Nariya Uchida

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. We also find a novel synchronized pattern with an oscillating phase shift. Our results shed light on the role of hydrodynamic interactions in biological systems, and could help in developing efficient mixing and transport strategies in microfluidic devices.

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. Our results suggest strategies for designing controllable microfluidic mixers using the emergent behavior of hydrodynamically coupled active components.

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. In particular, we argue that the primitive path analysis renormalizes a loosely to a tightly entangled system and provide a new explanation of the successful Lin-Noolandi packing conjecture for polymer melts.

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. Three-dimensional tracking of quantum dots enabled visualization of the left-handed corkscrewing of archaea in detail. An advanced analysis method combined with total internal reflection fluorescence microscopy, termed cross-kymography, was developed and revealed a right-handed helical structure of archaella with a rotation speed of 23 ± 5 Hz. Using these structural and kinetic parameters, we computationally reproduced the swimming and precession motion with a hydrodynamic model and estimated the archaellar motor torque to be 50 pN nm. Finally, in a tethered-cell assay, we observed intermittent pauses during rotation with ∼36° or 60° intervals, which we speculate may be a unitary step consuming a single adenosine triphosphate molecule, which supplies chemical energy of 80 pN nm when hydrolysed. From an estimate of the energy input as ten or six adenosine triphosphates per revolution, the efficiency of the motor is calculated to be ∼6–10%.

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. By a linear analysis, we derive the necessary and sufficient conditions for a pair of rotors to synchronize in phase. We also derive a non-linear evolution equation for their phase difference, which is reduced to minimization of an effective potential. The effective potential is calculated for a variety of trajectory shapes and geometries (either bulk or substrated), for which the stable and metastable states of the system are identified. Finite size of the trajectory induces asymmetry of the potential, which also depends sensitively on the tilt of the trajectory. Our results show that flexibility of cilia or flagella is not a requisite for their synchronized motion, in contrast to previous expectations. We discuss the possibility to directly implement the model and verify our results by optically driven colloids.Graphical abstract

Orientational ordering of buckling-induced microwrinkles on soft substrates

Orientational order in buckling-induced microwrinkles of elastic membranes on soft substrates is investigated both theoretically and experimentally. Anisotropic orientational correlation in wrinkles induced by isotropic compression is characterized using an orientational order parameter, and is explained by an effective elastic free energy that suppresses Gaussian curvature. We find that orientationally correlated domains tend to extend in ± 45° directions from the local wrinkle orientation. Excellent agreement is obtained between numerical, theoretical, and experimental results.

Elastic effects in disordered nematic networks

Elastic effects in a model of disordered nematic elastomers are numerically investigated in two dimensions. Networks crosslinked in the isotropic phase exhibit an unusual soft mechanical response against stretching. It arises from a gradual alignment of orientationally correlated regions that are elongated along the director. A sharp crossover to a macroscopically aligned state is obtained on further stretching. The effect of random internal stress is also discussed.

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. For α > d, the transition is smeared by the quenched disorder, and the macroscopic order parameter ψ decays slowly with g0 as |ψ| ∝ g(0)(2).

Casimir Effect in Fluids above the Isotropic-Lamellar Transition

We study fluctuation-induced interaction in confined fluids above the isotropic-lamellar transition. At an ideally continuous transition, the disjoining pressure has the asymptotic form Pi(d-->infinity) approximately -Ck(B)Tq(2)(0)/d, where d is the interwall distance, q(0) is the wave number of the scattering peak, and C = 1/4pi in the strong anchoring limit. The long-rangedness is enhanced due to continuous distribution of soft modes in the q space. An unconventionally strong Casimir force with a range of several lamella thicknesses is realistic above the transition. We also find an oscillatory force profile near a surface-induced transition.

Pattern formation in microphase-separating copolymer gels

Microphase separation in crosslinked diblock copolymers is investigated with a time-dependent Ginzburg–Landau model. Upon separation, polymers originally crosslinked in the homogeneous phase elongate parallel to the composition gradient. We take into account this elastic coupling as well as the random stress caused by the disordered network structure. The phase ordering process is numerically simulated to study the domain morphology. The random stress destroys the long-range orientational order of lamellae and creates jagged interfaces, which give rise to an asymmetric peak in the structure factor.