Publications
2021

(2021) Journal of Physics A: Mathematical and Theoretical. 54, 2, 025001. Abstract
The dynamics of a driven tracer in a quiescent bath subject to geometric confinement models a broad range of phenomena. We explore this dynamics in a 1D lattice model, where geometric confinement is tuned by varying the rate of particle overtaking. Previous studies of the model's stationary properties on a ring of L sites have revealed a phase in which the bath density profile extends over an similar to O(L) distance from the tracer and the tracer's velocity vanishes as similar to 1/L. Here, we study the model's long time dynamics in this phase for L > infinity. We show that the bath density profile evolves on a similar to root t timescale and, correspondingly, that the tracer's velocity decays as similar to 1/root t. Unlike the wellstudied case of a nondriven tracer, whose dynamics becomes diffusive whenever overtaking is allowed, we here find that driving the tracer preserves its hallmark subdiffusive singlefile dynamics, even in the presence of overtaking.
2020

(2020) Journal Of Statistical MechanicsTheory And Experiment. 2020, 6, 063216. Abstract
The effect of particle overtaking on transport in a narrow channel is studied using a 1D model of a driven tracer in a quiescent bath. In contrast with the wellstudied nondriven case, where the tracer's longtime dynamics changes from subdiffusive to diffusive whenever overtaking is allowed, the driven tracer is shown to exhibit a phase transition at a finite overtaking rate. The transition separates a phase in which the stationary bath density profile, as seen in the tracer's frame, is extended, as in the nonovertaking case, to a phase with a localized bath density profile. In the extended phase the tracer velocity vanishes in the thermodynamic limit while it remains finite in the localized phase. The phase diagram of the model, as well as the tracer velocity and the bath density profile in both phases, are studied, demonstrating their distinct features.
2019

(2019) Physical Review E. 100, 5, 052135. Abstract
The canonical phase diagram of the BlumeEmeryGriffiths model with infiniterange interactions is known to exhibit a fourthorder critical point at some negative value of the biquadratic interaction K <0. Here we study the microcanonical phase diagram of this model for K <0, extending previous studies which were restricted to positive K. A fourthorder critical point is found to exist at coupling parameters which are different from those of the canonical ensemble. The microcanonical phase diagram of the model close to the fourthorder critical point is studied in detail revealing some distinct features from the canonical counterpart.

(2019) Physical Review Letters. 123, 10, 100603. Abstract
We study an interacting system of N classical particles on a line at thermal equilibrium. The particles are confined by a harmonic trap and repel each other via pairwise interaction potential that behaves as a power law proportional to Sigma i not equal j(N) vertical bar x(i)  x(j)vertical bar(k) (with k > 2) of their mutual distance. This is a generalization of the wellknown cases of the onecomponent plasma (k = 1), Dyson's log gas (k > 0(+)), and the CalogeroMoser model (k = 2). Because of the competition between harmonic confinement and pairwise repulsion, the particles spread over a finite region of space for all k > 2. We compute exactly the average density profile for large N for all k > 2 and show that while it is independent of temperature for sufficiently low temperature, it has a rich and nontrivial dependence on k with distinct behavior for 2 <k <1, k > 1 and k = 1.

(2019) JOURNAL OF PHYSICS AMATHEMATICAL AND THEORETICAL. 52, 25, 254001. Abstract
Mixed order transitions are those which show a discontinuity of the order parameter as well as a divergent correlation length at the transition (critical) point. We show that the behavior of the order parameter correlation function along the transition line of mixed order transitions can change from normal critical behavior with power law decay, to fluctuationdominated phase ordering as a parameter is varied. The defining features of fluctuationdominated order are anomalous fluctuations which remain large in the thermodynamic limit, and correlation functions which approach a finite value through a cusp singularity as the separation scaled by the system size approaches zero. We demonstrate that fluctuationdominated order sets in along a portion of the transition line of an Ising model with truncated longrange interactions which was earlier shown to exhibit mixed order transitions. We also argue that this connection may hold more generally.

(2019) Physical Review E. 99, 1, 012124. Abstract
A recently developed nonlinear fluctuating hydrodynamics theory has been quite successful in describing various features of anomalous energy transport. However, the diffusion and the noise terms present in this theory are not derived from microscopic descriptions but rather added phenomenologically. We here derive these hydrodynamic equations with explicit calculation of the diffusion and noise terms in a onedimensional model. We show that in this model the energy current scales anomalously with system size L as similar to L2/3 in the leading order with a diffusive correction of order similar to L1. The crossover length l(c) from diffusive to anomalous transport is expressed in terms of microscopic parameters. Our theoretical predictions are verified numerically.
2018

(2018) Physical Review Letters. 121, 5, 058102. Abstract
We investigate the shape of a growing interface in the presence of an impenetrable moving membrane. The two distinct geometrical arrangements of the interface and membrane, obtained by placing the membrane behind or ahead of the interface, are not symmetrically related. On the basis of numerical results and an exact calculation, we argue that these two arrangements represent two distinct universality classes for interfacial growth: while the wellestablished KardarParisiZhang (KPZ) growth is obtained in the "ahead" arrangement, we find an arrested KPZ growth with a smaller roughness exponent in the "behind" arrangement. This suggests that the surface properties of growing cell membranes and expanding bacterial colonies, for example, are fundamentally distinct.

(2018) Journal of Physics A: Mathematical and Theoretical. 51, 8, 085001. Abstract
Instances of negative mobility, where a system responds to a perturbation in a way opposite to naive expectation, have been studied theoretically and experimentally in numerous nonequilibrium systems. In this work we show that absolute negative mobility (ANM), whereby current is produced in a direction opposite to the drive, can occur around equilibrium states. This is demonstrated with a simple onedimensional lattice model with a driven tracer. We derive analytical predictions in the linear response regime and elucidate the mechanism leading to ANM by studying the highdensity limit. We also study numerically a model of hard Brownian disks in a narrow planar channel, for which the lattice model can be viewed as a toy model. We find that the model exhibits negative differential mobility (NDM), but no ANM.
2017

(2017) Journal Of Statistical MechanicsTheory And Experiment. 013203. Abstract
A framework for studying the effect of the coupling to the heat bath in models exhibiting anomalous heat conduction is described. The framework is applied to the harmonic chain with momentum exchange model where the nontrivial temperature profile is calculated. In this approach one first uses the hydrodynamic (HD) equations to calculate the equilibrium currentcurrent correlation function in large but finite chains, explicitly taking into account the BCs resulting from the coupling to the heat reservoirs. Making use of a linear response relation, the anomalous conductivity exponent a and an integral equation for the temperature profile are obtained. The temperature profile is found to be singular at the boundaries with an exponent which varies continuously with the coupling to the heat reservoirs expressed by the BCs. In addition, the relation between the harmonic chain and a system of noninteracting Levy walkers is made explicit, where different BCs of the chain correspond to different reflection coefficients of the Levy particles.

(2017) Physical Review E. 95, 1, Abstract
Steadystate properties of a driven tracer moving in a narrow twodimensional (2D) channel of quiescent medium are studied. The tracer drives the system out of equilibrium, perturbs the density and pressure fields, and gives the bath particles a nonzero average velocity, creating a current in the channel. Three models in which the confining effect of the channel is probed are analyzed and compared in this study: the first is the simple symmetric exclusion process (SSEP), for which the stationary density profile and the pressure on the walls in the frame of the tracer are computed. We show that the tracer acts like a dipolar source in an average velocity field. The spatial structure of this 2D strip is then simplified to a onedimensional (1D) SSEP, in which exchanges of position between the tracer and the bath particles are allowed. Using a combination of meanfield theory and exact solution in the limit where no exchange is allowed gives good predictions of the velocity of the tracer and the density field. Finally, we show that results obtained for the 1D SSEP with exchanges also apply to a gas of overdamped hard disks in a narrow channel. The correspondence between the parameters of the SSEP and of the gas of hard disks is systematic and follows from simple intuitive arguments. Our analytical results are checked numerically.
2016

(2016) Physical Review E. 93, 5, 52130. Abstract
We study extremevalue statistics for spatially extended models exhibiting mixedorder phase transitions (MOT). These are phase transitions that exhibit features common to both firstorder (discontinuity of the order parameter) and secondorder (diverging correlation length) transitions. We consider here the truncated inverse distance squared Ising model, which is a prototypical model exhibiting MOT, and study analytically the extremevalue statistics of the domain lengths The lengths of the domains are identically distributed random variables except for the global constraint that their sum equals the total system size L. In addition, the number of such domains is also a fluctuating variable, and not fixed. In the paramagnetic phase, we show that the distribution of the largest domain length l(max) converges, in the large L limit, to a Gumbel distribution. However, at the critical point (for a certain range of parameters) and in the ferromagnetic phase, we show that the fluctuations of l(max) are governed by novel distributions, which we compute exactly. Our main analytical results are verified by numerical simulations.

(2016) JOURNAL OF PHYSICS AMATHEMATICAL AND THEORETICAL. 49, 15, 155002. Abstract
We study the effect of a onedimensional driving field on the interface between two coexisting phases in a two dimensional model. This is done by considering an Ising model on a cylinder with Glauber dynamics in all sites and additional biased Kawasaki dynamics in the central ring. Based on the exact solution of the twodimensional Ising model, we are able to compute the phase diagram of the driven model within a special limit of fast drive and slow spin flips in the central ring. The model is found to exhibit two phases where the interface is pinned to the central ring: one in which it fluctuates symmetrically around the central ring and another where it fluctuates asymmetrically. In addition, we find a phase where the interface is centered in the bulk of the system, either below or above the central ring of the cylinder. In the latter case, the symmetry breaking is 'stronger' than that found in equilibrium when considering a repulsive potential on the central ring. This equilibrium model is analyzed here by using a restricted solidonsolid model.

(2016) Journal of Statistical Mechanics: Theory and Experiment. 2016, 3, p. 033108 (31 pp.)033108 (31 pp.) Abstract
We consider a simple onedimensional stochastic model of heat transport which locally conserves both energy and momentum and which is coupled to heat reservoirs with different temperatures at its two ends. The steady state is analyzed and the model is found to obey the Fourier law with finite heat conductivity. In the infinite length limit, the steady state is described locally by an equilibrium Gibbs state. However finite size corrections to this local equilibrium state are present. We analyze these finite size corrections by calculating the onsite fluctuations of the momentum and the two point correlation of the momentum and energy. These correlations are long ranged and have scaling forms which are computed explicitly. We also introduce a multilane variant of the model in which correlations vanish in the steady state. The deviation from local equilibrium in this model as expressed in terms of the onsite momentum fluctuations is calculated in the large length limit.

