exact solution of a 1d asymmetric exclusion model using a matrix formulation several recent works have shown that the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions can be solved exactly in the case of open boundaries here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices with this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules they obtain several explicit forms for these non commuting matrices which are in the general case infinite dimensional their approach allows exact expressions to be derived for the current and density profiles finally they discuss briefly two possible generalizations of their results the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles

understanding the edge effect in tasep with mean field theoretic approaches we study a totally asymmetric simple exclusion process tasep with one defect site hopping rate q 1 near the system boundary regarding our system as a pair of uniform tasep s coupled through the defect we study various methods to match a finite tasep and an infinite one across a common boundary several approximation schemes are investigated utilizing the finite segment mean field fsmf method we set up a framework for computing the steady state current j as a function of the entry rate and q for the case where the defect is located at the entry site we obtain an analytical expression for j q which is in good agreement with monte carlo simulation results when the defect is located deeper in the bulk we refined the scheme of macdonald et al 1968 biopolymers 6 1 and find reasonably good fits to the density profiles before the defect site we discuss the strengths and limitations of each method as well as possible avenues for further studies

phase transitions in an exactly soluble one dimensional exclusion process we consider an exclusion process with particles injected with rate at the origin and removed with rate at the right boundary of a one dimensional chain of sites the particles are allowed to hop onto unoccupied sites to the right only for the special case of 1 the model was solved previously by derridaet al here we extend the solution to general the phase diagram obtained from our exact solution differs from the one predicted by the mean field approximation

asymmetric simple exclusion model with local inhomogeneity we study a totally asymmetric simple exclusion model with open boundary conditions and a local inhomogeneity in the bulk it consists of a one dimensional lattice with particles hopping stochastically with equal rates to the right at all lattice sites except one where the jump rate is different approximate stationary state solutions and phase diagrams are obtained and compared with monte carlo simulation results

totally asymmetric exclusion processes with particles of arbitrary size the steady state currents and densities of a one dimensional totally asymmetric exclusion process tasep with particles that occlude an integer number d of lattice sites are computed using various mean field approximations and monte carlo simulations taseps featuring particles of arbitrary size are relevant for modelling systems such as mrna translation vesicle locomotion along microtubules and protein sliding along dna we conjecture that the nonequilibrium steady state properties separate into low density high density and maximal current phases similar to those of the standard d 1 tasep a simple mean field approximation for steady state particle currents and densities is found to be inaccurate however we find local equilibrium particle distributions derived from a discrete tonks gas partition function yield apparently exact currents within the maximal current phase for the boundary limited phases the equilibrium tonks gas distribution cannot be used to predict currents phase boundaries or the order of the phase transitions however we employ a refined mean field approach to find apparently exact expressions for the steady state currents boundary densities and phase diagrams of the d 1 tasep extensive monte carlo simulations are performed to support our analytic mean field results

a time aggregation approach to markov decision processes we propose a time aggregation approach for the solution of infinite horizon average cost markov decision processes via policy iteration in this approach policy update is only carried out when the process visits a subset of the state space as in state aggregation this approach leads to a reduced state space which may lead to a substantial reduction in computational and storage requirements especially for problems with certain structural properties however in contrast to state aggregation which generally results in an approximate model due to the loss of markov property time aggregation suffers no loss of accuracy because the markov property is preserved single sample path based estimation algorithms are developed that allow the time aggregation approach to be implemented on line for practical systems some numerical and simulation examples are presented to illustrate the ideas and potential computational savings

exact steady states of disordered hopping particle models with parallel and ordered sequential dynamics a one dimensional driven lattice gas with disorder in the particle hopping probabilities is considered it has previously been shown that in the version of the model with random sequential updating a phase transition occurs from a low density inhomogeneous phase to a high density congested phase here the steady states for both parallel fully synchronous updating and ordered sequential updating are solved exactly the phase transition is shown to persist in both cases with the critical densities being higher than that for random sequential dynamics the steady state velocities are related to the fugacity of a bose system suggesting a principle of minimization of velocity a generalization of the dynamics to the case where the hopping probabilities depend on the number of empty sites in front of the particles is also solved exactly in the case of parallel updating the models have natural interpretations as simplistic descriptions of traffic flow the relation to more sophisticated traffic flow models is discussed

