Papers by Pedro L. Garrido
Physical Review Letters, Jul 31, 2002
Garrido and Hurtado Reply: In this Reply, we answer the Comment by Li et al. on our Letter ''Simp... more Garrido and Hurtado Reply: In this Reply, we answer the Comment by Li et al. on our Letter ''Simple Onedimensional Model of Heat Conduction which Obeys Fourier's Law'' . In that Letter, we studied the conductivity of a one-dimensional chain of N hard-point particles with alternating masses, proving that Fourier's law holds in this system. First, Li et al. study the conductivity N as a function of the system size N. They conclude that, as they do not observe saturation of the curve N even for N 8000 [instead, they fit N N 0:33 for large N], the large-N limit of N, 1 , must be divergent. In contrast, our conclusion was that finite size effects on N were too strong to conclude on 1 . In particular, we were able to fit both divergent and saturating laws to our data, thus demonstrating that this kind of study does not yield conclusive information on the value of 1 . Other authors have arrived at the same conclusions . Moreover, we can argue [2] that N 1 ÿ AN ÿ0:3 , so N 8000 is still far and away the asymptotic region. Hence, the fact that N in Li et al. data has not yet saturated for N 8000 does not involve a divergent conductivity. In their Comment, Li et al. also report measurements on the total energy current self-correlation function, Ct. They observe that Ct t ÿ , with 0:67, thus concluding, via the Green-Kubo formula, that 1 is divergent. However, Ct also shows important finite size effects . In particular, two different long time regions appear, the first one decaying algebraically as Ct t ÿ1ÿ , with 0:3, and the latest one decaying as Ct t ÿ , with 0:88. It can be shown that the first region (which yields a finite conductivity) is the relevant one in the thermodynamic limit, being the very long time decay Ct t ÿ , a result of finite size effects. It can also be shown that, contrary to the Li et al. claim, a close relation between Ct and the local energy current self-correlation, ct, exists; and it implies a common long time behavior of Ct and ct for our alternating masses system [4]. This system is believed to be ergodic . Thus, it is hard to believe that a change on the initial condition can yield a different decay exponent for Ct measured in equilibrium, as Li et al. claim. Let us now speak about the energy partition between light and heavy particles. Contrary to Li et al. claims, our results on this matter do not disagree with those of Kato and Jou . They found that, at the nonequilibrium stationary state of the open system, the average energy stored in heavy particles exceeds the average energy stored in light ones. On the other hand, in our Letter we studied how an energy pulse propagates through an isolated system, where there was no boundary thermalization. We observed how light particles respond dynamically to such perturbation, storing more energy on average than heavy particles. We think that both pictures are compatible (as Li et al. confirm in their figure), and reflect the nontrivial behavior of this system. The important fact is that our system responds to the perturbation trapping energy temporarily in light particles, thus allowing a diffusive transport of energy through the system. Furthermore, we have measured the mean square displacement of the energy distribution at each time, st. In Fig. , we plot st as a function of time, and we observe that, after an initial ballistic regime, the energy propagates diffusively, st t, and thus Fourier's law holds in this system. In conclusion, we think that Li et al. have analyzed their data in an erroneous way. Hence, we firmly support our previous results [2], i.e., that our one-dimensional system, which is momentum conserving and has a nonzero pressure, has a finite thermal conductivity in the thermodynamic limit, thus obeying Fourier's Law.
Jammed state of competitive sequential adsorption on a line
AIP Conference Proceedings, 2009
ABSTRACT
Physical review, Feb 22, 2019
arXiv (Cornell University), Jun 15, 2020
The Macroscopic Fluctuating Theory developed during the last thirty years is applied to generic s... more The Macroscopic Fluctuating Theory developed during the last thirty years is applied to generic systems described by continuum fields φ(x, t) that evolve by a Langevin equation that locally either conserves or not the field. The aim of this paper is to present well known concepts and results following a general framework in a practical and self consistent way. From the probability of a path we study general properties of the system's stationary state. In particular we focus on the study of the quasi-potential that defines the stationary distribution at the small noise limit. It is derived the system's adjoint dynamics that it is the time reversal Markov process of the system. The equilibrium is assumed to be the unique stationary state that is dynamically time reversal and therefore it can be reached by the system only when the adjoint dynamics is equal to the original one. This condition characterizes the dynamics of systems with equilibrium from the ones with nonequilibrium stationary states. That property is confronted with the macroscopic reversibility that occurs when the most probable path to create a fluctuation from the stationary state is equal to the time reversed path that relaxes it. The lack of this symmetry implies a nonequilibrium stationary state however the converse isn't true. Finally we study extensively the two-body correlations at the stationary state and we derive some generic properties at a variety of situations, including a discussion about the equivalence of ensembles in non-equilibrium systems.
