Paper | Original Paper


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, 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.


*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.

*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.

*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.


*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.

*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, 270 (2014).

[Summary] We have observed how the ciliate Paramecium attempts to retreat from the dead-end of a long capillary that is too narrow for turning. 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 ab eneficial 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.