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We show that domain walls separating coexisting extremal current phases in driven diffusive systems exhibit complex stochastic dynamics with a subdiffusive temporal growth of position fluctuations due to long-range anticorrelated current fluctuations and a weak pinning at long times. This weak pinning manifests itself in a saturated width of the domain wall position fluctuations that increases sublinearly with the system size. As a function of time t and system size L, the width w(t,L) has a scaling behavior w(t,L)=L^{3/4}f(t/L^{9/4}), with f(u) constant for u≫1 and f(u)∼u^{1/3} for u≪1. An Orstein-Uhlenbeck process with long-range anticorrelated noise is shown to capture this scaling behavior. The exponent 9/4 is a new dynamical exponent for relaxation processes in driven diffusive systems.

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The ribosome is one of the largest and most complex macromolecular machines in living cells. It polymerizes a protein in a step-by-step manner as directed by the corresponding nucleotide sequence on the template messenger RNA (mRNA) and this process is referred to as "translation" of the genetic message encoded in the sequence of mRNA transcript. In each successful chemomechanical cycle during the (protein) elongation stage, the ribosome elongates the protein by a single subunit, called amino acid, and steps forward on the template mRNA by three nucleotides called a codon. Therefore, a ribosome is also regarded as a molecular motor for which the mRNA serves as the track, its step size is that of a codon and two molecules of GTP and one molecule of ATP hydrolyzed in that cycle serve as its fuel. What adds further complexity is the existence of competing pathways leading to distinct cycles, branched pathways in each cycle, and futile consumption of fuel that leads neither to elongation of the nascent protein nor forward stepping of the ribosome on its track. We investigate a model formulated in terms of the network of discrete chemomechanical states of a ribosome during the elongation stage of translation. The model is analyzed using a combination of stochastic thermodynamic and kinetic analysis based on a graph-theoretic approach. We derive the exact solution of the corresponding master equations. We represent the steady state in terms of the cycles of the underlying network and discuss the energy transduction processes. We identify the various possible modes of operation of a ribosome in terms of its average velocity and mean rate of GTP hydrolysis. We also compute entropy production as functions of the rates of the interstate transitions and the thermodynamic cost for accuracy of the translation process.

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Dynamical universality classes are distinguished by their dynamical exponent z and unique scaling functions encoding space-time asymmetry for, e.g., slow-relaxation modes or the distribution of time-integrated currents. So far the universality class of the Nagel-Schreckenberg (NaSch) model, which is a paradigmatic model for traffic flow on highways, was not known. Only the special case v_{max}=1, where the model corresponds to the totally asymmetric simple exclusion process, is known to belong to the superdiffusive Kardar-Parisi-Zhang (KPZ) class with z=3/2. In this paper, we show that the NaSch model also belongs to the KPZ class for general maximum velocities v_{max}>1. Using nonlinear fluctuating hydrodynamics theory we calculate the nonuniversal coefficients, fixing the exact asymptotic solutions for the dynamical structure function and the distribution of time-integrated currents. The results of large-scale Monte Carlo simulations match the exact asymptotic KPZ solutions without any fitting parameter left. Additionally, we find that nonuniversal early-time effects or the choice of initial conditions might have a strong impact on the numerical determination of the dynamical exponent and therefore lead to inconclusive results. We also show that the universality class is not changed by extending the model to a two-lane NaSch model with lane-changing rules.

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Universality is a well-established central concept of equilibrium physics. However, in systems far away from equilibrium, a deeper understanding of its underlying principles is still lacking. Up to now, a few classes have been identified. Besides the diffusive universality class with dynamical exponent [Formula: see text], another prominent example is the superdiffusive Kardar-Parisi-Zhang (KPZ) class with [Formula: see text]. It appears, e.g., in low-dimensional dynamical phenomena far from thermal equilibrium that exhibit some conservation law. Here we show that both classes are only part of an infinite discrete family of nonequilibrium universality classes. Remarkably, their dynamical exponents [Formula: see text] are given by ratios of neighboring Fibonacci numbers, starting with either [Formula: see text] (if a KPZ mode exist) or [Formula: see text] (if a diffusive mode is present). If neither a diffusive nor a KPZ mode is present, all dynamical modes have the Golden Mean [Formula: see text] as dynamical exponent. The universal scaling functions of these Fibonacci modes are asymmetric Lévy distributions that are completely fixed by the macroscopic current density relation and compressibility matrix of the system and hence accessible to experimental measurement.