(2016) JOURNAL OF PHYSICS AMATHEMATICAL AND THEORETICAL. 49, 8, 085002. Abstract
We study the statistics of the gaps in the random average process on a ring with particles hopping symmetrically, except one tracer particle which could be driven. These particles hop either to the left or to the right by a random fraction eta of the space available till next particle in the respective directions. The random fraction eta is an element of [0, 1) is chosen from a distribution R(eta). For a nondriven tracer, when R(eta) satisfies a necessary and sufficient condition, the stationary joint distribution of the gaps between successive particles takes a universal form that is factorized except for a global constraint. Some interesting explicit forms of R(eta) are found which satisfy this condition. In the case of a driven tracer, the system reaches a currentcarrying steady state where such factorization does not hold. Analytical progress has been made in the thermodynamic limit, where we computed the single site distribution inside the bulk. We have also computed the two point gapgap correlation exactly in that limit. Numerical simulations support our analytical results.
2015

(2015) Journal of Statistical Mechanics: Theory and Experiment. 2015, 11, p. P11023 (28 pp.)P11023 (28 pp.) Abstract
We study the asymmetric zerorange process (ZRP) with L sites and open boundaries, conditioned to carry an atypical current. Using a generalized Doob htransform we compute explicitly the transition rates of an effective process for which the conditioned dynamics are typical. This effective process is a zerorange process with renormalized hopping rates, which are space dependent even when the original rates are constant. This leads to nontrivial density profiles in the steady state of the conditioned dynamics, and, under generic conditions on the jump rates of the unconditioned ZRP, to an intriguing supercritical bulk region where condensates can grow. These results provide a microscopic perspective on macroscopic fluctuation theory (MFT) for the weakly asymmetric case: it turns out that the predictions of MFT remain valid in the nonrigorous limit of finite asymmetry. In addition, the microscopic results yield the correct scaling factor for the asymmetry that MFT cannot predict.
2014

(2014) JOURNAL OF PHYSICS AMATHEMATICAL AND THEORETICAL. 47, 50, Abstract
In equilibrium, the effect of a spatially localized perturbation is typically confined around the perturbed region. Quite contrary to this, in a nonequilibrium stationary state often the entire system is affected. This appears to be a generic feature of nonequilibrium. We study such a nonlocal response in the stationary state of a lattice gas with a shear drive at the boundary, which keeps the system out of equilibrium. We show that a perturbation in the form of a localized blockage at the boundary induces an algebraically decaying density and current profile. In two examples, noninteracting particles and particles with simple exclusion, we analytically derive the powerlaw tail of the profiles.

(2014) Journal Of Statistical MechanicsTheory And Experiment. Abstract
Mixed order phase transitions (MOT), which display discontinuous order parameter and diverging correlation length, appear in several seemingly unrelated settings ranging from equilibrium models with longrange interactions to models far from thermal equilibrium. In a recent paper [1], an exactly soluble spin model with longrange interactions that exhibits MOT was introduced and analyzed both by a grand canonical calculation and a renormalization group analysis. The model was shown to form a bridge between two classes of 1D models exhibiting MOT, namely between spin models with inverse distance square interactions and surface depinning models. In this paper, we elaborate on the calculations performed in [1]. We also analyze the model in the canonical ensemble, which yields a better insight into the mechanism of MOT. In addition, we generalize the model to include Potts and general Ising spins and also consider a broader class of interactions that decay with distance using a power law different from 2.

(2014) Physical Review E. 90, 1, 12107. Abstract
We consider the onedimensional driven ABC model under particleconserving and particlenonconserving processes. Two limiting cases are studied: (a) The rates of the nonconserving processes are vanishingly slow compared with the conserving processes in the thermodynamic limit and (b) the two rates are comparable. For case (a) we provide a detailed analysis of the phase diagram and the large deviations function of the overall density, G(r). The phase diagram of the nonconserving model, derived from G(r), is found to be different from the conserving one. This difference, which stems from the nonconvexity of G(r), is analogous to ensemble inequivalence found in equilibrium systems with longrange interactions. An outline of the analysis of case (a) was given in an earlier letter. For case (b) we show that, unlike the conserving model, the nonconserving model exhibits a moving density profile in the steady state with a velocity that remains finite in the thermodynamic limit. Moreover, in contrast with case (a), the critical lines of the conserving and nonconserving models do not coincide. These are new features which are present only when the rates of the conserving and nonconserving processes are comparable. In addition, we analyze G(r) in case (b) using macroscopic fluctuations theory. Much of the derivation presented in this paper is applicable to any drivendiffusive system coupled to an external particle bath via a slow dynamics.

(2014) Physical Review E. 90, 1, 12109. Abstract
We show that the presence of a driven bond in an otherwise diffusive lattice gas with simple exclusion interaction results in longrange densitydensity correlation in its stationary state. In dimensions d > 1 we show that in the thermodynamic limit this correlation decays as C(r,s) similar to (r(2) + s(2))(d) at large distances r and s away from the drive with vertical bar r  s vertical bar >> 1. This is derived using an electrostatic analogy whereby C(r, s) is expressed as the potential due to a configuration of electrostatic charges distributed in 2d dimension. At bulk density rho = 1/2 we show that the potential is that of a localized quadrupolar charge. At other densities the same is correct in leading order in the strength of the drive and it is argued numerically to be valid at higher orders.

(2014) Physical Review Letters. 112, 1, 15701. Abstract
We introduce and analyze an exactly soluble onedimensional Ising model with long range interactions that exhibits a mixedorder transition, namely a phase transition in which the order parameter is discontinuous as in first order transitions while the correlation length diverges as in second order transitions. Such transitions are known to appear in a diverse classes of models that are seemingly unrelated. The model we present serves as a link between two classes of models that exhibit a mixedorder transition in one dimension, namely, spin models with a coupling constant that decays as the inverse distance squared and models of depinning transitions, thus making a step towards a unifying framework.
2013

(2013) Physical Review E. 88, 5, Abstract
We consider a longrange interacting system of N particles moving on a spherical surface under an attractive Heisenberglike interaction of infinite range and evolving under deterministic Hamilton dynamics. The system may also be viewed as one of globally coupled Heisenberg spins. In equilibrium, the system has a continuous phase transition from a lowenergy magnetized phase, in which the particles are clustered on the spherical surface, to a highenergy homogeneous phase. The dynamical behavior of the model is studied analytically by analyzing the Vlasov equation for the evolution of the singleparticle distribution and numerically by direct simulations. The model is found to exhibit longlived nonmagnetized quasistationary states (QSSs) which in the thermodynamic limit are dynamically stable within an energy range where the equilibrium state is magnetized. For finite N, these states relax to equilibrium over a time that increases algebraically with N. In the dynamically unstable regime, nonmagnetized states relax fast to equilibrium over a time that scales as ln N. These features are retained in presence of a global anisotropy in the magnetization.

(2013) Physical Review E. 87, 5, Abstract
We examine the effect of spatial correlations on the phenomenon of realspace condensation in driven masstransport 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 zerorange process (ZRP) in which, unlike the usual ZRP, the steady state is not a product measure. The validity of the mechanism in other masstransport models is discussed.
2012

(2012) Journal Of Statistical MechanicsTheory And Experiment. Abstract
It is well known that systems with longrange interactions may exhibit different phase diagrams when studied within two different ensembles. In many of the previously studied examples of ensemble inequivalence, the phase diagrams differ only when the transition in one of the ensembles is first order. By contrast, in a recent study of a generalized ABC model, the canonical and grandcanonical ensembles of the model were shown to differ even when they both exhibit a continuous transition. Here we show that the order of the transition where ensemble inequivalence may occur is related to the symmetry properties of the order parameter associated with the transition. This is done by analyzing the Landau expansion of a generic model with longrange interactions. The conclusions drawn from the generic analysis are demonstrated for the ABC model by explicit calculation of its Landau expansion.

(2012) Physical Review E. 86, 6, Abstract
The denaturation transition of circular DNA is studied within a PolandScheragatype approach, generalized to account for the fact that the total linking number (LK), which measures the number of windings of one strand around the other, is conserved. In the model the LK conservation is maintained by invoking both overtwisting and writhing (supercoiling) mechanisms. This generalizes previous studies, which considered each mechanism separately. The phase diagram of the model is analyzed as a function of the temperature and the elastic constant kappa associated with the overtwisting energy for any given loop entropy exponent c. As in the case where the two mechanisms apply separately, the model exhibits no denaturation transition for c 2 and kappa = 0 we find that the model exhibits a firstorder transition. The transition becomes of higher order for any kappa > 0. We also calculate the contribution of the two mechanisms separately in maintaining the conservation of the linking number and find that it is weakly dependent on the loop exponent c. DOI: 10.1103/PhysRevE.86.061904

(2012) Physical Review Letters. 109, 13, Abstract
The effect of a localized drive on the steady state of an interface separating two phases in coexistence is studied. This is done using a spinconserving kinetic Ising model on a twodimensional lattice with cylindrical boundary conditions, where a drive is applied along a single ring on which the interface separating the two phases is centered. The drive is found to induce an interface spontaneous symmetry breaking whereby the magnetization of the driven ring becomes nonzero. The width of the interface becomes finite and its fluctuations around the driven ring are nonsymmetric. The dynamical origin of these properties is analyzed in an adiabatic limit, which allows the evaluation of the large deviation function of the magnetization of the driven ring.

(2012) Journal Of Statistical MechanicsTheory And Experiment. Abstract
The condensation transition in a nonMarkovian zerorange process is studied in one and higher dimensions. In the meanfield approximation, corresponding to infiniterange hopping, the model exhibits condensation with a stationary condensate, as in the Markovian case, but with a modified phase diagram. In the case of nearestneighbor hopping, the condensate is found to drift by means of a 'slinky' motion from one site to the next. The mechanism of the drift is explored numerically in detail. A modified model with nearestneighbor hopping which allows exact calculation of the steady state is introduced. The steady state of this model is found to be a product measure, and the condensate is stationary.

(2012) Central European Journal of Physics. 10, 3, p. 582586 Abstract
A DNA molecule with freely fluctuating ends undergoes a sharp thermal denaturation transition upon heating. However, in circular DNA chains and some experimental setups that manipulate single DNA molecules, the total number of turns (linking number) is constant at all times. The consequences of this additional topological invariant on the melting behaviour are nontrivial. Below, we investigate the melting characteristics of a homogeneous DNA where the linking number along the melting curve is preserved by supercoil formation in duplex portions. We obtain the mass fraction and the number of loops and supercoils below and above the melting temperature. We also argue that a macroscopic loop appears at T (c) and calculate its size as a function of temperature.