Scientific Reports, Dec 13, 2016
Since the discovery of long-time tails, it has been clear that Fourier's law in low dimensions is... more Since the discovery of long-time tails, it has been clear that Fourier's law in low dimensions is typically anomalous, with a size-dependent heat conductivity, though the nature of the anomaly remains puzzling. The conventional wisdom, supported by renormalization-group arguments and moded momentum-conserving systems and belongs in the Lévy/Kardar-Parisi-Zhang universality class. Here we challenge this picture by using a novel scaling method to show unambiguously that universality d of gradients, densities and sizes all collapse onto an universal master curve, showing that (anomalous) Fourier's law holds even deep into the nonlinear regime. This allows to solve the macroscopic implies the existence of a bound on the heat current in terms of pressure. These results question the d, It's going to be 200 years since Fourier stated his seminal law 1 , but its microscopic understanding still poses one of the most important and challenging open problems in nonequilibrium statistical physics, with no rigorous mathematical derivation to date 2-7 . Fourier's law establishes the proportionality between the heat current and the local temperature gradient in a material, with the proportionality factor defining the heat conductivity κ, a key material property. While for bulk, three-dimensional materials κ is well characterized and measured, its status in low-dimensional structures is far from clear. In particular, for low-dimensional systems (d = 1, 2) with momentum conservation, the effective conductivity κ grows with the system size L, diverging in the thermodynamic limit and thus leading to anomalous heat transport . The understanding of this anomaly has attracted a lot of attention in recent years , not only because it is expected to shed light on the key ingredients behind Fourier's law at a fundamental level, but also because of its technological relevance in low-dimensional real-world materials, the most noteworthy being graphene [11] , but with other important examples ranging from molecular chains 13 and carbon nanotubes 14 to polymer fibers , nanowires and even spider silk 19 , to mention just a few; see 7 for a recent review. From a theoretical perspective, the low-dimensional anomaly in heat transport can be linked to the presence of strong dynamic correlations in these fluids and lattices , though a detailed understanding has remained elusive for decades. In 1d, clear signatures of this anomaly appear in a number of different phenomena 42 . For instance, the steady state heat current J of a 1d momentum-conserving system driven by a small boundary temperature gradient (i.e. in the linear regime) typically scales as L -1+γ for large enough system sizes L, with 0 ≤ γ < 1 an anomaly exponent, which can be interpreted in terms of a finite-size heat conductivity κ L ~ L γ . An exponent γ = 0 corresponds to standard diffusive transport, but typically γ > 0 is observed in 1d implying superdiffusive heat transport 42 . The low-dimensional transport anomaly is also apparent in equilibrium. In particular, the long-time tail of the equilibrium time correlation of the energy current decays in 1d in a nonintegrable, power-law way, 〈 J(0)J(t)〉 ~ t -1+δ as t → ∞ , with 0 ≤ δ < 1 another exponent. Green-Kubo relations for the transport coefficients hence imply a divergent value for the heat conductivity, in agreement with nonequilibrium results 6 . Additional signatures of anomalous transport have been also reported in the superdiffusive spreading of energy perturbations in equilibrium . A range of different values for the exponents γ and δ have been measured in simulations and experiments for different model systems , the main difficulty being extracting the large L asymptotics due to the strong and poorly understood finite-size effects affecting these measurements (which mix bulk and boundary finite-size corrections). The prevailing picture, however, is that the transport anomaly exponents are universal and within
Nucleation and Atmospheric Aerosols, 2003
We present preliminary results on the metastable behavior of a nonequilibrium ferromagnetic syste... more We present preliminary results on the metastable behavior of a nonequilibrium ferromagnetic system. The metastable state mean lifetime is a non-monotonous function of temperature; it shows a maximum at certain non-zero temperature which depends on the strengh of the nonequilibrium perturbation. This is in contrast with the equilibrium case in which lifetime increases monotonously as the temperature is decreasesed. We also report on avalanches during the decay from the metastable state. Assuming both free boundaries and nonequilibrium impurities, the avalanches exhibit power-law size and lifetime distributions. Such scale free behavior is very sensible. The chances are that our observations may be observable in real (i.e. impure) ferromagnetic nanoparticles.
