Publications

*Hiroshi Orihara, Yuko Harada, Fumiaki Kobayashi, Yuji Sasaki, Shuji Fujii, Yuki Satou, Yoshitomo Goto, and *Tomoyuki Nagaya,
Negative viscosity of a liquid crystal in the presence of turbulence,
Physical Review E, in press.

[Summary] We report on the discovery of enormous negative viscosity in a nematic liquid crystal in the presence of turbulence induced by electric fields. As the negative viscosity in this system is so large, we were able to observe several novel phenomena originating from it. For example, we observed a spontaneous shear flow that rotates the upper disc of a rheometer, as well as the reversal of the rotational direction upon applying an external torque in the opposite direction. Hysteresis loops were also observed in the shear stress-shear rate curves, which is reminiscent of those seen for ferromagnetic and ferroelectric materials. The similarities between the phenomena observed for our system and ferroic materials were comprehensively demonstrated, although the two systems are fundamentally different in that the former is out of equilibrium. We elucidate the origin of the negative viscosity and propose a simple model that reproduces the phenomena observed in this active fluid.

Takikawa Yoshinori, Yasuta Muneharu, Fujii Shuji, Orihara Hiroshi, Tanaka Yoshimi, and Nishinari Katsuyoshi,
Anomalous diffusion of particles dispersed in xanthan solutions subjected to shear flow,
Journal of the Physical Society of Japan 87, 054005/1-4 (2018).

[Summary] Xanthan gum exhibits viscoelastic and shear-thinning properties. We investigate the Brownian motion of particlesdispersed in xanthan gum solutions that are subjected to simple shear flow. The mean square displacements (MSDs) are obtained in both the flow and vorticity directions. In the absence of shear flow, subdiffusion is observed, MSD ∝ t^α with α < 1, where t is time. In the presence of shear flow, however, the exponent α becomes larger together with the MSD itself in both the flow and vorticity directions. We show that the diffusion is enhanced by Taylor dispersion in the flow direction, whereas in the vorticity direction it is enhanced by nonthermal self-diffusion.

Kazuya Maeda, Takayuki Narumi, Rinto Anugraha, Hirotaka Okabe, Kazuhiro Hara, *Yoshiki Hidaka,
Sub-Diffusion in Electroconvective Turbulence of Homeotropic Nematic Liquid Crystals,
Journal of the Physical Society of Japan 87, 014401/1-5 (2018).

[Summary] Diffusion resulting from turbulence corresponding to dynamic scattering mode 1 (DSM1) of electroconvection was studied in experiments on homeotropically aligned systems of nematic liquid crystals. In such systems, electroconvection displays peculiar nonlinear phenomena arising from the interaction between its convection and the nematic director yielding Nambu–Goldstone modes. From an analogy with Brownian motion, the motion of tagged particles driven by the turbulence was analyzed using the time-dependent coefficient of diffusion, defined as the mean-square displacement divided by time. The results indicate that sub-diffusion occurs in a certain time range, suggesting that turbulence causes particles to rebound. Detailed observations of turbulence structures revealed that rebounding is induced by characteristic linear structures of the nematic director caused by turbulence. This sub-diffusion arising from the interaction between the nematic director and turbulence is specific to nematic liquid crystals.

∗Yoshiki Hidaka, Kosuke Ijigawa, Seung-Yong Kwak, Noriko Oikawa, Hirotaka Okabe, Kazuhiro Hara,
Information Reduction for Chaotic Patterns,
Forma 33, S3-S7 (2018).

[Summary] To investigate the universality and diversity of spatiotemporal chaos, information reduction, which describes phenomena using generalized quantities such as amplitude and phase, is an important technique. Several methods of image analysis are presented for information reduction of experimental image data of spatiotemporal chaos.

*Yuji sasaki, Motoshi Ueda, Khoa V. Le, Reo Amano, Shin Sakane, Shuji Fujii, Fumito Araoka, and Hiroshi Orihara,
Polymer-stabilized micropixelated liquid crystals with tunable optical properties fabricated by double templating,
Advanced Materials 29, 1703054/1-7 (2017).

[Summary] Self-organized nano- and microstructures of soft materials are attracting　considerable attention because most of them are stimuli-responsive due to their soft nature. In this regard, topological defects in liquid crystals (LCs) are promising not only for self-assembling colloids and molecules but also for electro-optical applications such as optical vortex generation. However, there are currently few bottom-up methods for patterning a large number of defects periodically over a large area. It would be highly desirable to develop more effective techniques for high-throughput and low-cost fabrication. Here, a micropixelated LC structure consisting of a square array of topological defects is stabilized by photopolymerization. A polymer network is formed on the structure of a self-organized template of a nematic liquid crystal (NLC), and this in turn imprints other nonpolymerizable NLC molecules, which maintains their responses to electric field and temperature. Photocuring of specific local regions is used to create a designable template for the reproducible selforganization of defects. Moreover, a highly diluted polymer network (≈0.1 wt% monomer) exhibits instant on–off switching of the patterns. Beyond the mere stabilization of patterns, these results demonstrate that the incorporation of self-organized NLC patterns offers some unique and unconventional applications for anisotropic polymer networks.