dynamic dispersion curves for non homogeneous anisotropic beams with cross sections of arbitrary geometry abstract to accurately predict the dynamic behaviour of spanwise uniform non homogeneous anisotrophic beams with arbitrary cross sectional geometry is an important part of engineering analysis classical one dimensional beam theory fails in this endeavour and development of more sophisticated one dimensional theories is an important task a basis for development of improved one dimensional theory is the dispersion curve analysis a means to find the dispersion curves is discussed in this paper the code is developed to calculate the dispersion curves as well as corresponding mode shapes the code is based on finite element discretization over the cross sectional domain use of this code provides benchmark results for the testing of any existing one dimensional theory as well as facilitating the construction of new one dimensional theories dispersion information can also be useful in non destructive evaluation as an example of a case where non classical effects are particularly important results obtained from this code for an i beam are presented qualitative comparisons with the well known case of isotropic rectangular beam is provided features that are common for all beams are emphasized along with pointing out qualitative differences that exist for beams other than rectangular or circular

an asymptotically correct model for initially curved and twisted thin walled composite beams abstract the variational asymptotic method has been applied to develop an asymptotically correct model for initially curved and twisted thin walled composite beams of arbitrary cross sectional shapes and arbitrary anisotropic materials in a two step asymptotic reduction procedure the three dimensional strain energy is asymptotically reduced first to a two dimensional shell strain energy and then to a one dimensional beam strain energy this is a new attempt where initially curved and twisted thin walled composite beams with open or closed sections have been modeled in an asymptotically correct unified framework

exact results for the asymmetric simple exclusion process with a blockage we present new results for the current as a function of transmission rate in the one dimensional totally asymmetric simple exclusion process tasep with a blockage that lowers the jump rate at one site from one tor 1 exact finitevolume results serve to bound the allowed values for the current in the infinite system this proves the existence of a nonequilibrium phase transition corresponding to an immiscibility gap in the allowed values of the asymptotic densities which the infinite system can have in a stationary state a series expansion inr derived from the finite systems is proven to be asymptotic for all sufficiently large systems pade approximants based on this series which make specific assumptions about the nature of the singularity atr 1 match numerical data for the infinite system to 1 part in 104

totally asymmetric simple exclusion process with a shortcut in this paper we study the interplay of a totally asymmetric simple exclusion process tasep with a shortcut in its bulk under open boundary conditions two different models are introduced i model a for molecular motor motion and ii model b for vehicular traffic the phase diagrams and density profiles of both models are studied it is found that although the phase diagrams of both models can be classified into three regions the phases corresponding to these regions and the phase boundaries between these regions are quite different in these two models moreover the approximate stationary state solutions of model a have been carried out and it is shown that the analytical results are in good agreement with the results of monte carlo simulations

the control of a two level markov decision process by time aggregation the solution of markov decision processes mdps often relies on special properties of the processes for two level mdps the difference in the rates of state changes of the upper and lower levels has led to limiting or approximate solutions of such problems in this paper we solve a two level mdp without making any assumption on the rates of state changes of the two levels we first show that such a two level mdp is a non standard one where the optimal actions of different states can be related to each other then we give assumptions conditions under which such a specially constrained mdp can be solved by policy iteration we further show that the computational effort can be reduced by decomposing the mdp a two level mdp with m upper level states can be decomposed into one mdp for the upper level and m to m m 1 mdps for the lower level depending on the structure of the two level mdp the upper level mdp is solved by time aggregation a technique introduced in a recent paper cao x r ren z y bhatnagar s fu m marcus s 2002 a time aggregation approach to markov decision processes automatica 38 6 929 943 and the lower level mdps are solved by embedded markov chains

local inhomogeneity in asymmetric simple exclusion processes with extended objects totally asymmetric simple exclusion processes tasep with particles which occupy more than one lattice site and with a local inhomogeneity far away from the boundaries are investigated these non equilibrium processes are relevant for the understanding of many biological and chemical phenomena the steady state phase diagrams currents and bulk densities are calculated using a simple approximate theory and extensive monte carlo computer simulations it is found that the phase diagram for tasep with a local inhomogeneity is qualitatively similar to homogeneous models although the phase boundaries are significantly shifted the complex dynamics is discussed in terms of domain wall theory for driven lattice systems

best strip beam properties derivable from classical lamination theory this paper presents a simple method to extract classical beam properties for composite strips with general anisotropy from an asymptotically correct classical lamination theory derived using the variational asymptotic method none of the ad hoc approximations common in the literature of beam theory are used rather this approach discovers the necessary and su cient engineering assumptions for obtaining the correct cross sectional constants and stress recovery relations for a strip numerical examples are provided to illustrate that the resulting theory resulting elastic constants agree well with those from well established methods of calculating cross sectional constants and the accuracy deteriorates as the strip thickness to width ratio increases

