Genetically discrete populations of Trypanosoma congolense from livestock on the Kenyan coast

Twenty-seven stocks of Nannomonas trypanosomes isolated from livestock in 1982 on a ranch at Kilifi on the Kenyan coast were characterized by isoenzyme electrophoresis and by the abilities of the parasite's DNA to hybridize to two repetitive sequence DNA probes. Allthe Kilifi stocks which were examined had isoenzyme patterns which were markedly different from the 75 patterns previously described from 78 stocks of Trypanosoma congolense. On average only 15% of the enzyme bands present in the Kilifi stocks were present in those stocks of T. congolense which had previously been surveyed for isoenzymes. The DNA from all the Kilifi stocks which had been examined for isoenzymes hybridized with only the repetitive sequence probe isolated from a clone of a Kilifi stock. In contrast, the DNA from all 27 Kilifi stocks failed to hybridize with a repetitive sequence probe isolated from a clone from a different stock of T. congolense. Thus, the trypanosomes in all the Kilifi stocks examined were both phenotypically and genotypically discrete. These genetically discrete trypanosomes have also been detected in 2 stocks isolated from livestock from another location on the Kenyan coast. The results show that there is a wide range of genetic heterogeneity within the trypanosomes currently classified as T. congolense. We suggest that the limits of this genetic heterogeneity could represent incipient speciatio

p-species integrable reaction-diffusion processes

We consider a process in which there are p-species of particles, i.e. A_1,A_2,...,A_p, on an infinite one-dimensional lattice. Each particle $A_i$ can diffuse to its right neighboring site with rate $D_i$, if this site is not already occupied. Also they have the exchange interaction A_j+A_i --> A_i+A_j with rate $r_{ij}.$ We study the range of parameters (interactions) for which the model is integrable. The wavefunctions of this multi--parameter family of integrable models are found. We also extend the 2--species model to the case in which the particles are able to diffuse to their right or left neighboring sites.Comment: 16 pages, LaTe

An interacting spin flip model for one-dimensional proton conduction

A discrete asymmetric exclusion process (ASEP) is developed to model proton conduction along one-dimensional water wires. Each lattice site represents a water molecule that can be in only one of three states; protonated, left-pointing, and right-pointing. Only a right(left)-pointing water can accept a proton from its left(right). Results of asymptotic mean field analysis and Monte-Carlo simulations for the three-species, open boundary exclusion model are presented and compared. The mean field results for the steady-state proton current suggest a number of regimes analogous to the low and maximal current phases found in the single species ASEP [B. Derrida, Physics Reports, {\bf 301}, 65-83, (1998)]. We find that the mean field results are accurate (compared with lattice Monte-Carlo simulations) only in the certain regimes. Refinements and extensions including more elaborate forces and pore defects are also discussed.Comment: 13pp, 6 fig

Asymmetric exclusion process with next-nearest-neighbor interaction: some comments on traffic flow and a nonequilibrium reentrance transition

We study the steady-state behavior of a driven non-equilibrium lattice gas of hard-core particles with next-nearest-neighbor interaction. We calculate the exact stationary distribution of the periodic system and for a particular line in the phase diagram of the system with open boundaries where particles can enter and leave the system. For repulsive interactions the dynamics can be interpreted as a two-speed model for traffic flow. The exact stationary distribution of the periodic continuous-time system turns out to coincide with that of the asymmetric exclusion process (ASEP) with discrete-time parallel update. However, unlike in the (single-speed) ASEP, the exact flow diagram for the two-speed model resembles in some important features the flow diagram of real traffic. The stationary phase diagram of the open system obtained from Monte Carlo simulations can be understood in terms of a shock moving through the system and an overfeeding effect at the boundaries, thus confirming theoretical predictions of a recently developed general theory of boundary-induced phase transitions. In the case of attractive interaction we observe an unexpected reentrance transition due to boundary effects.Comment: 12 pages, Revtex, 7 figure

Single-File Diffusion of Atomic and Colloidal Systems: Asymptotic Laws

In this work we present a general derivation of the non-Fickian behavior for the self-diffusion of identically interacting particle systems with excluded mutual passage. We show that the conditional probability distribution of finding a particle at position $x_{t}$ after time $t$, when the particle was located at $x_{0}$ at $t=0$, follows a Gaussian distribution in the long-time limit, with variance $2W(t)\sim t^{1/2}$ for overdamped systems and with variance $2W(t)\sim t$ for classical systems. The asymptotic behavior of the mean-squared displacement, $W(t)$, is shown to be independent of the nature of interactions for homogeneous systems in the fluid state. Moreover, the long-time behavior of self-diffusion is determined by short-time and large scale collective density fluctuations.Comment: 4 page

Persistence in the One-Dimensional A+B -> 0 Reaction-Diffusion Model

The persistence properties of a set of random walkers obeying the A+B -> 0 reaction, with equal initial density of particles and homogeneous initial conditions, is studied using two definitions of persistence. The probability, P(t), that an annihilation process has not occurred at a given site has the asymptotic form $P(t) -> const + t^{-\theta}$, where $\theta$ is the persistence exponent (``type I persistence''). We argue that, for a density of particles $\rho >> 1$, this non-trivial exponent is identical to that governing the persistence properties of the one-dimensional diffusion equation, where $\theta \approx 0.1207$. In the case of an initially low density, $\rho_0 << 1$, we find $\theta \approx 1/4$ asymptotically. The probability that a site remains unvisited by any random walker (``type II persistence'') is also investigated and found to decay with a stretched exponential form, $P(t) \sim \exp(-const \rho_0^{1/2}t^{1/4})$, provided $\rho_0 << 1$. A heuristic argument for this behavior, based on an exactly solvable toy model, is presented.Comment: 11 RevTeX pages, 19 EPS figure

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