| 1. |
Yoichiro Kondo, Hiizu Nakanishi, Rattleback dynamics and its reversal time of rotation, Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 10.1103/PhysRevE.95.062207, 95, 6, 2017.06, A rattleback is a rigid, semielliptic toy which exhibits unintuitive behavior; when it is spun in one direction, it soon begins pitching and stops spinning, then it starts to spin in the opposite direction, but in the other direction, it seems to spin just steadily. This puzzling behavior results from the slight misalignment between the principal axes for the inertia and those for the curvature; the misalignment couples the spinning with the pitching and the rolling oscillations. It has been shown that under the no-slip condition and without dissipation the spin can reverse in both directions, and Garcia and Hubbard obtained the formula for the time required for the spin reversal tr [Proc. R. Soc. Lond. A 418, 165 (1988)1364-502110.1098/rspa.1988.0078]. In this work, we reformulate the rattleback dynamics in a physically transparent way and reduce it to a three-variable dynamics for spinning, pitching, and rolling. We obtain an expression of the Garcia-Hubbard formula for tr by a simple product of four factors: (1) the misalignment angle, (2) the difference in the inverses of inertia moment for the two oscillations, (3) that in the radii for the two principal curvatures, and (4) the squared frequency of the oscillation. We perform extensive numerical simulations to examine validity and limitation of the formula, and find that (1) the Garcia-Hubbard formula is good for both spinning directions in the small spin and small oscillation regime, but (2) in the fast spin regime especially for the steady direction, the rattleback may not reverse and shows a rich variety of dynamics including steady spinning, spin wobbling, and chaotic behavior reminiscent of chaos in a dissipative system.. |
| 2. |
Yumino Hayase, Takahiro Sakaue, and Hiizu Nakanishi, ``Compressive response and helix formation of a semiflexible polymer confined in a nanochannel'', Physical Review E, https://doi.org/10.1103/PhysRevE.95.052502, 95, 052502, 2017.05, Configurations of a single semiflexible polymer is studied when it is pushed into a nanochannel in the case where the polymer persistence length lp is much longer than the channel diameter D:lp/D≫1. Using numerical simulations, we show that the polymer undergoes a sequence of recurring structural transitions upon longitudinal compression: random deflection along the channel, a helix going around the channel wall, double-fold random deflection, double-fold helix, etc. We find that the helix transition can be understood as buckling of deflection segments, and the initial helix formation takes place at very small compression with no appreciable weak compression regime of the random deflection polymer.. |
| 3. |
Shin Ichiro Nagahiro, Hiizu Nakanishi, Negative pressure in shear thickening band of a dilatant fluid, Physical Review E, 10.1103/PhysRevE.94.062614, 94, 6, 2016.12, We perform experiments and numerical simulations to investigate spatial distribution of pressure in a sheared dilatant fluid of the Taylor-Couette flow under a constant external shear stress. In a certain range of shear stress, the flow undergoes the shear thickening oscillation around 20 Hz. We find that, during the oscillation, a localized thickened band rotates around the axis with the flow. Based upon experiments and numerical simulations, we show that a major part of the thickened band is under negative pressure even in the case of discontinuous shear thickening, which indicates that the thickening is caused by Reynolds dilatancy; the dilatancy causes the negative pressure in interstitial fluid, which generates contact structure in the granular medium, then frictional resistance hinders rearrangement of the structure and solidifies the medium.. |
| 4. |
