Activity statistics in a colloidal glass former: Experimental evidence for a dynamical transition.

In a dense colloidal suspension at a volume fraction below the glass transition, we follow the trajectories of an assembly of tracers over a large time window. We define a local activity, which quantifies the local tendency of the system to rearrange. We determine the statistics of the time integrated activity, and we argue that it develops a low activity tail that comes together with the onset of glassy-like behavior and heterogeneous dynamics. These rare events may be interpreted as the reflection of an underlying dynamic phase transition.

Long-Distance Rescue and Slow Extinction Dynamics Govern Multiscale Metapopulations.

Rare long-distance dispersal is known to be critical for species dynamics, but how the interplay between short- and long-distance colonization influences regional persistence in a fragmented habitat remains poorly understood. We propose a metapopulation model that combines local colonization within habitat islands and long-distance colonization between islands. We study how regional occupancy dynamics are affected by the multiscale colonization process. We find that the island size distribution (ISD) is a key driver of the long-term occupancy dynamics. When the ISD is heterogeneous-that is, when the size of islands is variable-we show that extinction dynamics become very slow. We demonstrate that this behavior is unrelated to the well-known extinction debt near the critical extinction threshold. Hence, this finding questions the equivalence between extinction debt and critical transitions in the context of metapopulation collapse. Furthermore, we show that long-distance colonization can rescue small islands from extinction and sustain a steady regional occupancy. These results provide novel theoretical and practical insights into extinction dynamics and persistence in fragmented habitats and are thus relevant for the design of conservation strategies.

Exit times of totally asymmetric simple exclusion processes.

We address the question of the time needed by N particles, initially located on the first sites of a finite one-dimensional lattice of size L, to exit that lattice when they move according to a TASEP transport model. Using analytical calculations and numerical simulations, we show that when N≪L, the mean exit time of the particles is asymptotically given by T_{N}(L)∼L+ß_{N}sqrt[L] for large lattices. Building upon exact results obtained for two particles, we devise an approximate continuous space and time description of the random motion of the particles that provides an analytical recursive relation for the coefficients ß_{N}. The results are shown to be in very good agreement with numerical results. This approach sheds some light on the exit dynamics of N particles in the regime where N is finite while the lattice size L→∞. This complements previous asymptotic results obtained by Johansson [Commun. Math. Phys. 209, 437 (2000)0010-361610.1007/s002200050027] in the limit where both N and L tend to infinity while keeping the particle density N/L finite.

Role of cilia activity and surrounding viscous fluid in properties of metachronal waves.

Large groups of active cilia collectively beat in a fluid medium as metachronal waves, essential for some microorganisms motility and for flow generation in mucociliary clearance. Several models can predict the emergence of metachronal waves, but what controls the properties of metachronal waves is still unclear. Here, we numerically investigate the respective impacts of active beating and viscous dissipation on the properties of metachronal waves in a collection of oscillators, using a simple model for cilia in the presence of noise on regular lattices in one and two dimensions. We characterize the wave using spatial correlation and the frequency of collective beating. Our results clearly show that the viscosity of the fluid medium does not affect the wavelength; the activity of the cilia does. These numerical results are supported by a dimensional analysis, which shows that the result of wavelength invariance is robust against the model taken for sustained beating and the structure of hydrodynamic coupling. Interestingly, the enhancement of cilia activity increases the wavelength and decreases the beating frequency, keeping the wave velocity almost unchanged. These results might have significance in understanding paramecium locomotion and mucociliary clearance diseases.

Injected power fluctuations in one-dimensional dissipative systems: role of ballistic transport.

This paper is a generalization of the models considered in J. Stat. Phys. 128, 1365 (2007). Using an analogy with free fermions, we compute exactly the large deviation function (LDF) of the energy injected up to time t in a one-dimensional dissipative system of classical spins, where a drift is allowed. The dynamics are T=0 asymmetric Glauber dynamics driven out of rest by an injection mechanism, namely, a Poissonian flipping of one spin. The drift induces anisotropy in the system, making the model more comparable to experimental systems with dissipative structures. We discuss the physical content of the results, specifically the influence of the rate of the Poisson injection process and the magnitude of the drift on the properties of the LDF. We also compare the results of this spin model to simple phenomenological models of energy injection (Poisson or Bernoulli processes of domain wall injection). We show that many qualitative results of the spin model can be understood within this simplified framework.

Role of spatial heterogeneity in the collective dynamics of cilia beating in a minimal one-dimensional model.