(2012) Physical Review E. 85, 5, Abstract
The statistical mechanics of DNA denaturation under fixed linking number is qualitatively different from that of unconstrained DNA. Quantitatively different melting scenarios are reached from two alternative assumptions, namely, that the denatured loops are formed at the expense of (i) overtwist or (ii) supercoils. Recent work has shown that the supercoiling mechanism results in a picture similar to BoseEinstein condensation where a macroscopic loop appears at Tc and grows steadily with temperature, while the nature of the denatured phase for the overtwisting case has not been studied. By extending an earlier result, we show here that a macroscopic loop appears in the overtwisting scenario as well. We calculate its size as a function of temperature and show that the fraction of the total sum of microscopic loops decreases above Tc, with a cusp at the critical point.

(2012) Journal Of Statistical MechanicsTheory And Experiment. Abstract
The equation which describes a particle diffusing in a logarithmic potential arises in diverse physical problems such as momentum diffusion of atoms in optical traps, condensation processes, and denaturation of DNA molecules. A detailed study of the approach of such systems to equilibrium via a scaling analysis is carried out, revealing three surprising features: (i) the solution is given by two distinct scaling forms, corresponding to a diffusive (x similar to root t) and a subdiffusive (x

(2012) Physical Review Letters. 108, 6, Abstract
The effect of particlenonconserving processes on the steady state of driven diffusive systems is studied within the context of a generalized ABC model. It is shown that in the limit of slow nonconserving processes, the large deviation function of the overall particle density can be computed by making use of the steadystate density profile of the conserving model. In this limit one can define a chemical potential and identify first order transitions via Maxwell's construction, similarly to what is done in equilibrium systems. This method may be applied to other driven models subjected to slow nonconserving dynamics.

(2012) Journal of Statistical Physics. 146, 2, p. 294313 Abstract
We investigate a new symmetry of the large deviation function of certain timeintegrated currents in nonequilibrium systems. The symmetry is similar to the wellknown GallavottiCohenEvansMorrisssymmetry for the entropy production, but it concerns a different functional of the stochastic trajectory. The symmetry can be found in a restricted class of Markov jump processes, where the network of microscopic transitions has a particular structure and the transition rates satisfy certain constraints. We provide three physical examples, where timeintegrated observables display such a symmetry. Moreover, we argue that the origin of the symmetry can be traced back to timereversal if stochastic trajectories are grouped appropriately.
2011

(2011) Physical Review E. 84, 6, 061151. Abstract
Longlived quasistationary states, associated with stationary stable solutions of the Vlasov equation, are found in systems with longrange interactions. Studies of the relaxation time in a model of N globally coupled particles moving on a ring, the Hamiltonian meanfield model (HMF), have shown that it diverges as N(gamma) for large N, with gamma similar or equal to 1.7 for some initial conditions with homogeneously distributed particles. We propose a method for identifying exact inhomogeneous steady states in the thermodynamic limit, based on analyzing models of uncoupled particles moving in an external field. For the HMF model, we show numerically that the relaxation time of these states diverges with N with the exponent gamma similar or equal to 1. The method, applicable to other models with globally coupled particles, also allows an exact evaluation of the stability limit of homogeneous steady states. In some cases, it provides a good approximation for the correspondence between the initial condition and the final steady state.

(2011) Physical Review E. 84, 5, 051136. Abstract
We show that the presence of a localized drive in an otherwise diffusive system results in steadystate density and current profiles that decay algebraically to their global average value, away from the drive in two or higher dimensions. An analogy to an electrostatic problem is established, whereby the density profile induced by a driving bond maps onto the electrostatic potential due to an electric dipole located along the bond. The dipole strength is proportional to the drive, and is determined selfconsistently by solving the electrostatic problem. The profile resulting from a localized configuration of more than one driving bond can be straightforwardly determined by the superposition principle of electrostatics. This picture is shown to hold even in the presence of exclusion interaction between particles.

(2011) JOURNAL OF PHYSICS AMATHEMATICAL AND THEORETICAL. 44, 41, 415004. Abstract
The ABC model is a driven diffusive exclusion model, composed of three species of particles that hop on a ring with local asymmetric rates. In the weak asymmetry limit, where the asymmetry vanishes with the length of the system, the model exhibits a phase transition between a homogeneous state and a phaseseparated state. We derive the exact solution for the density profiles of the three species in the hydrodynamic limit for arbitrary average densities. The solution yields the complete phase diagram of the model and allows the study of the nature of the firstorder phase transition found for average densities that deviate significantly from the point of equal densities.

(2011) Physical Review E. 84, 4, 041935. Abstract
The denaturation transition which takes place in circular DNA is analyzed by extending the PolandScheraga (PS) model to include the winding degrees of freedom. We consider the case of a homopolymer whereby the winding number of the doublestranded helix, released by a loop denaturation, is absorbed by supercoils. We find that as in the case of linear DNA, the order of the transition is determined by the loop exponent c. However the firstorder transition displayed by the PS model for c > 2 in linear DNA is replaced by a continuous transition with arbitrarily high order as c approaches 2, while the secondorder transition found in the linear case in the regime 1 <c

(2011) Physical Review E. 84, 4, 041111. Abstract
The latetime distribution function P(x, t) of a particle diffusing in a onedimensional 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 similar to t(1/2)) and a subdiffusive (x similar to t(gamma) with a given gamma <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.

(2011) Journal Of Statistical MechanicsTheory And Experiment. P03015. Abstract
Systems with longrange interactions, while relaxing towards equilibrium, sometimes get trapped in longlived nonBoltzmann quasistationary states (QSS) which have lifetimes that grow algebraically with the system size. Such states have been observed in models of globally coupled particles that move under Hamiltonian dynamics either on a unit circle or on a unit spherical surface. Here, we address the ubiquity of QSS in longrange systems by considering a different dynamical setting. Thus, we consider an anisotropic Heisenberg model consisting of classical Heisenberg spins with meanfield interactions and evolving under classical spin dynamics. Our analysis of the corresponding Vlasov equation for time evolution of the phase space distribution shows that in a certain energy interval, relaxation of a class of initial states occurs over a timescale which grows algebraically with the system size. We support these findings by extensive numerical simulations. This work further supports the generality of occurrence of QSS in longrange systems evolving under Hamiltonian dynamics.

(2011) Philosophical Transactions Of The Royal Society AMathematical Physical And Engineering Sciences. 369, 1935, p. 439452 Abstract
We introduce a model of uncoupled pendula, which mimics the dynamical behaviour of the Hamiltonian meanfield (HMF) model. This model has become a paradigm for longrange interactions, such as Coulomb or dipolar forces. As in the HMF model, this simplified integrable model is found to obey the Vlasov equation and to exhibit quasistationary states (QSSs), which arise after a 'collisionless' relaxation process. Both the magnetization and the singleparticle distribution function in these QSSs can be predicted using LyndenBell's theory. The existence of an extra conserved quantity for this model, the energy distribution function, allows us to understand the origin of some discrepancies of the theory with numerical experiments. It also suggests an improvement of LyndenBell's theory, which we fully implement for the zerofield case.
2010

(2010) Journal Of Statistical MechanicsTheory And Experiment. Abstract
The three species ABC model of driven particles on a ring is generalized to include vacancies and particlenonconserving processes. The model exhibits phase separation at high densities. For equal average densities of the three species, it is shown that although the dynamics is local, it obeys detailed balance with respect to a Hamiltonian with longrange interactions, yielding a nonadditive free energy. The phase diagrams of the conserving and nonconserving models, corresponding to the canonical and grandcanonical ensembles, respectively, are calculated in the thermodynamic limit. Both models exhibit a transition from a homogeneous to a phaseseparated state, although the phase diagrams are shown to differ from each other. This conforms with the expected inequivalence of ensembles in equilibrium systems with longrange interactions. These results are based on a stability analysis of the homogeneous phase and exact solution of the continuum equations of the models. They are supported by Monte Carlo simulations. This study may serve as a useful starting point for analyzing the phase diagram for unequal densities, where detailed balance is not satisfied and thus a Hamiltonian cannot be defined.

(2010) Journal Of Statistical MechanicsTheory And Experiment. P10008. Abstract
We study entropy production and fluctuation relations in the restricted solidonsolid growth model, which is a microscopic realization of the KardarParisiZhang (KPZ) equation. Solving the onedimensional model exactly on a particular line of the phase diagram we demonstrate that entropy production quantifies the distance from equilibrium. Moreover, as an example of a physically relevant current different from the entropy, we study the symmetry of the large deviation function associated with the interface height. In a special case of a system of length L = 4 we find that the probability distribution of the variation of height has a symmetric large deviation function, displaying a symmetry different from the GallavottiCohen symmetry.

(2010) Physical Review Letters. 105, 15, 150602. Abstract
A generalization of the ABC model, a onedimensional model of a driven system of three particle species with local dynamics, is introduced, in which the model evolves under either (i) densityconserving or (ii) nonconserving dynamics. For equal average densities of the three species, both dynamical models are demonstrated to exhibit detailed balance with respect to a Hamiltonian with longrange interactions. The model is found to exhibit two distinct phase diagrams, corresponding to the canonical (densityconserving) and grand canonical (density nonconserving) ensembles, as expected in longrange interacting systems. The implications of this result to nonequilibrium steady states, such as those of the ABC model with unequal average densities, are briefly discussed.

(2010) Physica AStatistical Mechanics And Its Applications. 389, 20, p. 43894405 Abstract
We review simple aspects of the thermodynamic and dynamical properties of systems with longrange pairwise interactions (LRI), which decay as 1/r(d+sigma) at large distances r in d dimensions. Two broad classes of such systems are discussed. (i) Systems with a slow decay of the interactions, termed "strong" LRI, where the energy is superextensive. These systems are characterized by unusual properties such as inequivalence of ensembles, negative specific heat, slow decay of correlations, anomalous diffusion and ergodicity breaking. (ii) Systems with faster decay of the interaction potential, where the energy is additive, thus resulting in less dramatic effects. These interactions affect the thermodynamic behavior of systems near phase transitions, where longrange correlations are naturally present. Longrange correlations are often present in systems driven out of equilibrium when the dynamics involves conserved quantities. Steady state properties of driven systems with local dynamics are considered within the framework outlined above. (C) 2010 Elsevier B.V. All rights reserved.