Schenz Daniel, Yasuaki Shima, Shigeru Kuroda, Toshiyuki Nakagaki and *Kei-ichi Ueda,
A mathematical model for adaptive vein formation during exploratory migration of Physarum polycephalum: routing while scouting,
Journal of Physics: Applied Physics 50, 434001/1-14 (2017).

[Summary] Exploring free space (scouting) ef ciently is a non-trivial task for organisms of limited perception, such as the amoeboid Physarum polycephalum. However, the strategy behind its exploratory behaviour has not yet been characterised. In this organism, as the extension of the frontal part into free space is directly supported by the transport of body mass from behind, the formation of transport channels (routing) plays the main role in that strategy. Here, we study the organism’s exploration by letting it expand through a corridor of constant width. When turning at a corner of the corridor, the organism constructed a main transport vein tracing a centre-in-centre line. We argue that this is ef cient for mass transport due to its short length, and check this intuition with a new algorithm that can predict the main vein’s position from the frontal tip’s progression. We then present a numerical model that incorporates reaction-diffusion dynamics for the behaviour of the organism’s growth front and current reinforcement dynamics for the formation of the vein network in its wake, as well as interactions between the two. The accuracy of the model is tested against the behaviour of the real organism and the importance of the interaction between growth tip dynamics and vein network development is analysed by studying variants of the model. We conclude by offering a biological interpretation of the well-known current reinforcement rule in the context of the natural exploratory behaviour of Physarum polycephalum.

Itsuki Kunita, *Kei-ichi Ueda, Dai Akita, Sshigeru Kuroda and Toshiyuki Nakagaki,
Behavioural differentiation induced by environmental variation when crossing a toxic zone in an amoeba,
Journal of Physics D: Applied Physics 50, 354002/1-15 (2017).

[Summary] Organisms choose from among various courses of action in response to a wide variety of environmental conditions and the mechanism by which various behaviours are induced is an open question. Interesting behaviour was recently reported: that a unicellular organism of slime mold Physarum polycephalum known as an amoeba had multiple responses (crossing, returning, etc) when the amoeba encounters a zone with toxic levels of quinine, even under carefully controlled conditions. We here examined this elegant example in more detail to obtain insight into behavioural differentiation. We found that the statistical distribution of passage times across a quinine zone switch from unimodal to bimodal (with peaks corresponding to fast crossing and no crossing) when a periodic light stimulation to modulate a biorhythm in amoeba is applied homogeneously across the space, even under the same level of chemical stimuli. Based on a mathematical model for cell movement in amoeba, we successfully reproduced the stimulation-induced differentiation, which was observed experimentally. These dynamics may be explained by a saddle structure around a canard solution. Our results imply that the differentiation of behavioural types in amoeba is modi ed step-by-step via the compounding of stimulation inputs. The complex behaviour like the differentiation in amoeba may provide a basis for understanding the mechanism of behaviour selection in higher animals from an ethological perspective.

Dai Akita, Daniel Schenz, Shigeru Kuroda, Katsuhiko Sato, Kei-Ichi Ueda, *Toshiyuki Nakagaki,
Current Reinforcement Model Reproduces Center-In-Center Vein Trajectory of Physarum Polycephalum,
Development, Growth & Differentation 59, 465-470 (2017).

[Summary] Vein networks span the whole body of the amoeboid organism in the plasmodial slime mould Physarum polycephalum, and the network topology is rearranged within an hour in response to spatio-temporal variations of the environment. It has been reported that this tube morphogenesis is capable of solving mazes, and a mathematical model, named the ‘current reinforcement rule’, was proposed based on the adaptability of the veins. Although it is known that this model works well for reproducing some key characters of the organism's maze-solving behaviour, one important issue is still open: In the real organism, the thick veins tend to trace the shortest possible route by cutting the corners at the turn of corridors, following a center-in-center trajectory, but it has not yet been examined whether this feature also appears in the mathematical model, using corridors of finite width. In this report, we confirm that the mathematical model reproduces the center-in-center trajectory of veins around corners observed in the maze-solving experiment.

*Mark Fricker, Dai Akita, Luke L. Heaton, Nick Jones, Barak Obara and Toshiyuki Nakagaki,
Automated analysis of Physarum network structure and dynamics,
Journal of Physics D: Applied Physics 50, 254005/1-14 (2017).

[Summary] We evaluate different ridge-enhancement and segmentation methods to automatically extract the network architecture from time-series of Physarum plasmodia withdrawing from an arena via a single exit. Whilst all methods gave reasonable results, judged by precision-recall analysis against a ground-truth skeleton, the mean phase angle (Feature Type) from intensity-independent, phase-congruency edge enhancement and watershed segmentation was the most robust to variation in threshold parameters. The resultant single pixel-wide segmented skeleton was converted to a graph representation as a set of weighted adjacency matrices containing the physical dimensions of each vein, and the inter-vein regions. We encapsulate the complete image processing and network analysis pipeline in a downloadable software package, and provide an extensive set of metrics that characterise the network structure, including hierarchical loop decomposition to analyse the nested structure of the developing network. In addition, the change in volume for each vein and intervening plasmodial sheet was used to predict the net flow across the network. The scaling relationships between predicted current, speed and shear force with vein radius were consistent with predictions from Murray's law. This work was presented at PhysNet 2015.

