take on at each point only one of two values thus yielding a shape recovery problem this article considers level set regularization for such problems however rather than explicitly integrating a time embedded pde to steady state which typically requires thousands of iterations methods based on gauss newton are applied more directly one of these can be viewed as damped gauss newton utilized to approximate the steady state equations which in turn are viewed as the necessary conditions of a tikhonov type regularization with a sharpening sub step at each iteration in practice this method is eclipsed however by a special finite time or levenberg marquardt type method which we call dynamic regularization applied to the output least squares formulation our stopping criterion for the iteration does not involve knowledge of the true solution the regularization functional is applied to the smooth level set function rather than to the discontinuous function to be recovered and the second focus of this article is on selecting this functional typical choices may lead to flat level sets that in turn cause ill conditioning we propose a new quartic non local regularization term that penalizes flatness and produces a smooth level set evolution and compare its performance to more usual choices two numerical test cases are considered a potential problem and the classical eit dc resistivity problem

inflating a flat toroidal membrane abstract a flat toroidal geometry composed of a stack of two flat annular membranes bonded together at the inner and outer boundaries equators is proposed the finite inflation mechanics of the composite membrane under uniform internal pressure is considered the membranes are assumed to be identical homogeneous and isotropic solids described by the gent hyperelastic model with a relaxed strain energy density function the variational inflation mechanics problem yields the governing equations and boundary conditions which are recast as a nonlinear two point boundary value problem in a suitable form for efficient computation the effects of the inflation pressure and material properties on the state of stretch and geometry of the inflated toroidal membrane are obtained which exhibit a number of desirable features the phenomenon of wrinkling instability is observed near the outer equator of the torus at low pressures in spite of a positive gaussian curvature which is exactly opposite to the behavior observed in a curved torus wrinkling at the inner equator at high pressure semi analytical expressions of the cauchy stress resultants are obtained which match well with the numerical computations further the limit point instability pressure of the toroidal membrane is shown to have a remarkable power law dependence on a geometric parameter of the uninflated flat torus and the material chain extensibility parameter involving two universal constants

on effective methods for implicit piecewise smooth surface recovery this paper considers the problem of reconstructing a piecewise smooth model function from given measured data the data are compared to a field which is given as a possibly nonlinear function of the model a regularization functional is added which incorporates the a priori knowledge that the model function is piecewise smooth and may contain jump discontinuities regularization operators related to total variation tv are therefore employed two popular methods are modified tv and huber s function both contain a parameter which must be selected the huber variant provides a more natural approach for selecting its parameter and we use this to propose a scheme for both methods our selected parameter depends both on the resolution and on the model average roughness thus it is determined adaptively its variation from one iteration to the next yields additional information about the progress of the regularization process the modified tv operator has a smoother generating function nonetheless we obtain a huber variant with comparable and occasionally better performance for large problems e g high resolution the resulting reconstruction algorithms can be tediously slow we propose two mechanisms to improve efficiency the first is a multilevel continuation approach aimed mainly at obtaining a cheap yet good estimate for the regularization parameter and the solution the second is a special multigrid preconditioner for the conjugate gradient algorithm used to solve the linearized systems encountered in the procedures for recovering the model function

a new numeric analytical principle for nonlinear deterministic and stochastic dynamical systems a new implicit local linearization method termed as the locally transversal linearization ltl is developed in the present paper for a numeric analytical integration of nonlinear dynamical systems under deterministic and or stochastic excitations the ltl procedure is developed in such a way that at a chosen time instant the ltl solution manifold transversally intersects the nonlinear solution manifold at that particular point or cross section in the state space where the solution vector needs to be obtained in general construction of the ltl equation is non unique and thus it is generally needed to substitute the conditionally linear ltl based solution into the given nonlinear ordinary differential equation ode at a specified time instant to ensure a transversal intersection in the present study however it is demonstrated that a transversal intersection at a given time instant may as well be ensured by just choosing a few specific forms of the ltl equation thereby eliminating the need for substitution this new variant of ltl is particularly suitable for discretization of stochastic differential equations sdes in that one simultaneously avoids dealing with formal derivatives of wiener processes while satisfying the nonlinear sde at discrete time points the stochastic ltl procedure is adaptable for obtaining strong pathwise solutions of a general nonlinear dynamical system with continuous but not necessarily differentiable vector fields under additive and or multiplicative excitations a specific advantage of the ltl method is that for a class of response regime herein referred to as the phase independent regime it can obtain an accurate description of response irrespective of the choice of the time step and without a propagation of local errors presently the method has been numerically illustrated for strong solutions of the hardening duffing oscillator under deterministic sinusoidal or additive stochastic white noise excitations or their combination limited numerical results on periodic solutions chaos with or without noise and stochastic resonance are included in this study the results presented are indicative of the sample path accuracy consistency stochastic numerical stability and a partial insensitivity to time step sizes of the proposed method

a new 3 d finite element for nonlinear elasticity using the theory of a cosserat point abstract the theory of a cosserat point has been used to formulate a new 3 d finite element for the numerical analysis of dynamic problems in nonlinear elasticity the kinematics of this element are consistent with the standard tri linear approximation in an eight node brick element specifically the cosserat point is characterized by eight director vectors which are determined by balance laws and constitutive equations for hyperelastic response the constitutive equations for the director couples are determined by derivatives of a strain energy function restrictions are imposed on the strain energy function which ensure that the element satisfies a nonlinear version of the patch test it is shown that the cosserat balance laws are in one to one correspondence with those obtained using a bubnov galerkin formulation nevertheless there is an essential difference between the two approaches in the procedure for obtaining the strain energy function specifically the cosserat approach determines the constitutive coefficients for inhomogeneous deformations by comparison with exact solutions or experimental data in contrast the bubnov galerkin approach determines these constitutive coefficients by integrating the 3 d strain energy function using the kinematic approximation it is shown that the resulting cosserat equations eliminate unphysical locking and hourglassing in large compression without the need for using assumed enhanced strains or special weighting functions

kronrod extensions with multiple nodes of quadrature formulas for fourier coefficients abstract we continue with analyzing quadrature formulas of high degree of precision for computing the fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials started recently by bojanov and petrova quadrature formulae for fourier coefficients j comput appl math 231 2009 378 391 and we extend their results construction of new gaussian quadrature formulas for the fourier coefficients of a function based on the values of the function and its derivatives is considered we prove the existence and uniqueness of kronrod extensions with multiple nodes of standard gaussian quadrature formulas with multiple nodes for several weight functions in order to construct some new generalizations of quadrature formulas for the fourier coefficients for the quadrature formulas for the fourier coefficients based on the zeros of the corresponding orthogonal polynomials we construct kronrod extensions with multiple nodes and highest algebraic degree of precision for this very desirable kind of extension there do not exist any results in the theory of standard quadrature formulas

