Metastability of multi-population Kuramoto-Sakaguchi oscillators.

An Ott-Antonsen reduced M-population of Kuramoto-Sakaguchi oscillators is investigated, focusing on the influence of the phase-lag parameter α on the collective dynamics. For oscillator populations coupled on a ring, we obtained a wide variety of spatiotemporal patterns, including coherent states, traveling waves, partially synchronized states, modulated states, and incoherent states. Back-and-forth transitions between these states are found, which suggest metastability.

Selective decision-making and collective behavior of fish by the motion of visual attention.

Collective motion provides a spectacular example of self-organization in Nature. Visual information plays a crucial role among various types of information in determining interactions. Recently, experiments have revealed that organisms such as fish and insects selectively utilize a portion, rather than the entirety, of visual information.

Flow patterns and defect dynamics of active nematic liquid crystals under an electric field.

The effects of an electric field on the flow patterns and defect dynamics of two-dimensional active nematic liquid crystals are numerically investigated. We found that field-induced director reorientation causes anisotropic active turbulence characterized by enhanced flow perpendicular to the electric field. The average flow speed and its anisotropy are maximized at an intermediate field strength.

Effect of mobility on collective phase dynamics of nonlocally coupled oscillators with a phase lag.

Nonlocally coupled oscillators with a phase lag self-organize into various patterns, such as global synchronization, the twisted state, and the chimera state. In this paper, we consider nonlocally coupled oscillators that move on a ring by randomly exchanging their positions with the neighbors and investigate the combined effects of phase lag and mobility on the collective phase dynamics. Spanning the whole range of phase lag and mobility, we show that mobility promotes synchronization for an attractive coupling, whereas it destroys coherence for a repulsive coupling.

Gait switching with phase reversal of locomotory waves in the centipede.

Crawling using locomotory waves is a common method of locomotion for limbless and many-legged invertebrates and stimulates the biomimetic engineering of flexible locomotion. It is generally believed that the direction of locomotory waves is fixed for a given species. However, we found that a centipede,, flexibly generated its gait to allow for locomotory waves that varied in direction, depending on (i) locomotion speed and (ii) the physical conditions of terrain.

Large-scale spatiotemporal patterns in a ring of nonlocally coupled oscillators with a repulsive coupling.

Nonlocally coupled oscillators with a phase lag exhibit various nontrivial spatiotemporal patterns such as the chimera states and the multitwisted states. We numerically study large-scale spatiotemporal patterns in a ring of oscillators with a repulsive coupling with a phase delay parameter α. We find that the multichimera state disappears when α exceeds a critical value.

Conditions for metachronal coordination in arrays of model cilia.

On surfaces with many motile cilia, beats of the individual cilia coordinate to form metachronal waves. We present a theoretical framework that connects the dynamics of an individual cilium to the collective dynamics of a ciliary carpet via systematic coarse graining. We uncover the criteria that control the selection of frequency and wave vector of stable metachronal waves of the cilia and examine how they depend on the geometric and dynamical characteristics of a single cilium, as well as the geometric properties of the array.

Hydrodynamic synchronization and collective dynamics of colloidal particles driven along a circular path.

We study theoretically the collective dynamics of particles driven by an optical vortex along a circular path. Phase equations of N particles are derived by taking into account both hydrodynamic and repulsive interactions between them. For N=2, the particles attract with each other and synchronize, forming a doublet that moves faster than a singlet.

Motor torque measurement of archaellar suggests a general model for ATP-driven rotary motors.

It is unknown how the archaellum-the rotary propeller used by Archaea for motility-works. To further understand the molecular mechanism by which the hexameric ATPase motor protein FlaI drives rotation of the membrane-embedded archaellar motor, we determined motor torque by imposition of various loads on archaella. Markers of different sizes were attached to single archaella, and their trajectories were quantified using three-dimensional tracking and high-speed recording.

Three-dimensional tracking of microbeads attached to the tip of single isolated tracheal cilia beating under external load.

To study the properties of tracheal cilia beating under various conditions, we developed a method to monitor the movement of the ciliary tip. One end of a demembranated cilium was immobilized on the glass surface, while the other end was capped with a polystyrene bead and tracked in three dimensions. The cilium, when activated by ATP, stably repeated asymmetric beating as in vivo.

