Dynamics of flowing 2D skyrmions

We investigate, numerically, the effects of externally imposed material flows on the structure and temporal evolution of liquid crystal (LC) skyrmions. The dynamics of a 2D system of skyrmions is modeled using the Ericksen–Leslie theory, which is based on two coupled equations, one for material flow and the other for the director field. As the time scales of the velocity and director fields differ by several orders of magnitude for realistic values of the system parameters, we have simplified the calculations by assuming that the velocity relaxes instantaneously when compared to the relaxation of the director field. Thus, we have used a finite-differences method known as artificial compressibility with adaptive time step to solve the velocity field and a fourth-order Runge-Kutta method for the director field. We characterized the skyrmion shape or configuration as a function of the time and the average velocity of the flow field. We found that for velocities above a certain threshold, the skyrmions stretch in the direction perpendicular to the flow, by contrast to the regime of weak flows where the skyrmions stretch along the streamlines of the flow field. These two regimes are separated by an abrupt (first-order) dynamical transition, which is robust with respect to e.g., the LC elastic anisotropy. Additionally, we have found how the presence of a second skyrmion affects the evolution of the shape of the skyrmions, by comparing the evolution of pairs of skyrmions to the evolution of a single-skyrmion

Wetting of a solid surface by active matter

A lattice model is used to study repulsive active particles at a planar surface. A rejection-free Kinetic Monte Carlo method is employed to characterize the wetting behaviour. The model predicts a motility-induced phase separation of active particles, and the bulk coexistence of dense liquid-like and dilute vapour-like steady states is determined. An “ensemble”, with a varying number of particles, analogous to a grand canonical ensemble in equilibrium, is introduced. The formation and growth of the liquid film between the solid surface and the vapour phase is investigated. At constant activity, as the system is brought towards coexistence from the vapour side, the thickness of the adsorbed film exhibits a divergent behaviour regardless of the activity. This suggests a complete wetting scenario along the full coexistence curve

Ordering of binary colloidal crystals by random potentials

Structural defects are ubiquitous in condensed matter, and not always a nuisance. For example, they underlie phenomena such as Anderson localization and hyperuniformity, and they are now being exploited to engineer novel materials. Here, we show experimentally that the density of structural defects in a 2D binary colloidal crystal can be engineered with a random potential. We generate the random potential using an optical speckle pattern, whose induced forces act strongly on one species of particles (strong particles) and weakly on the other (weak particles). Thus, the strong particles are more attracted to the randomly distributed local minima of the optical potential, leaving a trail of defects in the crystalline structure of the colloidal crystal. While, as expected, the crystalline ordering initially decreases with an increasing fraction of strong particles, the crystalline order is surprisingly recovered for sufficiently large fractions. We confirm our experimental results with particle-based simulations, which permit us to elucidate how this non-monotonic behavior results from the competition between the particle-potential and particle-particle interactions

Folding of small proteins: A matter of geometry?

We review some of our recent results obtained within the scope of simple lattice models and Monte Carlo simulations that illustrate the role of native geometry in the folding kinetics of two state folders.Comment: To appear in Molecular Physic

Collective variable model for the dynamics of liquid crystal skyrmions

Liquid crystal skyrmions are topologically protected spatially-localized distortions of the director field which exhibit particle-like properties including translational motion in oscillating electric fields. Here, we develop a collective variable model of the skyrmion dynamics, extending the approach of Long and Selinger proposed earlier for one dimensional systems. The model relates the skyrmion motion to a complex dynamics of the width of the twist wall around the skyrmion core. The width evolves in a non-reciprocal way, quantifying squirming deformations of the high twist region within on and off states of the field. We analyze in details the average skyrmion velocity as a function of the frequency and strength of the field as well as its duty cycle. The model predictions agrees qualitatively with experiments and results of numerical minimization of the Frank-Oseen model. Our results provide insights into the conditions necessary to observe velocity reversal as a function of the field parameters

Sculpting liquid crystal skyrmions with external flows

We investigate, using experiments and numerical simulations, the distortions and the alignment of skyrmions in liquid crystal under external flows for a range of average flow velocities. The simulations are based on the Landau-de Gennes Q-tensor theory both for isolated as well as for systems with many skyrmions. We found striking flow-driven elongation of an isolated skyrmion and flow alignment of skyrmions in the many-skyrmion system, both of which are also observed in the experiments. In the simulations, particular attention was given to the dissipation rate and to the various dissipation channels for a single skyrmion under external flow. This analysis provides insight on the observed scaling regime of the elongation of isolated flowing skyrmions and revealed a surprising plastic response at very short times, which may be relevant in applications based on the alignment of soft structures such as liquid crystal skyrmions