Nonlinearity, 2019
We consider a kinetic model whose evolution is described by a Boltzmannlike equation for the one-... more We consider a kinetic model whose evolution is described by a Boltzmannlike equation for the one-particle phase space distribution f (x, v, t). There are hard-sphere collisions between the particles as well as collisions with randomly fixed scatterers. As a result, this evolution does not conserve momentum but only mass and energy. We prove that the diffusively rescaled f ε (x, v, t) = f (ε −1 x, v, ε −2 t), as ε → 0 tends to a Maxwellian M ρ,0,T = ρ (2πT) 3/2 exp[− |v| 2 2T ], where ρ and T are solutions of coupled diffusion equations and estimate the error in L 2 x,v .
Analysis of heat conductivity in a 2D hard disk system
AIP Conference Proceedings, 2009
ABSTRACT Using numerical simulations, we study the heat conductivity in a 2d Hard Disk system. We... more ABSTRACT Using numerical simulations, we study the heat conductivity in a 2d Hard Disk system. We find nonlinear temperature profiles for diferent gradients, and use this profiles to obtain the empirical expresion of heat conductivity kappa(T,rho). We compare our results with predictions based on the Enskog theory, finding good agreement even for large gradients. Also we find that Henderson state equation for Hard Disk stands for our system.
Physical Review E
We study the behavior of stationary non-equilibrium two-body correlation functions for Diffusive ... more We study the behavior of stationary non-equilibrium two-body correlation functions for Diffusive Systems with equilibrium reference states (DSe). A DSe is described at the mesoscopic level by M locally conserved continuum fields that evolve through coupled Langevin equations with white noises. The dynamic is designed such that the system may reach equilibrium states for a set of boundary conditions. In this form, just by changing the equilibrium boundary conditions, we make the system driven to a non-equilibrium stationary state. We decompose the correlations in a known local equilibrium part and another one that contains the non-equilibrium behavior and that we call correlation's excessC(x, z). We formally derive the differential equations forC. We define a perturbative expansion around the equilibrium state to solve them order by order. We show that theC's first-order expansion,C (1) , is always zero for the unique field case, M = 1. MoreoverC (1) is always long-range or zero when M > 1. Surprisingly we show that their associated fluctuations, the space integrals ofC (1) , are always zero. Therefore, the fluctuations are dominated by the local equilibrium behavior up to second order in the perturbative expansion around the equilibrium. We derive the behaviors ofC (1) in real space for dimensions d = 1 and 2 explicitly, and we apply the analysis to a generic M = 2 case and, in particular, to a hydrodynamic model where we explicitly compute the two first perturbative orders,C (1),(2) , and its associated fluctuations.
Physical Review E
Convection is a key transport phenomenon important in many different areas, from hydrodynamics an... more Convection is a key transport phenomenon important in many different areas, from hydrodynamics and ocean circulation to planetary atmospheres or stellar physics. However, its microscopic understanding still remains challenging. Here we numerically investigate the onset of convective flow in a compressible (non-Oberbeck-Boussinesq) hard disk fluid under a temperature gradient in a gravitational field. We uncover a surprising two-step transition scenario with two different critical temperatures. When the bottom plate temperature reaches a first threshold, convection kicks in (as shown by a structured velocity field) but gravity results in hindered heat transport as compared to the gravity-free case. It is at a second (higher) temperature that a percolation transition of advection zones connecting the hot and cold plates triggers efficient convective heat transport. Interestingly, this picture for the convection instability opens the door to unknown piecewise-continuous solutions to the Navier-Stokes equations.
