Optimal external forces of the lock-in phenomena for flow past an inclined plate in uniform flow.

We theoretically studied the optimal control, frequency lock-in, and phase lock-in phenomena due to the spatially localized periodic forcing in flow past an inclined plate. Although frequency lock-in is evident in many fluid phenomena, especially fluid-structure interactions, not many researchers have investigated it using a theoretical approach based on flow details. We obtained detailed information on the lock-in phenomena to external periodic forcing using phase reduction theory, a mathematical method for extracting the dynamics near the limit cycle. Furthermore, the optimal forces applied to the velocity field were determined under the condition of the minimum forcing energy and maximum lock-in range. The study of uniform periodic forces applied within spatially confined regions led to the conclusion that the effective lock-in position, which includes both the upstream and downstream areas of the plate, depends on the principal frequency of the force. The frequency lock-in range of these forces was analyzed and compared with theoretical predictions.

Height-dependent oscillatory motion of a plastic cup with a camphor disk floated on water.

We have developed a self-propelled object, which is composed of a plastic cup and a camphor disk, on water to reflect its three-dimensional shape in the nature of motion. The self-propelled object, of which the driving force of motion is the difference in the surface tension, exhibited oscillatory motion between motion and rest. The period and the maximum speed of oscillatory motion increased and decreased depending on the height of the cup, h, respectively. Two types of diffusion coefficients were estimated based on the diffusion of camphor molecules which were indirectly visualized using 7-hydroxycoumarin. The experimental result on the period of oscillatory motion depending on h could be reproduced by the numerical calculation based on the diffusion of camphor molecules around the object and the diffusion coefficients which were experimentally estimated. The experimental results suggest that characteristic features of motion can be created based on the three-dimensional shape of the object.

Bioconvection pattern of Euglena under periodical illumination.

Microorganisms respond to environmental conditions and often spontaneously form highly ordered convection patterns. This mechanism has been well-studied from the viewpoint of self-organization. However, environmental conditions in nature are usually dynamic. Naturally, biological systems respond to temporal changes in environmental condition. To elucidate the response mechanisms in such a dynamic environment, we observed the bioconvection pattern of Euglena under periodical changes in illumination. It is known that Euglena shows localized bioconvection patterns under constant homogeneous illumination from the bottom. Periodical changes in light intensity induced two different types of spatiotemporal patterns: alternation of formation and decomposition over a long period and complicated transition of pattern over a short period. Our observations suggest that pattern formation in a periodically changing environment is of fundamental importance to the behavior of biological systems.

Long-time behavior of swimming Euglena gracilis in a heterogenous light environment.

The cell motion of Euglena gracilis in homogeneous and heterogeneous light environments was analyzed. Homogeneous and heterogeneous environments were prepared, with only a red color or with a red circle surrounded by brighter white regions, respectively. In a heterogeneous environment, the cells move into the red circle. Swimming orbits at 1/25 s intervals for 120 s were analyzed. The speed distribution of the 1 s-averaged cell orbits in a homogeneous environment was different from that in a heterogeneous environment, where the faster swimming fraction was enhanced. The relationship between speed and curvature radius was analyzed using a joint histogram. Histograms for short timescale motion, constructed by 1 s-averaged orbits, suggest that the cell swimming curves are not biased, while those for long timescale motion, constructed by 10 s-averaged orbits, suggest that the cell swimming curves are biased in the clockwise direction. Furthermore, the curvature radius determines the speed, which does not seem to depend on the light environment. The mean squared displacement in a heterogeneous environment is larger than that in a homogeneous environment on a 1 s timescale. These results will be the basis for constructing a model for the long-time behavior of photomovement for light differences.

Phase reduction technique on a target region.

We propose a phase reduction technique that provides the phase sensitivity function, which is one of the essential functions in phase reduction theory, on a target region. A system with a large degree of freedom and global coupling, such as an incompressible fluid system, is emphasized. Such a system poses challenges for the numerical calculation of the phase sensitivity function, which cannot be resolved using known algorithms such as the direct method or the adjoint method. A combination of the Jacobian-free algorithm and the Rayleigh-Ritz procedure is proposed to significantly reduce the computational cost and obtain a good approximation of the phase sensitivity function in a particular region of interest. In addition, the approximation can be assessed using the Ritz value. The breathing solution of a reaction-diffusion system and the flow past a flat plate are used to analyze the proposed methods, and the characteristics of the proposed method are discussed.

