Single File Diffusion of particles with long ranged interactions: damping and finite size effects

We study the Single File Diffusion (SFD) of a cyclic chain of particles that cannot cross each other, in a thermal bath, with long ranged interactions, and arbitrary damping. We present simulations that exhibit new behaviors specifically associated to systems of small number of particles and to small damping. In order to understand those results, we present an original analysis based on the decomposition of the particles motion in the normal modes of the chain. Our model explains all dynamic regimes observed in our simulations, and provides convincing estimates of the crossover times between those regimes.Comment: 30 pages, 9 figure

Diffusion et corrélations de particules confinées en interaction à longue portée

Describing the diffusion of brownian correlated objects is not a trivial issue in statistical physics. Long-ranged correlations indeed induce an "anomalous" diffusion, by definition not described by the usual statistical physics laws, which means that it has to be studied on a per cases base. This PhD is devoted to one particular example named Single-file Diffusion, refering to the diffusion of an ordered chain of particles that cannot cross each other. We report here molecular dynamics simulations and experimental results emphasizing the existence of several diffusive behaviors for the longitudinal or transverse fluctuations of particles in a SFD configuration. All our numerical and experimental results can be explained by an analytical model based on the decomposition of the thermal fluctuations on the vibrational eigenmodes of the system. This model can be used to describe real physical systems as it takes into account long-ranged interactions, the influence of the dissipation, the size of the system and the properties of both confinement forces. This eigenmodes analysis can explain the evolution of the transverse fluctuations during the zigzag transition and the structure of the system after the transition. Moreover, studying the transverse fluctuations also contributes to the understanding of the influence of a thermal noise on a pitchfork bifurcation.Décrire la diffusion d'objets browniens corrélés est un problème non trivial en physique statistique. La présence de corrélations à longue portée induit en effet une diffusion "anormale", par définition non décrite par les lois usuelles de la physique statistique et devant être étudiée au cas par cas. Cette thèse est consacrée à l'un de ces exemples, la Single-File Diffusion, désignant la diffusion d'une chaîne ordonnée de particules ne pouvant pas se croiser. Nous présentons des études numériques de dynamique moléculaire ainsi que des études expérimentales nous permettant de mettre en évidence et de caractériser plusieurs régimes de diffusion longitudinale et transverse rencontrés lors de ce phénomène de transport. L'ensemble de nos résultats numériques et expérimentaux est expliqué par un modèle analytique basé sur la décomposition des fluctuations thermiques sur les modes propres de vibration d'un système. Ce modèle s'applique aux systèmes physiques réels car il est valable pour des interactions entre particules à longue portée et tient compte de la dissipation, de la taille du système et des propriétés du potentiel de confinement. L'analyse en modes propres nous permet également de caractériser l'évolution des fluctuations thermiques transverses lors de la transition zizag et de prévoir la structure du système après la transition. Enfin, l'étude de la transition zigzag nous renseigne plus généralement sur les effets d'un bruit thermique sur une bifurcation

Collective behavior of strongly confined suspensions of squirmers

We run numerical simulations of strongly confined suspensions of model spherical swimmers called "squirmers". Because of the confinement, the Stokeslet dipoles generated by the particles are quickly screened and the far-field flow is dominated by the source dipole for all the different kinds of squirmers. However, we show that the collective behavior of the suspension still depends on the self-propelling mechanism of the swimmers as polar states can only be observed for neutral squirmers. We demonstrate that the near-field hydrodynamic interactions play a crucial role in the alignment of the orientation vectors of spherical particles. Moreover, we point out that the enstrophy and the fluid fluctuations of an active suspension also depend on the nature of the squirmers.This work is supported by the Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research KAKENHI.Peer reviewe

Enhanced fluctuations of interacting particles confined in a box

International audienceWe study the position fluctuations of interacting particles aligned in a finite cell that avoid any crossing in equilibrium with a thermal bath. The focus is put on the influence of the confining force directed along the cell length. We show that the system may be modeled as a 1D chain of particles with identical masses, linked with linear springs of varying spring constants. The confining force may be accounted for by linear springs linked to the walls. When the confining force range is increased toward the inside of the chain, a paradoxical behavior is exhibited. The outermost particles fluctuations are enhanced, whereas those of the inner particles are reduced. A minimum of fluctuations is observed at a distance of the cell extremities that scales linearly with the confining force range. Those features are in very good agreement with the model. Moreover, the simulations exhibit an asymmetry in their fluctuations which is an anharmonic effect. It is characterized by the measurement of the skewness, which is found to be strictly positive for the outer particles when the confining force is short ranged

Transverse single-file diffusion near the zigzag transition

International audienceWe study with numerical simulations the transverse fluctuations in quasi-one-dimensional systems of particles in a thermal bath, near the zigzag transition. We show that close to the zigzag threshold, the transverse fluctuations exhibit an anormal diffusion, characterized by a mean square displacement that increases as the square root of time. In contrast with the longitudinal fluctuations, this behavior of the transverse fluctuations cannot be explained by the single-file ordering. We provide an analytical modelization, and in the thermodynamic limit we demonstrate the existence of this subdiffusive regime near the zigzag transition, showing that it results from overdamped collective modes of the system. These calculations are extended to finite systems, in excellent agreement with the simulations data. We also exhibit some effects of the thermal fluctuations on the zigzag transition, and analyze them in the light of stochastic bifurcation theory