dynamical analysis of the exclusive queueing process recently the stationary state of a parallel update totally asymmetric simple exclusion process with varying system length which can be regarded as a queueing process with excluded volume effect exclusive queueing process was obtained c arita and d yanagisawa j stat phys 141 829 2010 in this paper we analyze the dynamical properties of the number of particles n t and the position of the last particle the system length l t using an analytical method generating function technique as well as a phenomenological description based on domain wall dynamics and monte carlo simulations the system exhibits two phases corresponding to linear convergence or divergence of n t and l t these phases can both further be subdivided into high density and maximal current subphases the predictions of the domain wall theory are found to be in very good agreement quantitively with results from monte carlo simulations in the convergent phase on the other hand in the divergent phase only the prediction for n t agrees with simulations

mathematical proof of closed form expressions for finite difference approximations based on taylor series taylor series based finite difference approximations of derivatives of a function have already been presented in closed forms with explicit formulas for their coefficients however those formulas were not derived mathematically and were based on observation of numerical results in this paper we provide a mathematical proof of those formulas by deriving them mathematically from the taylor series

numerical study of the wrinkling of a stretched thin sheet a thin sheet clamped at opposite ends and stretched develops wrinkles parallel to the direction of the applied tensile strain due to the hindered poisson lateral contraction at the clamps to study this phenomenon a variational model recently proposed by puntel deseri and fried is adopted the relevant energy functional includes bending and membranal contributions and is minimized subject to a constraint on the area of the mid surface of the sheet a fourth order partial differential equation is henceforth obtained and numerically implemented using b splines predictions are obtained concerning the number of wrinkles critical applied stretches and scaling relationships for wrinkle amplitude and wavelength both a linearized version of the boundary value problem based on the small slope approximation and a fully nonlinear one are considered their results are found to be in good agreement for the whole range of applied stretches taken into account comparisons with previous analytical results by puntel deseri and fried who used different boundary conditions and an ansatz on the deflection function are also provided the numerical results substantially confirm the validity of the analytical predictions the present work provides then an alternative numerical method for the study of wrinkling in thin sheets and supports the use of analytical and semi analytical solutions as viable options for specific geometries though further investigation particularly experimental is still needed extensive comparisons of the results with other studies available in the literature provide confirmation for the scaling laws and signal that predicted values of the critical stretches may only be accurate for higher length to width aspect ratios

a hierarchy of plate models derived from nonlinear elasticity by gamma convergence we derive a hierarchy of plate models from three dimensional nonlinear elasticity by convergence what distinguishes the different limit models is the scaling of the elastic energy per unit volume h where h is the thickness of the plate this is in turn related to the strength of the applied force h membrane theory derived earlier by le dret and raoult corresponds to 0 nonlinear bending theory to 2 von karman theory to 3 4 and linearized vk theory to 3 intermediate values of lead to certain theories with constraints a key ingredient in the proof is a generalization to higher derivatives of our rigidity result 29 which states that for maps v 0 1 3 3 the l2 distance of v from a single rotation is bounded by a multiple of the l2 distance from the set so 3 of all rotations

analysis of pulled axisymmetric membranes with wrinkling the nonlinear behavior of an axisymmetric hyperelastic membrane subjected to pulling forces is analyzed the membrane is considered to be ideal in the sense that it cannot carry compressive stress resultants if the membrane has a positive initial gaussian curvature the pulling gives rise to wrinkles which form over parts of the surface the full nonlinear equations governing the membrane behavior in the doubly tense and in the wrinkled regions are formulated and then solved using a numerical integration procedure solutions for various examples are presented with hookean and neo hookean constitutive behavior these include a few examples of wrinkled membranes with positive initial gaussian curvatures and one example of a membrane with a negative initial gaussian curvature where no wrinkles are formed

new numerical method for two dimensional partially wrinkled membranes based on the introduction of a nonnegative adjustable parameter into poisson s ratio a new numerical method is proposed to solve numerically the partially wrinkled membrane problems with arbitrary complex shapes three fundamental issues in this new method are addressed first a nonnegative adjustable parameter is introduced into the constitutive law automatically representing unwrinkled taut and wrinkled states of a membrane second a parametric variational principle is developed for the new membrane model third by the variational principle the original membrane problem is converted to a nonlinear mathematical programming problem the variational principle and the mathematical programming formulation lay a foundation for efficient numerical analysis of wrinkled membrane structures using finite element discretization three typical examples are given to show the effectiveness of this method

asymmetric inclusion process we introduce and explore the asymmetric inclusion process asip an exactly solvable bosonic counterpart of the fermionic asymmetric exclusion process asep in both processes random events cause particles to propagate unidirectionally along a one dimensional lattice of n sites in the asep particles are subject to exclusion interactions whereas in the asip particles are subject to inclusion interactions that coalesce them into inseparable clusters we study the dynamics of the asip derive evolution equations for the mean and probability generating function pgf of the sites occupancy vector obtain explicit results for the above mean at steady state and describe an iterative scheme for the computation of the pgf at steady state we further obtain explicit results for the load distribution in steady state with the load being the total number of particles present in all lattice sites finally we address the problem of load optimization and solve it under various criteria the asip model establishes bridges between statistical physics and queueing theory as it represents a tandem array of queueing systems with unlimited batch service and a tandem array of growth collapse processes

instability investigation on fluid loaded pre stretched cylindrical membranes this paper discusses the evaluation of instabilities on the quasi static equilibrium path of fluid loaded pre stretched cylindrical membranes and the switching to a secondary branch at a bifurcation point the membrane is represented by only the in plane stress components for which an incompressible isotropic hyperelastic material model is assumed the free inflation problem yields governing equations and boundary conditions which are discretized by finite differences and solved by a newton raphson method an incremental arclength cubic extrapolation method is used to find generalized equilibrium paths with different parametrizations limit points and bifurcation points are observed on the equilibrium path when fluid level is seen as the controlling parameter an eigen mode injection method is employed to switch to a secondary equilibrium branch at the bifurcation point a limit point with respect to fluid level is observed for a partially filled membrane when the aspect ratio length radius is high whereas for smaller aspect ratios the limit point with respect to fluid level is observed at over filling pre stretch is observed to have a stiffening effect in the pre limit zone and a softening effect in the post limit zone

higher order weak linearizations of stochastically driven nonlinear oscillators we present derivative free weak and strong solutions of stochastically driven nonlinear oscillators of engineering interest using higher order forms of the locally transversal linearization ltl method unlike strong solutions weak stochastic solutions attempt to predict only mathematical expectations of functions of the true solution and are obtainable with much less computational effort the linearized equations corresponding to the higher order implicit ltl schemes are arrived at using backward euler maruyama and newmark expansions in order to conditionally replace nonlinear drift and multiplicative diffusion vector fields we also briefly describe alterations through which explicit forms of such higher order linearizations are obtained in the weak forms the gaussian stochastic integrals appearing in the linearized solutions are replaced by random variables with simpler and discrete probability distributions the resulting local approximations to the true solution are of significantly higher formal order of accuracy as reflected through local error estimates numerical illustrations are presently provided for the duffing and van der pol oscillators driven by additive and multiplicative noises which are indicative of the numerical accuracy computational speed and algorithmic simplicity

