Dynamical phase transition for current statistics in a simple driven diffusive system

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.Comment: 12 pages, 6 figure

Symmetries in Fluctuations Far from Equilibrium

Fluctuations arise universally in Nature as a reflection of the discrete microscopic world at the macroscopic level. Despite their apparent noisy origin, fluctuations encode fundamental aspects of the physics of the system at hand, crucial to understand irreversibility and nonequilibrium behavior. In order to sustain a given fluctuation, a system traverses a precise optimal path in phase space. Here we show that by demanding invariance of optimal paths under symmetry transformations, new and general fluctuation relations valid arbitrarily far from equilibrium are unveiled. This opens an unexplored route toward a deeper understanding of nonequilibrium physics by bringing symmetry principles to the realm of fluctuations. We illustrate this concept studying symmetries of the current distribution out of equilibrium. In particular we derive an isometric fluctuation relation which links in a strikingly simple manner the probabilities of any pair of isometric current fluctuations. This relation, which results from the time-reversibility of the dynamics, includes as a particular instance the Gallavotti-Cohen fluctuation theorem in this context but adds a completely new perspective on the high level of symmetry imposed by time-reversibility on the statistics of nonequilibrium fluctuations. The new symmetry implies remarkable hierarchies of equations for the current cumulants and the nonlinear response coefficients, going far beyond Onsager's reciprocity relations and Green-Kubo formulae. We confirm the validity of the new symmetry relation in extensive numerical simulations, and suggest that the idea of symmetry in fluctuations as invariance of optimal paths has far-reaching consequences in diverse fields.Comment: 8 pages, 4 figure

Spectral signatures of symmetry-breaking dynamical phase transitions

Large deviation theory provides the framework to study the probability of rare fluctuations of time-averaged observables, opening new avenues of research in nonequilibrium physics. One of the most appealing results within this context are dynamical phase transitions (DPTs), which might occur at the level of trajectories in order to maximize the probability of sustaining a rare event. While the Macroscopic Fluctuation Theory has underpinned much recent progress on the understanding of symmetry-breaking DPTs in driven diffusive systems, their microscopic characterization is still challenging. In this work we shed light on the general spectral mechanism giving rise to continuous DPTs not only for driven diffusive systems, but for any jump process in which a discrete $\mathbb{Z}_n$ symmetry is broken. By means of a symmetry-aided spectral analysis of the Doob-transformed dynamics, we provide the conditions whereby symmetry-breaking DPTs might emerge and how the different dynamical phases arise from the specific structure of the degenerate eigenvectors. We show explicitly how all symmetry-breaking features are encoded in the subleading eigenvectors of the degenerate manifold. Moreover, by partitioning configuration space into equivalence classes according to a proper order parameter, we achieve a substantial dimensional reduction which allows for the quantitative characterization of the spectral fingerprints of DPTs. We illustrate our predictions in three paradigmatic many-body systems: (i) the 1D boundary-driven weakly asymmetric exclusion process (WASEP), which exhibits a particle-hole symmetry-breaking DPT for current fluctuations, (ii) the $3$ and $4$-state Potts model, which displays discrete rotational symmetry-breaking DPT for energy fluctuations, and (iii) the closed WASEP which presents a continuous symmetry-breaking DPT to a time-crystal phase characterized by a rotating condensate

Elaboració de material docent per a assignatures d'estadística industrial

La finalitat del projecte és elaborar material d'ajuda i suport a la docència per assignatures relacionades amb l'estadística industrial. Ens centrem fonamentalment en les assignatures “Mètodes estadístics de l’enginyeria 1”, d’enginyeria industrial, i “Estadística”, d’enginyera química, per la gran repercussió que tenen els canvis en aquestes assignatures (un total de 500 estudiants matriculats per any). El projecte es pot entendre com la continuació d’un altre projecte que va rebre un ajut de l’ICE i que es va desenvolupar durant el curs 2007-2008, titulat “Elaboració de material docent per a assignatures de control i millora de la qualitat” i coordinat per Lourdes Rodero de Lamo. La necessitat de creació de nou material sorgeix a partir de decidir canvis – alineats amb l’enfocament de l’EEES – en la metodologia docent. Els canvis venen motivats no només pel fet que aquestes dues assignatures entren en la fase pilot d’implantació de l’EEES a l’ETSEIB, sinó també – i sobretot – a partir de la constatació de fets que no ens agradaven als professors: poca assistència a classe, sensació de que els estudiants “no segueixen” l’assignatura, oblit ràpid del que s’ha aprés, etc.Peer Reviewe

Enzymatic degradation of starch thermoplastic blends using samples of different thickness

The material studied was a thermoplastic blend of corn starch with a poly(ethylene-vinyl alcohol) copolymer, SEVA-C. The influence of both the material’s exposed surface and enzyme concentration on degradation kinetics was studied. As α-amylase is present in the blood plasma, experiments were performed, varying the material thickness and the α-amylase between 50 and 100 units/l, at 37°C, lasting up to 90 days. Four different batches using SEVA-C and starch samples of different thickness were performed. The positive correlation between degradation rate and the exposed material surface was confirmed, since thin films with larger exposed surfaces were degraded faster than thick square plates having the same total mass. The degradation extent depends on the total amount of amorphous starch present in the formulation rather than on the amount of enzyme used and the minimum thickness to ensure maximum degradation was estimated to be close to 0.25 mm

Surface modification of starch based blends using potassium permanganate-nitric acid system and its effect on the adherence and proliferation of osteoblastic-like cells

The surface modification of three starch based polymeric biomaterials, using a KMnO4/NHO3 oxidizing system, and the effect of that modification on the osteoblastic cell adhesion has been investigated. The rationale of this work is as follows—starch based polymers have been proposed for use as tissue engineering scaffolds in several publications. It is known that in biodegradable systems it is quite difficult to have both cell adhesion and proliferation. Starch based polymers have shown to perform better than poly-lactic acid based materials but there is still room for improvement. This particular work is aimed at enhancing cell adhesion and proliferation on the surface of several starch based polymer blends that are being proposed as tissue engineering scaffolds. The surface of the polymeric biomaterials was chemically modified using a KMnO4/HNO3 system. This treatment resulted in more hydrophilic surfaces, which was confirmed by contact angle measurements. The effect of the treatment on the bioactivity of the surface modified biomaterials was also studied. The bioactivity tests, performed in simulated body fluid after biomimetic coating, showed that a dense film of calcium phosphate was formed after 30 days. Finally, human osteoblast-like cells were cultured on unmodified (control) and modified materials in order to observe the effect of the presence of higher numbers of polar groups on the adhesion and proliferation of those cells. Two of the modified polymers presented changes in the adhesion behavior and a significant increase in the proliferation rate kinetics when compared to the unmodified controls.FCT (Portugal) for providing the postdoctoral grant (BPD/8491/2002)