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For almost a decade the consensus has held that the random walk propagator for the elephant random walk (ERW) model is a Gaussian. Here we present strong numerical evidence that the propagator is, in general, non-Gaussian and, in fact, non-Lévy. Motivated by this surprising finding, we seek a second, non-Gaussian solution to the associated Fokker-Planck equation. We prove mathematically, by calculating the skewness, that the ERW Fokker-Planck equation has a non-Gaussian propagator for the superdiffusive regime. Finally, we discuss some unusual aspects of the propagator in the context of higher order terms needed in the Fokker-Planck equation.

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We examine the effect of spatial correlations on the phenomenon of real-space condensation in driven mass-transport systems. We suggest that in a broad class of models with a spatially correlated steady state, the condensate drifts with a nonvanishing velocity. We present a robust mechanism leading to this condensate drift. This is done within the framework of a generalized zero-range process (ZRP) in which, unlike the usual ZRP, the steady state is not a product measure. The validity of the mechanism in other mass-transport models is discussed.

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Using dynamical Monte Carlo simulations we observe the occurrence of an unexpected shock wave in driven diffusive systems with two conserved species of particles. This U shock is microscopically sharp, but does not satisfy the usual criteria for the stability of shocks. Exact analysis of the large-scale hydrodynamic equations of motion reveals the presence of an umbilical point which we show to be responsible for this phenomenon. We prove that such an umbilical point is a general feature of multispecies driven diffusive systems with reflection symmetry of the bulk dynamics. We argue that a U shock will occur whenever there are strong interactions between species such that the current-density relation develops a double well and the umbilical point becomes isolated.

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The late-time distribution function P(x,t) of a particle diffusing in a one-dimensional logarithmic potential is calculated for arbitrary initial conditions. We find a scaling solution with three surprising features: (i) the solution is given by two distinct scaling forms, corresponding to a diffusive (x∼t(1/2)) and a subdiffusive (x∼t(γ) with a given γ<1/2) length scale, respectively, (ii) the overall scaling function is selected by the initial condition, and (iii) depending on the tail of the initial condition, the scaling exponent that characterizes the scaling function is found to exhibit a transition from a continuously varying to a fixed value.

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Reactivity enhancement in a catalytic zeolite grain through molecular traffic control (MTC) rests on the basic notion that the reactant and product molecules prefer to diffuse along different channels inside the grain and therefore do not mutually hinder their transport in and out of the grain. We investigate the conditions of reactivity enhancement in the presence of MTC for a realistic channel topology that describes the pore structure of a TNU-9 zeolite. We compare the output current of an MTC system with a reference system, which does not show any channel selectivity. For a wide range of reaction rates and for different grain sizes, we find that there is a very significant enhancement of reactivity for the MTC system. This effect remains strong as the grain size increases. The mechanism behind reactivity enhancement is argued to be generic rather than being confined to the particular structure of TNU-9.

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The impact of temporally correlated dynamics on nonequilibrium condensation is studied using a non-Markovian zero-range process (ZRP). We find that memory effects can modify the condensation scenario significantly: (i) For mean-field dynamics, the steady state corresponds to that of a Markovian ZRP, but with modified hopping rates which can affect condensation; (ii) for nearest-neighbor hopping dynamics in one dimension, the condensate is found to occupy two adjacent lattice sites and to drift with a finite velocity. The validity of these results in a more general context is discussed.

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The zero-range process is a stochastic interacting particle system that is known to exhibit a condensation transition. We present a detailed analysis of this transition in the presence of quenched disorder in the particle interactions. Using rigorous probabilistic arguments, we show that disorder changes the critical exponent in the interaction strength below which a condensation transition may occur. The local critical densities may exhibit large fluctuations, and their distribution shows an interesting crossover from exponential to algebraic behavior.

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We consider the asymmetric simple exclusion process (ASEP) on a semi-infinite chain which is coupled at the end to a reservoir with a particle density that changes periodically in time. It is shown that the density profile assumes a time-periodic sawtoothlike shape. This shape does not depend on initial conditions and is found analytically in the hydrodynamic limit. In a finite system, the stationary state is shown to be governed by effective boundary densities and the extremal flux principle. Effective boundary densities are determined numerically via Monte Carlo simulations and compared with those given by mean-field approach and numerical integration of the hydrodynamic limit equation which is the Burgers equation. Our results extend straightforwardly beyond the ASEP to a wide class of driven diffusive systems with one conserved particle species.

