3,779 research outputs found

    Two-way traffic flow: exactly solvable model of traffic jam

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    We study completely asymmetric 2-channel exclusion processes in 1 dimension. It describes a two-way traffic flow with cars moving in opposite directions. The interchannel interaction makes cars slow down in the vicinity of approaching cars in other lane. Particularly, we consider in detail the system with a finite density of cars on one lane and a single car on the other one. When the interchannel interaction reaches a critical value, traffic jam occurs, which turns out to be of first order phase transition. We derive exact expressions for the average velocities, the current, the density profile and the kk- point density correlation functions. We also obtain the exact probability of two cars in one lane being distance RR apart, provided there is a finite density of cars on the other lane, and show the two cars form a weakly bound state in the jammed phase.Comment: 17 pages, Latex, ioplppt.sty, 11 ps figure

    Persistence in the Zero-Temperature Dynamics of the Diluted Ising Ferromagnet in Two Dimensions

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    The non-equilibrium dynamics of the strongly diluted random-bond Ising model in two-dimensions (2d) is investigated numerically. The persistence probability, P(t), of spins which do not flip by time t is found to decay to a non-zero, dilution-dependent, value P()P(\infty). We find that p(t)=P(t)P()p(t)=P(t)-P(\infty) decays exponentially to zero at large times. Furthermore, the fraction of spins which never flip is a monotonically increasing function over the range of bond-dilution considered. Our findings, which are consistent with a recent result of Newman and Stein, suggest that persistence in disordered and pure systems falls into different classes. Furthermore, its behaviour would also appear to depend crucially on the strength of the dilution present.Comment: some minor changes to the text, one additional referenc

    Correlation functions of the One-Dimensional Random Field Ising Model at Zero Temperature

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    We consider the one-dimensional random field Ising model, where the spin-spin coupling, JJ, is ferromagnetic and the external field is chosen to be +h+h with probability pp and h-h with probability 1p1-p. At zero temperature, we calculate an exact expression for the correlation length of the quenched average of the correlation function s0sns0sn\langle s_0 s_n \rangle - \langle s_0 \rangle \langle s_n \rangle in the case that 2J/h2J/h is not an integer. The result is a discontinuous function of 2J/h2J/h. When p=12p = {1 \over 2}, we also place a bound on the correlation length of the quenched average of the correlation function s0sn\langle s_0 s_n \rangle.Comment: 12 pages (Plain TeX with one PostScript figure appended at end), MIT CTP #220

    Directed polymer in a random medium of dimension 1+1 and 1+3: weights statistics in the low-temperature phase

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    We consider the low-temperature T<TcT<T_c disorder-dominated phase of the directed polymer in a random potentiel in dimension 1+1 (where Tc=T_c=\infty) and 1+3 (where Tc<T_c<\infty). To characterize the localization properties of the polymer of length LL, we analyse the statistics of the weights wL(r)w_L(\vec r) of the last monomer as follows. We numerically compute the probability distributions P1(w)P_1(w) of the maximal weight wLmax=maxr[wL(r)]w_L^{max}= max_{\vec r} [w_L(\vec r)], the probability distribution Π(Y2)\Pi(Y_2) of the parameter Y2(L)=rwL2(r)Y_2(L)= \sum_{\vec r} w_L^2(\vec r) as well as the average values of the higher order moments Yk(L)=rwLk(r)Y_k(L)= \sum_{\vec r} w_L^k(\vec r). We find that there exists a temperature Tgap<TcT_{gap}<T_c such that (i) for T<TgapT<T_{gap}, the distributions P1(w)P_1(w) and Π(Y2)\Pi(Y_2) present the characteristic Derrida-Flyvbjerg singularities at w=1/nw=1/n and Y2=1/nY_2=1/n for n=1,2..n=1,2... In particular, there exists a temperature-dependent exponent μ(T)\mu(T) that governs the main singularities P1(w)(1w)μ(T)1P_1(w) \sim (1-w)^{\mu(T)-1} and Π(Y2)(1Y2)μ(T)1\Pi(Y_2) \sim (1-Y_2)^{\mu(T)-1} as well as the power-law decay of the moments Yk(i)ˉ1/kμ(T) \bar{Y_k(i)} \sim 1/k^{\mu(T)}. The exponent μ(T)\mu(T) grows from the value μ(T=0)=0\mu(T=0)=0 up to μ(Tgap)2\mu(T_{gap}) \sim 2. (ii) for Tgap<T<TcT_{gap}<T<T_c, the distribution P1(w)P_1(w) vanishes at some value w0(T)<1w_0(T)<1, and accordingly the moments Yk(i)ˉ\bar{Y_k(i)} decay exponentially as (w0(T))k(w_0(T))^k in kk. The histograms of spatial correlations also display Derrida-Flyvbjerg singularities for T<TgapT<T_{gap}. Both below and above TgapT_{gap}, the study of typical and averaged correlations is in full agreement with the droplet scaling theory.Comment: 13 pages, 29 figure

    Number and length of attractors in a critical Kauffman model with connectivity one

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    The Kauffman model describes a system of randomly connected nodes with dynamics based on Boolean update functions. Though it is a simple model, it exhibits very complex behavior for "critical" parameter values at the boundary between a frozen and a disordered phase, and is therefore used for studies of real network problems. We prove here that the mean number and mean length of attractors in critical random Boolean networks with connectivity one both increase faster than any power law with network size. We derive these results by generating the networks through a growth process and by calculating lower bounds.Comment: 4 pages, no figure, no table; published in PR

    Zero Temperature Dynamics of the Weakly Disordered Ising Model

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    The Glauber dynamics of the pure and weakly disordered random-bond 2d Ising model is studied at zero-temperature. A single characteristic length scale, L(t)L(t), is extracted from the equal time correlation function. In the pure case, the persistence probability decreases algebraically with the coarsening length scale. In the disordered case, three distinct regimes are identified: a short time regime where the behaviour is pure-like; an intermediate regime where the persistence probability decays non-algebraically with time; and a long time regime where the domains freeze and there is a cessation of growth. In the intermediate regime, we find that P(t)L(t)θP(t)\sim L(t)^{-\theta'}, where θ=0.420±0.009\theta' = 0.420\pm 0.009. The value of θ\theta' is consistent with that found for the pure 2d Ising model at zero-temperature. Our results in the intermediate regime are consistent with a logarithmic decay of the persistence probability with time, P(t)(lnt)θdP(t)\sim (\ln t)^{-\theta_d}, where θd=0.63±0.01\theta_d = 0.63\pm 0.01.Comment: references updated, very minor amendment to abstract and the labelling of figures. To be published in Phys Rev E (Rapid Communications), 1 March 199
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