Takuya Umedachi, Kentaro Ito, Ryo Kobayashi, Akio Ishiguro and Toshiyuki Nakagaki,
Response to Various Periods of Mechanical Stimuli in Physarum Plasmodium,
Journal of Physics D: Applied Physics 50, 254002/1-7 (2017).

[Summary] Response to mechanical stimuli is a fundamental and critical ability for living cells to survive in hazardous conditions or to form adaptive and functional structures against force(s) from the environment. Although this ability has been extensively studied by molecular biology strategies, it is also important to investigate the ability from the viewpoint of biological rhythm phenomena so as to reveal the mechanisms that underlie these phenomena. Here, we use the plasmodium of the true slime mold Physarum polycephalum as the experimental system for investigating this ability. The plasmodium was repetitively stretched for various periods during which its locomotion speed was observed. Since the plasmodium has inherent oscillation cycles of protoplasmic streaming and thickness variation, how the plasmodium responds to various periods of external stretching stimuli can shed light on the other biological rhythm phenomena. The experimental results show that the plasmodium exhibits response to periodic mechanical stimulation and changes its locomotion speed depending on the period of the stretching stimuli.

*Hiroshi Orihara, Nobutaka Sakurai, Yuji Sasaki, and Tomoyuki Nagaya,
Direct observation of coupling between orientation and flow fluctuations in a nematic liquid crystal at equilibrium,
Physical Review E 95, 042705/1-6 (2017).

[Summary] Nematic liquid crystals (NLCs) have long-range orientational order, and the average direction of their rod-like molecules is designated by the so-called director. One of the most remarkable properties in NLCs is the coupling between director and flow: a change in the director can induce flow and vice versa. To demonstrate the coupling between orientation and flow fluctuations in a nematic liquid crystal at equilibrium, we simultaneously observe the intensity change due to director fluctuations under a polarizing microscope and theBrownian motion of a fluorescent particle trapped weakly by optical tweezers. The calculated cross-correlationfunction of the particle position and the spatial gradient of the intensity is nonzero, clearly indicating the existenceof coupling.

*Bernd Meyer, Cedrick Ansorge and Toshiyuki Nakagaki,
The Role of Noise in Self-organized Decision Making by the True Slime Mold Physarum polycephalum,
PLOS ONE 12, e0172933 (2017).

[Summary] Self-organized mechanisms are frequently encountered in nature and known to achieve flexible, adaptive control and decision-making. Noise plays a crucial role in such systems: It can enable a self-organized system to reliably adapt to short-term changes in the environ- ment while maintaining a generally stable behavior. This is fundamental in biological sys- tems because they must strike a delicate balance between stable and flexible behavior. In the present paper we analyse the role of noise in the decision-making of the true slime mold Physarum polycephalum, an important model species for the investigation of computational abilities in simple organisms. We propose a simple biological experiment to investigate the reaction of P. polycephalum to time-variant risk factors and present a stochastic extension of an established mathematical model for P. polycephalum to analyze this experiment. It predicts that—due to the mechanism of stochastic resonance—noise can enable P. polyce- phalum to correctly assess time-variant risk factors, while the corresponding noise-free sys- tem fails to do so. Beyond the study of P. polycephalum we demonstrate that the influence of noise on self-organized decision-making is not tied to a specific organism. Rather it is a general property of the underlying process dynamics, which appears to be universal across a wide range of systems. Our study thus provides further evidence that stochastic reso- nance is a fundamental component of the decision-making in self-organized macroscopic and microscopic groups and organisms.

K. Sato, I. Kunita, Y. Takikawa, D. Takeuchi, Y. Tanaka, T. Nakagaki and *H. Orihara,
Direct observation of orientation distributions of actin filaments in a solution undergoing shear banding,
Soft Matter 13, 2708-2716 (2017).

[Summary] Shear banding is frequently observed in complex fluids. However, the configuration of macromoleculesin solutions undergoing shear banding has not yet been directly observed. In this study, by using the factthat F-actin solutions exhibit shear banding and actin filaments are visualized by fluorescent labels, wedirectly observed the intrinsic states of an actin solution undergoing shear banding. By combining the 3Dimaging of labeled actin filaments and particle image velocimetry (PIV), we obtained orientation distributionsof actin filaments in both high and low shear rate regions, whose quantitative differences are indicated.In addition, by using the orientation distributions and applying stress expression for rod-like polymers, weestimated stress tensors in both high and low shear rate regions. This evaluation indicates that differentorientation distributions of filamentous macromolecules can exhibit a common shear stress.

Makoto Iima, Hiroshi Kori and Toshiyuki Nakagaki,
Studies of the phase gradient at the boundary of the phase diffusion equation, motivated by peculiar wave patterns of rhythmic contraction in the amoeboid movement of Physarum polycephalum,
Journal of Physics D: Applied Physics 50, 154004/1-10 (2017).

