We study the velocity distribution of unicellular swimming algae Euglena gracilis using optical microscopy and theory. To characterize a peculiar feature of the experimentally observed distribution at small velocities we use the concept of active fluctuations, which was recently proposed for the description of stochastically self-propelled particles [Romanczuk, P. and Schimansky-Geier, L., Phys. Rev. Lett. 106, 230601 (2011)]. In this concept, the fluctuating forces arise due to internal random performance of the propulsive motor. The fluctuating forces are directed in parallel to the heading direction, in which the propulsion acts. In the theory, we introduce the active motion via the depot model [Schweitzer et al., Phys. Rev. Lett. 80, 23, 5044 (1998)]. We demonstrate that the theoretical predictions based on the depot model with active fluctuations are consistent with the experimentally observed velocity distributions. In addition to the model with additive active noise, we obtain theoretical results for a constant propulsion with multiplicative noise.

Structure and ordering in swarms of active particles have much in common with condensed matter systems like magnets or liquid crystals. A number of important characteristics of such materials can be obtained via dynamic tests such as hysteresis. In this work, we show that dynamic hysteresis can be observed also in swarms of active particles and possesses similar properties to the counterparts in magnetic materials. To study the swarm dynamics, we use computer simulations of the active Brownian particle model with dissipative interactions. The swarm is confined to a narrow linear channel and the one-dimensional polar order parameter is measured. In an oscillating external field, the order parameter demonstrates dynamic hysteresis with the shape of the loop and its area varying with the amplitude and frequency of the applied field, swarm density and the noise intensity. We measure the scaling exponents for the hysteresis loop area, which can be associated with the controllability of the swarm. Although the exponents are non-universal and depend on the system's parameters, their limiting values can be predicted using a generic model of dynamic hysteresis. We also discuss similarities and differences between the swarm ordering dynamics and two-dimensional magnets.