Flagellated bacteria such as Escherichia coli and Bacillus subtilis exhibit effective mechanisms for swimming in fluids and exploring the surrounding environment. In isotropic fluids such as water, the bacteria change swimming direction through the run-and-tumble process. Lyotropic chromonic liquid crystals (LCLCs) have been introduced recently as an anisotropic environment in which the direction of preferred orientation, the director, guides the bacterial trajectories. In this work, we describe the behavior of bacteria B. subtilis in a homeotropic LCLC geometry, in which the director is perpendicular to the bounding plates of a shallow cell. We demonstrate that the bacteria are capable of overcoming the stabilizing elastic forces of the LCLC and swim perpendicularly to the imposed director (and parallel to the bounding plates). The effect is explained by a finite surface anchoring of the director at the bacterial body; the role of surface anchoring is analyzed by numerical simulations of a rod realigning in an otherwise uniform director field. Shear flows produced by a swimming bacterium cause director distortions around its body, as evidenced both by experiments and numerical simulations. These distortions contribute to a repulsive force that keeps the swimming bacterium at a distance of a few micrometers away from the bounding plates. The homeotropic alignment of the director imposes two different scenarios of bacterial tumbling: one with an 180°r eversal of the horizontal velocity and the other with the realignment of the bacterium by two consecutive 90°turns. In the second case, the angle between the bacterial body and the imposed director changes from 90°to 0°and then back to 90°; the new direction of swimming does not correlate with the previous swimming direction. with a relatively flat rigid polyaromatic core and polar groups at the periphery [11][12][13]. In water, these molecules aggregate face-to-face in order to minimize the areas of unfavorable contact with water. Unlike their surfactantbased micellar and thermotropic counterparts, the LCLCs are not toxic to biological organisms [14].Recent experiments demonstrate that the prevailing direction of swimming is parallel to the directorn, i.e. to the average direction of LCLC orientation ( º -n n, = |ˆ| n 1) [7,8]. The orientational order of the LCLC environment can be controlled by temperature, the concentration of liquid crystal organic molecules, external electromagnetic fields and by surface alignment of the director [9,11,12]. The dispersion of swimming bacteria in LCLC, also called a living liquid crystal [8], offers new opportunities to control the dynamic behavior of the bacteria.The studies of swimming bacteria in LCLCs have been performed mostly for sandwich-type cells, in which the LCLC is confined between two glass plates, with the director being uniformly aligned along a certain direction in the plane of the cell (planar alignment). It has been shown that rod-like flagellated bacteria prefer to swim along the director [7,8,15,16]. It is ass...

Outermost occupied electron shells of chemical elements can have symmetries resembling that of monopoles, dipoles, quadrupoles and octupoles corresponding to filled s-, p-, d- and f-orbitals. Theoretically, elements with hexadecapolar outer shells could also exist, but none of the known elements have filled g-orbitals. On the other hand, the research paradigm of ‘colloidal atoms' displays complexity of particle behaviour exceeding that of atomic counterparts, which is driven by DNA functionalization, geometric shape and topology and weak external stimuli. Here we describe elastic hexadecapoles formed by polymer microspheres dispersed in a liquid crystal, a nematic fluid of orientationally ordered molecular rods. Because of conically degenerate boundary conditions, the solid microspheres locally perturb the alignment of the nematic host, inducing hexadecapolar distortions that drive anisotropic colloidal interactions. We uncover physical underpinnings of formation of colloidal elastic hexadecapoles and describe the ensuing bonding inaccessible to elastic dipoles, quadrupoles and other nematic colloids studied previously.

Active matter, both synthetic and biological, demonstrates complex spatiotemporal self-organization and the emergence of collective behavior. A coherent rotational motion, the vortex phase, is of great interest because of its ability to orchestrate well-organized motion of self-propelled particles over large distances. However, its generation without geometrical confinement has been a challenge. Here, we show by experiments and computational modeling that concentrated magnetic rollers self-organize into multivortex states in an unconfined environment. We find that the neighboring vortices more likely occur with the opposite sense of rotation. Our studies provide insights into the mechanism for the emergence of coherent collective motion on the macroscale from the coupling between microscale rotation and translation of individual active elements. These results may stimulate design strategies for self-assembled dynamic materials and microrobotics.

We use a variational principle to derive a mathematical model for a nematic electrolyte in which the liquid crystalline component is described in terms of a second-rank order parameter tensor. The model extends the previously developed director-based theory and accounts for presence of disclinations and possible biaxiality. We verify the model by considering a simple but illustrative example of liquid crystal-enabled electro-osmotic flow around a stationary dielectric spherical particle placed at the center of a large cylindrical container filled with a nematic electrolyte. Assuming homeotropic anchoring of the nematic on the surface of the particle and uniform distribution of the director on the surface of the container, we consider two configurations with a disclination equatorial ring and with a hyperbolic hedgehog, respectively. The computed electro-osmotic flows show a strong dependence on the director configurations and on the anisotropies of dielectric permittivity and electric conductivity of the nematic, characteristic of liquid crystal-enabled electrokinetics. Further, the simulations demonstrate space charge separation around the dielectric sphere, even in the case of isotropic permittivity and conductivity. This is in agreement with the induced-charge electro-osmotic effect that occurs in an isotropic electrolyte when an applied field acts on the ionic charge it induces near a polarizable surface.