[Summary] The boundary of a cell is the interface with its surroundings and plays a key role in controlling the cell movement adaptations to different environments. We propose a study of the boundary effects on the patterns and waves of the rhythmic contractions in plasmodia of Physarum polycephalum, a tractable model organism of the amoeboid type. Boundary effects are defined as the effects of both the boundary conditions and the boundary shape. The rhythmicity of contraction can be modulated by local stimulation of temperature, light and chemicals, and by local deformation of cell shape via mechanosensitive ion channels as well. First, we examined the effects of boundary cell shapes in the case of a special shape resembling a tadpole, while requiring that the natural frequency in the proximity of the boundary is slightly higher and uniform. The simulation model reproduced the approximate propagated wave, from the tail to the head, while the inward waves were observed only near the periphery of the head section of the tadpole-shape. A key finding was that the frequency of the rhythmic contractions depended on the local shape of cell boundary. This implies that the boundary conditions of the phase were not always homogeneous. To understand the dependency, we reduced the two-dimensional model into a one-dimensional continuum model with Neumann boundary conditions. Here, the boundary conditions reflect the frequency distribution at the boundary. We described the analytic solutions and calculated the relationship between the boundary conditions and the wave propagation for a one-dimensional model of the continuous oscillatory field and a discrete coupled oscillator system. The results obtained may not be limited to cell movement of Physarum, but may be applicable to the other physical systems since the analysis used a generic phase diffusion equation.

Shigeru Kuroda, Seiji Takagi, Tetsu Saigusa and *Toshiyuki Nakagaki,
Physical ethology of unicellular organism,
Brain Evolution by Design -, 3-23 (2017).

[Summary] In this chapter, some behaviours of unicellular organisms that appear to be smart or intelligent are reported. Two topics are the focus from two major groups of eukaryotic unicellular organisms, amoebae and ciliates: (1) anticipatory capacity of periodic environmental events in an amoeba and (2) environment- induced development of a new type of behaviour in a ciliate. A mechanism of these behaviours is discussed, based on a mechanical equation of motion. Ethology (the science of animal behaviour) of unicellular organisms is recently being studied from a physical point of view. We propose to call this kind of study physical ethology. Physical ethology may give us some hints about the origin of primitive intelligence.

Yoriaki Nishioka, Fumiaki Kobayashi, Nobutaka Sakurai, *Yuji Sasaki, and Hiroshi Orihara,
Microscopic characterisation of self-assembled colloidal particles in electrohydrodynamic convection of a low-birefringence nematic liquid crystal,
Liquid Crystals 43(4), 427-435 (2016).

[Summary] Electrokinetics of small particles immersed in anisotropic fluids is attracting attention in recent years. Here we focus on microscopic appearance of single as well as self-assembled particles moving in the electrohydrodynamic convection (EHC) of a nematic liquid crystal with low birefringence. Characterisation of the birefringent properties is made by polarised light microscopy under different illumination conditions. Because of the small optical anisotropy, the director distortion around the particles clearly exhibits distinctive colours on both sides depending on the height in the cell. The observation can be explained as the change in the net phase retardation of the light. It is also found that a caterpillar-like motion is possible by tuning temperature, although the horizontal size of the EHC rolls is relatively narrow.

Dai Akita, Itsuki Kunita, Mark D Fricker, Shigeru Kuroda, Katsuhiko Sato and *Toshiyuki Nakagaki,
Experimental models for Murray’s law,
Journal of Physics D: Applied Physics 50, 024001 (2016).

[Summary] Transport networks are ubiquitous in multicellular organisms and include leaf veins, fungal mycelia and bloodvessels. While transport of materials and signals through the network plays a crucial role in maintaining theliving system, the transport capacity of the network can best be understood in terms of hydrodynamics. Wereport here that plasmodium from the large, single-celled amoeboid Physarum was able to construct ahydrodynamically optimized veinnetwork when evacuating biomass from confined arenas of various shapes througha narrow exit. Increasingly thick veins developed towards the exit, and the network spanned the arena viarepetitive bifurcations to give a branching tree. The Hausdorff distance from all parts of the plasmodium tothe vein network was kept low, whilst the hydrodynamic conductivity from distal parts of the network to theexit was equivalent, irrespective of the arena shape. This combination of spatial patterning and differentialvein thickening served to evacuate biomass at an equivalent rate across the entire arena. The scalingrelationship at the vein branches was determined experimentally to be 2.53.3.29, consistent with predictionsfrom Murray’s law. Furthermore, we show that mathematical models for self-organised, adaptive transport inPhysarum simulate the experimental network organisation well if the scaling coefficient of thecurrent-reinforcement rule is set to 3. In simulations, this resulted in rapid development of an optimalnetwork that minimised the combined volume and frictional energy in comparison with other scalingcoefficients. This would predict that the boundary shear forces within each vein are constant throughout thenetwork, and would be consistent with a feedback mechanism based on a sensing a threshold shear at the veinwall.

Yuji Sasaki, *V.S.R. Jampani, Chiharu Tanaka, Nobutaka Sakurai, Shin Sakane, Khoa V. Le, *Fumito Araoka, and *Hiroshi Orihara,
Large-scale self-organization of reconfigurable topological defect networks in nematic liquid crystals,
Nature Communications 7, 13238 (2016).

