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

the invertibility of rotation invariant radon transforms let r denote the radon transform on rn that integrates a function over hyperplanes in given smooth positive measures depending on the hyperplane we characterize the measures for which r is rotation invariant we prove rotation invariant transforms are all one to one and hence invertible on the domain of square integrable functions of compact support l02 rn we prove the hole theorem if f l02rn and r f 0 for hyperplanes not intersecting a ball centered at the origin then f is zero outside of that ball using the theory of fourier integral operators we extend these results to the domain of distributions of compact support on rn our results prove invertibility for a mathematical model of positron emission tomography and imply a hole theorem for the constantly attenuated radon transform as well as invertibility for other radon transforms

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

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

a dual mixed approximation method for a three field model of a nonlinear generalized stokes problem in this work a dual mixed approximation of a nonlinear generalized stokes problem is studied the problem is analyzed in sobolev spaces which arise naturally in the problem formulation existence and uniqueness results are given and error estimates are derived it is shown that both lowest order and higher order mixed finite elements are suitable for the approximation method numerical experiments that support the theoretical results are presented

analysis of a pseudostress based mixed finite element method for the brinkman model of porous media flow in this paper we introduce and analyze a new mixed finite element method for the two dimensional brinkman model of porous media flow with mixed boundary conditions we use a dual mixed formulation in which the main unknown is given by the pseudostress the original velocity and pressure unknowns are easily recovered through a simple postprocessing in addition since the neumann boundary condition becomes essential we impose it in a weak sense which yields the introduction of the trace of the fluid velocity over the neumann boundary as the associated lagrange multiplier we apply the babuska brezzi theory to establish sufficient conditions for the well posedness of the resulting continuous and discrete formulations in particular a feasible choice of finite element subspaces is given by raviart thomas elements of order k ge 0 k 0 for the pseudostress and continuous piecewise polynomials of degree k 1 k 1 for the lagrange multiplier we also derive a reliable and efficient residual based a posteriori error estimator for this problem suitable auxiliary problems the continuous inf sup conditions satisfied by the bilinear forms involved a discrete helmholtz decomposition and the local approximation properties of the raviart thomas and clement interpolation operators are the main tools for proving the reliability then helmholtz s decomposition inverse inequalities and the localization technique based on triangle bubble and edge bubble functions are employed to show the efficiency finally several numerical results illustrating the performance and the robustness of the method confirming the theoretical properties of the estimator and showing the behaviour of the associated adaptive algorithm are provided

spontaneous symmetry breaking in two channel asymmetric exclusion processes with narrow entrances multi particle non equilibrium dynamics in two channel asymmetric exclusion processes with narrow entrances is investigated theoretically particles move on two parallel lattices in opposite directions without changing them while the channels are coupled only at the boundaries a particle cannot enter the corresponding lane if the exit site of the other lane is occupied stationary phase diagrams particle currents and densities are calculated in a mean field approximation it is shown that there are four stationary phases in the system with two of them exhibiting spontaneous symmetry breaking phenomena extensive monte carlo computer simulations confirm qualitatively our predictions although the phase boundaries and stationary properties deviate from the mean field results computer simulations indicate that several dynamic and phase properties of the system have a strong size dependence and one of the stationary phases predicted by the mean field theory probably disappears in the thermodynamic limit

inf sup conditions for twofold saddle point problems necessary and sufficient conditions for existence and uniqueness of solutions are developed for twofold saddle point problems which arise in mixed formulations of problems in continuum mechanics this work extends the classical saddle point theory to accommodate nonlinear constitutive relations and the twofold saddle structure application to problems in incompressible fluid mechanics employing symmetric tensor finite elements for the stress approximation is presented

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

synchronization of kinks in the two lane totally asymmetric simple exclusion process with open boundary conditions we study the motion of kinks in a two lane model of the totally asymmetric simple exclusion process with open boundaries we analytically study the motion of the kinks by a decoupling approximation in terms of the decoupling approximation we find that the positions of the kinks become synchronized though the difference in the number of particles between lanes remains non zero when the rate of lane change is asymmetric the validity of this result is confirmed for small asymmetric cases through the monte carlo simulation

numerical approximation of a quasi newtonian stokes flow problem with defective boundary conditions in this article we study the numerical approximation of a quasi newtonian stokes flow problem where only the flow rates are specified at the inflow and outflow boundaries a variational formulation of the problem using lagrange multipliers to enforce the stated flow rates is given the existence and the uniqueness to the continuous and discrete variational formulations of the solution are shown an error analysis for the numerical approximation is also given numerical computations are included which demonstrate the approximation scheme studied