a hierarchical optical flow estimation algorithm based on the interlevel motion smoothness constraint abstract an optical flow estimation algorithm is proposed based on the multiresolution representation of the image i e the image pyramid since the image pyramid consists of several low pass filtered versions of the image sequence the motion vector at each pyramid level is also the low pass filtered versions of the motion vector at the finest level thus the interlevel motion smoothness constraint is introduced in the motion estimation by defining the operators to establish an appropriate relationship between two adjacent pyramid levels the employment of the image pyramid allows us to estimate the large flow vectors and to adopt easily the multigrid technique to improve the convergence speed of the proposed algorithm the simulation results reveal that the proposed algorithm provides more accurate motion estimation compared to the methods using the smoothness constraints such as horn and schunck s algorithm in addition the theoretical analysis of the convergence behavior of the proposed algorithm is also provided in this paper

asymmetric exclusion process and extremal statistics of random sequences a mapping is established between sequence alignment one of the most commonly used tools of computational biology at a certain choice of scoring parameters and the asymmetric exclusion process one of the few exactly solvable models of nonequilibrium physics the statistical significance of sequence alignments is characterized through studying the total hopping current of the discrete time and space version of the asymmetric exclusion process

finding a control parameter in one dimensional parabolic equations an inverse problem concerning diffusion equation with source control parameter is considered several finite difference schemes are presented for identifying the control parameter which produces at each time a desired temperature at a given point in a spatial domain these schemes are based on the second order 3 point forward time centred space ftcs explicit formula and the fourth order 5 point ftcs explicit scheme and the second order 3 point backward time centred space btcs implicit technique and the fourth order 3 3 crandall s implicit formula the 5 point ftcs scheme has a bounded range of stability but its fourth order accuracy is significant the 3 point btcs method uses less central processor cpu time than the 3 3 crandall s technique but it is only second order accurate the basis of analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach developed from the 1974 work of warming and hyett this allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference schemes the results of a numerical experiment are presented and accuracy and the cpu time needed for the parabolic inverse problem are discussed

equilibrium shapes of inflated inextensible membranes this paper proposes an effective method for directly determining the final equilibrium shapes of closed inextensible membranes subjected to internal pressures with reference to new high performance textile materials we assume that the mechanical response of a fabric membrane can be accurately represented by regarding it as a two state material in the active state the membrane is subject to tensile stresses and is virtually inextensible vice versa in the passive state it is unable to sustain any compressive stress so it contracts freely equilibrium of the membrane in the final configuration is enforced by recourse to the minimum total potential energy principle the lagrange multipliers method is used to solve the minimum problem by accounting for the aforesaid nonlinear constitutive law the set of governing equations is solved for the unknown coordinates of the equilibrium surface points closed form solutions are obtained for fully wrinkled cylindrical and axisymmetric membranes under homogeneous boundary conditions while a simple iterative procedure is used to numerically solve cases of axisymmetric membranes under various inhomogeneous boundary conditions the soundness of the proposed method is verified by comparing the results with solutions available in the literature

a pseudo dynamical systems approach to a class of inverse problems in engineering a pseudo dynamical approach for a class of inverse problems involving static measurements is proposed and explored following linearization of the minimizing functional associated with the underlying optimization problem the new strategy results in a system of linearized ordinary differential equations odes whose steady state solutions yield the desired reconstruction we consider some explicit and implicit schemes for integrating the odes and thus establish a deterministic reconstruction strategy without an explicit use of regularization a stochastic reconstruction strategy is then developed making use of an ensemble kalman filter wherein these odes serve as the measurement model finally we assess the numerical efficacy of the developed tools against a few linear and nonlinear inverse problems of engineering interest

remarks on a theory of elasticity for fluid films a theory of elastic fluid films that generalizes classical notions of capillarity is described for the purely mechanical problem restrictions on energy minimizing states are obtained these restrictions are in accord with the experimental findings of kwok et al 1994

modified backward differentiation methods of the adams type based on exponential interpolation abstract for the numerical solution of first order differential equations multistep methods of the adams type are established which integrate exactly the functions exp kx x j j 0 1 n where k is a parameter these methods have stepsize dependent coefficients which also depend on k within each integration segment one can choose for k the value which minimizes in a certain sense the local truncation error in this way the new method leads to highly accurate results in comparison with the classical methods of the adams type especially when the solution of the differential equation shows an exponential behaviour numerical examples are provided to illustrate this

stochastic queueing theory approach to human dynamics recently numerous studies have shown that human dynamics cannot be described accurately by exponential laws for instance barabasi nature london 435 207 2005 demonstrates that waiting times of tasks to be performed by a human are more suitably modeled by power laws he presumes that these power laws are caused by a priority selection mechanism among the tasks priority models are well developed in queueing theory e g for telecommunication applications and this paper demonstrates the quasi immediate applicability of such a stochastic priority model to human dynamics by calculating generating functions and by studying them in their dominant singularity we prove that nonexponential tails result naturally contrary to popular belief however these are not necessarily triggered by the priority selection mechanism

normalization of temporal distance parameters in pediatric gait several techniques for the normalization of temporal distance parameters in pediatric gait are given the resulting normalized data can be used to compare or discriminate individuals or groups of individuals without the effect of variables such as age and height the normalization with respect to a reference data set or with respect to the data set itself can be accommodated three novel techniques for normalization of gait data have been given offset decorrelation and detrending for normalization of stride length with respect to height all three are superior to the commonly accepted technique of dividing by the height the offset technique has obscure units and will have a residual correlation the decorrelation technique also has obscure units but will have zero correlation provided it is being normalized using a linear model or piecewise linear model fitted to the data in a least squares sense the detrending technique will also result in a zero correlation if piecewise linear or polynomial models fitted to the data in a least squares sense are used the detrending technique is the most useful of the three techniques proposed as it will also generate the same units as the original data set and can be easily scaled so that its magnitude is also comparable with the original data both the decorrelation and detrending techniques can be used simultaneously to normalize data with respect to two or more variables

new finite difference formulas for numerical differentiation conventional numerical differentiation formulas based on interpolating polynomials operators and lozenge diagrams can be simplified to one of the finite difference approximations based on taylor series and closed form expressions of these finite difference formulas have already been presented in this paper we present new finite difference formulas which are more accurate than the available ones especially for the oscillating functions having frequency components near the nyquist frequency closed form expressions of the new formulas are given for arbitrary order a comparison of the previously available three types of approximations is given with the presented formulas a computer program written in mathematica based on new formulas is given in the appendix for numerical differentiation of a function at a specified mesh point

occupancy correlations in the asymmetric simple inclusion process the asymmetric simple inclusion process asip a lattice gas model for unidirectional transport with irreversible aggregation has been proposed as an inclusion counterpart of the asymmetric simple exclusion process and as a batch service counterpart of the tandem jackson network to date the analytical tractability of the model has been limited while the average particle density in the model is easy to compute very little is known about the joint occupancy distribution to partially bridge this gap we study occupancy correlations in the asip we take an analytical approach to this problem and derive an exact formula for the covariance matrix of the steady state occupancy vector we verify the validity of this formula numerically in small asip systems where monte carlo simulations can provide reliable estimates for correlations in reasonable time and further use it to draw a comprehensive picture of spatial occupancy correlations in asip systems of arbitrary size