[Summary] Topological defects in nematic liquid crystals are ubiquitous. The defects are important in understanding the fundamental properties of the systems, as well as in practical applications, such as colloidal self-assembly, optical vortex generation and templates for molecular self-assembly. Usually, spatially and temporally stable defects require geometrical frustration imposed by surfaces; otherwise, the system relaxes because of the high cost of the elastic energy. So far, multiple defects are kept in bulk nematic liquid crystals by top-down lithographic techniques. In this work, we stabilize a large number of umbilical defects by doping with an ionic impurity. This method does not require pre-patterned surfaces. We demonstrate that molecular reorientation controlled by an AC voltage induces periodic density modulation of ions accumulated at an electrically insulating polymer interface, resulting in self-organization of a two-dimensional square array of umbilical defects that is reconfigurable and tunable.

*Takayuki Narumi, Yosuke Mikami, Tomoyuki Nagaya, Hirotaka Okabe, Kazuhiro Hara, and Yoshiki Hidaka,
Relaxation with long-period oscillation in defect turbulence of planar nematic liquid crystals,
Physical Review E 94, 042701/1-6 (2016).

[Summary] Through experiments, we studied defect turbulence, a type of spatiotemporal chaos in planar systems of nematic liquid crystals, to clarify the chaotic advection of weak turbulence. In planar systems of large aspect ratio, structural relaxation, which is characterized by the dynamic structure factor, exhibits a long-period oscillation that is described well by a combination of a simple exponential relaxation and underdamped oscillation. The simple relaxation arises as a result of the roll modulation while the damped oscillation is manifest in the repetitive gliding of defect pairs in a local area. Each relaxation is derived analytically by the projection operator method that separates turbulent transport into a macroscopic contribution and fluctuations. The analysis proposes that the two relaxations are not correlated. The nonthermal fluctuations of defect turbulence are consequently separated into two independent Markov processes. Our approach sheds light on diversity and universality from a unified viewpoint for weak turbulence.

Koutaro Nakagome, Katsuhiko Sato, Seine A. Shintani, *Shin’ichi Ishiwata,
Model simulation of the SPOC wave in a bundle of striated myofibrils,
Biophysics and Physicobiology 13, 217-226 (2016).

[Summary] SPOC (spontaneous oscillatory contraction) is a phenomenon observed in striated muscle under intermediateactivation conditions. Recently, we constructed a theoretical model of SPOC for a sarcomere, a unit sarcomeremodel, which explains the behavior of SPOC at each sarcomere level. We also constructed a single myofibrilmodel, which visco-elastically connects the unit model in series, and explains the behaviors of SPOC at themyofibril level. In the present study, to understand the SPOC properties in a bundle of myofibrils, weextended the single myofibril model to a two-dimensional (2D) model and a three-dimensional (3D) model, inwhich myofibrils were elastically connected side-by-side through cross-linkers between the Z-lines andM-lines. These 2D and 3D myofibril models could reproduce various patterns of SPOC waves experimentallyobserved in a 2D sheet and a 3D bundle of myofibrils only by choosing different values of elastic constants ofthe cross-linkers and the external spring. The results of these 2D and 3D myofibril models provide insightinto the SPOC properties of the higher-ordered assembly of myofibrils.

*Tomoyuki Nagaya, Yuki Satou, Yoshitomo Goto, Yoshiki Hidaka, and Hiroshi Orihara,
Viscosity of Liquid Crystal Mixtures in the Presence of Electroconvection,
Journal of the Physical Society of Japan 85, 074002/1-4 (2016).

[Summary] We have experimentally investigated the viscosity of nematic liquid crystal mixtures of p-methoxybenzylidene-pA-n- butylaniline (MBBA) and p-ethoxybenzylidene-pA-cyanoaniline (EBCA) in the presence of electroconvection under an ac electric field with 60Hz. Although the viscosity of the mixtures with negative dielectric anisotropy shows a characteristic decrease in the high-voltage regime, that with positive dielectric anisotropy shows a monotonic increase as the applied voltage is increased. The experimental results suggest that the decrease in viscosity observed only for the mixtures with negative dielectric anisotropy is attributed to the negative contribution of electric stress caused by the anisotropic director distribution of the turbulent state.

Itsuki Kunita, Tatsuya Yamaguchi, Atsushi Tero, Masakazu Akiyama, Shigeru Kuroda and *Toshiyuki Nakagaki,
A ciliate memorizes the geometry of a swimming arena,
The Royal Soc. Interface 13, 20160155/1-7 (2016).

[Summary] Previous studies on adaptive behaviour in single-celled organisms have given hints to the origin of their memorizing capacity. Here we report evidence that a protozoan ciliate Tetrahymena has the capacity to learn the shape and size of its swimming space. Cells confined in a small water dro-plet for a short period were found to recapitulate circular swimming trajectories upon release. The diameter of the circular trajectories and their duration reflected the size of the droplet and the period of confinement. We suggest a possible mechanism for this adaptive behaviour based on a Ca2þ channel. In our model, repeated collisions with the walls of a confining droplet result in a slow rise in intracellular calcium that leads to a long-term increase in the reversal frequency of the ciliary beat.