free vibration analysis of civil engineering structures by component wise models abstract higher order beam models are used in this paper to carry out free vibration analysis of civil engineering structures refined kinematic fields are developed using the carrera unified formulation cuf which allows for the implementation of any order theory without the need for ad hoc formulations the principle of virtual displacements in conjunction with the finite element method fem is used to formulate stiffness and mass matrices in terms of fundamental nuclei the nuclei depend neither on the adopted class of beam theory nor on the fem approximation along the beam axis this paper focuses on a particular class of cuf models that makes use of lagrange polynomials to discretize cross sectional displacement variables this class of models are referred to as component wise cw in recent works according to the cw approach each structural component e g columns walls frame members and floors can be modeled by means of the same 1d formulation a number of typical civil engineering structures e g simple beams arches truss structures and complete industrial and civil buildings are analyzed and cw results are compared to classical beam theories euler bernoulli and timoshenko refined beam models based on taylor like expansions of the displacements on the cross section and classical solid shell fem solutions from the commercial code msc nastran the results highlight the enhanced capabilities of the proposed formulation it is in fact demonstrated that cw models are able to replicate 3d solid results with very low computational efforts

disordered totally asymmetric simple exclusion process exact results we study the effect of quenched spatial disorder on the current carrying steady states of a totally asymmetric simple exclusion process with spatially disordered jump rates expressions for the steady state weights and the current are derived for this model in one dimension these solutions are exploited to study analytically the exact symmetries of the system in particular we confirm the recent numerical observation of tripathy and barma phys rev e 58 1911 1998 that the magnitude of the steady state current is left invariant when the direction of all the allowed particle jumps are reversed

validation of the variational asymptotic beam sectional analysis the computer program vabs variational asymptotic beam section analysis uses the variational asymptotic method to split a three dimensional nonlinear elasticity problem into a twodimensional linear cross sectional analysis and a one dimensional nonlinear beam problem this is accomplished by taking advantage of certain small parameters inherent to beam like structures vabs is able to calculate the one dimensional cross sectional stiffness constants with transverse shear and vlasov refinements for initially twisted and curved beams with arbitrary geometry and material properties several validation cases are presented first an elliptic bar is modeled with transverse shear refinement using the variational asymptotic method and the solution is shown to be identical to that obtained from the theory of elasticity the shear center locations calculated by vabs for various cross sections agree well with those obtained from common engineering analyses comparisons with other composite beam theories prove that it is unnecessary to introduce ad hoc kinematic assumptions to build an accurate beam model for numerical validation values of the one dimensional variables are extracted from an abaqus model and compared with results from a one dimensional beam analysis using cross sectional constants from vabs furthermore point wise three dimensional stress and strain fields are recovered using vabs and the correlation with the three dimensional results from abaqus is excellent finally classical theory is shown to be insufficient for general purpose beam modeling appropriate refined theories are recommended for some classes of problems

characteristics of the asymmetric simple exclusion process in the presence of quenched spatial disorder we investigate the effect of quenched spatial disordered hopping rates on the characteristics of the asymmetric simple exclusion process with open boundaries both numerically and by extensive simulations disorder averages of the bulk density and current are obtained in terms of various input and output rates we study the binary and uniform distributions of disorder it is verified that the effect of spatial inhomogeneity is generically to enlarge the size of the maximal current phase this is in accordance with the mean field results obtained by harris and stinchcombe phys rev e 70 016108 2004 furthermore we obtain the dependence of the current and the bulk density on the characteristics of the disorder distribution function it is shown that the impact of disorder crucially depends on the particle input and out rates in some situations disorder can constructively enhance the current

