Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and algae. For artificial microswimmers, alternative concepts to convert chemical energy or heat into directed motion can be employed, which are potentially more efficient. The dynamics of microswimmers comprises many facets, which are all required to achieve locomotion. In this article, we review the physics of locomotion of biological and synthetic microswimmers, and the collective behavior of their assemblies. Starting from individual microswimmers, we describe the various propulsion mechanism of biological and synthetic systems and address the hydrodynamic aspects of swimming. This comprises synchronization and the concerted beating of flagella and cilia. In addition, the swimming behavior next to surfaces is examined. Finally, collective and cooperate phenomena of various types of isotropic and anisotropic swimmers with and without hydrodynamic interactions are discussed.

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of "active matter" in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano-and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics.

-The structural and dynamical properties of suspensions of self-propelled Brownian particles of spherical shape are investigated in three spatial dimensions. Our simulations reveal a phase separation into a dilute and a dense phase, above a certain density and strength of selfpropulsion. The packing fraction of the dense phase approaches random close packing at high activity, yet the system remains fluid. Although no alignment mechanism exists in this model, we find long-lived cooperative motion of the particles in the dense regime. This behavior is probably due to an interface-induced sorting process. Spatial displacement correlation functions are nearly scale-free for systems with densities close to or above the glass transition density of passive systems.

The conformational properties of single polyelectrolyte chains of various lengths in the presence of counterions are investigated by molecular dynamics simulations. For Coulomb interaction strengths below the critical value for Manning condensation, the molecular chain exhibits an increase of the radius of gyration and of the end-to-end distance with increasing interaction strength. Above this critical value, counterions condense on the chain and ion pairs are formed. The ion pairs possess a net attraction such that beyond a certain interaction strength the chain with the condensed ions collapses into a dense coil. The scaling behavior of the radius of gyration and the end-to-end distance with changes in the number of bonds is discussed for various Coulomb interaction strengths. [S0031-9007(98)05910-9] PACS numbers: 36.20.Ey, 87.15.ByCharged macromolecules (polyelectrolytes and polyampholytes) constitute a large class of materials which are particularly important for biological systems. Among these proteins and nucleic acids are well known. A variety of theoretical studies have been undertaken to elucidate the structural properties of such molecules [1][2][3][4] and to gain insight into the coil to rod transition behavior. However, to predict the conformational properties of a charged macromolecule is a very complex problem due to the long range nature of the Coulomb interaction. This is particularly true for highly charged chains, where the interaction with the counterions has to be taken into account. Recent experimental and theoretical studies demonstrate that the condensation of counterions and the formation of ion pairs significantly influence the conformation of a chain [5][6][7]. The Coulomb interaction and the counterions add new length scales to those of the neutral polymer. This complicates scaling theories and other theoretical approaches considerably. Thus, a microscopic understanding of the underlying physical phenomena is currently only possible by computer simulations.To elucidate the conformational properties of highly charged polyelectrolytes in the presence of counterions, we performed a series of molecular dynamics simulations. We particularly investigated the distribution of the counterions for various interaction strengths between the chain molecule and the ions. For highly charged chains all the counterions are condensed on the chains, and compact globules are formed. As demonstrated below, the formation of ion pairs associated with dipole moments is essential for the collapse of the chain.In this Letter, we present simulation results for a polyelectrolyte chain without salt but taking into account the counterions explicitly. The chain comprises N (N 2 1 being the number of bonds) harmonically bound mass points. The excluded volume interaction between the masses of the chain and with an equal number of counterions is taken into account by a purely repulsive Lennard-Jones potential. In addition, each monomer of the chain carries a charge e and the counterions a charge 2e. Hence, the charges o...

The dynamic structure factor for molecular chains with variable stiffness in a dilute solution is investigated. In the limit of small scattering vectors q only the overall translational motion of the macromolecules contributes to the dynamic structure factor. The translational diffusion coefficient D exhibits a chain length dependence D∼1/√L for flexible chains and D∼ln L/L+const/L for rodlike chains. For flexible chains there is an intermediate scattering vector regime in which the decay rate or spectral linewidth of the dynamic structure factor is proportional to q3 indicating that stretching modes are dominant. Such an intermediate scattering vector regime cannot be observed for semiflexible or rodlike chains. At large scattering vectors q/2p≳1.5, where 1/2p is the persistence length of the macromolecules, the chain stiffness becomes important for any kind of molecules, i.e., even for very flexible ones. The dynamic structure factor and the decay rate are compared with experimental results of quasielastic neutron and light scattering experiments on different natural and synthetic macromolecules. These experimental results are in good agreement with the theoretical predictions. Furthermore, we determine the persistence length of F-actin from a dynamic light scattering experiment.