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

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

non abelian symmetries of stochastic processes derivation of correlation functions for random vertex models and disordered interacting particle systems we consider systems of particles hopping stochastically on d dimensional lattices with space dependent probabilities we map the master equation onto an evolution equation in a fock space where the dynamics are given by a quantum hamiltonian continuous time or a transfer matrix discrete time using non abelian symmetries of these operators we derive duality relations expressing the time evolution of a given initial configuration in terms of correlation functions of simpler dual processes particularly simple results are obtained for the time evolution of the density profile as a special case we show that for any su 2 symmetric system the two point and three point density correlation functions in the n particle steady state can be computed from the probability distribution of a single particle moving in the same environment we apply our results to various models among them partial exclusion a simple diffusion reaction system and the two dimensional six vertex model with space dependent vertex weights for a random distribution of the vertex weights one obtains a version of the random barrier model describing diffusion of particles in disordered media we derive exact expressions for the averaged two point density correlation functions in the presence of weak correlated disorder

cubulating graphs of free groups with cyclic edge groups we prove that if g is a group that splits as a finite graph of finitely generated free groups with cyclic edge groups and g has no non euclidean baumslag solitar subgroups then g is the fundamental group of a compact nonpositively curved cube complex in addition if g is also word hyperbolic i e if g contains no baumslag solitar subgroups of any type we show that g is linear in fact is a subgroup of sl n z

exact solution of the asymmetric exclusion model with particles of arbitrary size a generalization of the simple exclusion asymmetric model is introduced in this model an arbitrary mixture of molecules with distinct sizes s 0 1 2 dots in units of lattice space diffuses asymmetrically on the lattice a related surface growth model is also presented variations of the distribution of the molecules sizes may change the excluded volume almost continuously we solve the model exactly through the bethe ansatz and the dynamical critical exponent z is calculated from the finite size corrections of the mass gap of the related quantum chain our results show that for an arbitrary distribution of molecules the dynamical critical behavior is on the kardar parizi zhang universality

exclusion process for particles of arbitrary extension hydrodynamic limit and algebraic properties the behaviour of extended particles with exclusion interaction on a one dimensional lattice is investigated the basic model is called l asep as a generalization of the asymmetric exclusion process asep to particles of arbitrary length l stationary and dynamical properties of the l asep with periodic boundary conditions are derived in the hydrodynamic limit from microscopic properties of the underlying stochastic many body system in particular the hydrodynamic equation for the local density evolution and the time dependent diffusion constant of a tracer particle are calculated as a fundamental algebraic property of the symmetric exclusion process the su 2 symmetry is generalized to the case of extended particles

large deviations for noninteracting infinite particle systems a large deviation property is established for noninteracting infinite particle systems previous large deviation results obtained by the authors involved a singlei function because the cases treated always involved a unique invariant measure for the process in the context of this paper there is an infinite family of invariant measures and a corresponding infinite family ofi functions governing the large deviations

exact results for one dimensional totally asymmetric diffusion models several types of totally asymmetric diffusion models with and without exclusion are considered for some models conditional probabilities of finding n particles on lattice sites at time t with initial occupation at time t 0 are expressed in a determinant form on the other hand the q boson totally asymmetric diffusion model is introduced which interpolates the free boson model and the model with exclusion like interaction the effects of the interaction are compared for the case of two particle diffusion

certain summation and transformation formulas for generalized hypergeometric series we derive summation formulas for generalized hypergeometric series of unit argument one of which upon specialization reduces to minton s summation theorem as an application we deduce a reduction formula for a certain kampe de feriet function that in turn provides a kummer type transformation formula for the generalized hypergeometric function pf p x

complex temperature plane zeros in the mean field approximation we derive asymptotic expressions for the complex temperature plane zeros of the infinite range ising model in the scaling regime the results also apply to high dimensional short range ising systems for thenth zero in a system ofn spins the leading asymptotic result istn n n 1 2 1 i

on the reducibility of the kampe deferiet function the existing list of reducible cases of double hypergeometric functions is supplemented by the use of summation theorems for nearly poised hypergeometric functions a few new relations for single hypergeometric functions emerge as special cases relations of this type are useful for computing purposes

irreducible affine varieties over a free group i irreducibility of quadratic equations and nullstellensatz the object of this paper which consists of two parts is to describe irreducible varieties over free groups and to characterize finitely generated fully residually free groups we prove that any variety over a free group f can be defined by a finite number of systems of equations s 1 in triangular form where quadratic words play the role of leading terms algebraically irreducible varieties are exactly the varieties whose coordinate groups are fully residually f the crucial point of the classification of fully residually free groups is to prove that the coordinate groups of irreducible varieties are embeddable into lyndon s free z x group f since every finitely generated fully residually free group is a free factor of the coordinate group of an irreducible variety and the group f is fully residually f we obtain a characterization of finitely generated fully residually free groups as subgroups of f the group f and its subgroups have been studied extensively during the last several years in particular every finitely generated subgroup of f hence every finitely generated fully residually free group can be obtained from free abelian groups of finite rank by finitely many free products with amalgamation and hnn extensions of the type where amalgamated and associated subgroups are free abelian of finite rank in particular this implies that every finitely generated fully residually free group is finitely presented there are three parts to this paper algebraic geometry over free groups the theory of free exponential groups and makanin razborov s machinery to deal with equations over free groups 11 14 13 the algebraic geometry approach has been shown to be very usefull in dealing with equations over groups it provides necessary topological means and a method to transcribe geometric notions into pure group theoretic language following baumslag myasnikov remeslennikov 1 we use the standard algebraic geometry notions such as variety zariski topology irreducibility of varieties radicals and coordinate groups some of the ideas of the algebraic geometry approach go back to r lyndon 9 e rips j stallings 16