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

sensitivity analysis for simulations via likelihood ratios we present a simple method of estimating the sensitivity of quantities obtained from simulation with respect to a class of parameters here sensitivity means the derivative of an expectation with respect to a parameter the class of parameters includes for example poisson rates discrete probabilities and the mean and variance of a normal distribution the method is extremely well suited to regenerative simulation and can be implemented on extant simulations with little effort increase in running time or memory requirements it is based on some change of measure formulas derived from likelihood ratios in addition to the theorems that underly the technique we present some numerical examples

smoothly varying hopping rates in driven flow with exclusion we consider the one dimensional totally asymmetric simple exclusion process tasep with position dependent hopping rates the problem is solved in a mean field adiabatic approximation for a general smooth form of spatial rate variation numerical simulations of systems with hopping rates varying linearly against position constant rate gradient for both periodic and open boundary conditions provide detailed confirmation of theoretical predictions concerning steady state average density profiles and currents as well as open system phase boundaries to excellent numerical accuracy

light traffic derivatives via likelihood ratios the steady state behavior of open queuing systems with poisson arrival processes in light traffic that is as the arrival rate tends to zero is considered expressions are provided for the derivatives with respect to the arrival rate of various quantities of interest such as moments of steady state sojourn times and queue lengths evaluated at an arrival rate of zero these expressions are obtained using the regenerative structure of the queuing system and a change of measure formula based on likelihood ratios the derivatives which can be used in interpolation approximations can be evaluated analytically in simple cases and by simulation in general

solving average cost markov decision processes by means of a two phase time aggregation algorithm abstract this paper introduces a two phase approach to solve average cost markov decision processes which is based on state space embedding or time aggregation in the first phase time aggregation is applied for policy optimization in a prescribed subset of the state space and a novel result is applied to expand the evaluation to the whole state space this evaluation is then used in the second phase in a policy improvement step and the two phases are then alternated until convergence is attained some numerical experiments illustrate the results

a relationship of mean field theory for a driven lattice gas to an exact equilibrium density functional we consider the totally asymmetric exclusion process tasep of particles on a one dimensional lattice that interact with site exclusion and are driven into one direction only the mean field approximation of the dynamical equation for the one particle density of this model is shown to be equivalent to the exact euler lagrange equations for the equilibrium density profiles of a binary mixture in this mixture particles occupy one two lattice sites and correspond to resting moving particles in the tasep despite the strict absence of bulk phase transitions in the equilibrium mixture the influence of density dependent external potentials is shown to induce abrupt changes in the one body density that are equivalent to the exact out of equilibrium phase transitions between steady states in the tasep with open boundaries

scaling approach to related disordered stochastic and free fermion models motivated by mapping from a stochastic system with spatially random rates we consider disordered non conserving free fermion systems using a scaling procedure for the equations of motion this approach demonstrates disorder induced localization acting in competition with the asymmetric driving we discuss the resulting implications for the original stochastic system

a simulation study of an asymmetric exclusion model with open boundaries and random rates using numerical simulations we study the asymmetric exclusion model with open boundaries particlewise disorder and parallel dynamics at each time step particles are injected at the left boundary with probability removed on the right with probability and jump in the bulk with probability where is a random rate associated with each injected particle the parameter interpolates between fully parallel and random sequential dynamics the phase diagram in the plane displays high density low density and maximum current phases with the first order transition line between high and low density phases shifted away from the line within the low density phase a platoon phase transition occurs many features of which can be explained using exact results for asymmetric exclusion with particlewise disorder on the ring in a certain region of parameter space the disorder induces a cusp in the current density relation at maximum flow our simulations indicate that this does not affect the topology of the phase diagram nor the familiar decay of the density profile in the maximum current phase

on asymptotically correct linear laminated plate theory abstract the focus of this paper is the development of asymptotically correct theories for laminated plates the material properties of which vary through the thickness and for which each lamina is orthotropic this work is based on the variational asymptotical method a mathematical technique by which the three dimensional analysis of plate deformation can be split into two separate analyses a one dimensional through the thickness analysis and a two dimensional plate analysis the through the thickness analysis includes elastic constants for use in the plate theory and approximate closed form recovering relations for all three dimensional field variables expressed in terms of plate variables in general the specific type of plate theory that results from this procedure is determined by the procedure itself however in this paper only reissner like plate theories are considered often called first order shear deformation theories this paper makes three main contributions first it is shown that construction of an asymptotically correct reissner like theory for laminated plates of the type considered is not possible in general second a new point of view on the variational asymptotical method is presented leading to an optimization procedure that permits a derived theory to be as close to asymptotical correctness as possible third numerical results from such an optimum reissner like theory are presented these results include comparisons of plate displacement as well as of three dimensional field variables and are the best of all extant reissner like theories indeed they even surpass results from theories that carry many more generalized displacement variables