(2010) Physical Review E. 82, 3, 36112. Abstract
A model for epidemic spreading on rewiring networks is introduced and analyzed for the case of scale free steady state networks. It is found that contrary to what one would have naively expected, the rewiring process typically tends to suppress epidemic spreading. In particular it is found, that as in static networks under a meanfield approximation, rewiring networks with degree distribution exponent gamma>3 exhibit a threshold in the infection rate below which epidemics die out in the steady state. However the threshold is higher in the rewiring case. For 2

(2010) Journal Of Statistical MechanicsTheory And Experiment. P08026. Abstract
Longrange interacting systems, while relaxing towards equilibrium, may get trapped in nonequilibrium quasistationary states (QSS) for a time which diverges algebraically with the system size. These intriguing nonBoltzmann states have been observed under deterministic Hamiltonian evolution of a paradigmatic system, the Hamiltonian meanfield (HMF) model. We study here the robustness of QSS with respect to stochastic processes beyond deterministic dynamics within a microcanonical ensemble. To this end, we generalize the HMF model by allowing for stochastic threeparticle collision dynamics in addition to the deterministic ones. By analyzing the resulting Boltzmann equation for the phase space density, we demonstrate that, in the presence of stochasticity, QSS occur only as a crossover phenomenon over a finite time determined by the strength of the stochastic process. In particular, we argue that the relaxation time to equilibrium does not scale algebraically with the system size. We propose a scaling form for the relaxation time which is in very good agreement with results of extensive numerical simulations. The broader validity of these results is tested on a different stochastic HMF model involving microcanonical Monte Carlo dynamical moves.

(2010) Physica AStatistical Mechanics And Its Applications. 389, 15, p. 30023006 Abstract
We investigate the impact of supercoil period and nonzero supercoil formation energy on the thermal denaturation of a circular DNA. Our analysis is based on a recently proposed generalization of the Poland Scheraga model that allows the DNA melting to be studied for plasmids with circular topology, where denaturation is accompanied by formation of supercoils. We find that the previously obtained firstorder melting transition persists under the generalization discussed. The dependence of the size of the orderparameter jump at the transition point and the associated melting temperature are obtained analytically. (C) 2010 Elsevier B.V. All rights reserved.

(2010) Physical Review Letters. 105, 4, 40602. Abstract
Quasistationary states are longlived nonequilibrium states, observed in some systems with longrange interactions under deterministic Hamiltonian evolution. These intriguing nonBoltzmann states relax to equilibrium over times which diverge algebraically with the system size. To test the robustness of this phenomenon to nondeterministic dynamical processes, we have generalized the paradigmatic model exhibiting such a behavior, the Hamiltonian meanfield model, to include energyconserving stochastic processes. Analysis, based on the Boltzmann equation, a scaling approach, and numerical studies, demonstrates that in the long time limit the system relaxes to the equilibrium state on time scales which do not diverge algebraically with the system size. Thus, quasistationarity takes place only as a crossover phenomenon on times determined by the strength of the stochastic process.
2009

(2009) JOURNAL OF PHYSICS AMATHEMATICAL AND THEORETICAL. 42, 48, Abstract
A simple twospecies asymmetric exclusion model in one dimension with bulk and boundary exchanges of particles is investigated for the existence of spontaneous symmetry breaking. The model is a generalization of the 'bridge' model for which earlier studies have confirmed the existence of symmetrybroken phases, and the motivation here is to check the robustness of the observed symmetry breaking with respect to additional dynamical moves, in particular, the boundary exchange of the two species of particle. Our analysis, based on general considerations, meanfield approximation and numerical simulations, shows that the symmetry breaking in the bridge model is sustained for a range of values of the boundary exchange rate. Moreover, the mechanism through which symmetry is broken is similar to that in the bridge model. Our analysis allows us to plot the complete phase diagram of the model, demarcating regions of symmetric and symmetrybroken phases.

(2009) Journal of Statistical Physics. 137, 6May, p. 11661204 Abstract
The three species asymmetric ABC model was initially defined on a ring by Evans, Kafri, Koduvely, and Mukamel, and the weakly asymmetric version was later studied by Clincy, Derrida, and Evans. Here the latter model is studied on a onedimensional lattice of N sites with closed (zero flux) boundaries. In this geometry the local particle conserving dynamics satisfies detailed balance with respect to a canonical Gibbs measure with long range asymmetric pair interactions. This generalizes results for the ring case, where detailed balance holds, and in fact the steady state measure is known, only for the case of equal densities of the different species: in the latter case the stationary states of the system on a ring and on an interval are the same. We prove that in the limit N > a the scaled density profiles are given by (pieces of) the periodic trajectory of a particle moving in a quartic confining potential. We further prove uniqueness of the profiles, i.e., the existence of a single phase, in all regions of the parameter space (of average densities and temperature) except at low temperature with all densities equal; in this case a continuum of phases, differing by translation, coexist. The results for the equal density case apply also to the system on the ring, and there extend results of Clincy et al.

(2009) Physical Review Letters. 103, 9, Abstract
The impact of temporally correlated dynamics on nonequilibrium condensation is studied using a nonMarkovian zerorange process (ZRP). We find that memory effects can modify the condensation scenario significantly: (i) For meanfield dynamics, the steady state corresponds to that of a Markovian ZRP, but with modified hopping rates which can affect condensation; (ii) for nearestneighbor 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.

(2009) Physical Review E. 80, 1, Abstract
We generalize the PolandScheraga model to the case of a circular DNA, taking into account the twisting of the two strains around each other. Guided by recent singlemolecule experiments on DNA strands, we assume that the torsional stress induced by denaturation enforces the formation of supercoils whose writhe absorbs the linking number expelled by the loops. Our model predicts that when the entropy parameter of a loop satisfies c 2, a firstorder denaturation transition is consistent with our model and may take place in the actual system, as in the case with no supercoils. These results are in contrast with other treatments of circular DNA melting where denaturation is assumed to be accompanied by an increase in twist rather than writhe on the bound segments.

(2009) Journal Of Statistical MechanicsTheory And Experiment. Abstract
The pressure components of 'soft' disks in a twodimensional narrow channel are analyzed in the dilute gas regime using the Mayer cluster expansion and molecular dynamics. Channels with either periodic or reflecting boundaries are considered. It is found that when the twobody potential, u(r), is singular at some distance r(0), the dependence of the pressure components on the channel width exhibits a singularity at one or more channel widths which are simply related to r(0). In channels with periodic boundary conditions and for potentials which are discontinuous at r(0), the transverse and longitudinal pressure components exhibit a 1/2 and a 3/2 singularity, respectively. Continuous potentials with a powerlaw singularity result in weaker singularities of the pressure components. For channels with reflecting boundary conditions the singularities are found to be weaker than those corresponding to periodic boundaries.

(2009) Journal Of PhysicsCondensed Matter. 21, 3, Abstract
The dynamics of loops at the DNA denaturation transition is studied. A scaling argument is used to evaluate the asymptotic behavior of the autocorrelation function of the state of complementary bases (either open or closed). The longtime asymptotic behavior of the autocorrelation function is expressed in terms of the entropy exponent, c, of a loop. The validity of the scaling argument is tested using a microscopic model of an isolated loop and a toy model of interacting loops. This suggests a method for measuring the entropy exponent using singlemolecule experiments such as fluorescence correlation spectroscopy.
2008

(2008) JOURNAL OF PHYSICS AMATHEMATICAL AND THEORETICAL. 41, 43, Abstract
We introduce a class of 1D models mimicking a singlelane bridge with two junctions and two particle species driven in opposite directions. The model exhibits spontaneous symmetry breaking (SSB) for a range of injection/extraction rates. In this phase the steadystate currents of the two species are not equal. Moreover, there is a coexistence region in which the symmetrybroken phase coexists with a symmetric phase. Along a path in which the extraction rate is varied, keeping the injection rate fixed and large, hysteresis takes place. The meanfield phase diagram is calculated and supporting Monte Carlo simulations are presented. One of the transition lines exhibits a kink, a feature which cannot exist in transition lines of equilibrium phase transitions.

(2008) Physical Biology. 5, 3, 036001. Abstract
Nuclear pore complexes are constantly confronted by large fluxes of macromolecules and macromolecular complexes that need to get into and out of the nucleus. Such bidirectional traffic occurring in a narrow channel can easily lead to jamming. How then is passage between the nucleus and cytoplasm maintained under the varying conditions that arise during the lifetime of the cell? Here, we address this question using computer simulations in which the behaviour of the ensemble of transporting cargoes is analysed under different conditions. We suggest that traffic can exist in two distinct modes, depending on the concentration of cargoes and dissociation rates of the transport receptorcargo complexes from the pores. In one mode, which prevails when dissociation is quick and cargo concentration is low, transport in either direction proceeds uninterrupted by transport in the other direction. The result is that the overall traffic direction fluctuates rapidly and unsystematically between import and export. Remarkably, when cargo concentrations are high and disassociation is slow, another mode takes over in which traffic proceeds in one direction for a certain extent of time, after which it flips direction for another period. The switch between this, more regulated, mode of transport and the other, quickly fluctuating state, does not require an active gating mechanism but rather occurs spontaneously through the dynamics of the transported particles themselves. The determining factor for the behaviour of traffic is found to be the exit rate from the pore channel, which is directly related to the activity of the Ran system that controls the loading and release of cargo in the appropriate cellular compartment.

(2008) JOURNAL OF PHYSICS AMATHEMATICAL AND THEORETICAL. 41, 20, Abstract
The steady state distributions and dynamical behaviour of zero range processes with hopping rates which are non monotonic functions of the site occupation are studied. We consider two classes of non monotonic hopping rates. The first results in a condensed phase containing a large ( but subextensive) number of mesocondensates each containing a subextensive number of particles. The second results in a condensed phase containing a finite number of extensive condensates. We study the scaling behaviour of the peak in the distribution function corresponding to the condensates in both cases. In studying the dynamics of the condensate we identify two timescales: one for creation, the other for evaporation of condensates at a given site. The scaling behaviour of these timescales is studied within the Arrhenius law approach and by numerical simulations.

(2008) Physical Review E. 77, 1, Abstract
We study a generalized isotropic XY model which includes both two and fourspin meanfield interactions. This model can be solved in the microcanonical ensemble. It is shown that in certain parameter regions the model exhibits gaps in the magnetization at fixed energy, resulting in ergodicity breaking. This phenomenon has previously been reported in anisotropic and discrete spin models. The entropy of the model is calculated and the microcanonical phase diagram is derived, showing the existence of firstorder phase transitions from the ferromagnetic to a paramagnetic disordered phase. It is found that ergodicity breaking takes place in both the ferromagnetic and paramagnetic phases. As a consequence, the system can exhibit a stable ferromagnetic phase within the paramagnetic region, and conversely a disordered phase within the magnetically ordered region.