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The susceptible-infectious-recovered (SIR) model describes the evolution of three species of individuals which are subject to an infection and recovery mechanism. A susceptible S can become infectious with an infection rate beta by an infectious I type provided that both are in contact. The I type may recover with a rate gamma and from then on stay immune. Due to the coupling between the different individuals, the model is nonlinear and out of equilibrium. We adopt a stochastic individual-based description where individuals are represented by nodes of a graph and contact is defined by the links of the graph. Mapping the underlying master equation onto a quantum formulation in terms of spin operators, the hierarchy of evolution equations can be solved exactly for arbitrary initial conditions on a linear chain. In the case of uncorrelated random initial conditions, the exact time evolution for all three individuals of the SIR model is given analytically. Depending on the initial conditions and reaction rates beta and gamma , the I population may increase initially before decaying to zero. Due to fluctuations, isolated regions of susceptible individuals evolve, and unlike in the standard mean-field SIR model, one observes a finite stationary distribution of the S type even for large population size. The exact results for the ensemble-averaged population size are compared with simulations for single realizations of the process and also with standard mean-field theory, which is expected to be valid on large fully connected graphs.

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We investigate the conditions for reactivity enhancement of catalytic processes in porous solids by the use of molecular traffic control (MTC). With dynamic Monte-Carlo simulations and continuous-time master equation theory applied to the high concentration regime, we obtain a quantitative description of the MTC effect for a network of intersecting single-file channels in a wide range of grain parameters and for optimal external operating conditions. Implementing the concept of MTC in models with specially designed alternating bimodal channels, we find the efficiency ratio (compared with a topologically and structurally similar reference system without MTC) to be enhanced with increasing grain diameter, a property verified for the first time for a MTC system. Even for short intersection channels, MTC leads to a reactivity enhancement of up to approximately 65%. This suggests that MTC may significantly enhance the efficiency of a catalytic process for small as well as large porous particles with a suitably chosen binary channel topology.

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We determine all families of Markovian three-state lattice gases with pair interaction and a single local conservation law. One such family of models is an asymmetric exclusion process where particles exist in two different nonconserved states. We derive conditions on the transition rates between the two states such that the shock has a particularly simple structure with minimal intrinsic shock width and random walk dynamics. We calculate the drift velocity and diffusion coefficient of the shock.

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We investigate the change of critical behavior of two-level hierarchy systems in which the second level (B) is unidirectionally coupled to the first (A) by the coupling dynamics A --> A + nB with n = 1 or 2. The first level belongs to the directed percolation or the parity-conserving (PC) universality class, the second to PC. If both levels are critical, the active region of the second level becomes heterogeneous. In the so-called coupled region the first level feeds particles to the second, while in the uncoupled region the second level evolves autonomously. Measuring dynamic critical exponents in both regions, we show to what extent the critical behavior of the second level depends on the universality class of the first. These results suggest a simple criterion for the emergence of unusual critical behavior of unidirectionally coupled nonequilibrium systems.

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We consider a discrete-time random walk where the random increment at time step t depends on the full history of the process. We calculate exactly the mean and variance of the position and discuss its dependence on the initial condition and on the memory parameter p . At a critical value p((1) )(c ) =1/2 where memory effects vanish there is a transition from a weakly localized regime [where the walker (elephant) returns to its starting point] to an escape regime. Inside the escape regime there is a second critical value where the random walk becomes superdiffusive. The probability distribution is shown to be governed by a non-Markovian Fokker-Planck equation with hopping rates that depend both on time and on the starting position of the walk. On large scales the memory organizes itself into an effective harmonic oscillator potential for the random walker with a time-dependent spring constant k=(2p-1)/t . The solution of this problem is a Gaussian distribution with time-dependent mean and variance which both depend on the initiation of the process.

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Using a generalized Rubinstein-Duke model, we prove rigorously that kinematic disorder leaves the prediction of the standard reptation theory for the scaling of the diffusion constant in the limit for long polymer chains D proportional to L(-2) unaffected. Based on an analytical calculation as well as on Monte Carlo simulations, we predict kinematic disorder to affect the center-of-mass diffusion constant of an entangled polymer in the limit for long chains by the same factor as single particle diffusion in a random barrier model.

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The scaling of the viscosity of polymer melts is investigated with regard to the molecular weight. We present a generalization of the Rubinstein-Duke model, which takes constraint releases into account and calculates the effects on the viscosity by the use of the density matrix renormalization group algorithm. Using input from Rouse theory, the rates for the constraint releases are determined in a self-consistent way. We conclude that shape fluctuations of the tube caused by constraint release are not a likely candidate for improving Doi's crossover theory for the scaling of the polymer viscosity.