new computational approaches for wrinkled and slack membranes the static response of thin wrinkled membranes is studied using both a tension field approximation based on plane stress conditions and a 3d nonlinear elasticity formulation discretized through 8 noded cosserat point elements while the tension field approach only obtains the wrinkled slack regions and at best a measure of the extent of wrinkliness the 3d elasticity solution provides in principle the deformed shape of a wrinkled slack membrane however since membranes barely resist compression the discretized and linearized system equations via both the approaches are ill conditioned and solutions could thus be sensitive to discretizations errors as well as other sources of noises imperfections we propose a regularized pseudo dynamical recursion scheme that provides a sequence of updates which are almost insensitive to the regularizing term as well as the time step size used for integrating the pseudo dynamical form this is borne out through several numerical examples wherein the relative performance of the proposed recursion scheme vis a vis a regularized newton strategy is compared the pseudo time marching strategy when implemented using 3d cosserat point elements also provides a computationally cheaper numerically accurate and simpler alternative to that using geometrically exact shell theories for computing large deformations of membranes in the presence of wrinkles

on a connection between symmetric polynomials generalized stirling numbers and the newton general divided difference interpolation polynomial this paper gives a connection between symmetric polynomials generalized stirling numbers and the newton general divided difference interpolation polynomial the generalized stirling numbers of the first and second kind denoted s n k a and s n k a respectively are given symbolically for the case n 5 as an illustrative example by using maple programming maple v r3 programming reference manual these numbers depend on n k and n distinct values a 1 a 2 a n the ordinary stirling numbers s n k and s n k may be obtained as special cases by taking a i i 1 i 1 1 n

the asymmetric simple exclusion process an integrable model for non equilibrium statistical mechanics the asymmetric simple exclusion process asep plays the role of a paradigm in non equilibrium statistical mechanics we review exact results for the asep obtained by the bethe ansatz and put emphasis on the algebraic properties of this model the bethe equations for the eigenvalues of the markov matrix of the asep are derived from the algebraic bethe ansatz using these equations we explain how to calculate the spectral gap of the model and how global spectral properties such as the existence of multiplets can be predicted an extension of the bethe ansatz leads to an analytic expression for the large deviation function of the current in the asep that satisfies the gallavotti cohen relation finally we describe some variants of the asep that are also solvable by the bethe ansatz

tensor based finite element formulation for geometrically nonlinear analysis of shell structures in the present study a finite element computational model for the nonlinear analysis of shell structures is presented a tensor based finite element formulation is presented to describe the mathematical model of a shell in a natural and simple way by using curvilinear coordinates in addition a family of high order elements with lagrangian interpolations is used to avoid membrane and shear locking and no mixed interpolations are employed a first order shell theory with seven parameters is derived with exact nonlinear deformations and under the framework of the lagrangian description this approach takes into account thickness stretching and therefore 3d constitutive equations are utilized numerical simulations and comparisons of the present results with those found in the literature for typical benchmark problems involving isotropic and laminated composites as well as functionally graded shells are found to be excellent and show the validity of the developed finite element model moreover the simplicity of this approach makes it attractive for applications in contact mechanics and damage propagation of shells

general explicit difference formulas for numerical differentiation through introducing the generalized vandermonde determinant the linear algebraic system of a kind of vandermonde equations is solved analytically by use of the basic properties of this determinant and then we present general explicit finite difference formulas with arbitrary order accuracy for approximating first and higher derivatives which are applicable to unequally or equally spaced data comparing with other finite difference formulas the new explicit difference formulas have some important advantages basic computer algorithms for the new formulas are given and numerical results show that the new explicit difference formulas are quite effective for estimating first and higher derivatives of equally and unequally spaced data

the modeling and numerical analysis of wrinkled membranes in this paper three fundamental issues regarding modeling and analysis of wrinkled membranes are addressed first a new membrane model with viable young s modulus and poisson s ratio is proposed which physically characterizes stress relaxation phenomena in membrane wrinkling and expresses taut wrinkled and slack states of a membrane in a systematic manner second a parametric variational principle is developed for the new membrane model third by the variational principle the original membrane problem is converted to a non linear complementarity problem in mathematical programming a parametric finite element discretization and a smoothing newton method are then used for numerical solution the proposed membrane model and numerical method are capable of delivering convergent results for membranes with a mixture of wrinkled and slack regions without iteration of membrane stresses three numerical examples are provided

on generalized averaged gaussian formulas we present a simple numerical method for constructing the optimal generalized averaged gaussian quadrature formulas which are the optimal stratified extensions of gauss quadrature formulas these extensions exist in many cases in which real positive kronrod formulas do not exist for the jacobi weight functions w x w x 1 x 1 x 1 we give a necessary and sufficient condition on the parameters a and such that the optimal averaged gaussian quadrature formulas are internal

zero range model of traffic flow a multicluster model of traffic flow is studied in which the motion of cars is described by a stochastic master equation assuming that the escape rate from a cluster depends only on the cluster size the dynamics of the model is directly mapped to the mathematically well studied zero range process knowledge of the asymptotic behavior of the transition rates for large clusters allows us to apply an established criterion for phase separation in one dimensional driven systems the distribution over cluster sizes in our zero range model is given by a one step master equation in one dimension it provides an approximate mean field dynamics which however leads to the exact stationary state based on this equation we have calculated the critical density at which phase separation takes place we have shown that within a certain range of densities above the critical value a metastable homogeneous state exists before coarsening sets in within this approach we have estimated the critical cluster size and the mean nucleation time for a condensate in a large system the metastablity in the zero range process is reflected in a metastable branch of the fundamental flux density diagram of traffic flow our work thus provides a possible analytical description of traffic jam formation as well as important insight into condensation in the zero range process

parallel techniques for a boundary value problem with non classic boundary conditions new parallel techniques are developed for obtaining approximate solutions to an initial boundary value problem for the three dimensional parabolic partial differential equation pde with non classic boundary conditions while sharing some common features with the one dimensional models the solution of three dimensional equations are substantially more difficult thus some considerations are taken to be able to extend some ideas of one dimensional case using a suitable transformation the solution of this problem is equivalent to the solution of two other problems the former which is a one dimensional non classic boundary value problem giving the value of m through using an unconditionally stable explicit scheme using this result the second problem will be changed to a classical three dimensional diffusion equation with neumann s boundary conditions which will be solved numerically by using the method of lines semi discretization approach the space derivatives in the pde are approximated by finite difference replacements the solution of the resulting system of first order linear ordinary differential equations satisfies a recurrence relation which involves a matrix exponential function the accuracy in time is controlled by choosing several subdiagonal pade approximants to replace this matrix exponential term numerical techniques are developed to compute the required solution using a splitting method leading to algorithms for sequential and parallel implementation the algorithms are tested on a model problem and the resulting numerical experiments are also presented the central processor unit times needed are also reported and are compared