Takahiro Umeki, Masahiko Ohata, Hiizu Nakanishi & Masatoshi Ichikawa, Dynamics of microdroplets over the surface of hot water, Scientific Reports 5 (2015) 8046, 10.1038/srep08046, 2015.01, When drinking a cup of coffee under the morning sunshine, you may notice white membranes of steam floating on the surface of the hot water. They stay notably close to the surface and appear to almost stick to it. Although the membranes whiffle because of the air flow of rising steam, peculiarly fast splitting events occasionally occur. They resemble cracking to open slits approximately 1 mm wide in the membranes, and leave curious patterns. We studied this phenomenon using a microscope with a high-speed video camera and found intriguing details: i) the white membranes consist of fairly monodispersed small droplets of the order of 10 μm; ii) they levitate above the water surface by 10 ~ 100 μm; iii) the splitting events are a collective disappearance of the droplets, which propagates as a wave front of the surface wave with a speed of 1 ~ 2 m/s; and iv) these events are triggered by a surface disturbance, which results from the disappearance of a single droplet.. |
| 5. |
Ken-ichi Mizuochi, Hiizu Nakanishi and Takahiro Sakaue, Dynamical scaling of polymerized membranes, EPL 107 (2014) 38003, 10.1209/0295-5075/107/38003, 2014.07, Monte Carlo simulations have been performed to analyze the sub-diffusion dynamics of a tagged monomer in self-avoiding polymerized membranes in the flat phase. By decomposing the mean square displacement into the out-of-plane and the in-plane components, we obtain good data collapse with two distinctive diffusion exponents and , and the roughness exponents and , respectively for each component. Their values are consistent with the relation from the rotational symmetry. We derive the generalized Langevin equations to describe the sub-diffusional behaviors of a tagged monomer in the intermediate time regime where the collective effect of internal modes in the membrane dominate the dynamics to produce negative memory kernels with a power law. We also briefly discuss how the long-range hydrodynamic interactions alter the exponents.. |
| 6. |
Hiizu Nakanishi, Takahiro Sakaue, Jun'ichi Wakou, Hamilton-Jacobi method for molecular distribution function in a chemical oscillator, J. Chem. Phys. 139, 214105 (2013)[11 pages], http://dx.doi.org/10.1063/1.4834636, 2013.12, Using the Hamilton-Jacobi method, we solve chemical Fokker-Planck equations within the Gaussian approximation and obtain a simple and compact formula for a conditional probability distribution. The formula holds in general transient situations, and can be applied not only to a steady state but also to an oscillatory state. By analyzing the long time behavior of the solution in the oscillatory case, we obtain the phase diffusion constant along the periodic orbit and the steady distribution perpendicular to it. A simple method for numerical evaluation of these formulas are devised, and they are compared with Monte Carlo simulations in the case of Brusselator as an example. Some results are shown to be identical to previously obtained expressions.. |
| 7. |
Hiroyuki Kitagishi, Takahiro Sakaue, Hiizu Nakanishi, Jun'ichi Wakou, Inelastic collapse in one-dimensional driven systems under gravity, Phys. Rev. E87 (2013) 042201 [11 pages]., http://dx.doi.org/10.1103/PhysRevE.87.042201, 2013.04, We study inelastic collapse in a one-dimensional N-particle system when the system is driven from below under gravity. We investigate the hard-sphere limit of inelastic soft-sphere systems by numerical simulations to find how the collision rate per particle ncoll increases as a function of the elastic constant of the sphere k when the restitution coefficient e is kept constant. For systems with large enough N≳20, we find three regimes in e depending on the behavior of ncoll in the hard-sphere limit: (i) an uncollapsing regime for 1≥e>ec1, where ncoll converges to a finite value, (ii) a logarithmically collapsing regime for ec1>e>ec2, where ncoll diverges as ncoll∼logk, and (iii) a power-law collapsing regime for ec2>e>0, where ncoll diverges as ncoll∼kα with an exponent α that depends on N. The power-law collapsing regime shrinks as N decreases and seems not to exist for the system with N=3, while, for large N, the size of the uncollapsing and the logarithmically collapsing regime decreases as ec1≃1–2.6/N and ec2≃1–3.0/N. We demonstrate that this difference between large and small systems exists already in the inelastic collapse without external drive and gravity.. |