*Shigeru Kuroda, Seiji Takagi, Toshiyuki Nakagaki and Tetsuo Ueda,
Allometry in Physarum plasmodium during free locomotion: size versus shape, speed and rhythm,
Journal of Experimental Biology 218, 3729-3738 (2015).

[Summary] Physarum plasmodium is a giant unicellular organism whose lengthcan vary by more than three orders of magnitude. Using plasmodiaranging in size from 100 μm to 10 cm, we investigated the sizedependency of their thickness distributions and locomotion speedsduring free locomotion. (1) In the longitudinal direction, the organismis thickest close to the front, and decreases exponentially in thicknesstowards the rear. The slenderness ratio varies with body sizeaccording to a power law, such that large plasmodia are long andflat, whereas small plasmodia are short and thick. (2) The meanlocomotion speed is proportional to the mean maximum thickness ofthe frontal part. By conducting a dimensional analysis, possiblephysical models are discussed. (3) The intrinsic period of thethickness oscillation, which is related to shuttle streaming (period1–2 min), increases logarithmically with body size. (4) Variouscharacteristics exhibit size-independent, long-period (20±10 min)oscillations, including speed, shape and intrinsic thicknessoscillation period. These variations are closely coupled to formationof the entire cell shape, including undulation of thickness along thelongitudinal axis and timing of branching of the frontal tip. Based onthese experimental results and those reported previously, wepropose a simple mathematical model for cell locomotion.

*Yoshiki Hidaka, Megumi Hashiguchi, Noriko Oikawa, Shoichi Kai,
Lagrangian chaos and particle diffusion in electroconvection of planar nematic liquid crystals,
Physical Review E 92, 032909/1-6 (2015).

[Summary] Two types of spatiotemporal chaos in the electroconvection of nematic liquid crystals, such as defect turbulence and spatiotemporal intermittency, have been statistically investigated according to the Lagrangian picture. Here fluctuations are traced using the motion of a single particle driven by chaotic convection. In the defect turbulence (fluctuating normal rolls), a particle is mainly trapped in a roll but sometimes jumps to a neighboring roll. Its activation energy is then obtained from the jumping (hopping) rate. This research clarifies that diffusion in the defect turbulence regime in electroconvection can be regarded as a kind of hopping process. The spatiotemporal intermittency appears as a coexistent state of ordered grid domains and turbulent domains. The motion of a single particle shows weak and strong diffusion, respectively, in the ordered and turbulent domains. The diffusion characteristics intermittently change from one to another with certain durations as the domains change. This research has found that the distribution function of the duration that a particle remains in an ordered area has a power-law decay for which the index is different from that obtained by the Eulerian measurement.

Misato Iino, *Yoshiki Hidaka, Fahrudin Nugroho, Rinto Anugraha, Hirotaka Okabe, Kazuhiro Hara,
Responses of spatiotemporal chaos to oscillating forces,
Physical Review E 92, 012916/1-5 (2015).

[Summary] The responses of soft-mode turbulence, a kind of spatiotemporal chaos seen in electroconvection of a nematic liquid crystal, to alternating-current magnetic fields is investigated to uncover the dynamical properties of spatiotemporal chaos. The dynamical responses can be measured by an order parameter, Mp(t), which indicates ordering in the convective roll pattern induced by the magnetic field. Determined by properties of the liquid crystal in a magnetic field, Mp(t) oscillates in accordance with the square of the magnetic field. The relaxation time of the system was obtained by fitting the frequency dependence of the complex susceptibility for the pattern obtained from the oscillation of Mp(t) to the Debye-type relaxation spectra. However, for the high-frequency regime, the susceptibility deviates from the spectra because slow and large fluctuations of Mp(t) contribute to the oscillation. The properties of this type of fluctuation were investigated by introducing a dynamic ordering parameter defined as the period average of Mp(t).

Jaka Fajar Fatriansyah and *Hiroshi Orihara,
Electric-field-induced flow-aligning state in a nematic liquid crystal,
Physical Review E 91, 042508/1-7 (2015).

[Summary] The response of shear stress to a weak ac electric field as a probe is measured in a nematic liquid crystal undershear flow and dc electric fields. Two states with different responses are clearly observed when the dc electricfield is changed at a constant shear rate: the flow aligning and non–flow aligning states. The director lies in theshear plane in the flow aligning state and out of the plane in the non–flow aligning state. Through applicationof dc electric field, the non–flow aligning state can be changed to the flow aligning state. In the transition fromthe flow aligning state to the non–flow aligning state, it is found that the response increases and the relaxationtime becomes longer. Here, the experimental results in the flow aligning state are discussed on the basis of theEricksen-Leslie theory.

*Jean-Paul Rieu, Helene Delano-Ayari, Seiji Takagi, Yoshimi Tanaka, Toshiyuki Nakagaki,
Periodic traction in migrating large amoeba of Physarum Polycephalum,
Journal of Royal Society Interface 12, 20150099 (2015).