a priori and a posteriori error analyses of augmented twofold saddle point formulations for nonlinear elasticity problems abstract in this paper we introduce and analyze new augmented mixed finite element methods allowing much more flexibility in the choice of the corresponding finite dimensional subspaces for a class of nonlinear elasticity problems arising in hyperelasticity the starting mixed method is based on the incorporation of the strain tensor as an auxiliary unknown which together with the usual stress displacement rotation approach employed in linear elasticity yields a nonlinear twofold saddle point operator equation as the resulting weak formulation we first extend known results on the well posedness of the associated galerkin scheme with peers of order k 0 to the case k 1 then the augmented schemes are obtained by adding consistent galerkin type terms arising first from the constitutive equation and then from the equilibrium equation and the relations defining the rotation in terms of the displacement and the strain tensor as independent unknown all of them multiplied by suitably chosen stabilization parameters we apply classical results on the solvability analysis of nonlinear saddle point and strongly monotone operator equations to prove that the corresponding continuous and discrete augmented schemes are well posed more precisely and as the main advantages of our present approach we show that the well posedness of a partially augmented galerkin scheme is ensured by any finite element subspace for the strain tensor together with the peers space of order k 0 for the remaining unknowns whereas any finite element subspace of the whole continuous space will do in the case of a fully augmented scheme then we derive reliable and efficient residual based a posteriori error estimators for all the schemes finally we provide several numerical results illustrating the good performance of the mixed finite element methods confirming the theoretical properties of the estimators and showing the behaviour of the associated adaptive algorithms

a posteriori estimators for mixed finite element approximations of a fluid obeying the power law we study a posteriori error estimation in the approximation by the finite element method of a fluid which obeys the power law 2 d u r 2d u p f u 0 1 r 2 abstract and calculable a posteriori estimators are given in two fields and in a three fields version of this problem furthermore we give some examples of fe spaces satisfying the inf sup condition which relates the discrete space of tensors and the discrete space of velocities needed for this formulation

on stability of probability laws with univariate stable marginals examples of d marcus in 2 dispel the belief that a probability measure on d is stable if and only if all its univariate marginals are stable however in d in fact in fairly general linear spaces a probability measure whose two dimensional marginals are all infinitely divisible is stable if and only if all its univariate marginals are stable

the robustness of spontaneous symmetry breaking in a bridge model a simple two species asymmetric exclusion model in one dimension with bulk and boundary exchanges of particles is investigated for the existence of spontaneous symmetry breaking the model is a generalization of the bridge model for which earlier studies have confirmed the existence of symmetry broken phases and the motivation here is to check the robustness of the observed symmetry breaking with respect to additional dynamical moves in particular the boundary exchange of the two species of particle our analysis based on general considerations mean field approximation and numerical simulations shows that the symmetry breaking in the bridge model is sustained for a range of values of the boundary exchange rate moreover the mechanism through which symmetry is broken is similar to that in the bridge model our analysis allows us to plot the complete phase diagram of the model demarcating regions of symmetric and symmetry broken phases

a low order mixed finite element method for a class of quasi newtonian stokes flows part i a priori error analysis abstract this is the second part of a work dealing with a low order mixed finite element method for a class of nonlinear stokes models arising in quasi newtonian fluids in the first part we showed that the resulting variational formulation is given by a twofold saddle point operator equation and that the corresponding galerkin scheme becomes well posed with piecewise constant functions and raviart thomas spaces of lowest order as the associated finite element subspaces in this paper we develop a bank weiser type a posteriori error analysis yielding a reliable estimate and propose the corresponding adaptive algorithm to compute the mixed finite element solutions several numerical results illustrating the efficiency of the method are also provided

non stable laws with all projections stable is the characterist ic function of a probabi l i ty law on ir 2 we then show that for 0 4 define functions on ir 2 as follows

dual mixed finite element approximation of stokes and nonlinear stokes problems using trace free velocity gradients in this work a finite element method for a dual mixed approximation of stokes and nonlinear stokes problems is studied the dual mixed structure which yields a twofold saddle point problem arises in a formulation of this problem through the introduction of unknown variables with relevant physical meaning the method approximates the velocity its gradient and the total stress tensor but avoids the explicit computation of the pressure which can be recovered through a simple postprocessing technique this method improves an existing approach for these problems and uses raviart thomas elements and discontinuous piecewise polynomials for approximating the unknowns existence uniqueness and error results for the method are given and numerical experiments that exhibit the reduced computational cost of this approach are presented

residual a posteriori error estimator for a three field model of a non linear generalized stokes problem in this article we propose and analyze an a posteriori error estimator for a three field model of a generalized stokes problem the components of the a posteriori error estimator are defined via a non linear projection of the residues of the variational equations both upper and lower bounds for the approximation error are derived in terms of the components of the a posteriori error estimator the non linear projections do not need to be explicitly computed to construct the a posteriori error estimates