| 8. |
Hiizu Nakanishi, Shin-ichiro Nagahiro, Namiko Mitarai, `Experimental observation of shear thickening oscillation', EPL 104 (2013) 28002 [6 pages], http://dx.doi.org/10.1209/0295-5075/104/28002, 2013.04, We report experimental observations of the shear thickening oscillation, i.e. the spontaneous macroscopic oscillation in the shear flow of severe shear thickening fluid. Using a density-matched starch-water mixture, in the cylindrical shear flow of a few centimeters flow width, we observed that well-marked vibrations of frequency around 20 Hz appear via a Hopf bifurcation upon increasing externally applied shear stress. The parameter range and the frequency of the vibration are consistent with those expected by a simple phenomenological model of the dilatant fluid.. |
| 9. |
Ryota Nishino, Takahiro Sakaue, Hiizu Nakanishi, Transcription Fluctuation effects on biochemical oscillations, PLOS ONE 8(4) (2013) e60938, 10.1371/journal.pone.0060938, 2013.03, Some biochemical systems show oscillation. They often consist of feedback loops with repressive transcription regulation. Such biochemical systems have distinctive characteristics in comparison with ordinary chemical systems: i) numbers of molecules involved are small, ii) there are typically only a couple of genes in a cell with a finite regulation time. Due to the fluctuations caused by these features, the system behavior can be quite different from the one by deterministic rate equations, because the rate equations ignore molecular fluctuations and thus are exact only in the infinite molecular number limit. The molecular fluctuations on a free-running circadian system have been studied by Gonze et al. (2002) by introducing a scale parameter for the system size. They consider, however, only the first effect, assuming that the gene process is fast enough for the second effect to be ignored, but this has not been examined systematically yet. Here we study fluctuation effects due to the finite gene regulation time by introducing a new scale parameter , which we take as the unbinding time of a nuclear protein from the gene. We focus on the case where the fluctuations due to small molecular numbers are negligible. In simulations on the same system studied by Gonze et al., we find the system is unexpectedly sensitive to the fluctuation in the transcription regulation; the period of oscillation fluctuates about 30 min even when the regulation time scale is around 30 s, that is even smaller than 1/1000 of its circadian period. We also demonstrate that the distribution width for the oscillation period and amplitude scales with , and the correlation time scales with in the small regime. The relative fluctuations for the period are about half of that for the amplitude, namely, the periodicity is more stable than the amplitude.. |
| 10. |
N. Mitarai and H. Nakanishi, ``Granular flow: Dry and wet'', Eur. Phys. J. Special Topics 204 (2012) 5-17, 2012.04, Granular material is a collection of macroscopic particles that are visible with naked eyes. The non-equilibrium nature of the granular materials makes their rheology quite different from that of molecular systems. In this minireview, we present the unique features of granular materials focusing on the shear flow of dry granular materials and granule-liquid mixture.. |
| 11. |
Hiizu Nakanishi, Shin-ichiro Nagahiro, and Namiko Mitarai,, ``Fluid dynamics of dilatant fluids'', Phys. Rev. E 85, 011401 (2012), 2012.01, A dense mixture of granules and liquid often shows a severe shear thickening and is called a dilatant fluid. We construct a fluid dynamics model for the dilatant fluid by introducing a phenomenological state variable for a local state of dispersed particles. With simple assumptions for an equation of the state variable, we demonstrate that the model can describe basic features of the dilatant fluid such as the stress-shear rate curve that represents discontinuous severe shear thickening, hysteresis upon changing shear rate, and instantaneous hardening upon external impact. An analysis of the model reveals that the shear thickening fluid shows an instability in a shear flow for some regime and exhibits the shear thickening oscillation (i.e., the oscillatory shear flow alternating between the thickened and the relaxed states). The results of numerical simulations are presented for one- and two-dimensional systems.. |
