Hysteretic dynamics of active particles in a periodic orienting field

Active motion of living organisms and artificial self-propelling particles has been an area of intense research at the interface of biology, chemistry and physics. Significant progress in understanding these phenomena has been related to the observation that dynamic self-organization in active systems has much in common with ordering in equilibrium condensed matter such as spontaneous magnetization in ferromagnets. The velocities of active particles may behave similar to magnetic dipoles and develop global alignment, although interactions between the individuals might be completely different. In this work, we show that the dynamics of active particles in external fields can also be described in a way that resembles equilibrium condensed matter. It follows simple general laws, which are independent of the microscopic details of the system. The dynamics is revealed through hysteresis of the mean velocity of active particles subjected to a periodic orienting field. The hysteresis is measured in computer simulations and experiments on unicellular organisms. We find that the ability of the particles to follow the field scales with the ratio of the field variation period to the particles'' orientational relaxation time, which, in turn, is related to the particle self-propulsion power and the energy dissipation rate. The collective behaviour of the particles due to aligning interactions manifests itself at low frequencies via increased persistence of the swarm motion when compared with motion of an individual. By contrast, at high field frequencies, the active group fails to develop the alignment and tends to behave like a set of independent individuals even in the presence of interactions. We also report on asymptotic laws for the hysteretic dynamics of active particles, which resemble those in magnetic systems. The generality of the assumptions in the underlying model suggests that the observed laws might apply to a variety of dynamic phenomena from the motion of synthetic active particles to crowd or opinion dynamics.     

不同粒径微米/亚微米颗粒布朗运动的实验研究

利用显微粒子追踪测速系统(Micro-PTV)对四种不同粒径(2μm、1μm、0.71μm、0.52μm)的颗粒在纯水中的布朗运动进行了实验研究.使用波长为532nm的连续激光器、电子倍增CCD(EMCCD)相机以及放大倍率为63倍的显微物镜得到颗粒图像.对原始图像进行处理,借助于Video Spot Tracker软件获得相邻两帧图像中示踪颗粒的单步位移,在此基础上计算颗粒在纯水中的实验扩散系数,分别为0.191μm2/s,0.391μm2/s,0.579μm2/s及0.746μm2/s.将计算结果与采用Stokes-Einstein公式计算的无限大空间单个颗粒理论扩散系数进行了比对,偏差在10%以内,实验值略小.实验结果能够正确反映微米(μm)/亚微米颗粒布朗运动的特征.     

Motion of inertial particles in Gaussian fields driven by an infinite-dimensional fractional Brownian motion

We study the motion of an inertial particle in a fractional Gaussian random field. The motion of the particle is described by Newton's second law, where the force is proportional to the difference between the background fluid velocity and the particle velocity. The fluid velocity satisfies a linear stochastic partial differential equation driven by an infinite-dimensional fractional Brownian motion with an arbitrary Hurst parameter H?∈?(0,?1). The usefulness of such random velocity fields in simulations is that we can create random velocity fields with desired statistical properties, thus generating artificial images of realistic turbulent flows. This model also captures the clustering phenomenon of preferential concentration, observed in real world and numerical experiments, i.e. particles cluster in regions of low-vorticity and high-strain rate. We prove almost sure existence and uniqueness of particle paths and give sufficient conditions to rewrite this system as a random dynamical system with a global random pullback attractor. Finally, we visualize the random attractor through a numerical experiment.     

Emergent behavioural phenotypes of swarming models revealed by mimicking a frustrated anti-ferromagnet

Self-propelled particle (SPP) models are often compared with animal swarms. However, the collective animal behaviour observed in experiments often leaves considerable unconstrained freedom in the structure of a proposed model. Essentially, multiple models can describe the observed behaviour of animal swarms in simple environments. To tackle this degeneracy, we study swarms of SPPs in non-trivial environments as a new approach to distinguish between candidate models. We restrict swarms of SPPs to circular (periodic) channels where they polarize in one of two directions (like spins) and permit information to pass through windows between neighbouring channels. Co-alignment between particles then couples the channels (anti-ferromagnetically) so that they tend to counter-rotate. We study channels arranged to mimic a geometrically frustrated anti-ferromagnet and show how the effects of this frustration allow us to better distinguish between SPP models. Similar experiments could therefore improve our understanding of collective motion in animals. Finally, we discuss how the spin analogy can be exploited to construct universal logic gates, and therefore swarming systems that can function as Turing machines.     

Hot Brownian Motion of Thermoresponsive Microgels in Optical Tweezers Shows Discontinuous Volume Phase Transition and Bistability

Microgels are soft microparticles that often exhibit thermoresponsiveness and feature a transformation at a critical temperature, referred to as the volume phase transition temperature. Whether this transformation occurs as a smooth or as a discontinuous one is still a matter of debate. This question can be addressed by studying individual microgels trapped in optical tweezers. For this aim, composite particles are obtained by decorating  Poly-N-isopropylacrylamide (pNIPAM) microgels with iron oxide nanocubes. These composites become self-heating when illuminated by the infrared trapping laser, performing hot Brownian motion within the trap. Above a certain laser power, a single decorated microgel features a volume phase transition that is discontinuous, while the usual continuous sigmoidal-like dependence is recovered after averaging over different microgels. The collective sigmoidal behavior enables the application of a power-to-temperature calibration and provides the effective drag coefficient of the self-heating microgels, thus establishing these composite particles as potential micro-thermometers and micro-heaters. Moreover, the self-heating microgels also exhibit an unexpected and intriguing bistability behavior above the critical temperature, probably due to partial collapses of the microgel. These results set the stage for further studies and the development of applications based on the hot Brownian motion of soft particles.