[Summary] The slime mould Physarum polycephalum is a giant multinucleated cell exhibiting well-known Ca2þ-dependent actomyosin contractions of its vein network driving the so-called cytoplasmic shuttle streaming. Its actomyosinnetwork forms both a filamentous cortical layer and large fibrils. In order to understand the role of each structure in the locomotory activity, we performedbirefringence observations and traction force microscopy on excised fragments of Physarum. After several hours, these microplasmodia adopt three main morphologies: flat motile amoeba, chain types with round contractile heads connected by tubes and motile hybrid types. Each typeexhibits oscillations with a period of about 1.5 min of cell area, traction forces and fibril activity (retardance) when fibrils are present. The amoeboid types show only peripheral forces while the chain types present a neverreported force pattern with contractile rings far from the cell boundary under the spherical heads. Forces are mostly transmitted where the actomyosin cortical layer anchors to the substratum, but fibrils maintain highly invaginated structures and contribute to forces by increasing the length of the anchorage line. Microplasmodia are motile only when there is an asymmetry in the shape and/or the force distribution.

*Yuji Sasaki, Hikaru Hoshikawa, Takafumi Seto, Fumiaki Kobayashi, V. S. R. Jampani, Stephan Herminghaus, Christian Bahr, and Hiroshi Orihara,
Direct visualization of spatiotemporal structure of self-assembled colloidal particles in electrohydrodynamic flow of a nematic liquid crystal,
Langmuir 31, 3815-3819 (2015).

[Summary] Characterization of spatiotemporal dynamics is of vital importance to soft matter systems far from equilibrium. Using a confocal laser scanning microscopy, we directly reveal three-dimensional motion of surface-modified particles in the electrohydrodynamic convection of a nematic liquid crystal. Particularly, visualizing a caterpillar-like motion of a self-assembled colloidal chain demonstrates the mechanism of the persistent transport enabled by the elastic, electric, and hydrodynamic contributions. We also precisely show how the particles’ trajectory is spatially modified by simply changing the surface boundary condition.

*Yang Ho Na, Yuki Aburaya, Hiroshi Orihara, Kazuyuki Hiraoka, and Youngbae Han,
Electrically induced deformation in chiral smectic elastomers with different domain structures,
Physical Review E 90, 062507/1-6 (2014).

[Summary] Electrical actuation is investigated in two kinds of chiral smectic liquid-crystal elastomers (LCEs) with different domain structures LCE1 and LCE2: The latter is better than the former in orientational order. Tracking fluorescent beads dispersed on the samples enables us to measure the two-dimensional strain tensors in ferroelectric elastomer films. It turns out that the electric-field-induced strain is polarity dependent and the type of molecular orientation responsible for the strain is specified. In LCE1 the shear strain is dominant, whereas in LCE2 it is comparable to the elongation strain, which is explained by the rotation of the principal axes. The essential differences of the two elastomers are observed in the eigenvalues of the strain tensors. The absolute values for LCE1 are larger than those for LCE2. The difference is discussed on the basis of the domain structures.

Yuji Sasaki, Yoshinori Takikawa, V. S. R. Jampani, Hikaru Hoshikawa, Takafumi Seto, Christian Bahr, Stephan Herminghaus, Yoshiki Hidaka, and *Hiroshi Orihara,
Colloidal caterpillars for cargo transportation,
Soft Matter 10, 8813–8820 (2014).

[Summary] Tunable transport of tiny objects in fluid systems is demanding in diverse fields of science such as drug delivery,active matter far from equilibrium, and lab-on-a-chip applications. Here, we report the directed motion ofcolloidal particles and self-assembled colloidal chains in a nematic liquid crystal matrix using electrohydrodynamic convection (EHC) rolls. The asymmetric distortion of the molecular orientation around the particles results – for single particles – in a hopping motion from one EHC roll to the next and – for colloidal chains – in a caterpillar-like motion in the direction perpendicular to the roll axes. We demonstrate the use of colloidal chains as microtraction engines for the transport of various types of microcargo.

Jaka Fajar Fatriansyah, Yuji Sasaki, and *Hiroshi Orihara,
Nonequilibrium steady-state response of a nematic liquid crystal under simple shear flow and electric fields,
Physical Review E 90, 032504/1-8 (2014).

[Summary] The effect of a dc electric field on the response of a nematic liquid crystal under shear flow has been investigated by measuring the shear stress response to an ac electric field used as a probe. It was found that both the first- and second-order responses do not vanish at high frequencies, but have constant nonzero values. The experimental results are in good agreement with calculations based on the Ericksen-Leslie theory. The role of the Parodi relation (which is derived from the Onsager reciprocal relation) in the stress response is discussed.

*Yoshiki Hidaka and Noriko Oikawa,
Chaos and Spatiotemporal Chaos in Convective Systems,
FORMA 29, 29-32 (2014).

[Summary] Much of early research on chaos from the viewpoint of physics was performed using spatially confined convective systems. In spatially extended convective systems, on the other hand, spatiotemporal chaos occurs. However, there is no unified definition for the term spatiotemporal chaos as for chaos. To unify definition, a property common to the three kinds of spatiotemporal chaos observed in electroconvection of nematic liquid crystals is presented.