Single-file diffusion of particles in a box: Transient behaviors

International audienceWe consider a finite number of particles with soft-core interactions, subjected to thermal fluctuations and confined in a box with excluded mutual passage. Using numerical simulations, we focus on the influence of the longitudinal confinement on the transient behavior of the longitudinal mean squared displacement. We exhibit several power laws for its time evolution according to the confinement range and to the rank of the particle in the file. We model the fluctuations of the particles as those of a chain of springs and point masses in a thermal bath. Our main conclusion is that actual system dynamics can be described in terms of the normal oscillation modes of this chain. Moreover, we obtain complete expressions for the physical observables, in excellent agreement with our simulations. The correct power laws for the time dependency of the mean squared displacement in the various regimes are recovered, and analytical expressions of the prefactors according to the relevant parameters are given

Noisy zigzag transition, fluctuations, and thermal bifurcation threshold

International audienceWe study the zigzag transition in a system of particles with screened electrostatic interaction, submitted to a thermal noise. At finite temperature, this configurational phase transition is an example of noisy supercritical pitchfork bifurcation. The measurements of transverse fluctuations allow a complete description of the bifurcation region, which takes place between the deterministic threshold and a thermal threshold beyond which thermal fluctuations do not allow the system to flip between the symmetric zigzag configurations. We show that a divergence of the saturation time for the transverse fluctuations allows a precise and unambiguous definition of this thermal threshold. Its evolution with the temperature is shown to be in good agreement with theoretical predictions from noisy bifurcation theory. Many systems exhibit a topological transition as soon as a parameter β, which controls this transition, reaches a threshold β ZZ. An example of such transitions is the " zigzag bifurcation, " which involves a quasi-one-dimensional (1D) chain of interacting particles confined in a narrow channel that forbids any particle crossing [1]. At T = 0 K and for an infinite system, the particles remain aligned until the transverse component of the interparticle forces exceeds the transverse confinement, which may be expressed as β > β ZZ if β is the transverse stiffness [see Fig. 1(a)]. The bifurcation occurs when these two contributions are equal, β = β ZZ. Beyond that, for β β ZZ to a finite value y(β) = ±(β ZZ − β) 1/2 as the difference β ZZ − β increases. This bifurcation is purely mechanical. The zigzag threshold β ZZ is called the deterministic threshold and noted β ZZ (0) ≡ β ZZ (T = 0). When the confined particles interact with a thermal bath, the topological properties are no longer sufficient to describe the states of the system. Although the equilibrium configurations are independent of the temperature, the thermal fluctuations directly modify the bifurcation scheme. Far from the threshold, when the system is strongly stable, these fluctuations do not modify the stability of the system, but they have a large influence near the bifurcation since the system is then very sensitive to any small perturbation. In particular, just beyond the deterministic bifurcation threshold [β 0 K, β ZZ (T) is not so accurate since the y(β) curve is broadened by the thermal fluctuations which smooth out th

Active cluster crystals

We study the appearance and properties of cluster crystals (solids in which the unit cell is occupied by a cluster of particles) in a two-dimensional system of self-propelled active Brownian particles with repulsive interactions. Self-propulsion deforms the clusters by depleting particle density inside, and for large speeds it melts the crystal. Continuous field descriptions at several levels of approximation allow us to identify the relevant physical mechanisms.We acknowledge financial support from grants LAOP, CTM2015-66407-P (AEI/FEDER, EU) and ESOTECOS, FIS2015-63628-C2-1-R (AEI/FEDER, EU).Peer reviewe

Single-file diffusion of interacting particles in a finite-sized channel

International audienceWe study the dynamics of charged macroscopic particles millimetric steel balls confined in a linear channel of finite length, sufficiently narrow to avoid particles crossing. We show that their individual response to thermal fluctuations strongly depends either on their position in the channel or the local potential they experience. Three different dynamical regimes are identified. At small times, a " free regime " takes place, with the outermost particles exhibiting the highest diffusion coefficient. This effect results from an " echo " of the thermal fluctuations reflected by the channel wall. Then, forbidden crossing induces a correlated regime similar to single file diffusion. Surprisingly, the corresponding mobility increases with the local potential. Lastly, the finite length of the channel induces the saturation of fluctuations. We show that those behaviors may be described heuristically with the help of models for N hard-core interacting particles diffusing in a finite channel of length L, provided that we replace the uniform interparticle distance L / N by a characteristic distance k B T / K 1/2 built upon the temperature T and the stiffness K of the local potential. It provides a very satisfactory estimate for the fluctuations sizes, whereas they are greatly overestimated assuming hard-core interactions