Statistical mechanics of systems with long range interactions(2008) Dynamics And Thermodynamics Of Systems With LongRange Interactions: Theory And Experiments. 970, p. 2238 Abstract
Recent theoretical studies of statistical mechanical properties of systems with long range interactions are briefly reviewed. In these systems the interaction potential decays with a rate slower than 1/r(d) at large distances r in d dimensions. As a result, these systems are nonadditive and they display unusual thermodynamic and dynamical properties which are not present in systems with short range interactions. In particular, the various statistical mechanical ensembles are not equivalent and the microcanonical specific heat may be negative. Long range interactions may also result in breaking of ergodicity, making the maximal entropy state inaccessible from some regions of phase space. In addition, in many cases long range interactions result in slow relaxation processes, with time scales which diverge in the thermodynamic limit. Various models which have been found to exhibit these features are discussed.
2007

(2007) Journal Of Statistical MechanicsTheory And Experiment. Abstract
We consider several models with long range interactions evolving via Hamiltonian dynamics. The microcanonical dynamics of the basic Hamiltonian mean field (HMF) model and perturbed HMF models with either global anisotropy or an onsite potential are studied both analytically and numerically. We find that, in the magnetic phase, the initial zero magnetization state remains stable above a critical energy and is unstable below it. In the dynamically stable state, these models exhibit relaxation timescales that increase algebraically with the number N of particles, indicating the robustness of the quasistationary state seen in previous studies. In the unstable state, the corresponding timescale increases logarithmically in N.

(2007) Physical Review B. 76, 6, Abstract
We study theoretically layered spin systems where longrange dipolar interactions play a relevant role. By choosing a specific sample shape, we are able to reduce the complex Hamiltonian of the system to that of a much simpler coupled rotator model with shortrange and meanfield interactions. This latter model has been studied in the past because of its interesting dynamical and statistical properties related to exotic features of longrange interactions. It is suggested that experiments could be conducted such that within a specific temperature range the presence of longrange interactions crucially affects the behavior of the system.

(2007) Journal Of Statistical MechanicsTheory And Experiment. Abstract
The zero range process, in which particles hop between sites on a lattice under conserving dynamics, is a prototypical model for studying real space condensation. Within this model the system is critical only at the transition point. Here we consider a non conserving zero range process which is shown to exhibit generic critical phases which exist in a range of creation and annihilation parameters. The model also exhibits phases characterized by mesocondensates, each of which contains a subextensive number of particles. A detailed phase diagram, delineating the various phases, is derived.

(2007) Physical Review Letters. 98, 3, Abstract
The dynamics of a loop in DNA molecules at the denaturation transition is studied by scaling arguments and numerical simulations. The autocorrelation function of the state of complementary bases (either closed or open) is calculated. The longtime decay of the autocorrelation function is expressed in terms of the loop exponent c both for homopolymers and heteropolymers. This suggests an experimental method for measuring the exponent c using florescence correlation spectroscopy.
2006

(2006) Journal Of Statistical MechanicsTheory And Experiment. Abstract
We investigate two distinct universality classes for probe particles that move stochastically in a onedimensional driven system. If the random force that drives the probe particles is fully generated by the current fluctuations of the driven fluid, such as when the probe particles are embedded in a ring, they inherit the dynamical exponent of the fluid, which generically is z = 3/2. On the other hand, if the random force has a part that is temporally uncorrelated, the resulting motion can be described by a dynamical exponent z = 2 as considered in previous work.

(2006) Journal Of Statistical MechanicsTheory And Experiment. Abstract
A class of nonlocal contact processes is introduced and studied using the mean field approximation and numerical simulations. In these processes particles are created at a rate which decays algebraically with the distance from the nearest particle. It is found that the transition into the absorbing state is continuous and is characterized by continuously varying critical exponents. This model differs from the previously studied nonlocal directed percolation model, where particles are created by unrestricted Levy flights. It is motivated by recent studies of nonequilibrium wetting indicating that such nonlocal processes play a role in the unbinding transition. Other nonlocal processes which have been suggested to exist within the context of wetting are considered as well.

(2006) Physica AStatistical Mechanics And Its Applications. 365, 1, p. 120127 Abstract
The effect of nearestneighbor coupling on the thermodynamic and dynamical properties of the ferromagnetic Hamiltonian mean field model (HMF) is studied. For a range of anti ferromagnetic nearestneighbor coupling, a canonical firstorder transition is observed, and the canonical and microcanonical ensembles are nonequivalent. In studying the relaxation time of nonequilibrium states it is found that as in the HMF model, a class of nonmagnetic states is quasistationary, with an algebraic divergence of their lifetime with the number of degrees of freedom N. The lifetime of metastable states is found to increase exponentially with N as expected. (c) 2006 Elsevier B.V. All rights reserved.
2005

(2005) Physical Review Letters. 95, 24, Abstract
The thermodynamic and dynamical properties of an Ising model with both shortrange and longrange, meanfieldlike, interactions are studied within the microcanonical ensemble. It is found that the relaxation time of thermodynamically unstable states diverges logarithmically with system size. This is in contrast with the case of shortrange interactions where this time is finite. Moreover, at sufficiently low energies, gaps in the magnetization interval may develop to which no microscopic configuration corresponds. As a result, in local microcanonical dynamics the system cannot move across the gap, leading to breaking of ergodicity even in finite systems. These are general features of systems with longrange interactions and are expected to be valid even when the interaction is slowly decaying with distance.

(2005) Physical Review E. 72, 4, Abstract
Zerorange processes, in which particles hop between sites on a lattice, are closely related to rewiring networks, in which rewiring of links between nodes takes place. Both systems exhibit a condensation transition for appropriate choices of the dynamical rules. The transition results in a macroscopically occupied site for zerorange processes and a macroscopically connected node for networks. Criticality, characterized by a scalefree distribution, is obtained only at the transition point. This is in contrast with the widespread scalefree complex networks. Here we propose a generalization of these models whereby criticality is obtained throughout an entire phase, and the scalefree distribution does not depend on any finetuned parameter.

(2005) Journal of Statistical Physics. 120, 6May, p. 759778 Abstract
We calculate the exact stationary distribution of the onedimensional zerorange process with open boundaries for arbitrary bulk and boundary hopping rates. When such a distribution exists, the steady state has no correlations between sites and is uniquely characterized by a spacedependent fugacity which is a function of the boundary rates and the hopping asymmetry. For strong boundary drive the system has no stationary distribution. In systems which on a ring geometry allow for a condensation transition, a condensate develops at one or both boundary sites. On all other sites the particle distribution approaches a product measure with the finite critical density r(c). In systems which do not support condensation on a ring, strong boundary drive leads to a condensate at the boundary. However, in this case the local particle density in the interior exhibits a complex algebraic growth in time. We calculate the bulk and boundary growth exponents as a function of the system parameters.

(2005) Journal Of Physics AMathematical And General. 38, 29, p. L523L529 Abstract
Condensation transition in twospecies driven systems in a ring geometry is studied in the case where the currentdensity relation of a domain of particles exhibits two degenerate maxima. It is found that the two maximalcurrent phases coexist both in the fluctuating domains of the fluid and in the condensate; when it exists. This has a profound effect on the steadystate properties of the model. In particular, phase separation becomes more favourable, as compared with the case of a single maximum in the currentdensity relation. Moreover, a selection mechanism imposes equal currents flowing out of the condensate, resulting in a neutral fluid even when the total numbers of particles of the two species are not equal. In this case, the particle imbalance shows up only in the condensate.

(2005) Europhysics Letters. 70, 5, p. 565571 Abstract
The effective interaction between two probe particles in a onedimensional driven system is studied. The analysis is carried out using an asymmetric simple exclusion process with nearestneighbor interactions. It is found that the driven fluid mediates an effective longrange attraction between the two probes, with a force that decays at large distances x as b/x, where b is a function of the interaction parameters. Depending on the amplitude b, the two probes may form one of three states: a) an unbound state, where the distance grows diffusively with time; b) a weakly bound state, in which the distance grows subdiffusively; and c) a strongly bound state, where the average distance stays finite in the longtime limit. Similar results are found for the behavior of any finite number of probes.

(2005) Physical Review E. 71, 2, Abstract
It is argued that some phase transitions observed in models of nonequilibrium wetting phenomena are related to contact processes with longrange interactions. This is investigated by introducing a model where the activation rate of a site at the edge of an inactive island of length l is 1+al(sigma). Meanfield analysis and numerical simulations indicate that for sigma>1 the transition is continuous and belongs to the universality class of directed percolation, while for 0
2004

(2004) Journal of Statistical Physics. 117, 6May, p. 819830 Abstract
It is suggested that the question of existence of a jamming phase transition in a broad class of singlelane cellularautomaton traffic models may be studied using a correspondence to the asymmetric chipping model. In models where such correspondence is applicable, jamming phase transition does not take place. Rather, the system exhibits a smooth crossover between freeflow and jammed states, as the car density is increased.

(2004) Physica AStatistical Mechanics And Its Applications. 340, 4, p. 636646 Abstract
The recently suggested correspondence between domain dynamics of traffic models and the asymmetric chipping model is reviewed. It is observed that in many cases traffic domains perform the two characteristic dynamical processes of the chipping model, namely chipping and diffusion. This correspondence indicates that jamming in traffic models in which all dynamical rates are nondeterministic takes place as a broad crossover phenomenon, rather than a sharp transition. Two traffic models are studied in detail and analyzed within this picture. (C) 2004 Elsevier B.V. All rights reserved.

(2004) European Physical Journal B. 41, 2, p. 223230 Abstract
The recently introduced correspondence between onedimensional twospecies driven models and the ZeroRange Process is extended to study the case where the densities of the two species need not be equal. The correspondence is formulated through the length dependence of the current emitted from a particle domain. A direct numerical method for evaluating this current is introduced, and used to test the assumptions underlying this approach. In addition, a model for isolated domain dynamics is introduced, which provides a simple way to calculate the current also for the nonequal density case. This approach is demonstrated and applied to a particular twospecies model, where a phase separation transition line is calculated.

(2004) Physical Review E. 69, 6, Abstract
The thermodynamic and dynamical behavior of a gas of hard disks in a narrow channel is studied theoretically and numerically. Using a virial expansion, we find that the pressure and collision frequency curves exhibit a singularity at a channel width corresponding to twice the disk diameter. As expected, the maximum Lyapunov exponent is also found to display a similar behavior. At high density, these curves are dominated by solidlike configurations which are different from the bulk ones, due to the channel boundary conditions.