limit laws for the asymmetric inclusion process the asymmetric inclusion process asip is a unidirectional lattice gas flow model which was recently introduced as an exactly solvable bosonic counterpart of the fermionic asymmetric exclusion process an iterative algorithm that allows the computation of the probability generating function pgf of the asip s steady state exists but practical considerations limit its applicability to small asip lattices large lattices on the other hand have been studied primarily via monte carlo simulations and were shown to display a wide spectrum of intriguing statistical phenomena in this paper we bypass the need for direct computation of the pgf and explore the asip s asymptotic statistical behavior we consider three different limiting regimes heavy traffic regime large system regime and balanced system regime in each of these regimes we obtain analytically and in closed form stochastic limit laws for five key asip observables traversal time overall load busy period first occupied site and draining time the results obtained yield a detailed limit laws perspective of the asip numerical simulations demonstrate the applicability of these laws as useful approximations

modified stieltjes polynomials and gauss kronrod quadrature rules modified stieltjes polynomials are defined and used to construct suboptimal extensions of gaussian rules with one or two degrees less of polynomial exactness than the corresponding kronrod extension we prove that for wide classes of weight functions and a sufficiently large number of nodes the extended quadratures have positive weights and simple nodes on the interval 1 1 the classes of weight functions considered complement those for which the gauss kronrod rule is known to exist also strong asymptotic representations on the whole interval 1 1 are given for the modified stieltjes polynomials which prove that they behave asymptotically as orthogonal polynomials finally we provide some numerical examples

occupation probabilities and fluctuations in the asymmetric simple inclusion process the asymmetric simple inclusion process asip a lattice gas model of unidirectional transport and aggregation was recently proposed as an inclusion counterpart of the asymmetric simple exclusion process in this paper we present an exact closed form expression for the probability that a given number of particles occupies a given set of consecutive lattice sites our results are expressed in terms of the entries of catalan s trapezoids number arrays which generalize catalan s numbers and catalan s triangle we further prove that the asip is asymptotically governed by the following i an inverse square root law of occupation ii a square root law of fluctuation and iii a rayleigh law for the distribution of interexit times the universality of these results is discussed

exact dynamical state of the exclusive queueing process with deterministic hopping the exclusive queueing process eqp has recently been introduced as a model for the dynamics of queues that takes into account the spatial structure of the queue it can be interpreted as a totally asymmetric exclusion process of varying length here we investigate the case of deterministic bulk hopping p 1 that turns out to be one of the rare cases where exact nontrivial results for the dynamical properties can be obtained using a time dependent matrix product form we calculate several dynamical properties e g the density profile of the system

a historical note on gauss kronrod quadrature the idea of gauss kronrod quadrature in a germinal form is traced back to an 1894 paper of r skutsch

determination of hourglass coefficients in the theory of a cosserat point for nonlinear elastic beams abstract the theory of a cosserat point has recently been used int j solids struct 38 2001 4395 to formulate the numerical solution of problems of nonlinear elastic beams in that theory the constitutive equations for inhomogeneous elastic deformations included undetermined constants associated with hourglass modes which can occur due to nonuniform cross sectional extension and nonuniform torsion the objective of this paper is to determine these hourglass coefficients by matching exact solutions of pure bending and pure torsion applied in different directions on each of the surfaces of the element it is shown that the resulting constitutive equations in the cosserat theory do not exhibit unphysical stiffness increases due to thinness of the beam mesh refinement or incompressibility that are present in the associated bubnov galerkin formulation also example problems of a bar hanging under its own weight and a bar attached to a spinning rigid hub are analyzed

taylor series based finite difference approximations of higher degree derivatives a new type of taylor series based finite difference approximations of higher degree derivatives of a function are presented in closed forms with their coefficients given by explicit formulas for arbitrary orders characteristics and accuracies of presented approximations and already presented central difference higher degree approximations are investigated by performing example numerical differentiations it is shown that the presented approximations are more accurate than the central difference approximations especially for odd degrees however for even degrees central difference approximations become attractive as the coefficients of the presented approximations of even degrees do not correspond to equispaced input samples

numerical solution of one dimensional parabolic inverse problem this paper is concerned with numerical techniques for the solution of a one dimensional parabolic inverse problem with a control parameter the discrete approximation of the problem is based on the finite difference schemes these techniques are presented for identifying the control parameter which produces at each time a desired temperature at a given point in a spatial domain the main idea behind the finite difference methods for obtaining the solution of a given partial differential equation is to approximate the derivatives appearing in the equation by a set of values of the function at a selected number of points the most usual way to generate these approximations is through the use of taylor series the methods developed here are based on the modified equivalent partial differential equation as described by warming and hyett j comput phys 14 2 1974 159 this approach allows the simple determination of the theoretical order of accuracy thus allowing methods to be compared with one another also from the truncation error of the modified equivalent equation it is possible to eliminate the dominant error terms associated with the finite difference equations that contain free parameters weights thus leading to more accurate methods the results of a numerical experiment are presented and accuracy and the central processor cpu time needed for the parabolic inverse problem are discussed

nineteen dubious ways to compute the exponential of a matrix twenty five years later in principle the exponential of a matrix could be computed in many ways methods involving approximation theory differential equations the matrix eigenvalues and the matrix characteristic polyn

chaotic motion of a parametrically forced simple pendulum abstract this paper describes the behavior of a simple pendulum with support in a steady and rather slow circular motion in a vertical plane the governing equation of this model is nonlinear and its motion is about the direction of gravity in the equation of motion there are three parameters which are related to the radius and angular velocity of the circular motion the length of the pendulum and the damping constant for some combinations of these parameters this model is found to have chaotic motion by numerical integration this paper not only draws the time series and poincare map to show the characteristics of regular and chaotic motions but also explores the feasibility of using the amplitude probability distribution by numerical method to diagnose whether the motion is chaotic the effect of geometry and damping constant on the motion of the system is investigated furthermore whether the poincare map and amplitude probability distribution depend sensitively on the initial conditions is also studied

nonequilibrium steady states of matrix product form a solver s guide we consider the general problem of determining the steady state of stochastic nonequilibrium systems such as those that have been used to model among other things biological transport and traffic flow we begin with a broad overview of this class of driven diffusive systems which includes exclusion processes focusing on interesting physical properties such as shocks and phase transitions we then turn our attention specifically to those models for which the exact distribution of microstates in the steady state can be expressed in a matrix product form in addition to a gentle introduction to this matrix product approach how it works and how it relates to similar constructions that arise in other physical contexts we present a unified pedagogical account of the various means by which the statistical mechanical calculations of macroscopic physical quantities are actually performed we also review a number of more advanced topics including nonequilibrium free energy functionals the classification of exclusion processes involving multiple particle species existence proofs of a matrix product state for a given model and more complicated variants of the matrix product state that allow various types of parallel dynamics to be handled we conclude with a brief discussion of open problems for future research