The influence of nonequilibrium bulk conditions on the properties of the interfaces exhibited by ... more The influence of nonequilibrium bulk conditions on the properties of the interfaces exhibited by a kinetic Ising--like model system with nonequilibrium steady states is studied. The system is maintained out of equilibrium by perturbing the familiar spin--flip dynamics at temperature T with completely--random flips; one may interpret these as ideally simulating some (dynamic) impurities. We find evidence that, in the present case, the nonequilibrium mechanism adds to the basic thermal one resulting on a renormalization of microscopic parameters such as the probability of interfacial broken bonds. On this assumption, we develop theory for the nonequilibrium "surface tension", which happens to show a non--monotonous behavior with a maximum at some finite T. It ensues, in full agreement with Monte Carlo simulations, that interface fluctuations differ qualitatively from the equilibrium case, e.g., the interface remains rough at zero--T. We discuss on some consequences of these ...
Journal of Statistical Mechanics: Theory and Experiment, 2021
The macroscopic fluctuating theory developed during the last 30 years is applied to generic syste... more The macroscopic fluctuating theory developed during the last 30 years is applied to generic systems described by continuum fields ϕ(x, t) that evolve by a Langevin equation that locally either conserves or does not conserve the field. This paper aims to review well-known basic concepts and results from a pedagogical point of view by following a general framework in a practical and self-consistent way. From the probability of a path, we study the general properties of the system’s stationary state. In particular, we focus on the study of the quasipotential that defines the stationary distribution at the small noise limit. To discriminate between equilibrium and non-equilibrium stationary states, the system’s adjoint dynamics are defined as the system’s time-reversal Markov process. The equilibrium is then defined as the unique stationary state that is dynamically time-reversible, and therefore its adjoint dynamics are equal to those of the original one. This property is confronted wi...
arXiv: Statistical Mechanics, 2018
We do a generic study of the behavior of a hard disk system under the action of a thermal gradien... more We do a generic study of the behavior of a hard disk system under the action of a thermal gradient in presence of an uniform gravity field. We observe the conduction-convection transition and measure the main system observables and fields as the thermal current, global pressure, velocity field, temperature field,... We can highlight two of the main results of this overall work: (1) for large enough thermal gradients and a given gravity, we show that the hydrodynamic fields (density, temperature and velocity) have a natural scaling form with the gradient. And (2) we show that local equilibrium holds if the mechanical pressure and the thermodynamic one are not equal, that is, the Stoke's assumption does not hold in this case. Moreover we observe that the best fit to the data is obtained when the bulk viscosity depends on the mechanical pressure.
Journal of Statistical Mechanics: Theory and Experiment, 2021
We assume that a system at a mesoscopic scale is described by a field ϕ(x, t) that evolves by a L... more We assume that a system at a mesoscopic scale is described by a field ϕ(x, t) that evolves by a Langevin equation with a white noise whose intensity is controlled by a parameter 1 / Ω . The system stationary state distribution in the small noise limit (Ω → ∞) is of the form P st [ϕ] ≃ exp(−ΩV 0[ϕ]), where V 0[ϕ] is called the quasipotential. V 0 is the unknown of a Hamilton–Jacobi equation. Therefore, V 0 can be written as an action computed along a path that is the solution from Hamilton’s equation that typically cannot be solved explicitly. This paper presents a theoretical scheme that builds a suitable canonical transformation that permits us to do such integration by deforming the original path into a straight line and including some weights along with it. We get the functional form of such weights through conditions on the existence and structure of the canonical transformation. We apply the scheme to get the quasipotential algebraically for several one-dimensional nonequilibri...