(2004) Journal Of Statistical MechanicsTheory And Experiment. Abstract
Recent studies have indicated that the coarse grained dynamics of a large class of traffic models and driven  diffusive systems may be described by urn models. We consider a class of onedimensional urn models whereby particles hop from an urn to its nearest neighbour at a rate which decays with the occupation number k of the departure site as ( 1+ b/ k). In addition a diffusion process takes place, whereby all particles in an urn may hop to an adjacent one at some rate a. A condensation transition which may take place in this model is studied and the (b, alpha) phase diagram is calculated within the mean field approximation and by numerical simulations. A driven  diffusive model whose coarse grained dynamics corresponds to this urn model is considered.

(2004) Journal Of Statistical MechanicsTheory And Experiment. Abstract
Condensation occurs in nonequilibrium steady states when a finite fraction of the particles in the system occupies a single lattice site. We study condensation transitions in a onedimensional zerorange process with a single defect site. The system is analysed in the grand canonical and canonical ensembles and the two are contrasted. Two distinct condensation mechanisms are found in the grand canonical ensemble. Discrepancies between the infinite and large but finite systems' particle current versus particle density diagrams are investigated and an explanation for how the finite current goes above a maximum value predicted for infinite systems is found in the canonical ensemble.
2003

(2003) Physical Review E. 68, 6, Abstract
A simple onedimensional microscopic model of the depinning transition of an interface from an attractive hard wall is introduced and investigated. Upon varying a control parameter, the critical behavior observed along the transition line changes from a directedpercolation type to a multiplicativenoise type. Numerical simulations allow for a quantitative study of the multicritical point separating the two regions. Meanfield arguments and the mapping on yet a simpler model provide some further insight on the overall scenario.

(2003) Physical Review E. 68, 4, Abstract
We report a detailed account of the phase diagram of a recently introduced model for nonequilibrium wetting in (1+1) dimensions [H. Hinrichsen, R. Livi, D. Mukamel, and A. Politi, Phys. Rev. Lett. 79, 2710 (1997)]. A meanfield approximation is shown to reproduce the main features of the phase diagram, while providing indications for the behavior of the wetting transition in higher dimensions. The meanfield phase diagram is found to exhibit an extra transition line which does not exist in (1+1) dimensions. The line separates a phase in which the interface height distribution decays exponentially at large heights from a superexponentially decaying phase. Implications to wetting in dimensions higher than (1+1) are discussed.

(2003) Physical Review E. 68, 3, Abstract
A class of models of twospecies driven diffusive systems which is shown to exhibit phase separation in d=1 dimensions is introduced. Unlike previously studied models exhibiting similar phenomena, here the relative density of the two species is fluctuating within the macroscopic domain of the phase separtated state. The nature of the phase transition from the homogeneous to the phaseseparated state is discussed in view of a recently introduced criterion for phase separation in onedimensional driven systems.

(2003) Physical Review Letters. 91, 5, Abstract
Griffiths singularities occurring in the unbinding of strongly disordered heteropolymers are studied. A model with two randomly distributed binding energies, 1 and v, is introduced and studied analytically by analyzing the LeeYang zeros of the partition sum. It is demonstrated that in the limit v>infinity the model exhibits a Griffiths type singularity at a temperature TG=O(1) corresponding to melting of long homogeneous domains of the low binding energy. For finite v>1 the model is expected to exhibit an additional, unbinding, transition at a high temperature TM=O(v).


(2003) Physical Review E. 67, 2, Abstract
The distance distribution between complementary base pairs of the two strands of a DNA molecule is studied near the melting transition. Scaling arguments are presented for a generalized PolandScheragatype model that includes selfavoiding interactions. At the transition temperature and for a large distance r, the distribution decays as 1/r(kappa) with kappa=1+(c2)/nu. Here nu is the selfavoiding walk correlation length exponent and c is the exponent associated with the entropy of an open loop in the chain. Results for the distribution function just below the melting point are also presented. Numerical simulations that fully take into account the selfavoiding interactions are in good agreement with the scaling approach.
2002

(2002) Journal Of Physics AMathematical And General. 35, 30, p. L459L466 Abstract
Models of onedimensional driven diffusive systems sometimes exhibit. an abrupt increase in the correlation length to an anomalously large but finite value as the parameters of the model are varied. This behaviour may be misinterpreted as a genuine phase transition. A simple mechanism for this sharp increase is presented. The mechanism is introduced within the framework of a recently suggested correspondence between driven diffusive systems and zerorange processes. It is shown that when the dynamics of the model is such that small domains are suppressed in the steadystate distribution, anomalously large correlation lengths may build up. The mechanism is examined in detail in two models.

(2002) Journal Of Physics AMathematical And General. 35, 29, p. L433L438 Abstract
An asymmetric exclusion process comprising positive particles, negative particles and vacancies is introduced. The model is defined on a ring and the dynamics does not conserve the number of particles. We solve the steady state exactly and show that it can exhibit a continuous phase transition in which the density of vacancies decreases to zero. The model has no absorbing state and furnishes an example of a onedimensional phase transition in a homogeneous nonconserving system which does not belong to the absorbing state universality classes.

(2002) Physical Review Letters. 89, 3, Abstract
A general criterion for the existence of phase separation in driven densityconserving onedimensional systems is proposed. It is suggested that phase separation is related to the size dependence of the steadystate currents of domains in the system. A quantitative criterion for the existence of phase separation is conjectured using a correspondence made between driven diffusive models and zerorange processes. The criterion is verified in all cases where analytical results are available, and predictions for other models are provided.

(2002) European Physical Journal B. 27, 1, p. 135146 Abstract
Existing experimental studies of the thermal denaturation of DNA yield sharp steps in the melting curve suggesting that the melting transition is first order. This transition has been theoretically studied since. the early sixties, mostly within an approach in which the microscopic configurations of a DNA molecule consist of an alternating sequence of noninteracting bound segments and denaturated loops. Studies of these models neglect the repulsive, selfavoiding, interaction between different loops and segments and have invariably yielded continuous denaturation transitions. In the present study we take into account in an approximate way the excludedvolume interaction between denaturated loops and the rest of the chain. This is done by exploiting recent results on scaling properties of polymer networks of arbitrary topology. We also ignore the heterogeneity of the polymer. We obtain a firstorder melting transition in d = 2 dimensions and above, consistent with the experlincrital results. We also consider within our approach the unzipping transition, which takes place when the two DNA strands are pulled apart by an external force acting on one end. We find that the under equilibrium condition the unzipping transition is also first order. Although the denaturation and unzipping transitions are thermodynamically first order, they do exhibit critical fluctuations in some of their properties. For instance, the loop size distribution decays algebraically at the transition and the length of the denaturated end segment diverges as the transition is approached. We evaluate these critical properties within our approach,

(2002) Physica AStatistical Mechanics And Its Applications. 306, 4Jan, p. 3950 Abstract
When DNA molecules are heated they undergo a denaturation transition by which the two strands of the molecule are separated and become unbound. Experimental studies strongly indicate that the denaturation transition is first order. The main theoretical approach to study this transition, introduced in the early 1960s, considers microscopic configurations of a DNA molecule as given by an alternating sequence of noninteracting bound segments and denaturated loops. Studies of this model usually neglect the repulsive, selfavoiding, interaction between different loops and segments and have invariably yielded continuous denaturation transitions. It is shown that the excluded volume interaction between denaturated loops and bound segments may be taken into account using recent results on the scaling properties of polymer networks of arbitrary topology. These interactions are found to drive the transition first order, compatible with experimental observations. The unzipping transition of DNA which takes place when the two strands are pulled apart by an external force acting on one end may also be considered within this approach, again yielding a firstorder transition. Although the denaturation and unzipping transitions are thermodynamically first order, they do exhibit critical fluctuations in some of their properties. This appears, for example, in the algebraic decay of the loop size distribution at the thermal denaturation and in the divergence of the length of the end segment as the transition is approached in both thermal and forceinduced transitions. (C) 2002 Published by Elsevier Science B.V.
2001

(2001) Journal Of Physics AMathematical And General. 34, 47, p. 99239937 Abstract
In this paper we study a twospecies driven diffusive system with open boundaries that exhibits spontaneous symmetry breaking in one dimension. In a symmetry broken state the currents of the two species are not equal, although the dynamics is symmetric. A meanfield theory predicts a sequence of two transitions from a strong symmetry broken state through an intermediate symmetry broken state to a symmetric state. However, a recent numerical study has questioned the existence of the intermediate state and instead suggested a single discontinuous transition. We present an extensive numerical study that supports the existence of the intermediate phase but shows that this phase and the transition to the symmetric phase are qualitatively different from the meanfield predictions.

(2001) Physical Review E. 64, 2, Abstract
The evolution of a twodimensional driven latticegas model is studied on an L(x)xL(y) lattice. Scaling arguments and extensive numerical simulations are used to show that starting from random initial configuration the model evolves via two stages: (a) an early stage in which alternating stripes of particles and vacancies are formed along the direction y of the driving field, and (b) a stripe coarsening stage, in which the number of stripes is reduced and their average width increases. The number of stripes formed at the end of the first stage is shown to be a function of Lx/Ly(phi), with phi similar or equal to0.2. Thus, depending on this parameter, the resulting state could be either single or multistriped. In the second, stripe coarsening stage, the coarsening time is found to be proportional to Ly, becoming infinitely long in the thermodynamic limit. This implies that the multistriped state is thermodynamically stable. The results put previous studies of the model in a more general framework.

(2001) Physical Review Letters. 87, 3, Abstract
We study the global phase diagram of the Infiniterange BlumeEmeryGriffiths model both in the canonical and in the microcanonical ensembles. The canonical phase diagram shows firstorder and continuous transition lines separated by a tricritical point. We find that below the tricritical point, when the canonical transition is first order, the phase diagrams of the two ensembles disagree. In this region the microcanonical ensemble exhibits energy ranges with negative specific heat and temperature jumps at transition energies. These results can be extended to weakly decaying nonintegrable interactions.

(2001) Physical Review E. 63, 2, p. art. no.21704 Abstract
A Landau model is used to study the phase behavior of the surface layer for magnetic and cholesteric liquidcrystal systems that are at or near a Lifshitz point marking the boundary between modulated and homogeneous bulk phases. The model incorporates surface and bulk fields and includes a term in the free energy proportional to the square of the second derivative of the order parameter in addition to the usual term involving the square of the first derivative. In the limit of vanishing bulk field, three distinct types of surface ordering are possible: a wetting layer, a nonwet layer having a small deviation from bulk order, and a different nonwet layer with a large deviation from bulk order that decays nonmonotonically as the distance from the wall increases. In particular, the large deviation nonwet layer is a feature of systems at the Lifshitz point and also those systems having only homogeneous bulk phases.
2000

(2000) Physical Review Letters. 85, 23, p. 49884991 Abstract
We study a model for the denaturation transition of DNA in which the molecules are considered as being composed of a sequence of alternating bound segments and denaturated loops. We take into account the excludedvolume interactions between denaturated loops and the rest of the chain by exploiting recent results on scaling properties of polymer networks of arbitrary topology. The phase transition is found to be first order in d = 2 dimensions and above, in agreement with experiments and at variance with previous theoretical results, in which only excludedvolume interactions within denaturated loops were taken into account. Our results agree with recent numerical simulations.