inflation of nonlinearly deformed annular elastic membranes abstract the inflation of an isotropic nonlinear elastic membrane by means of a volume independent hydrostatic pressure is studied in particular we consider annular membranes which on the inner boundary have been subjected to an axial twist and a displacement normal to the plane of the membrane with the outer boundary fixed a direct two dimensional approach is adopted and by introducing a relaxed strain energy function the occurrence of wrinkled solutions is considered the governing equations are found to reduce to a system of first order differential equations which are then solved numerically for a mooney rivlin material over a range of boundary value problems

anisotropic membrane wrinkling theory and analysis abstract a complete theory of wrinkling of anisotropic elastic membranes is presented based on the notion of relaxed energy function the theory is obtained as a particular case of a general theory of saturated elasticity it is shown that when any given hyperelastic constitutive law is supplemented with a saturation condition the right cauchy green strain tensor abides by an additive decomposition law governed by a normality rule for the case of wrinkling these results are implemented into a numerical procedure and examples are presented

a novel variational algorithmic formulation for wrinkling at finite strains based on energy minimization application to mesh adaption this paper is concerned with an efficient novel algorithmic formulation for wrinkling at finite strains in contrast to previously published numerical implementations the advocated method is fully variational more precisely the parameters describing wrinkles or slacks together with the unknown deformation mapping are computed jointly by minimizing the potential energy of the considered mechanical system furthermore the wrinkling criteria are naturally included within the presented variational framework the proposed method allows to employ three dimensional constitutive models without any additional modification i e a projection in plane stress space is not required analogously to the wrinkling parameters the non vanishing out of plane component of the strain tensor results conveniently from relaxing the respective helmholtz energy of the membrane the proposed framework is very general and does not rely on any assumption regarding the symmetry of the material i e arbitrary anisotropic hyperelastic models can be consistently taken into account the advantages associated with such a variational method are manifold for instance it opens up the possibility of applying standard optimization algorithms to the numerical implementation this is especially important for highly non linear or singular problems such as wrinkling on the other hand minimization principles provide a suitable basis for a posteriori error estimation and thus for adaptive finite element formulations as a prototype a variational error indicator leading to an efficient h adaption for wrinkling is briefly discussed the performance of the wrinkling approach is demonstrated by selected finite element analyses

efficient sub grid scale modeling of membrane wrinkling by a projection method abstract considering wrinkling as an analogue to perfect plasticity this study employs the projection method from inelasticity model to take into account wrinkling of thin membranes along the additive strain decomposition the total strains within the wrinkled membranes are divided into an elastic part and a wrinkling part the projection method removes the wrinkling strain part which has zero strain energy from the total strains as a consequence the outcome is a modified constitutive tensor which represents only energy of the elastic strain part due to its simplicity this method is advantageous for implementation and combines a good rate of convergence and low computational costs within this work the incremental constitutive equation is derived in a general form which is applicable both for isotropic and orthotropic materials the potential of the proposed wrinkling model is verified via various numerical analyses of wrinkled membranes furthermore the model is attractive to be implemented into commercial finite element programs

on the computational complexity of the empirical mode decomposition algorithm abstract it has been claimed that the empirical mode decomposition emd and its improved version the ensemble emd eemd are computation intensive in this study we will prove that the time complexity of the emd eemd which has never been analyzed before is actually equivalent to that of the fourier transform numerical examples are presented to verify that emd eemd is in fact a computationally efficient method

incremental stresses in loaded orthotropic circular membrane tubes i theory abstract starting from the equations of general elastic nonlinear membrane theory in intrinsic form the equations governing the incremental state of stress in an orthotropic circular membrane tube are derived and discussed the tube is initially subjected to uniform internal pressure and to longitudinal extension which lead to large homogeneous deformation then some changes in loading and or geometry are considered e g an additional load is applied the shape of the boundary is changed or a slit is formed in the membrane these changes are regarded as small perturbations on the initial homogeneous state of stress the general form as well as some simplified forms of the equations are presented leading finally to a set of two equations in terms of two scalar potential functions two different variational formulations for the problem are also presented each of which may serve as a basis for numerical treatment

a variational formulation for finite deformation wrinkling analysis of inelastic membranes this paper is concerned with a novel fully variational formulation for finite deformation analysis of inelastic membranes with wrinkling in contrast to conventional approaches every aspect of the physical problem derives from minimization of suitable energy functionals a variational formulation of finite strain plasticity theory which leads to a minimization problem for the constitutive updates serves as the starting point for the derivations in order to take into account the kinematics induced by wrinkles and slacks a relaxed version of the finite strain functional is postulated in effect the local incremental stress strain relations are established via differentiation of the relaxed energy functional with respect to the strains hence the presented formulation is fully analogous to that of hyperelasticity with the sole exception that the aforementioned functional depends on history variables and accordingly it is path dependent the advantages associated with the developed variational method are manifold from a practical point of view the possibility of applying standard optimization algorithms to solve the minimization problem describing inelastic membranes is remunerative from a mathematical point of view on the other hand the energy of the system induces some sort of natural metric representing an essential requirement for error estimation and thus for adaptive finite element methods the presented derivation of the model allows to consider possible material symmetries in the elastic as well as plastic response of the material as a prototype a von mises type model is implemented the efficiency and performance of the resulting algorithm are demonstrated by means of numerical examples

analytic study of clustering in shaken granular material using zero range processes abstract we show that models used to describe granular clustering due to vertical shaking belong to the class of zero range processes this correspondence allows us to derive analytically in the large particle number limit in a very easy and straightforward manner a number of properties of the models like particle distribution functions phase diagram and characteristic time of clusterization

elastic surface substrate interactions a theory for three dimensional finite deformations of elastic solids with conforming elastic films attached to their bounding surfaces is described the gurtin murdoch theory incorporating elastic resistance of the film to strain is generalized to account for the effects of intrinsic flexural resistance this modification yields a model that can be used to describe equilibrium deformations in the presence of compressive surface stress fields an associated variational theory is given and material symmetry considerations are discussed the theory is illustrated by examples

an exact solution of a one dimensional asymmetric exclusion model with open boundaries a simple asymmetric exclusion model with open boundaries is solved exactly in one dimension the exact solution is obtained by deriving a recursion relation for the steady state if the steady state is known for all system sizes less thann then our equation 8 gives the steady state for sizen using this recursion we obtain closed expressions 48 for the average occupations of all sites the results are compared to the predictions of a mean field theory in particular for infinitely large systems the effect of the boundary decays as the distance to the power 1 2 instead of the inverse of the distance as predicted by the mean field theory