large deviations for poisson systems of independent random walks we prove large deviation theorems for occupation time functionals of independent random walks started from a poisson field on zd in dimensions 1 and 2 the large deviation tails are larger than exponential exact asymptotics are derived

zeros of the finite size scaling region partition function for a model with a wetting transition we derive a finite size scaling representation for the partition function for an onsager temperley string model with a wetting transition and analyze the zeros of this partition function in the complex scaled coupling parameter of relevance the system models the one dimensional interface between two phases in a rectangular two dimensional region x y 2 l y l o x n the two phases are at coexistence the string or interface has a surface tension 2kkt per unit length and an extra boltzmann weighta per unit length if it touches the surfaces aty l there is a critical valueac 1 2k and fora ac the string is confined to one of the surfaces while fora ac the string moves roughly in the rectangular region the finite size scaling parameters are a c 2 n l2 and l a ac a c 2 we find that for large the zeros of the scaled partition function lie close to the lines arg 4 with re 0 we discuss the motion of all the zeros as changes by both analytic and numerical arguments

a summation formula for clausen s series 3f2 1 with an application to goursat s function 2f2 x a new summation formula for clausen s series 3f2 1 is derived in two different ways and used to obtain a reduction formula for the kampe de feriet function fp 2 0q 2 0 x x the specialization p q 0 of the latter result reduces to a kummer type transformation formula for the generalized hypergeometric function 2f2 x which has recently been deduced by r b paris who employed other methods

irreducible affine varieties over a free group ii systems in triangular quasi quadratic form and description of residually free groups abstract we shall prove the conjecture of myasnikov and remeslennikov 4 which states that a finitely generated group is fully residually free every finite set of nontrivial elements has nontrivial images under some homomorphism into a free group if and only if it is embeddable in the lyndon s exponential groupfz x which is thez x completion of the free group herez x is the ring of polynomials of one variable with integer coefficients historically lyndon s attempts to solve tarski s famous problem concerning the elementary equivalence of free groups of different ranks led him to introducefz x an free group is a groupgsuch that the class of formulas true ing is the same as the class of formulas true in a nonabelian free group a finitely generated group is free if and only if it is fully residually free 22 our result gives an algebraic description of free groups we shall give an algorithm to represent a solution set of an arbitrary system of equations overfas a union of finite number of irreducible components in the zariski topology onfn the solution set for every system is contained in the solution set of a finite number of systems in triangular form with quadratic words as leading terms the possibility of such a decomposition for a solution set was conjectured by razborov in 20 and also by rips we shall give a description of systems of equations determining irreducible components using methods developed in 13 19 it is possible to find some of these methods in 18 we are thankful to e rips for attracting our attention to these techniques

brownian walkers within subdiffusing territorial boundaries inspired by the collective phenomenon of territorial emergence whereby animals move and interact through the scent marks they deposit we study the dynamics of a 1d brownian walker in a random environment consisting of confining boundaries that are themselves diffusing anomalously we show how to reduce in certain parameter regimes the non markovian many body problem of territoriality to the analytically tractable one body problem studied here the mean square displacement msd of the 1d brownian walker within subdiffusing boundaries is calculated exactly and generalizes well known results when the boundaries are immobile furthermore under certain conditions if the boundary dynamics are strongly subdiffusive we show the appearance of an interesting nonmonotonicity in the time dependence of the msd giving rise to transient negative diffusion

cubulating malnormal amalgams let g be a group splitting as a graph of groups where each vertex group acts properly on a cat 0 cube complex when g is hyperbolic relative to virtually abelian subgroups we examine conditions producing a proper action of g on a cat 0 cube complex when g is hyperbolic this action is also cocompact

cubulating hyperbolic free by cyclic groups the irreducible case let v be a nite graph and let v v be an irreducible train track map whose mapping torus has word hyperbolic fundamental group g then g acts freely and cocompactly on a cat 0 cube complex hence if f is a nite rank free group and f f an irreducible monomorphism so that g f is word hyperbolic then g acts freely and cocompactly on a cat 0 cube complex this holds in particular if is an irreducible automorphism with g f o z word hyperbolic