Jacobian-free algorithm to calculate the phase sensitivity function in the phase reduction theory and its applications to Kármán's vortex street.

Phase reduction theory has been applied to many systems with limit cycles; however, it has limited applications in incompressible fluid systems. This is because the calculation of the phase sensitivity function, one of the fundamental functions in phase reduction theory, has a high computational cost for systems with a large degree of freedom. Furthermore, incompressible fluid systems have an implicit expression of the Jacobian. To address these issues, we propose a new algorithm to numerically calculate the phase sensitivity function. This algorithm does not require the explicit form of the Jacobian along the limit cycle, and the computational time is significantly reduced, compared with known methods. Along with the description of the method and characteristics, two applications of the method are demonstrated. One application is the traveling pulse in the FitzHugh Nagumo equation in a periodic domain and the other is the Kármán's vortex street. The response to the perturbation added to the Kármán's vortex street is discussed in terms of both phase reduction theory and fluid mechanics.

Active lift inversion process of heaving wing in uniform flow by temporal change of wing kinematics.

The transition of the vortex pattern and the lift generated by a heaving wing in a uniform flow was investigated numerically. As a fundamental problem constituting the insects' flight maneuverability, we studied the relationship between a temporal change in the heaving wing motion and the change in the global vortex pattern. At a Strouhal number that generates an asymmetric vortex pattern, we found that temporal angular frequency reduction causes inversion of both the global vortex pattern and the lift sign. The inversion is initiated by the transfer of the leading-edge vortex, which interferes with the vortex pattern generated at the trailing edge. Successful inversion is conditioned on the starting phase and the time interval of the frequency reduction. The details of the process during the transition are discussed.

Surface switching statistics of rotating fluid: Disk-rim gap effects.

We examined the influence of internal noise on the irregular switching of the shape of the free surface of fluids in an open cylindrical vessel driven by a bottom disk rotating at constant speed [Suzuki, Iima, and Hayase, Phys. Fluids 18, 101701 (2006)PHFLE61070-663110.1063/1.2359740]. A slight increase in the disk-rim gap (less than 3% of the disk radius) was established experimentally to cause significant changes in this system, specifically, frequent appearance of the surface descending event connecting a nonaxisymmetric shape in strong mixing flow (turbulent flow) and an axisymmetric shape in laminar flow, as well as a shift in critical Reynolds number that define the characteristic states. The physical mechanism underlying the change is analyzed in terms of flow characteristics in the disk-rim gap, which acts as a noise source, and a mathematical model established from measurements of the surface height fluctuations with noise term.

The Flux of Euglena gracilis Cells Depends on the Gradient of Light Intensity.

We have quantified the photomovement behavior of a suspension of Euglena gracilis representing a behavioral response to a light gradient. Despite recent measurements of phototaxis and photophobicity, the details of macroscopic behavior of cell photomovements under conditions of light intensity gradients, which are critical to understand recent experiments on spatially localized bioconvection patterns, have not been fully understood. In this paper, the flux of cell number density under a light intensity gradient was measured by the following two experiments. In the first experiment, a capillary containing the cell suspension was illuminated with different light intensities in two regions. In the steady state, the differences of the cell numbers in the two regions normalized by the total number were proportional to the light difference, where the light intensity difference ranged from 0.5-2.0 µmol m-2 s-1. The proportional coefficient was positive (i.e., the bright region contained many microorganisms) when the mean light intensity was weak (1.25 µmol m-2 s-1), whereas it was negative when the mean intensity was strong (13.75 µmol m-2 s-1). In the second experiment, a shallow rectangular container of the suspension was illuminated with stepwise light intensities. The cell number density distribution exhibited a single peak at the position where the light intensity was about Ic ≃ 3.8 µmol m-2 s-1. These results suggest that the suspension of E. gracilis responded to the light gradient and that the favorable light intensity was Ic.

Florigen distribution determined by a source-sink balance explains the diversity of inflorescence structures in Arabidopsis.