Direct observation of rotation and steps of the archaellum in the swimming halophilic archaeon Halobacterium salinarum.

Motile archaea swim using a rotary filament, the archaellum, a surface appendage that resembles bacterial flagella structurally, but is homologous to bacterial type IV pili. Little is known about the mechanism by which archaella produce motility. To gain insights into this mechanism, we characterized archaellar function in the model organism Halobacterium salinarum.

Hydrodynamic synchronization between objects with cyclic rigid trajectories.

Synchronization induced by long-range hydrodynamic interactions is attracting attention as a candidate mechanism behind coordinated beating of cilia and flagella. Here we consider a minimal model of hydrodynamic synchronization in the low Reynolds number limit. The model consists of rotors, each of which assumed to be a rigid bead making a fixed trajectory under periodically varying driving force.

Many-body theory of synchronization by long-range interactions.

Synchronization of coupled oscillators on a d-dimensional lattice with the power-law coupling G(r) = g0/rα and randomly distributed intrinsic frequency is analyzed. A systematic perturbation theory is developed to calculate the order parameter profile and correlation functions in powers of ϵ = α/d-1. For α ≤ d, the system exhibits a sharp synchronization transition as described by the conventional mean-field theory.

Generic conditions for hydrodynamic synchronization.

Synchronization of actively oscillating organelles such as cilia and flagella facilitates self-propulsion of cells and pumping fluid in low Reynolds number environments. To understand the key mechanism behind synchronization induced by hydrodynamic interaction, we study a model of rigid-body rotors making fixed trajectories of arbitrary shape under driving forces that are arbitrary functions of the phase. For a wide class of geometries, we obtain the necessary and sufficient conditions for synchronization of a pair of rotors.

Synchronization and collective dynamics in a carpet of microfluidic rotors.

We study synchronization of an array of rotors on a substrate that are coupled by hydrodynamic interaction. Each rotor, which is modeled by an effective rigid body, is driven by an internal torque and exerts an active force on the surrounding fluid. The long-ranged nature of the hydrodynamic interaction between the rotors causes a rich pattern of dynamical behaviors including phase ordering and self-proliferating spiral waves.

Viscoelasticity and primitive path analysis of entangled polymer liquids: from F-actin to polyethylene.

We combine computer simulations and scaling arguments to develop a unified view of polymer entanglement based on the primitive path analysis of the microscopic topological state. Our results agree with experimentally measured plateau moduli for three different polymer classes over a wide range of reduced polymer densities: (i) semidilute theta solutions of synthetic polymers, (ii) the corresponding dense melts above the glass transition or crystallization temperature, and (iii) solutions of semiflexible (bio)polymers such as F-actin or suspensions of rodlike viruses. Together, these systems cover the entire range from loosely to tightly entangled polymers.

Numerical simulation of the twist-grain-boundary phase of chiral liquid crystals.

We study the structure of the twist-grain-boundary phase of chiral liquid crystals by numerically minimizing the Landau-de Gennes free energy. We analyze the morphology of layers at the grain boundary, to better understand the mechanism of frustration between the smectic layer order and chirality. As the chirality increases, the layer compression energy strongly increases while the effective layer bending rigidity is reduced due to unlocking of the layer orientation and the director.

Boundary conditions for equilibrating incommensurate periodic patterns.

Simulation of periodic patterns often suffer from artifacts due to incommensurability of the intrinsic length scale and the system size. We introduce a simple numerical scheme to avoid this problem in finding equilibrium domain morphologies from a Ginzburg-Landau-type free energy. In this scheme, the boundary values are determined only by the local equilibrium condition at the adjacent bulk sites.

Dynamics of orientational ordering in fluid membranes.

We study the dynamics of orientational phase ordering in fluid membranes. Through numerical simulation we find an unusually slow coarsening of topological texture, which is limited by subdiffusive propagation of membrane curvature. The growth of the orientational correlation length xi obeys a power law xi proportional, variant t(w) with w<1/4 in the late stage.

Pattern formation in phase-separating gels with spontaneous shear.

We study pattern formation in gels undergoing simultaneous phase separation and orientational ordering. A 2D numerical simulation is performed using a minimal model of nonlinear elasticity with density-anisotropy coupling. For strong positive coupling, the collapsed phase elongates along the phase boundary and buckle, creating a folded structure with paired topological defects.