Phase Coexistence in Driven One Dimensional Transport

We study a one-dimensional totally asymmetric exclusion process with random particle attachments and detachments in the bulk. The resulting dynamics leads to unexpected stationary regimes for large but finite systems. Such regimes are characterized by a phase coexistence of low and high density regions separated by domain walls. We use a mean-field approach to interpret the numerical results obtained by Monte-Carlo simulations and we predict the phase diagram of this non-conserved dynamics in the thermodynamic limit.Comment: 4 pages, 3 figures. Accepted for publication on Phys. Rev. Let

Bethe ansatz solution of zero-range process with nonuniform stationary state

The eigenfunctions and eigenvalues of the master-equation for zero range process with totally asymmetric dynamics on a ring are found exactly using the Bethe ansatz weighted with the stationary weights of particle configurations. The Bethe ansatz applicability requires the rates of hopping of particles out of a site to be the $q$-numbers $[n]_q$. This is a generalization of the rates of hopping of noninteracting particles equal to the occupation number $n$ of a site of departure. The noninteracting case can be restored in the limit $q\to 1$. The limiting cases of the model for $q=0,\infty$ correspond to the totally asymmetric exclusion process, and the drop-push model respectively. We analyze the partition function of the model and apply the Bethe ansatz to evaluate the generating function of the total distance travelled by particles at large time in the scaling limit. In case of non-zero interaction, $q \ne 1$, the generating function has the universal scaling form specific for the Kardar-Parizi-Zhang universality class.Comment: 7 pages, Revtex4, mistypes correcte

Boundary-induced nonequilibrium phase transition into an absorbing state

We demonstrate that absorbing phase transitions in one dimension may be induced by the dynamics of a single site. As an example we consider a one-dimensional model of diffusing particles, where a single site at the boundary evolves according to the dynamics of a contact process. As the rate for offspring production at this site is varied, the model exhibits a phase transition from a fluctuating active phase into an absorbing state. The universal properties of the transition are analyzed by numerical simulations and approximation techniques.Comment: 4 pages, 4 figures; minor change

Numerical Study of Phase Transition in an Exclusion Model with Parallel Dynamics

A numerical method based on Matrix Product Formalism is proposed to study the phase transitions and shock formation in the Asymmetric Simple Exclusion Process with open boundaries and parallel dynamics. By working in a canonical ensemble, where the total number of the particles is being fixed, we find that the model has a rather non-trivial phase diagram consisting of three different phases which are separated by second-order phase transition. Shocks may evolve in the system for special values of the reaction parameters.Comment: 8 pages, 3 figure

Gene Structure, cDNA Sequence, and mRNA Distribution

The rat HNF-3 (hepatocyte nuclear factor 3) gene family encodes three transcription factors known to be important in the regulation of gene expression in liver and lung. We have cloned and characterized the mouse genes and cDNAs for HNF-3α, β, and γ and analyzed their expression patterns in various adult tissues and mouse embryonic stages. The HNF-3 proteins are highly conserved between mouse and rat, with the exception of the amino terminus of HNF-3γ, which in mouse is more similar to those of HNF-3α and β than to the amino termini of the rat HNF-3γ protein. The mouse HNF-3 genes are small and contain only two or three (HNF-3β) exons with conserved intron-exon boundaries. The proximal promoter of the mouse HNF3β gene is remarkably similar to that of the previously cloned rat HNF-3β gene, but is different from the promoters of the HNF-3α and γ genes. The mRNA distribution of the mouse HNF-3 genes was analyzed by quantitative RNase protection with gene-specific probes. While HNF-3α and β are restricted mainly to endoderm-derived tissues (lung, liver, stomach, and small intestine), HNF-3γ is more extensively expressed, being present additionally in ovary, testis, heart, and adipose tissue, but missing from lung. Transcripts for HNF-3β and α are detected most abundantly in midgestation embryos (Day 9.5), while HNF-3γ expression peaks around Day 15.5 of gestation

Exact time-dependent correlation functions for the symmetric exclusion process with open boundary

As a simple model for single-file diffusion of hard core particles we investigate the one-dimensional symmetric exclusion process. We consider an open semi-infinite system where one end is coupled to an external reservoir of constant density $\rho^\ast$ and which initially is in an non-equilibrium state with bulk density $\rho_0$. We calculate the exact time-dependent two-point density correlation function $C_{k,l}(t)\equiv -$ and the mean and variance of the integrated average net flux of particles $N(t)-N(0)$ that have entered (or left) the system up to time $t$. We find that the boundary region of the semi-infinite relaxing system is in a state similar to the bulk state of a finite stationary system driven by a boundary gradient. The symmetric exclusion model provides a rare example where such behavior can be proved rigorously on the level of equal-time two-point correlation functions. Some implications for the relaxational dynamics of entangled polymers and for single-file diffusion in colloidal systems are discussed.Comment: 11 pages, uses REVTEX, 2 figures. Minor typos corrected and reference 17 adde

Exact solution of a one-parameter family of asymmetric exclusion processes

We define a family of asymmetric processes for particles on a one-dimensional lattice, depending on a continuous parameter $\lambda \in [0,1]$, interpolating between the completely asymmetric processes [1] (for $\lambda =1$) and the n=1 drop-push models [2] (for $\lambda =0$). For arbitrary \la, the model describes an exclusion process, in which a particle pushes its right neighbouring particles to the right, with rates depending on the number of these particles. Using the Bethe ansatz, we obtain the exact solution of the master equation .Comment: 14 pages, LaTe

Time-dependent correlation functions in a one-dimensional asymmetric exclusion process

We study a one-dimensional anisotropic exclusion process describing particles injected at the origin, moving to the right on a chain of $L$ sites and being removed at the (right) boundary. We construct the steady state and compute the density profile, exact expressions for all equal-time n-point density correlation functions and the time-dependent two-point function in the steady state as functions of the injection and absorption rates. We determine the phase diagram of the model and compare our results with predictions from dynamical scaling and discuss some conjectures for other exclusion models.Comment: LATEX-file, 32 pages, Weizmann preprint WIS/93/01/Jan-P

Weakly disordered absorbing-state phase transitions

The effects of quenched disorder on nonequilibrium phase transitions in the directed percolation universality class are revisited. Using a strong-disorder energy-space renormalization group, it is shown that for any amount of disorder the critical behavior is controlled by an infinite-randomness fixed point in the universality class of the random transverse-field Ising models. The experimental relevance of our results are discussed.Comment: 4 pages, 2 eps figures; (v2) references and discussion on experiments added; (v3) published version, minor typos corrected, some side discussions dropped due to size constrain

The asymmetric exclusion model with sequential update

We present a solution for the stationary state of an asymmetric exclusion model with sequential update and open boundary conditions. We solve the model exactly for random hopping in both directions by applying a matrix-product formalism which was recently used to solve the model with sublattice-parallel update[1]. It is shown that the matrix-algebra describing the sequential update and sublattice-parallel update are identical and can be mapped onto the random sequential case treated by Derrida et al[2].Comment: 7 pages, Late