(2000) Physical Review E. 62, 6, p. 76197626 Abstract
The coarsening process in a class of driven systems exhibiting striped structures is studied. The dynamics is governed by the motion of the driven interfaces between the stripes. When two interfaces meet they coalesce thus giving rise to a coarsening process in which l(t), the average width of a stripe, grows with time. This is a generalization of the reactiondiffusion process A + A > A to the case of extended coalescing objects, namely, the interfaces. Scaling arguments which relate the coarsening process to the evolution of a single driven interface are given, yielding growth laws for l(t), for both short and long times. We introduce a simple microscopic model for this process. Numerical simulations of the model confirm the scaling picture and growth laws. The results are compared to the case where the stripes are not driven and different growth laws arise.

(2000) European Physical Journal B. 16, 4, p. 669676 Abstract
The coarsening process in a class of driven systems is studied. These systems have previously been shown to exhibit phase separation and slow coarsening in one dimension. We consider generalizations of this class of models to higher dimensions. In particular we study a system of three types of particles that diffuse under local conserving dynamics in two dimensions. Arguments and numerical studies are presented indicating that the coarsening process in any number of dimensions is logarithmically slow in time. A key feature of this behavior is that the interfaces separating: the various growing domains are macroscopically smooth (well approximated by a Fermi function). This implies that the coarsening mechanism in one dimension is readily extendible to higher dimensions.

(2000) Physical Review E. 61, 3, p. 27532758 Abstract
We study the Landau model of the class of incommensurate systems with a scalar order parameter where the modulated phase is driven by a gradientsquared term with negative coefficient. For example, theoretical studies of cholesteric liquid crystals in a field (electric or magnetic) suggest that such an modulated phase should exist at high chirality. The bulk phase diagram in the presence of a bulk external field which couples linearly to the order parameter exhibits a modulated phase inside a loop in the temperatureheld plane, and a homogeneous phase outside. On analyzing the same model for a semiinfinite system, we fmd a surprising result; the system exhibits surface states in a region where the bulk phase is homogeneous (but close to the modulated region). These states are very different from the wellknown surface states induced either by a surface field or by enhanced interactions at the surface, for they exist and are energetically favored even when the sole effect of the surface is to terminate the bulk, as expressed by free boundary conditions taken at the surface. Near the surface, the surfacestate order parameter is very different from the bulk value (in fact, it has the opposite sign). When the temperature or the bulk field are varied to move away from the modulated state, we find a surface phase transition at which the surface states become energetically unfavorable, though they continue to exist as metastable states. We then study how a surface field changes the surface phase diagram.

(2000) Physical Review E. 61, 2, p. R1032R1035 Abstract
A model for nonequilibrium wetting in 1+1 dimensions is introduced. It comprises adsorption and desorption processes with a dynamics that generically does not obey detailed balance. Depending on the rates of the dynamical processes the wetting transition is either of first or second order. It is found that the wet (unbound) and the nonwet (pinned) states coexist and are both thermodynamically stable in a domain of the dynamical parameters that define the model. This is in contrast with equilibrium transitions where coexistence of thermodynamically stable states takes place only on the transition line.

(2000) Soft And Fragile Matter: Nonequilibrium Dynamics, Metastability And Flow. 53, p. 237258 Abstract
Keywords: ASYMMETRIC EXCLUSION MODEL; SPONTANEOUS SYMMETRYBREAKING; DRIVEN DIFFUSIVE SYSTEMS; OPEN BOUNDARIES; CELLULAR AUTOMATA; TRANSLATIONAL INVARIANCE; STATIONARY STATES; PARALLEL DYNAMICS; STEADYSTATES; ISINGMODELS
1999

(1999) Physical Review Letters. 82, 1, p. 1013 Abstract
We investigate the nonequilibrium stationary state of a translationally invariant onedimensional driven lattice gas with shortrange interactions. The phase diagram is found to exhibit a line of continuous transitions from a disordered phase to a phase with spontaneous symmetry breaking. At the phase transition the correlation length is infinite and density correlations decay algebraically. Depending on the parameters which define the dynamics, the transition either belongs to the universality class of directed percolation or to a universality class of a growth model which preserves the local minimal height. Consequences of mappings to other models are briefly discussed. [S00319007(98)081009].
1998

(1998) Physical Review E. 58, 3, p. 27642778 Abstract
A driven system of three species of particles diffusing on a ring is studied in detail. The dynamics is local and conserves the three densities. A simple argument suggesting that the model should phase separate and break the translational symmetry is given. We show that for the special case where the three densities are equal the model obeys detailed balance, and the steadystate distribution is governed by a Hamiltonian with asymmetric longrange interactions. This provides an explicit demonstration of a simple mechanism for breaking of ergodicity in one dimension. The steady state of finitesize systems is studied using a generalized matrix product ansatz. The coarsening process leading to phase separation is studied numerically and in a meanfield model. The system exhibits slow dynamics due to trapping in metastable states whose number is exponentially large in the system size. The typical domain size is shown to grow logarithmically in time. Generalizations to a larger number of species are discussed.

(1998) Physical Review E. 57, 5, p. 49975012 Abstract
A class of solidonsolid growth models with shortrange interactions and sequential updates is studied. The models exhibit both smooth and rough phases in dimension d=1. Some of the features of the roughening transition which takes place in these models are related to contact processes or directed percolation type problems. The models are analyzed using a mean field approximation, scaling arguments, and numerical simulations. In the smooth phase the symmetry of the underlying dynamics is spontaneously broken. A family of order parameters which are not conserved by the dynamics is defined, as well as conjugate fields which couple to these order parameters. The corresponding critical behavior is studied, and novel exponents identified and measured. We also show how continuous symmetries can be broken in one dimension. A field theory appropriate for studying the roughening transition is introduced and discussed.

(1998) Physical Review Letters. 80, 3, p. 425429 Abstract
A driven diffusive model of three types of particles that exhibits phase separation on a ring is introduced. The dynamics is local and comprises nearestneighbor exchanges that conserve each of the three species. For the case in which the three densities are equal, it is shown that the model obeys detailed balance. The Hamiltonian governing the steady state distribution in this case is given and is found to have long range asymmetric interactions. The partition sum and bounds on some correlation functions are calculated analytically demonstrating phase separation.
1997

(1997) Physical Review Letters. 79, 14, p. 27102713 Abstract
A simple twodimensional (2D) model of a phase growing on a substrate is introduced. The model is characterized by an adsorption rate q, and a desorption rate p. It exhibits a wetting transition which may be viewed as an unbinding transition of an interface from a wall. For p = 1, the model may be mapped onto an exactly soluble equilibrium model exhibiting complete wetting with critical exponents gamma = 1/3 for the diverging interface width and x(0) = 1 for the zerolevel occupation. For 0 <p not equal 1 a crossover to different exponents is observed which is related to a KardarParisiZhangtype nonlinearity.

(1997) Physical Review E. 56, 2, p. 17731783 Abstract
The phase diagram of a bull; cholesteric liquid crystal in an electric or magnetic field applied perpendicular to the pitch axis is studied. This is an example of a system which exhibits different types of phase transitions between various modulated and homogeneous states. Possible transitions are of three types: (1) first order, (2) continuous and described as a condensation of solitons with repulsive interaction, or (3) continuous but characterized by a small order parameter. The detailed behavior of the temperaturefield phase diagram is found to be strongly dependent on the intrinsic chirality, where the existence of an undulating state is predicted at high chirality. The relevant temperature, electric field, and chirality ranges are experimentally attainable.

(1997) Physical Review E. 55, 2, p. 17831793 Abstract
A model for the motion of ringshaped DNA in a gel is introduced and studied by numerical simulations and a meanfield approximation. The ring motion is mediated by fingershaped loops that move in an amoebalike fashion around the gel obstructions. This constitutes an extension of previous reptation tube treatments. It is shown that tension is essential for describing the dynamics in the presence of loops. It is included in the model as longrange interactions over stretched DNA regions. The mobility of ringshaped DNA is found to saturate much as in the wellstudied case of linear DNA. Experiments in agarose gels, however, show that the mobility drops exponentially with the DNA ring size. This is commonly attributed to dangling ends in the gel that can impale the ring. The predictions of the present model are expected to apply to artificial twodimensional obstacle arrays [W. D. Volkmuth and R. H. Austin, Nature 358, 600 (1992)] which have no dangling ends. In the zerofield case an exact solution of the model steady state is obtained, and quantities such as the average ring size are calculated. An approximate treatment of the ring dynamics is given, and the diffusion coefficient is derived. The model is also discussed in the context of spontaneous symmetry breaking in one dimension.
1996

(1996) Physical Review Letters. 76, 15, p. 27462749 Abstract
A class of nonequilibrium models with shortrange interactions and sequential updates is presented. The models describe onedimensional growth processes which display a roughening transition between a smooth and a rough phase. This transition is accompanied by spontaneous symmetry breaking, which is described by an order parameter whose dynamics is nonconserving. Some aspects of models in this class are related to directed percolation in 1 + 1 dimensions, although unlike directed percolation the models have no absorbing states. Scaling relations are derived and compared with Monte Carlo simulations.

(1996) Physical Review E. 53, 3, p. 25952602 Abstract
Modulated structures have been observed in nonchiral systems such as Langmuir monolayers and freely suspended smectic films, and a mechanism involving spontaneous chiral symmetry breaking has recently been suggested to account for the occurrence of these structures. We study a simple model corresponding to this mechanism in the meanfield approximation. We find that the model exhibits two uniaxially modulated phases (the director field is colinear or noncolinear) and a vortexlattice phase, in addition to the two uniform ordered phases (one chiral and one nonchiral) and the disordered phase. The hightemperature transition from the uniform nonchiral phase to the noncolinear uniaxial phase is found to be of third order; it belongs to a peculiar, intermediate class of transitions that has previously been suggested to occur in chiral systems. The lowtemperature transition from the noncolinear uniaxial phase to the uniform chiral phase is second order, but also peculiar, because the wave number vanishes linearly at the transition; the modulated phase just above the transition is best described as a spatially varying commensurate phase with walls.