self regularized pseudo time marching schemes for structural system identification with static measurements we explore the application of pseudo time marching schemes involving either deterministic integration or stochastic filtering to solve the inverse problem of parameter identification of large dimensional structural systems from partial and noisy measurements of strictly static response solutions of such non linear inverse problems could provide useful local stiffness variations and do not have to confront modeling uncertainties in damping an important yet inadequately understood aspect in dynamic system identification problems the usual method of least square solution is through a regularized gauss newton method gnm whose results are known to be sensitively dependent on the regularization parameter and data noise intensity finite time recursive integration of the pseudo dynamical gnm pd gnm update equation addresses the major numerical difficulty associated with the near zero singular values of the linearized operator and gives results that are not sensitive to the time step of integration therefore we also propose a pseudo dynamic stochastic filtering approach for the same problem using a parsimonious representation of states and specifically solve the linearized filtering equations through a pseudo dynamic ensemble kalman filter pd enkf for multiple sets of measurements involving various load cases we expedite the speed of thepd enkf by proposing an inner iteration within every time step results using the pseudo dynamic strategy obtained through pd enkf and recursive integration are compared with those from the conventional gnm which prove that the pd enkf is the best performer showing little sensitivity to process noise covariance and yielding reconstructions with less artifacts even when the ensemble size is small

time needed to board an airplane a power law and the structure behind it a simple model for the boarding of an airplane is studied passengers have reserved seats but enter the airplane in arbitrary order queues are formed along the aisle as some passengers have to wait to reach the seats for which they have reservation we label a passenger by the number of his or her reserved seat in most cases the boarding process is much slower than for the optimal situation where passenger and seat orders are identical we study this dynamical system by calculating the average boarding time when all permutations of n passengers are given equal weight to first order the boarding time for a given permutation ordering of the passengers is given by the number s of sequences of monotonically increasing values in the permutation we show that the distribution of s is symmetric on 1 n which leads to an average boarding time n 1 2 we have found an exact expression for s and have shown that the full distribution of s approaches a normal distribution as n increases however there are significant corrections to the first order results due to certain correlations between passenger ordering and the substrate seat ordering this occurs for some cases in which the sequence of the seats is partially mirrored in the passenger ordering these cases with correlations have a boarding time that is lower than predicted by the first order results the large number of cases with reduced boarding times have been classified we also give some indicative results on the geometry of the correlations with sorting into geometry groups with increasing n both the number of correlation types and the number of cases belonging to each type increase rapidly using enumeration we find that as a result of these correlations the average boarding time behaves like n with 0 69 as compared with 1 0 for the first order approximation

finite element analysis of dynamic response of wrinkling membranes a new iterative scheme for finite element analysis of wrinkling membranes originally devised for static analysis is extended for analyzing dynamic response of wrinkling membranes the scheme is found to be successfully implemented with an explicit total lagrangian finite element code based upon the central difference method the finite element implementation of the scheme is straightforward and only minor modifications are needed for existing membrane finite element codes in light of application for contact impact discussed are a couple of existing contact algorithms which are well suited for treating contact impact of wrinkling membranes with rigid bodies the validity of the scheme is demonstrated via a numerical simulation of an inflating automotive airbag made of orthotropic membranes under impulse pressure loading

differential equation for the amplitude of wrinkles introduction t he renewed interest in the phenomenonof wrinkling of membranes fueled by applications to the aerospace industry has spurred considerable activity on both the theoretical and computational aspectsof the subject althoughthe wrinklingphenomenonis known to be a case of shell buckling it seems unwise to utilize this knowledge in actual computations because treating the membrane as a shell with a vanishinglysmall thickness leads to the frustrating effects of numerical instability there exist on the other hand techniques based on themembrane theory alone that permit us to obtain with relative ease and numerical robustness not only the extent of thewrinkledzones but also the eldof directionsof thewrinkles 1i4 all that is needed therefore is a means for calculating the amplitude and wavelength of the wrinkles in an already known wrinkled domain in this note we derive an ordinary differential equation whose solution delivers such information for clarity of the presentation the equation is obtained under a number of simplifying assumptions mostly involving the smallness of the deformations however the method is straightforwardlyextendable to the general case our guiding principle has been to keep only those aspects of the model that are clearly determinant of the result while leaving all other aspects for future re nement we believe that this philosophy will serve to highlight the essential features rather than the technicalities of the proposedequation note that even under a geometrically andmaterially linear regime the resultingdifferentialequation is highly nonlinear the physical reason for this nonlinearityis to be foundin that becausewrinklingentailsno stress in thedirectionperpendicular to the wrinkles there exists a severe constraint between the wavelength and amplitude of the wrinkles this can be phrased intuitively as follows for a given amount of wrinkling strain the larger the number of wrinkles the smaller their amplitude to the best of our knowledge the only attempt in a direction similar to the one proposed herein is due to wong and pellegrino in their work these authors present a model basedmainly on the particular case of shearing of a rectangular panel their results are very valuable and will be used here as a benchmark for validation purposes

totally asymmetric exclusion process with extended objects a model for protein synthesis the process of protein synthesis in biological systems resembles a one dimensional driven lattice gas in which the particles have spatial extent covering more than one lattice site we expand the well studied totally asymmetric exclusion process in which particles typically cover a single lattice site to include cases with extended objects exact solutions can be determined for a uniform closed system we analyze the uniform open system through two approaches first a continuum limit produces a modified diffusion equation for particle density profiles second an extremal principle based on domain wall theory accurately predicts the phase diagram and currents in each phase finally we briefly consider approximate approaches to a nonuniform open system with quenched disorder in the particle hopping rates and compare these approaches with monte carlo simulations

analyses of wrinkled and slack membranes through an error reproducing mesh free method a mesh free approximation of large deformations of flexible membrane structures within the tension field theory is considered in this paper a modification of the wrinkling theory originally proposed by roddeman et al 1987 roddeman d g drukker j oomens c w j janssen j d 1987 the wrinkling of thin membranes part i theory part ii numerical analysis asme j appl mech 54 884 892 is proposed to study the behaviour of an isotropic membrane under the mixed state of stress taut wrinkled and slack using the facts that the state of stress is not uniform across an element and that the deformation gradient is a spatially continuous and possibly non differentiable tensor the proposed model uses a continuously modified deformation gradient to capture the location and orientation of wrinkles more precisely while the deformation gradient need not be everywhere differentiable in a wrinkled membrane it is argued that the fictive non wrinkled non slack surface may be looked upon as an everywhere taut surface in the limit as the minor and major principal tensile stresses over the wrinkled slack portions go to zero accordingly the modified deformation gradient is thought of as the limit of a sequence of everywhere differentiable tensors the weighted residual from the governing equations are presently solved via a mesh free method where the entire domain is discretized only by a set of grid points a non uniform rational b spline nurbs based error reproducing kernel method erkm has been used to approximate the field variable over the domain the first step in the method is to approximate a function and its derivatives through nurbs basis functions however since nurbs functions neither reproduce any polynomial nor interpolate the grid points also referred to as control or nodal points the approximated functions result in uncontrolled errors over the domain including the grid points accordingly the error functions in the nurbs approximation and its derivatives are reproduced via a family of non nurbs basis functions the non nurbs basis functions are constructed using a polynomial reproduction condition and added to the nurbs approximation of the function obtained in the first step several numerical examples on wrinkled and or slack membranes are also provided