Journal of Statistical Physics, 2020
Hard particle systems are among the most successful, inspiring and prolific models of physics. Th... more Hard particle systems are among the most successful, inspiring and prolific models of physics. They contain the essential ingredients to understand a large class of complex phenomena, from phase transitions to glassy dynamics, jamming, or the physics of liquid crystals and granular materials, to mention just a few. As we discuss in this paper, their study also provides crucial insights on the problem of transport out of equilibrium. A main tool in this endeavour are computer simulations of hard particles. Here we review some of our work in this direction, focusing on the hard disks fluid as a model system. In this quest we will address, using extensive numerical simulations, some of the key open problems in the physics of transport, ranging from local equilibrium and Fourier's law to the transition to convective flow in the presence of gravity, the efficiency of boundary dissipation, or the universality of anomalous transport in low dimensions. In particular, we probe numerically the macroscopic local equilibrium hypothesis, which allows to measure the fluid's equation of state in nonequilibrium simulations, uncovering along the way subtle nonlocal corrections to local equilibrium and a remarkable bulk-boundary decoupling phenomenon in fluids out of equilibrium. We further show that the the hydrodynamic profiles that a system develops when driven out of equilibrium by an arbitrary temperature gradient obey universal scaling laws, a result that allows the determination of transport coefficients with unprecedented precission and proves that Fourier's law remains valid in highly nonlinear regimes. Switching on a gravity field against the temperature gradient, we investigate numerically the transition to convective flow. We uncover a surprising two-step transition scenario with two different critical thresholds for the hot bath temperature, a first one where convection kicks but gravity hinders heat transport, and a second critical temperature where a percolation transition of streamlines connecting the hot and cold baths triggers efficient convective heat transport. We also address numerically the efficiency of boundary heat baths to dissipate the energy provided by a bulk driving mechanism. As a bonus track, we depart from the hard disks model to study anomalous transport in a related hard-particle system, the 1d diatomic hard-point gas. We show unambiguously that the universality conjectured for anomalous transport in 1d breaks down for this model, calling into question recent theoretical predictions and offering a new perspective on anomalous transport in low dimensions. Our results show how carefully-crafted numerical simulations Dedicated to Joel L. Lebowitz to celebrate his key role as leading editor of the Journal of Statistical Physics.
The European Physical Journal Special Topics, 2018
Physical Review Letters, 2017
Physical Review E, 2016
The additivity principle (AP) allows to compute the current distribution in many one-dimensional ... more The additivity principle (AP) allows to compute the current distribution in many one-dimensional (1d) nonequilibrium systems. Here we extend this conjecture to general d-dimensional driven diffusive systems, and validate its predictions against both numerical simulations of rare events and microscopic exact calculations of three paradigmatic models of diffusive transport in d = 2. Crucially, the existence of a structured current vector field at the fluctuating level, coupled to the local mobility, turns out to be essential to understand current statistics in d > 1. We prove that, when compared to the straightforward extension of the AP to high-d, the so-called weak AP always yields a better minimizer of the macroscopic fluctuation theory action for current statistics.
Thermodynamics of Currents in Nonequilibrium Diffusive Systems: Theory and Simulation
Journal of Statistical Physics, 2013
Physical Review E, 2013
We consider fluctuations of the time-averaged current in the one-dimensional weakly-asymmetric ex... more We consider fluctuations of the time-averaged current in the one-dimensional weakly-asymmetric exclusion process on a ring. The optimal density profile which sustains a given fluctuation exhibits an instability for low enough currents, where it becomes time-dependent. This instability corresponds to a dynamical phase transition in the system fluctuation behavior: while typical current fluctuations result from the sum of weakly-correlated local events and are still associated with the flat, steady-state density profile, for currents below a critical threshold the system self-organizes into a macroscopic jammed state in the form of a coherent traveling wave, that hinders transport of particles and thus facilitates a time-averaged current fluctuation well below the average current. We analyze in detail this phenomenon using advanced Monte Carlo simulations, and work out macroscopic fluctuation theory predictions, finding very good agreement in all cases. In particular, we study not only the current large deviation function, but also the critical current threshold, the associated optimal density profiles and the traveling wave velocity, analyzing in depth finite-size effects and hence providing a detailed characterization of the dynamical transition.
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Papers by Pedro L. Garrido