hard rod gas with long range interactions exact predictions for hydrodynamic properties of continuum systems from discrete models one dimensional hard rod gases are explicitly constructed as the limits of discrete systems exclusion processes involving particles of arbitrary length those continuum many body systems in general do not exhibit the same hydrodynamic properties as the underlying discrete models considering as examples a hard rod gas with additional long range interaction and the generalized asymmetric exclusion process for extended particles it is shown how a correspondence between continuous and discrete systems must be established instead this opens up a possibility to exactly predict the hydrodynamic behavior of this continuum system under eulerian scaling by solving its discrete counterpart with analytical or numerical tools as an illustration simulations of the totally asymmetric exclusion process are compared to analytical solutions of the model and applied to the corresponding hard rod gas the case of short range interaction is treated separately

a kummer type transformation for a 2 f 2 hypergeometric function we obtain a kummer type transformation for the 2 f 2 x hypergeometric function with general parameters in the form of a sum of 2 f 2 x functions this result is specialised to the case where one pair of parameters differs by unity to generalize a recent result of miller j comput appl math 157 2003 507

letter to the editor on a kummer type transformation for the generalized hypergeometric function 2 f 2 a kummer type transformation formula for the generalized hypergeometric function 2f2 deduced by exton is rederived in two simple and transparent ways

a generalized master equation approach to modelling anomalous transport in animal movement we present some models of random walks with internal degrees of freedom that have the potential to find application in the context of animal movement and stochastic search the formalism we use is based on the generalized master equation which is particularly convenient here because of its inherent coarse graining procedure whereby a random walker position is averaged over the internal degrees of freedom we show some instances in which non local jump probabilities emerge from the coupling of the motion to the internal degrees of freedom and how the tuning of one parameter can give rise to sub super and normal diffusion at long times remarks on the relation between the generalized master equation continuous time random walks and fractional diffusion equations are also presented

on the motion of the first lee yang zero in the d dimensional ferromagnetic ising and 4 systems the motion of the first lee yang zero when the lattice size tends to infinity is studied in particular a power law behavior at the critical point which is distinct from those in noncritical points is elucidated

finite size scaling and universality for the totally asymmetric simple exclusion process the applicability of the concepts of finite size scaling and universality to nonequilibrium phase transitions is considered in the framework of the one dimensional totally asymmetric simple exclusion process with open boundaries in the thermodynamic limit there are boundary induced transitions both of the first and second order between steady state phases of the model we derive finite size scaling expressions for the current near the continuous phase transition and for the local density near the first order transition under different stochastic dynamics and compare them to establish the existence of universal functions next we study numerically the finite size behavior of the lee yang zeros of the normalization factor for the different steady state probabilities

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

codimension 1 subgroups and splittings of groups abstract we show that under certain circumstances a codimension 1 subgroup h of a finitely generated group g either provides a splitting of g as an amalgam or provides a codimension 1 subgroup of h in particular if g is hyperbolic and h is quasiconvex one gets a descending sequence of codimension 1 subgroups terminating at a splitting in the process we settle a conjecture of kropholler and roller for the case of quasiconvex subgroups of hyperbolic groups

a combination theorem for special cube complexes we prove that certain compact cube complexes have special nite covers this means they have nite covers whose fundamental groups are quasiconvex subgroups of right angled artin groups as a result we obtain linearity and the separability of quasiconvex subgroups for the groups we consider our result applies in particular to a compact negatively curved cube complex whose hyperplanes do not self intersect for a cube complex with word hyperbolic fundamental group we show that it is virtually special if and only if its hyperplane stabilizers are separable in a nal application we show that the fundamental groups of every simple type uniform arithmetic hyperbolic manifolds are cubical and virtually special

transformations of kummer type for 2f2 series and their q analogues linearization method and series rearrangement are employed to review the transformations of kummer type for the generalized hypergeometric f22 series due to exton on the reducibility of the kampe de feriet function j comput appl math 83 1997 119 miller on a kummer type transformation for the generalized hypergeometric function f22 j comput appl math 157 2003 507 and paris a kummer type transformation for a f22 hypergeometric function j comput appl math 173 2005 379 several new transformation formulae as well as their q analogues for the same f22 series are also established

anomalous tag diffusion in the asymmetric exclusion model with particles of arbitrary sizes anomalous behavior of correlation functions of tagged particles are studied in generalizations of the one dimensional asymmetric exclusion problem in these generalized models the range of the hard core interactions are changed and the restriction of relative ordering of the particles is partially broken the models probing these effects are those of biased diffusion of particles having size s 0 1 2 dots or an effective negative size s ensuremath 1 ensuremath 2 dots in units of lattice space our numerical simulations show that irrespective of the range of the hard core potential as long some relative ordering of particles are kept we find suitable sliding tag correlation functions whose fluctuations growth with time anomalously slow t 1 3 when compared with the normal diffusive behavior t 1 2 these results indicate that the critical behavior of these stochastic models are in the kardar parisi zhang kpz universality class moreover a previous bethe ansatz calculation of the dynamical critical exponent z for size sg 0 particles is extended to the case sl0 and the kpz result z frac 3 2 is predicted for all values of s ensuremath in z