guidelines and recommendations to construct theories for metallic and composite plates this work has evaluated the refinement of some classical theories such as the kirchhoff and reissner mindlin theories adding generalized displacement variables up to fourth order to the taylor type expansion in the thickness plate direction isotropic orthotropic and laminated plates have been analyzed varying the thickness ratio orthotropic ratio and stacking sequence of the layout higher order theories have been implemented according to the compact scheme known as the carrera unified formulation the results have been restricted to simply supported orthotropic plates subjected to harmonic distributions of transverse pressure for which closed form solutions are available for a given plate problem isotropic orthotropic or laminated the effectiveness of each employed generalized displacement variable has been established comparing the error obtained accounting for and removing the variable in the plate governing equations a number of theories have therefore been constructed imposing a given error with respect to the available best results guidelines and recommendations that are focused on the proper selection of the displacement variables that have to be retained in refined plate theories are then furnished it has been found that the terms that have to be used according to a given error vary from problem to problem but they also vary when the variable that has to be evaluated displacement stress components is changed diagrams errors in terms of geometrical and orthotopic ratios and graphical schemes have been built to establish the appropriate theories with respect to the data of the problem under consideration

discrete stochastic models for traffic flow we investigate a probabilistic cellular automaton model which has been introduced recently this model describes single lane traffic flow on a ring and generalizes the asymmetric exclusion process models we study the equilibrium properties and calculate the so called fundamental diagrams flow versus density for parallel dynamics this is done numerically by computer simulations of the model and by means of an improved mean field approximation which takes into account short range correlations for cars with a maximum velocity of 1 the simplest nontrivial approximation gives the exact result for higher velocities the analytical results obtained by iterated application of the approximation scheme are in excellent agreement with the numerical simulations

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

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

hydrodynamic mean field solutions of 1d exclusion processes with spatially varying hopping rates we analyse the open boundary partially asymmetric exclusion process with smoothly varying internal hopping rates in the infinite size mean field limit the mean field equations for particle densities are written in terms of ricatti equations with the steady state current j as a parameter these equations are solved both analytically and numerically upon imposing the boundary conditions set by the injection and extraction rates the currents j are found self consistently we find a number of cases where analytic solutions can be found exactly or approximated results for j from asymptotic analyses for slowly varying hopping rates agree extremely well with those from extensive monte carlo simulations suggesting that mean field currents asymptotically approach the exact currents in the hydrodynamic limit as the hopping rates vary slowly over the lattice if the forward hopping rate is greater than or less than the backward hopping rate throughout the entire chain the three standard steady state phases are preserved our analysis reveals the sensitivity of the current to the relative phase between the forward and backward hopping rate functions

asymptotic theory for static behavior of elastic anisotropic i beams abstract end effects for prismatic anisotropic beams with thin walled open cross sections are analyzed by the variational asymptotic method the decay rates for disturbances at the ends of prismatic beams are evaluated and the most influential end disturbances are incorporated into a refined beam theory thus the foundations of vlasovs theory as well as restrictions on its applicability are obtained from the variational asymptotic point of view vlasovs theory is proved to be asymptotically correct for isotropic i beams the asymptotically correct generalization of vlasovs theory for static behavior of anisotropic beams is presented in light of this development various published generalizations of vlasovs theory for thin walled anisotropic beams are discussed comparisons with a numerical 3 d analysis are provided showing that the present approach gives the closest agreement of all published theories the procedure can be applied to any thin walled beam with open cross sections

steady state properties of a totally asymmetric exclusion process with periodic structure we study the steady state behavior of totally asymmetric simple exclusion processes taseps that contain periodically varying movement rates in this model particles move to the right at one of two rates p 2 if the particle occupies one of a periodically arranged set of lattice sites p 1 otherwise approximate mean field approaches are used to study the steady state currents and bulk densities of this model these mean field methods are found to provide results in good agreement with data derived from monte carlo simulations finally the condition for particle hole symmetry in the tasep with periodically varying movement rates is specified and the changes in the locations of the boundary limited to maximal current transition lines due to symmetry violation are investigated

performance gradient estimation for the very large finite markov chains using an embedded markov chain the steady state performance gradient estimation for very large markov chains is decomposed into two smaller problems one solved by the stochastic recursive sr method and the other by the likelihood ratio lr method the combination named sr lr can have several magnitudes of lower space requirement than the sr and several magnitudes of lower time consumptions than the lr both the lr and the sr are the extreme cases of the combined algorithm the authors demonstrate the sr lr methods on markov chains with hundreds of millions of states which are created using queuing networks

