Brownian motion in a growing population of ballistic particles.

We investigate the motility of a growing population of cells in a idealized setting: We consider a system of hard disks in which new particles are added according to prescribed growth kinetics, thereby dynamically changing the number density. As a result, the expected Brownian motion of the hard disks is modified. We compute the density-dependent friction of the hard disks and insert it in an effective Langevin equation to describe the system, assuming that the intercollision time is smaller than the timescale of the growth. We find that the effective Langevin description captures the changes in motility, in agreement with the simulation results. Our framework can be extended to other systems in which the transport coefficient varies with time.

Mesoscopic simulations of anisotropic chemically powered nanomotors.

Chemically powered self-propelled colloids generate a motor force by converting locally a source of energy into directed motion, a process that has been explored both in experiments and in computational models. The use of active colloids as building blocks for nanotechnology opens the doors to interesting applications, provided we understand the behavior of these elementary constituents. We build a consistent mesoscopic simulation model for self-propelled colloids of complex shape with the aim of resolving the coupling between their translational and rotational motion. Considering a passive L-shaped colloidal particle, we study its Brownian dynamics and locate its center of hydrodynamics, the tracking point at which translation and rotation decouple. The active L particle displays the same circling trajectories that have been found experimentally, a result which we compare with the Brownian dynamics model. We put forward the role of hydrodynamics by comparing our results with a fluid model in which the particles' velocities are reset randomly. There, the trajectories only display random orientations. We obtain these original simulation results without any parametrization of the algorithm, which makes it a useful method for the preliminary study of active colloids, prior to experimental work.

Passive and active colloidal chemotaxis in a microfluidic channel: mesoscopic and stochastic models.

Chemotaxis is the response of a particle to a gradient in the chemical composition of the environment. While it was originally observed for biological organisms, it is of great interest in the context of synthetic active particles such as nanomotors. Experimental demonstration of chemotaxis for chemically-powered colloidal nanomotors was reported in the literature in the context of chemo-attraction in a still fluid or in a microfluidic channel where the gradient is sustained by a specific inlet geometry. In this work, we use mesoscopic particle-based simulations of the colloid and solvent to demonstrate chemotaxis in a microfluidic channel. On the basis of this particle-based model, we evaluate the chemical concentration profiles in the presence of passive or chemically active colloids, compute the chemotactic force acting upon them and propose a stochastic model that rationalises our findings on colloidal chemotaxis. Our model is also able to explain the results of an earlier simulation work that uses a simpler geometry and to extend its interpretation.

Sustainable computational science: the ReScience initiative.

Computer science offers a large set of tools for prototyping, writing, running, testing, validating, sharing and reproducing results; however, computational science lags behind. In the best case, authors may provide their source code as a compressed archive and they may feel confident their research is reproducible. But this is not exactly true. James Buckheit and David Donoho proposed more than two decades ago that an article about computational results is advertising, not scholarship. The actual scholarship is the full software environment, code, and data that produced the result. This implies new workflows, in particular in peer-reviews. Existing journals have been slow to adapt: source codes are rarely requested and are hardly ever actually executed to check that they produce the results advertised in the article. ReScience is a peer-reviewed journal that targets computational research and encourages the explicit replication of already published research, promoting new and open-source implementations in order to ensure that the original research can be replicated from its description. To achieve this goal, the whole publishing chain is radically different from other traditional scientific journals. ReScience resides on GitHub where each new implementation of a computational study is made available together with comments, explanations, and software tests.

Generalized maximum entropy approach to quasistationary states in long-range systems.

Systems with long-range interactions display a short-time relaxation towards quasistationary states (QSSs) whose lifetime increases with the system size. In the paradigmatic Hamiltonian mean-field model (HMF) out-of-equilibrium phase transitions are predicted and numerically detected which separate homogeneous (zero magnetization) and inhomogeneous (nonzero magnetization) QSSs. In the former regime, the velocity distribution presents (at least) two large, symmetric bumps, which cannot be self-consistently explained by resorting to the conventional Lynden-Bell maximum entropy approach. We propose a generalized maximum entropy scheme which accounts for the pseudoconservation of additional charges, the even momenta of the single-particle distribution. These latter are set to the asymptotic values, as estimated by direct integration of the underlying Vlasov equation, which formally holds in the thermodynamic limit. Methodologically, we operate in the framework of a generalized Gibbs ensemble, as sometimes defined in statistical quantum mechanics, which contains an infinite number of conserved charges. The agreement between theory and simulations is satisfying, both above and below the out-of-equilibrium transition threshold. A previously unaccessible feature of the QSSs, the multiple bumps in the velocity profile, is resolved by our approach.