three dimensional analysis of wrinkled membranes using modification scheme of stress strain tensor three dimensional finite element analysis using conventional membrane elements tends to be numerically unstable because of their lack of bending stiffness additionally membrane structures are highly susceptible to localized buckling posing further numerical difficulties in this paper a modified stress strain tensor recently proposed by the authors to account for membrane wrinkling is applied to three dimensional finite element analysis of membrane structures with the aim to overcome the preceding numerical difficulties it is found through numerical investigations that the use of the modified stress strain tensor renders the iterative solution process remarkably stable and enables one to obtain the converged solution for those problems that are difficult to solve using conventional membrane elements

applications of little s law to stochastic models of gene expression the intrinsic stochasticity of gene expression can lead to large variations in protein levels across a population of cells to explain this variability different sources of messenger rna mrna fluctuations poisson and telegraph processes have been proposed in stochastic models of gene expression both poisson and telegraph scenario models explain experimental observations of noise in protein levels in terms of bursts of protein expression correspondingly there is considerable interest in establishing relations between burst and steady state protein distributions for general stochastic models of gene expression in this work we address this issue by considering a mapping between stochastic models of gene expression and problems of interest in queueing theory by applying a general theorem from queueing theory little s law we derive exact relations which connect burst and steady state distribution means for models with arbitrary waiting time distributions for arrival and degradation of mrnas and proteins the derived relations have implications for approaches to quantify the degree of transcriptional bursting and hence to discriminate between different sources of intrinsic noise in gene expression to illustrate this we consider a model for regulation of protein expression bursts by small rnas for a broad range of parameters we derive analytical expressions validated by stochastic simulations for the mean protein levels as the levels of regulatory small rnas are varied the results obtained show that the degree of transcriptional bursting can in principle be determined from changes in mean steady state protein levels for general stochastic models of gene expression

identifying a control function in two dimensional parabolic inverse problems numerical solution of the parabolic partial differential equations with an unknown parameter play a very important role in engineering applications this study presents numerical schemes for solving two two dimensional parabolic inverse problems i e for the determination of some unknown functions in the parabolic partial differential equations these schemes are developed for determining the parameter p t which satisfy u t u x x u y y p t email protected in rx 0 t u x y 0 f x y x y r 0 1 2 it is assumed that u is known on the boundary of r and subject to the integral overspecification over a portion of the spatial domain 0 email protected 0 1u x y t dxdy e t 0

tension field theory a general theory of the tension field is developed for application to the analysis of wrinkling in isotropic elastic membranes undergoing finite deformations the principal contribution is a partial differential equation describing a geometrical property of tension trajectories this is one of a system of two equations which describes the state of stress independently of the deformation this system is strongly elliptic at any stable solution whereas the deformation is described by a system of parabolic type controllable solutions i e those states that can be maintained in any isotropic elastic material by application of edge tractions and lateral pressure alone are obtained the general axisymmetric problem is solved implicitly and the theory is applied to the solution of two representative examples existing small strain theories are shown to correspond to a singular limit of the general theory at which the underlying system changes from elliptic to parabolic type

phase space linearization for non linear oscillators deterministic and stochastic systems abstract a new and efficient semi analytical phase space linearization psl scheme for a class of non linear oscillators is developed in this paper the method is based on replacement of the non linear vector field by a set of linear ones each valid over a short segment of the evolving trajectory or over sufficiently small interval of time based on this concept a few explicit and implicit integration schemes are first proposed and applied to a class of low dimensional non linear dynamical systems to accurately determine their response trajectories this approach of local linearization is further extended to non linear oscillators excited by formal derivatives of one or a combination of gauss markov processes since the present methodology reduces the non linear operator by a set of linear operators it is also demonstrated that the principles of linear random vibration may be suitable exploited to arrive at a faster and semi analytical monte carlo scheme for computing the response statistics both in stationary and non stationary regimes limited examples are presented and compared with exact solutions whenever available to illustrate the efficiency and versatility of the proposed schemes

an analytical and numerical method for solving linear and nonlinear vibration problems a direct analytical and numerical method independent of the existing classical methods for solving linear and nonlinear vibration problems is given with the introduction of a piecewise constant argument nt n a new numerical method which produces sufficiently accurate results with good convergence is introduced development of the formulae for numerical calculations is based on the original governing differential equations

michaelis menten reaction scheme as a unified approach towards the optimal restart problem we study the effect of restart and retry on the mean completion time of a generic process the need to do so arises in various branches of the sciences and we show that it can naturally be addressed by taking advantage of the classical reaction scheme of michaelis and menten stopping a process in its midst only to start it all over again may prolong leave unchanged or even shorten the time taken for its completion here we are interested in the optimal restart problem i e in finding a restart rate which brings the mean completion time of a process to a minimum we derive the governing equation for this problem and show that it is exactly solvable in cases of particular interest we then continue to discover regimes at which solutions to the problem take on universal details independent forms which further give rise to optimal scaling laws the formalism we develop and the results obtained can be utilized when optimizing stochastic search processes and randomized computer algorithms an immediate connection with kinetic proofreading is also noted and discussed

bridging genetic networks and queueing theory one of the main challenges facing biology today is the understanding of the joint action of genes proteins and rna molecules interwoven in intricate interdependencies commonly known as genetic networks to this end several mathematical approaches have been introduced to date in addition to developing the analytical tools required for this task anew one can utilize knowledge found in existing disciplines specializing in the representation and analysis of systems featuring similar aspects we suggest queueing theory as a possible source of such knowledge this discipline which focuses on the study of workloads forming in a variety of scenarios offers an assortment of tools allowing for the derivation of the statistical properties of the inspected systems we argue that a proper adaptation of modeling techniques and analytical methods used in queueing theory can contribute to the study of genetic regulatory networks this is demonstrated by presenting a queueing inspired model of a genetic network of arbitrary size and structure for which the probability distribution function is derived this model is further applied to the description of the lac operon regulation mechanism in addition we discuss the possible benefits stemming for queueing theory from the interdisciplinary dialogue with molecular biology in particular the incorporation of various dynamical behaviours into queueing networks

traffic of molecular motors through tube like compartments the traffic of molecular motors through open tube like compartments is studied using lattice models these models exhibit boundary induced phase transitions related to those of the asymmetric simple exclusion process asep in one dimension the location of the transition lines depends on the boundary conditions at the two ends of the tubes three types of boundary conditions are studied a periodic boundary conditions which correspond to a closed torus like tube b fixed motor densities at the two tube ends where radial equilibrium holds locally and c diffusive motor injection at one end and diffusive motor extraction at the other end in addition to the phase diagrams we also determine the profiles for the bound and unbound motor densities using mean field approximations and monte carlo simulations our theoretical predictions are accessible to experiments

a new computational framework for materials with different mechanical responses in tension and compression and its applications abstract materials possessing tension compression asymmetric behavior can be simulated by a bi modulus constitutive relation which assumes the materials have different moduli in tension and compression traditional iteration methods struggle for the convergence difficulty for such kind of constitutive model in this paper a new computational framework is established solution procedures under both small and finite deformations which have asymptotically quadratic rate of convergence have also been proposed and implemented in abaqus with umat numerical examples show that the proposed computational framework can be applied successfully to simulate the wrinkling analysis of thin plane membranes and explain some unusual cell mechanosensing phenomena