The ability to continue flowering after loss of inductive environmental cues that trigger flowering is termed floral commitment. Reversible transition involving a switch from floral development back to vegetative development has been found in Arabidopsis mutants and many plant species. Although the molecular basis for floral commitment remains unclear, recent studies suggest that the persistent activity of FLOWERING LOCUS T (FT) at inflorescences is required for floral commitment in Arabidopsis thaliana. Because FT encodes a mobile signal, florigen, which is generally transported from leaves to meristems through the phloem, understanding the transportation dynamics of FT is required to explore the role of FT on floral commitment. Here we developed a transportation model of leaf- and inflorescence-derived florigen and sucrose based on pressure-flow hypothesis. Depending on the demanded level of florigen supply for floral commitment of each floral meristem, the model predicted the change in inflorescence pattern from stable commitment to flower, transient flowering, and complete reversion. FT activity in inflorescence partly suppressed floral reversion, but complete suppression was achieved only when inflorescence became a source of sucrose. This finding highlights the importance of monitoring the spatio-temporal sucrose distribution and floral stimulus to understand inflorescence development mechanism.

Effects of structural flexibility of wings in flapping flight of butterfly.

The objective of this paper is to clarify the effects of structural flexibility of wings of a butterfly in flapping flight. For this purpose, a dynamics model of a butterfly is derived by Lagrange's method, where the butterfly is considered as a rigid multi-body system. The panel method is employed to simulate the flow field and the aerodynamic forces acting on the wings. The mathematical model is validated by the agreement of the numerical result with the experimentally measured data. Then, periodic orbits of flapping-of-wings flights are parametrically searched in order to fly the butterfly models. Almost periodic orbits are found, but they are unstable. Deformation of the wings is modeled in two ways. One is bending and its effect on the aerodynamic forces is discussed. The other is passive wing torsion caused by structural flexibility. Numerical simulations demonstrate that flexible torsion reduces the flight instability.

Peristaltic transport and mixing of cytosol through the whole body of Physarum plasmodium.

We study how the net transport and mixing of chemicals occur in a relatively large amoeba, the true slime mold Physarum polycephalum. The shuttle streaming of the amoeba is characterized by a rhythmic flow of the order of 1 µm/s in which the protoplasm streams back and forth. To explain the experimentally observed transport of chemicals, we formulate a simplified model to consider the mechanism by which net transport can be induced by shuttle (or periodic) motion inside the amoeba. This model is independent from the details of fluid property as it is based on the mass conservation law only. Even in such a simplified model, we demonstrate that sectional oscillations play an important role in net transport and discuss the effects of the sectional boundary motion on net transport in the microorganism.

Minimum-risk path finding by an adaptive amoebal network.

When two food sources are presented to the slime mold Physarum in the dark, a thick tube for absorbing nutrients is formed that connects the food sources through the shortest route. When the light-avoiding organism is partially illuminated, however, the tube connecting the food sources follows a different route. Defining risk as the experimentally measurable rate of light-avoiding movement, the minimum-risk path is exhibited by the organism, determined by integrating along the path. A model for an adaptive-tube network is presented that is in good agreement with the experimental observations.

A two-dimensional aerodynamic model of freely flying insects.

Possible free flights of insects by a single flapping motion were studied. It is well-known that insects utilize vortices generated by flapping, by which they generate larger lift than that evaluated by the ordinary aerodynamic theory. However, the effect of the motion of the center of mass (CM) of the insect on its flight has not been clarified. To clarify the effect, numerical simulation was performed for a simple model considering the coupling between the vertical CM motion and the separation vortices generated by flapping wing. As a result, it is shown that the flapping flight has the following interesting features. First, despite a single flapping motion, the model exhibits two types of flapping flight: a steady flight in which the CM velocity oscillates and a wandering flight in which the CM velocity varies irregularly. These two types of flights are selected by the initial conditions even when all the parameters are the same. Second, at a certain critical parameter value, the steady flight loses its stability and undergoes an abrupt transition to the wandering flight. Interestingly, at this critical value, the steady flight can be regarded as hovering. The possible flights are analyzed in terms of bifurcation, and the bifurcation structure is qualitatively explained based on a simple assumption. These results suggest the significance of the effect of CM motion.