a family of higher order mixed finite element methods for plane elasticity the dirichler problem for the equations of plane elasticity is approximated by a mixed finite element method using a new family of composite finite elements having properties analogous to those possessed by the raviart thomas mixed finite elements for a scalar second order elliptic equation estimates of optimal order and minimal regularity are derived for the errors in the displacement vector and the stress tensor inl 2 and optimal order negative norm estimates are obtained inh s for a range ofs depending on the index of the finite element space an optimal order estimate inl for the displacement error is given also a quasioptimal estimate is derived in an appropriate space all estimates are valid uniformly with respect to the compressibility and apply in the incompressible case the formulation of the elements is presented in detail

a hybrid high order method for a class of quasi newtonian stokes equations on general meshes abstract in this paper we introduce a hybrid high order hho discrete scheme for numerically solving a class of incompressible quasi newtonian stokes equations in r 2 the presented hho method depends on hybrid discrete velocity unknowns at cells and edges and pressure unknowns at cells benefiting from the hybridization of unknowns the computation cost can be reduced by the technique of static condensation and the solvability of the static condensation algebra system is proved furthermore we study the hho scheme by polynomials of arbitrary degrees k k 1 on the general meshes and geometries the unique solvability of the discrete scheme is proved additionally the optimal a priori error estimates for the velocity gradient and pressure approximations are obtained finally we provide several numerical results to verify the good performance of the proposed hho scheme and confirm the optimal approximation properties on a variety of meshes and geometries

exact domain wall theory for deterministic tasep with parallel update we develop an exact domain wall theory dwt for the totally asymmetric exclusion process tasep with parallel update and deterministic p 1 bulk motion remarkably the dynamics of this system can be described by the motion of a domain wall not only on the coarse grained level but also exactly on the microscopic scale for arbitrary system size all properties of this tasep not only stationary but also time dependent are shown to follow from the solution of a bivariate master equation whose variables are not only the position but also the velocity of the domain wall in the continuum limit this exactly soluble model then allows us to perform a first principle derivation of a fokker planck equation for the position of the wall

totally asymmetric exclusion process with long range hopping generalization of the one dimensional totally asymmetric exclusion process tasep with open boundary conditions in which particles are allowed to jump l sites ahead with the probability p l ensuremath sim 1 l ensuremath sigma 1 is studied by monte carlo simulations and the domain wall approach for ensuremath sigma g1 the standard tasep phase diagram is recovered but the density profiles display additional features when 1l ensuremath sigma l2 at the first order transition line the domain wall is localized and phase separation is observed in the maximum current phase the profile has an algebraic decay with a ensuremath sigma dependent exponent within the ensuremath sigma ensuremath le 1 regime where the transitions are found to be absent analytical results in the continuum mean field approximation are derived in the limit ensuremath sigma ensuremath 1

a priori and a posteriori error analyses of a velocity pseudostress formulation for a class of quasi newtonian stokes flows abstract in this paper we introduce and analyze new mixed finite element schemes for a class of nonlinear stokes models arising in quasi newtonian fluids the methods are based on a non standard mixed approach in which the velocity the pressure and the pseudostress are the original unknowns however we use the incompressibility condition to eliminate the pressure and set the velocity gradient as an auxiliary unknown which yields a twofold saddle point operator equation as the resulting dual mixed variational formulation in addition a suitable augmented version of the latter showing a single saddle point structure is also considered we apply known results from nonlinear functional analysis to prove that the corresponding continuous and discrete schemes are well posed in particular we show that raviart thomas elements of order k 0 for the pseudostress and piecewise polynomials of degree k for the velocity and its gradient ensure the well posedness of the associated galerkin schemes moreover we prove that any finite element subspace of the square integrable tensors can be employed to approximate the velocity gradient in the case of the augmented formulation then we derive a reliable and efficient residual based a posteriori error estimator for each scheme finally we provide several numerical results illustrating the good performance of the resulting mixed finite element methods confirming the theoretical properties of the estimator and showing the behaviour of the associated adaptive algorithms

cylindrical levy processes in banach spaces cylindrical probability measures are flnitely additive measures on banach spaces that have sigma additive projections to euclidean spaces of all dimensions they are naturally associated to notions of weak cylindrical random variable and hence weak cylindrical stochastic processes in this paper we focus on cylindrical levy processes these have weak levy it o decompositions and an associated levy khintchine formula if the process is weakly square integrable its covariance oper ator can be used to construct a reproducing kernel hilbert space in which the pro cess has a decomposition as an inflnite series built from a sequence of uncorrelated bona flde one dimensional levy processes this series is used to deflne cylindrical stochastic integrals from which cylindrical ornstein uhlenbeck processes may be constructed as unique solutions of the associated cauchy problem we demonstrate that such processes are cylindrical markov processes and study their cylindrical invariant measures