Cilia are elastic hairlike protuberances of the cell membrane found in various unicellular organisms and in several tissues of most living organisms. In some tissues such as the airway tissues of the lung, the coordinated beating of cilia induces a fluid flow of crucial importance as it allows the continuous cleaning of our bronchia, known as mucociliary clearance. While most of the models addressing the question of collective dynamics and metachronal wave consider homogeneous carpets of cilia, experimental observations rather show that cilia clusters are heterogeneously distributed over the tissue surface. The purpose of this paper is to investigate the role of spatial heterogeneity on the coherent beating of cilia using a very simple one-dimensional model for cilia known as the rower model. We systematically study systems consisting of a few rowers to hundreds of rowers and we investigate the conditions for the emergence of collective beating. When considering a small number of rowers, a phase drift occurs, hence, a bifurcation in beating frequency is observed as the distance between rower clusters is changed. In the case of many rowers, a distribution of frequencies is observed. We found in particular the pattern of the patchy structure that shows the best robustness in collective beating behavior, as the density of cilia is varied over a wide range.

Finite-size effects and intermittency in a simple aging system.

We study the intermittent dynamics and the fluctuations of the dynamic correlation function of a simple aging system. Given its size L and its coherence length xi , the system can be divided into N independent subsystems, where N= (L/xi)(d), and d is the dimension of space. Each of them is considered as an aging subsystem which evolves according to an activated dynamics between energy levels. We compute analytically the distribution of trapping times for the global system, which can take power-law, stretched-exponential or exponential forms according to the values of N and the regime of times considered. An effective number of subsystems at age t(w), N(eff) (t(w)), can be defined, which decreases as t(w) increases, as well as an effective coherence length, xi (t(w)) approximately tw ((1-mu)/d), where mu<1 characterizes the trapping times distribution of a single subsystem. We also compute the probability distribution functions of the time intervals between large decorrelations, which exhibit different power-law behaviors as t(w) increases (or N decreases), and which should be accessible experimentally. Finally, we calculate the probability distribution function of the two-time correlator. We show that in a phenomenological approach, where N is replaced by the effective number of subsystems N(eff) (t(w)), the same qualitative behaviour as in experiments and simulations of several glassy systems can be obtained.

Structure factor of polymers interacting via a short range repulsive potential: application to hairy wormlike micelles.

We use the random phase approximation to compute the structure factor S(q) of a solution of chains interacting through a soft and short range repulsive potential V. Above a threshold polymer concentration, whose magnitude is essentially controlled by the range of the potential, S(q) exhibits a peak whose position depends on the concentration. We take advantage of the close analogy between polymers and wormlike micelles and apply our model, using a Gaussian function for V, to quantitatively analyze experimental small angle neutron scattering profiles of solutions of hairy wormlike micelles. These samples, which consist in surfactant self-assembled flexible cylinders decorated by amphiphilic copolymer, provide indeed an appropriate experimental model system to study the structure of sterically interacting polymer solutions.

Glassy behavior of a homopolymer from molecular dynamics simulations.

We study at- and out-of-equilibrium dynamics of a single homopolymer chain at low temperature using molecular dynamics. The main quantities of interest are the average root mean square displacement of the monomers below the theta point, and the structure factor, as a function of time. The observation of these quantities show a close resemblance to those measured in structural glasses and suggest that the polymer chain in its low temperature phase is in a glassy phase, with its dynamics dominated by traps. In equilibrium, at low temperature, we observe the trapping of the monomers and a slowing down of the overall motion of the polymer as well as nonexponential relaxation of the structure factor. Out of equilibrium, at low temperatures, we compute the two-time quantities and observe breaking of ergodicity in a range of waiting times, with the onset of aging.

Transport on a lattice with dynamical defects.

Many transport processes in nature take place on substrates, often considered as unidimensional lanes. These unidimensional substrates are typically nonstatic: Affected by a fluctuating environment, they can undergo conformational changes. This is particularly true in biological cells, where the state of the substrate is often coupled to the active motion of macromolecular complexes, such as motor proteins on microtubules or ribosomes on mRNAs, causing new interesting phenomena. Inspired by biological processes such as protein synthesis by ribosomes and motor protein transport, we introduce the concept of localized dynamical sites coupled to a driven lattice gas dynamics. We investigate the phenomenology of transport in the presence of dynamical defects and find a regime characterized by an intermittent current and subject to severe finite-size effects. Our results demonstrate the impact of the regulatory role of the dynamical defects in transport not only in biology but also in more general contexts.

Driving kinetically constrained models into nonequilibrium steady states: Structural and slow transport properties.

Complex fluids in shear flow and biased dynamics in crowded environments exhibit counterintuitive features which are difficult to address both at a theoretical level and by molecular dynamic simulations. To understand some of these features we study a schematic model of a highly viscous liquid, the two-dimensional Kob-Andersen kinetically constrained model, driven into nonequilibrium steady states by a uniform non-Hamiltonian force. We present a detailed numerical analysis of the microscopic behavior of the model, including transversal and longitudinal spatial correlations and dynamic heterogeneities. In particular, we show that at high particle density the transition from positive to negative resistance regimes in the current vs field relation can be explained via the emergence of nontrivial structures that intermittently trap the particles and slow down the dynamics. We relate such spatial structures to the current vs field relation in the different transport regimes.