A parallel algorithm for step- and chain-growth polymerization in molecular dynamics.

Classical Molecular Dynamics (MD) simulations provide insight into the properties of many soft-matter systems. In some situations, it is interesting to model the creation of chemical bonds, a process that is not part of the MD framework. In this context, we propose a parallel algorithm for step- and chain-growth polymerization that is based on a generic reaction scheme, works at a given intrinsic rate and produces continuous trajectories. We present an implementation in the ESPResSo++ simulation software and compare it with the corresponding feature in LAMMPS. For chain growth, our results are compared to the existing simulation literature. For step growth, a rate equation is proposed for the evolution of the crosslinker population that compares well to the simulations for low crosslinker functionality or for short times.

Absence of thermalization for systems with long-range interactions coupled to a thermal bath.

We investigate the dynamics of a small long-range interacting system, in contact with a large long-range thermal bath. Our analysis reveals the existence of striking anomalies in the energy flux between the bath and the system. In particular, we find that the evolution of the system is not influenced by the kinetic temperature of the bath, as opposed to what happens for short-range collisional systems. As a consequence, the system may get hotter also when its initial temperature is larger than the bath temperature. This observation is explained quantitatively in the framework of the collisionless Vlasov description of toy models with long-range interactions and shown to be valid whenever the Vlasov picture applies, from cosmology to plasma physics..

Phoretic self-propulsion: a mesoscopic description of reaction dynamics that powers motion.

The fabrication of synthetic self-propelled particles and the experimental investigations of their dynamics have stimulated interest in self-generated phoretic effects that propel nano- and micron-scale objects. Theoretical modeling of these phenomena is often based on a continuum description of the solvent for different phoretic propulsion mechanisms, including, self-electrophoresis, self-diffusiophoresis and self-thermophoresis. The work in this paper considers various types of catalytic chemical reaction at the motor surface and in the bulk fluid that come into play in mesoscopic descriptions of the dynamics. The formulation is illustrated by developing the mesoscopic reaction dynamics for exothermic and dissociation reactions that are used to power motor motion. The results of simulations of the self-propelled dynamics of composite Janus particles by these mechanisms are presented.

Effectiveness of mixing in violent relaxation.

Relaxation processes in collisionless dynamics lead to peculiar behavior in systems with long-range interactions such as self-gravitating systems, non-neutral plasmas, and wave-particle systems. These systems, adequately described by the Vlasov equation, present quasistationary states (QSS), i.e., long lasting intermediate stages of the dynamics that occur after a short significant evolution called "violent relaxation." The nature of the relaxation, in the absence of collisions, is not yet fully understood. We demonstrate in this article the occurrence of stretching and folding behavior in numerical simulations of the Vlasov equation, providing a plausible relaxation mechanism that brings the system from its initial condition into the QSS regime. Area-preserving discrete-time maps with a mean-field coupling term are found to display a similar behavior in phase space as the Vlasov system.

Self-consistent inhomogeneous steady states in Hamiltonian mean-field dynamics.

Long-lived quasistationary states, associated with stationary stable solutions of the Vlasov equation, are found in systems with long-range interactions. Studies of the relaxation time in a model of N globally coupled particles moving on a ring, the Hamiltonian mean-field model (HMF), have shown that it diverges as N(γ) for large N, with γ1.7 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 γ ~/= 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.

Statistical mechanics of collisionless relaxation in a non-interacting system.

We introduce a model of uncoupled pendula, which mimics the dynamical behaviour of the Hamiltonian mean-field (HMF) model. This model has become a paradigm for long-range 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 quasi-stationary states (QSSs), which arise after a 'collisionless' relaxation process. Both the magnetization and the single-particle distribution function in these QSSs can be predicted using Lynden-Bell'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 Lynden-Bell's theory, which we fully implement for the zero-field case.