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

analyse numerique des ecoulements quasi newtoniens dont la viscosite obeit a la loi puissance ou la loi de carreau we prove abstract error estimates for the approximation of the velocity and the pressure by a mixed fem of quasi newtonian flows whose viscosity obeys the power law or the carreau law these estimates are optimal in some cases they can be applied to most finite elements used for the solution of stokes s problem on prouve des estimations d erreur abstraites pour l approximation de la vitesse et la pression par une mef mixtes d ecoulements quasi newtoniens dont la viscosite obeit a la loi puissance ou la loi de carreau ces estimations sont optimales dans certains cas elles peuvent etre appliquees a la plupart des elements finis utilises pour la resolution du probleme de stokes

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

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

characteristic functions of random variables attracted to 1 stable laws the domain of attraction of a 1 stable law on r d is characterized by the expansions of the characteristic functions of its elements

distances between measures from 1 dimensional projections as implied by continuity of the inverse radon transform distances between measures on ir d are determined from distances between their 1 dimensional projections the method employed involves considering the 1 dimensional projections to be the radon transform of the measures crucial to the main theorem is a continuity result for the inverse radon transform focus is restricted to the prohorov dual bounded lipschitz and d k metrics which metrize weak convergence of probability measures these metrics are related to each other and to the sobolev norms the d k results extend from measures to generalized functions

numerical analysis of a three fields model for a quasi newtonian flow abstract we study a finite element approximation of a non linear three fields version of stokes system for incompressible fluids such a problem arises when one considers a white metzner type model for a viscoelastic fluid flow and sets the relaxation time to zero the non linear aspect comes from the fact that a fraction of the viscosity of the fluid depends on the second invariant of the rate of deformation tensor we give existence and unicity results for the continuous problem and its approximation and we prove the error bound

a priori and a posteriori error analyses of a pseudostress based mixed formulation for linear elasticity in this paper we present the a priori and a posteriori error analyses of a non standard mixed finite element method for the linear elasticity problem with non homogeneous dirichlet boundary conditions more precisely the approach introduced here is based on a simplified interpretation of the pseudostress displacement formulation originally proposed in arnold and falk 1988 which does not require symmetric tensor spaces in the finite element discretization in addition physical quantities such as the stress the strain tensor of small deformations and the rotation are computed through a simple postprocessing in terms of the pseudostress variable furthermore we also introduce a second element by element postprocessing formula for the stress which yields an optimally convergent approximation of this unknown with respect to the broken h div norm we apply the classical babuska brezzi theory to prove that the corresponding continuous and discrete schemes are well posed in particular raviart thomas spaces of order k 0 for the pseudostress and piecewise polynomials of degree k for the displacement can be utilized moreover we remark that in the 3d case the number of unknowns behaves approximately as 9 times the number of elements tetrahedra of the triangulation when k 0 this factor increases to 12 5 when one uses the classical peers next we derive a reliable and efficient residual based a posteriori error estimator for the mixed finite element scheme finally several numerical results illustrating the performance of the method confirming the theoretical properties of the estimator and showing the expected behaviour of the associated adaptive algorithm are provided

analysis of a velocity pressure pseudostress formulation for the stationary stokes equations abstract we consider a non standard mixed approach for the stokes problem in which the velocity the pressure and the pseudostress are the main unknowns alternatively the pressure can be eliminated from the original equations thus yielding an equivalent formulation with only two unknowns in this paper we develop a priori and a posteriori error analyses of both approaches we first apply the babuska brezzi theory to prove the well posedness of the continuous and discrete formulations in particular we show that raviart thomas elements of order k 0 for the pseudostresses and piecewise polynomials of degree k for the velocities and the pressures ensure unique solvability and stability of the associated galerkin schemes then we derive reliable and efficient residual based a posteriori error estimators for both schemes without and with pressure unknown finally we provide several numerical results illustrating the good performance of the resulting mixed finite element methods confirming the theoretical properties of the estimators and showing the behaviour of the associated adaptive algorithms

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

two channel totally asymmetric simple exclusion processes totally asymmetric simple exclusion processes consisting of two coupled parallel lattice chains with particles interacting with hard core exclusion and moving along the channels and between them are considered in the limit of strong coupling between the channels the particle currents density profiles and a phase diagram are calculated exactly by mapping the system into an effective one channel totally asymmetric exclusion model for intermediate couplings a simple approximate theory that describes the particle dynamics in vertical clusters of two corresponding parallel sites exactly and neglects the correlations between different vertical clusters is developed it is found that similarly to the case of one channel totally asymmetric simple exclusion processes there are three stationary state phases although the phase boundaries and stationary properties strongly depend on inter channel coupling extensive computer monte carlo simulations fully support the theoretical predictions

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