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

exact dynamic stiffness elements based on one dimensional higher order theories for free vibration analysis of solid and thin walled structures in this paper an exact dynamic stiffness formulation using one dimensional 1d higher order theories is presented and subsequently used to investigate the free vibration characteristics of solid and thin walled structures higher order kinematic fields are developed using the carrera unified formulation which allows for straightforward implementation of any order theory without the need for ad hoc formulations classical beam theories euler bernoulli and timoshenko are also captured from the formulation as degenerate cases the principle of virtual displacements is used to derive the governing differential equations and the associated natural boundary conditions an exact dynamic stiffness matrix is then developed by relating the amplitudes of harmonically varying loads to those of the responses the explicit terms of the dynamic stiffness matrices are also presented the resulting dynamic stiffness matrix is used with particular reference to the wittrick williams algorithm to carry out the free vibration analysis of solid and thin walled structures the accuracy of the theory is confirmed both by published literature and by extensive finite element solutions using the commercial code msc nastran

disordered asymmetric simple exclusion process mean field treatment we provide two complementary approaches to the treatment of disorder in a fundamental nonequilibrium model the asymmetric simple exclusion process first a mean field steady state mapping is generalized to the disordered case where it provides a mapping of probability distributions and demonstrates how disorder results in a new flat regime in the steady state current density plot for periodic boundary conditions this effect was earlier observed by phys rev e 58 1911 1998 but we provide a treatment for more general distributions of disorder including both numerical results and analytic expressions for the width 2 delta c of the flat section we then apply an argument based on moving shock fronts europhys lett 48 257 1999 to show how this leads to an increase in the high current region of the phase diagram for open boundary conditions second we show how equivalent results can be obtained easily by taking the continuum limit of the problem and then using a disordered version of the well known cole hopf mapping to linearize the equation within this approach we show that adding disorder induces a localization transformation verified by numerical scaling and delta c maps to an inverse localization length helping to give a physical interpretation to the problem

lateral torsional buckling of cantilevered elastically coupled composite strip and i beams the lateral torsional buckling of composite strip and i beams is considered the geometrically exact governing equations are simplified by consistently regarding certain configuration parameters as small the assumption that these parameters are indeed small is equivalent to the assumption that the square of the maximum prebuckling cross sectional rotation due to bending is small compared to unity the analysis takes into account various refinements of previously published results including the vlasov eaect elastic coupling the oaset of the load from the centroid and of course prebuckling deflections the analysis is thereby reduced to a single fourth order diaerential equation and boundary conditions all of which are derivable from a corresponding energy expression from the form of matched asymptotic expansions of the buckling mode when small parameters are ignored altogether a single comparison function is found which gives the correct buckling load to within 1 for a wide range of the warping rigidity using this comparison function a formula for the buckling load as a function of the small parameters of the problem is found and validated with certain exceptions regarding the load oaset parameter the formula provides results which agree quite well with the numerical solution of the exact equations as long as all the small parameters remain small however the load oaset parameter always appears in the governing equations as multiplied by a ratio of stianesses which can become large especially for composite i beams for this case a special treatment is required 2001 elsevier science ltd all rights reserved

vehicular traffic flow at a non signalized intersection we have developed a modified nagel schreckenberg cellular automata model for describing a conflicting vehicular traffic flow at the intersection of two streets no traffic lights control the traffic flow the approaching cars to the intersection yield to each other to avoid collision closed boundary condition is applied to the streets extensive monte carlo simulation is taken into account to find the model characteristics in particular we obtain the fundamental diagrams and show that the effect of the interaction of two streets can be regarded as a dynamic impurity located at the intersection point our results suggest that yielding mechanism gives rise to a high total flow throughout the intersection especially in the low density regime

spontaneous symmetry breaking in totally asymmetric simple exclusion processes on two intersected lattices this paper studies totally asymmetric simple exclusion processes taseps on two intersected lattices three different models are introduced model a for molecular motor motion and models b and c for vehicle traffic extensive monte carlo simulations are carried out phase diagrams and density profiles of the three models are investigated it is shown that phase diagrams of all the three models are divided into three regions the phase boundaries are calculated by an approximate mean field approach it is found that the analytic solutions are in good agreement with the results of monte carlo simulations for models b and c spontaneous symmetry breaking is identified the particle density histograms and qualitative domain wall explanation are presented to describe the spontaneous symmetry breaking phenomenon finally in model c the effect of lane changing probability p on spontaneous symmetry breaking is investigated a threshold of p for the occurrence of symmetry breaking is obtained