Scaling and selection in cellular structures and living polymers(1996) Fluctuating Geometries In Statistical Mechanics And Field Theory. p. 9951009 Abstract
Keywords: Mechanics; Physics, Condensed Matter; Physics, Particles & Fields
1995

SPONTANEOUS SYMMETRYBREAKING  EXACT RESULTS FOR A BIASED RANDOMWALK MODEL OF AN EXCLUSION PROCESS(1995) Journal Of Physics AMathematical And General. 28, 21, p. 60396071 Abstract
It has been recently suggested that a totally asymmetric exclusion process with two species on an open chain could exhibit spontaneous symmetry breaking in some range of the parameters defining its dynamics. The symmetry breaking is manifested by the existence of a phase in which the densities of the two species are not equal. In order to provide a more rigorous basis to these observations we consider the limit of the process when the rate at which particles leave the system goes to zero. In this limit the process reduces to a biased random walk in the positive quarter plane, with specific boundary conditions. The stationary probability measure of the position of the walker in the plane is shown to be concentrated around two symmetrically located points, one on each axis, corresponding to the fact that the system is typically in one of the two states of broken symmetry in the exclusion process. We compute the average time for the walker to traverse the quarter plane from one axis to the other, which corresponds to the average time separating two flips between states of broken symmetry in the exclusion process. This time is shown to diverge exponentially with the size of the chain.

(1995) Journal of Statistical Physics. 80, 2Jan, p. 69102 Abstract
A simple twospecies asymmetric exclusion model is introduced. It consists of two types of oppositely charged particles driven by an electric field and hopping on an open chain. The phase diagram of the model is calculated in the meanfield approximation and by Monte Carlo simulations. Exact solutions are given for special values of the parameters defining its dynamics. The model is found to exhibit two phases in which spontaneous symmetry breaking takes place, where the two currents of the two species are not equal.


1994

RECTIFIED MOTIONINDUCED BY AC FORCES IN PERIODIC STRUCTURES(1994) Journal De Physique I. 4, 10, p. 15511561 Abstract
A particle in a periodic potential can be set into macroscopic motion by an ac force of zero mean value if the potential is asymmetric in space or the ac force is asymmetric in time. We analyze features of the resulting complex behaviour at zero and low temperatures within the framework of a simple sawtooth potential. This allows us to suggest experiments promoting separation methods and analysis of motor protein assemblies.

(1994) Physical Review E. 50, 2, p. 774779 Abstract
The steady state distribution of polymer (or micelle) lengths under nonequilbrium conditions in which monomers are continuously extracted from a system is studied. The dynamical equations describing this process exhibit a oneparameter family of steady state distributions. A study of the dynamical equations suggests that they exhibit either a linear marginal or nonlinear marginal selection, depending on the control parameters of the model. The selection is explicitly demonstrated for a simplified linear version of the dynamical equations.

(1994) Physical Review Letters. 72, 18, p. 28672870 Abstract
The late time evolution and structure of 2D RayleighTaylor and RichtmyerMeshkov bubble fronts is calculated, using a new statistical merger model based on the potential flow equations. The merger model dynamics are shown to reach a scale invariant regime. It is found that the RayleighTaylor front reaches a constant acceleration. growing as 0.05gt2, while the RichtmyerMeshkov front grows as at0.4 where a depends on the initial perturbation. The model results are in good agreement with experiments and simulations.
1993

(1993) Journal Of Physics AMathematical And General. 26, 19, p. 49114918 Abstract
The onedimensional fully asymmetric exclusion model, which describes a system of particles hopping in a preferred direction with hard core interactions, is considered on a ring of size N. The steady state of this system is known (all configurations have equal weight), which allows for easy computation of the average velocity of a particle in the steady state. Here an exact expression for the diffusion constant of a particle is obtained for arbitrary number of particles and system size, by using a matrix formulation. Two limits of infinite system size N are discussed: firstly, when the number of particles remains finite as N > infinity the diffusion constant remains dependent on the exact number of particles due to correlations between successive collisions; secondly, when the density rho of particles is nonzero (i.e. when the number of particles is equal to Nrho as N > infinity) the diffusion constant scales as N1/2 . The exponent  1 /2 is related to the dynamic exponent z = 3/2 of the KPZ equation in (1+1) dimensions.

(1993) Physical Review E. 48, 2, p. 10081014 Abstract
A statistical model of RayleighTaylor bubble fronts in two dimensions is introduced. Float and merger of bubbles lead to a scaleinvariant regime, with a stable distribution of scaled bubble radii and a constant front acceleration. The model is solved for a simple merger law, showing that a family of such stable distributions exists. The basins of attraction of each of these are mapped. The properties of the scaleinvariant distributions for various merger laws, including a merger law derived from the SharpWheeler model, are analyzed. The results are in good agreement with computer simulations. Finally, it is shown that for some merger laws, a runaway bubble regime develops. A criterion for the appearance of runaway growth is presented.

(1993) Physical Review Letters. 70, 23, p. 36073610 Abstract
The analogy between temporally periodic phases of noisy extended driven systems and smooth interfaces in growth models is used to derive results for both problems, viz., stable, temporally quasiperiodic phases with longrange spatial order can in fact occur for noisy, shortrange, isotropic rules in dimensions d > 2. For d = 2, temporally quasiperiodic phases have algebraic, rather than longrange, order, and occur only in anisotropic systems. Anisotropic rules can also produce smooth, commensurately growing interfaces with d greaterthanorequalto 2 dimensions for generic parameter values.

(1993) Physical Review E. 47, 2, p. 812819 Abstract
Evolving random cellular structures are observed to reach a universal scaling regime. A meanfield approach to finding fixedpoint distributions in cellside number is extended to distributions for the average area of cells with a given number of sides. This approach leads to simplified equations that can be analyzed analytically and numerically. The theory's results are compared to experimental results on dynamics and distributions in soap froths and good agreement is achieved.

(1993) Physica Scripta. T49B, p. 622628 Abstract
The effect of a localized defect on the profile of a onedimensional growing interface is considered. The (q, q') phase diagram of a restricted solidonsolid growth model is studied within the mean field approximation, where q' and q are the intrinsic growth rates of the defect site and of all other sites, respectively. It is found that the model exhibits two types of phase transitions: One separating vanishing slope and nonvanishing slope interfaces, and the other separating interfaces whose slope varies continuously with the defect parameter q' from those whose slope is independent of q'.
1992

(1992) Journal of Statistical Physics. 69, 4Mar, p. 667687 Abstract
A simple asymmetric exclusion model with open boundaries is solved exactly in one dimension. The exact solution is obtained by deriving a recursion relation for the steady state: if the steady state is known for all system sizes less than N, then our equation (8) gives the steady state for size N. Using this recursion, we obtain closed expressions (48) for the average occupations of all sites. The results are compared to the predictions of a mean field theory. In particular, for infinitely large systems, the effect of the boundary decays as the distance to the power  1/2 instead of the inverse of the distance, as predicted by the mean field theory.

(1992) Europhysics Letters. 20, 4, p. 325329 Abstract
The effect of a localized defect on the profile of a onedimensional growing surface is studied. It is found that the width of the average profile scales with the distance R from the defect as R(gamma). A phase transition is observed as the velocity of propagation at the defect site is increased. For small velocities gamma <1, while above a critical value the profile becomes linear (gamma = 1). This system provides a very interesting example of a phase transition in a onedimensional probabilistic dynamical system.

(1992) PHYSICA D. 59, 3Jan, p. 177184 Abstract
We review current attempts at understanding the scaling behaviour of fully developed turbulence through studying simple, scalar, translationally invariant, deterministic coupledmap interface models. The universality classes of such model systems are discussed.

(1992) Physical Review A. 46, 8, p. 47914796 Abstract
We explore the similarities between the dynamics of rough interfaces and fully developed hydrodynamical turbulence. In particular, we introduce a simple system of coupled mappings that (1) is chaotic with an attractor whose dimension grows proportionally to the system size, (2) generates smallscale structure, and (3) has structure functions that grow as power laws. We discuss the universality classes that determine the largedistance longtime behavior by computing the exponents for the scaling of the interface width.

(1992) Physical Review A. 45, 8, p. 57835788 Abstract
The structure of the modulated phases that can occur in systems like chiral tilted smectic films and monolayers of tilted amphiphiles is studied numerically within the meanfield approximation. Two types of modulated phases, uniaxial and hexagonal, are considered. The uniaxial phase is composed of an array of nontopological line defects and is therefore different from modulated structures occurring near ordinary commensurateincommensurate phase transitions. The hexagonal phase displays point defects and topological piline defects. We discuss the energetics of these structures and the nature of the modulatedsmecticC phase transition.

(1992) Europhysics Letters. 18, 3, p. 269274 Abstract
A model corresponding to the recently observed wrinkling transition in partially polymerized membranes is presented. In this model the quenched random internal disorder induced by the polymerization is coupled linearly to the local curvature of the membrane. It is argued that within the meanfield approximation the theory can be reduced to a Heisenberg spinglass with random DzyaloshinskyMoriya interactions. It exhibits crumpled, flat, spinglass (and mixed) phases with a phase transition from the flat to the glass (or mixed) phase. It is argued that these conclusions should also hold for nonselfavoiding membranes in D = 2.
1991

(1991) Europhysics Letters. 15, 5, p. 479484 Abstract
The time evolution of a wide variety of physical systems exhibiting twodimensional cellular structures has recently been studied and found to lead to a universal distribution x(l) of the number of sides, l, of the cells. A simple model for the evolution of these structures is presented and analysed. The model exhibits a oneparameter family of fixedpoint distributions x(l)*(sigma). Within this model, universality is maintained by a mechanism in which a particular marginally stable fixed point is selected. The predictions of the model compare well with experimental observations in soap froths.
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1979



PHASETRANSITIONS IN 2DIMENSIONALLY MODULATED SYSTEMS(1979) Physical Review B. 19, 3, p. 16011609 Abstract


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1970

(1970) Physical Review BSolid State. 2, 11, p. 46794685 Abstract
The appearance of ferroelectricity in conjunction with a paramagnetictoantiferromagnetic transition in centrosymmetric crystals is considered. Ferroelectricity is forbidden in centrosymmetric crystals. As a result of a magnetic transition such crystals may lose their center of symmetry. Hence, ferroelectricity, which is forbidden in the paramagnetic phase, may appear in the magnetically ordered one. To illustrate this effect from a symmetry point of view, an antiferromagnetic transition in a structure belonging to the space group Pmma is discussed in detail. An estimation of the ferroelectric moment in a model crystal with some "reasonably real" properties yields a moment of 10(8) C/cm(2). It is also shown that a discontinuity in the dielectric constant may occur at the transition point, due to the ferroelectric moment. This discontinuous change is expected to be Delta epsilon/epsilon approximate to 10(6).