＊Itsuki Kunita, Shigeru Kuroda, Kaito Ooki, Toshiyuki Nakagaki,
Attempts to retreat from a dead-ended long capillary by backward swimming in Paramecium,
Frontiers in Microbiology 5, Article 270 (1-8) (2014).

[Summary] We have observed how the ciliate {\it Paramecium} attempts to retreat from the dead-end of a long capillary that is too narrow in which to turn. After many trial-and-error episodes of short-term backward swimming (SBS), which is the conventional avoidance behavior exhibited in free swimming when an obstacle is faced, long-term backward swimming (LBS) that lasted five to ten times longer was developed. LBS may have a beneficial effect for complete withdrawal from the capillary space, although in our experiment it was impossible for the organism to do so due to the capillary length. In order to identify a physically possible mechanism for LBS, we propose model equations for the membrane potential of Hodgkin-Huxley type, which describe the control of ciliary movement. The physiological implications and physical mechanism of the development of LBS are discussed.

Satoshi Aya, Yuji Sasaki, Damian Pociecha, Fumito Araoka, Ewa Gorecka, Kenji Ema, Igor Musevic, Hiroshi Orihara, Ken Ishikawa, and *Hideo Takezoe,
Stepwise heat-capacity change at an orientation transition in liquid crystals,
Physical Review E 89, 022512 (2014).

[Summary] During a phase transition in a bulk material, heat is exchanged with matter to balance the changes in the internal energy and the entropy of the system. Here we report on the thermal detection of a surface-mediated anchoring transition, a spontaneous and discontinuous orientation change between planar (P) and homeotropic (H) alignments within a single nematic phase by changing temperature. In this case a stepwise change in the heat flow, similar to a glass transition, is observed by means of high-resolution differential scanning calorimetry. We found that the jump in the specific heat does not depend on the sample volume, although the contribution of molecules in the vicinity of surfaces, which trigger the transition, becomes less with increasing the sample volume. This means that different molecular orientations, H and P, with respect to surfaces have different thermodynamic free energies. We also address why the anchoring transition occurs by means of Grazing-incidence x-ray diffraction measurements, which clearly reveal the formation of quasi-smectic layers parallel to surfaces in the nematic phase.

Yoshinori Takikawa and *Hiroshi Orihara,
Persistence of Brownian motion in shear flow,
Physical Review E 88, 062111/1-5 (2013).

[Summary] The persistence of a Brownian particle in a shear flow is investigated. The persistence probability P(t) , which is the probability that the particle does not return to its initial position up to time t, is known to obey a power law . Since the displacement of a particle along the flow direction due to convection is much larger than that due to Brownian motion, we define an alternative displacement in which the convection effect is removed. We derive theoretically the two-time correlation function and the persistence exponent  of this displacement. The exponent has different values at short and long times. The theoretical results are compared with experiment and a good agreement is found.

Masaru Suzuki, Hiroshi Sueto, Yusaku Hosokawa, Naoyuki Muramoto, Takayuki Narumi, Yoshiki Hidaka, and Shoichi Kai,
Duality of diffusion dynamics in particle motion in soft-mode turbulence,
Physical Review E 88, 42147 (2013).

[Summary] Nonthermal Brownian motion is investigated experimentally by injecting a particle into soft-mode turbulence (SMT), in the electroconvection of a nematic liquid crystal. It is clarified that the particle motion can be classified into two phases: fast motion, where particles move with the local convective flow, and slow motion, where they are carried by global slow pattern dynamics. We propose a simplified model to clarify the mechanism of the short-time and asymptotic behavior of diffusion. In our model, the correlation time is estimated as a function of a control parameter ɛ. The scaling of the SMT pattern correlation time, τ_d ∼ ɛ^−1, is estimated from the particle dynamics, which is consistent with a previous report observed from the Eulerian viewpoint. The origin of the non-Gaussian distribution of the displacement in the short-time regime is also discussed and an analytical curve is introduced that quantitatively agrees with the experimental data. Our results clearly illustrate the characteristics of diffusive motion in SMT, which are considerably different from the conventional Brownian motion.

Jaka Fajar Fatriansyah and *Hiroshi Orihara,
Dynamical properties of nematic liquid crystals subjected to shear flow and magnetic fields: Tumbling instability and non-equilibrium fluctuations,
Physival Review E 88, 012510/1-9 (2013).

[Summary] We investigate the dynamical properties of monodomain nematic liquid crystals under shear flow and magnetic fields on the basis of the Ericksen-Leslie theory. Stable and unstable states appear depending on the magnetic field and the shear rate. The trajectory of the unstable state shows tumbling motion. The phase diagram of these states is plotted as a function of the three components of the magnetic field at a constant shear rate. The phase diagram changes depending on the viscous properties of different types of nematic liquid crystals. In this non-equilibrium steady state, we calculate the correlation function of director fluctuations and the response function, and discuss the non-equilibrium fluctuations and the modified fluctuation dissipation relation in connection with non-conservative forces due to shear flow.