| 12. |
Ludvig Lizana, Namiko Mitarai, Kim Sneppen, and Hiizu Nakanishi,, ``Modeling the spatial dynamics of culture spreading in the presence of cultural strongholds '', Phys. Rev. E 83, 066116 (2011), 2011.06, Cultural competition has throughout our history shaped and reshaped the geography of boundaries between humans. Language and culture are intimately connected and linguists often use distinctive keywords to quantify the dynamics of information spreading in societies harboring strong culture centers. One prominent example, which is addressed here, is Kyoto’s historical impact on Japanese culture. We construct a minimal model, based on shared properties of linguistic maps, to address the interplay between information flow and geography. We show that spreading of information over Japan in the premodern time can be described by an Eden growth process with noise levels corresponding to coherent spatial patches of sizes given by a single day’s walk (~15 km), and that new words appear in Kyoto at times comparable to the time between human generations (~30 yr).. |
| 13. |
Hiizu Nakanishi and Namiko Mitarai,, ``Shear Thickening Oscillation in a Dilatant Fluid'', J. Phys. Soc. Jpn. 80 (2011) 033801, 2011.02, By introducing a state variable, we construct a phenomenological fluid dynamical model of a dilatant fluid, i.e., a dense mixture of fluid and granules that shows severe shear thickening. We demonstrate that the fluid shows shear thickening oscillation, namely, the fluid flow oscillates owning to the coupling between the fluid dynamics and the internal dynamics of state. We also demonstrate that the jamming leads to a peculiar response to an external impact on the fluid.. |
| 14. |
Namiko Mitarai and Hiizu Nakanishi,, "Simple Interaction Model for Partially Wet Granular Materials", AIP Conf. Proc. -- May 5, 2010 -- Volume 1227, pp. 214-220, 2010.05. |
| 15. |
Namiko Mitarai and Hiizu Nakanishi,, Simple model for wet granular materials with liquid clusters, Europhys. Lett. 88 (2009) 64001, 2009.11. |
| 16. |
Hiizu Nakanishi, Margit Pedersen, Anne K Alsing, and Kim Sneppen,, Modeling of the genetic switch of bacteriophage TP901-1: A heteromer of CI and MOR ensures robust bistability, J. Mol. Biol. 394 (2009) 15--28., 2009.10. |
| 17. |
Kenji Shimomura, Hiizu Nakanishi, and Namiko Mitarai, Nonideal behavior of the intramolecular structure factor of dilute polymers in a theta solvent, Phys. Rev. E 80 (2009) 051804-1 -- 7., 2009.10. |
| 18. |
Yoichiro Kondo, Namiko Mitarai, and Hiizu Nakanishi,, Loewner driving functions for off-critical percolation clusters, Phys. Rev. E 80 (2009) 050102(R)., 2009.09. |
| 19. |
Hiizu Nakanishi, Namiko Mitarai, and Kim Sneppen, Dynamical Analysis on Gen Activity in the Presence of
Repressors and an Interfering Promoter, Biophysical Journal 95 (2008) 4228–4240, 2008.06. |
| 20. |
Yasuhiro Imafuku, Namiko Mitarai, Katsuhisa Tawada, and Hiizu Nakanishi, Anomalous Fluctuations in Sliding Motion of Cytoskeletal Filaments Driven by Molecular Motors: Model Simulations, J. Phys. Chem. B(2008) 1487 -1493., 112 (2008) 1487 -1493, 2008.01. |
| 21. |
Ryo Kawahara and Hiizu Nakanishi,, Slow relaxation in two dimensional electron plasma under strong magnetic field, J. Phys. Soc. Jpn. 76 No. 7 (2007), 2007.07.  |
| 22. |
Namiko Mitarai and Hiizu Nakanishi, Velocity correlations in the dense granular shear flows: Effects on energy dissipation and normal stress, Phys. Rev. E, 75 (2007) 31305-1 --- 9, 2007.03. |
| 23. |
Hiizu Nakanishi, Ryo Yamamoto, Yumino Hayase, and Namiko Mitarai, Lattice Model of Sweeping Interface for Drying Process in Water-Granule Mixture, J. Phys. Soc. Jpn. 76 (2007) 024003-1 -- 7, 2007.01. |
| 24. |
T. Iwashita, Y. Hayase, and H. Nakanishi,, Phase Field Model for Dynamics of Sweeping Interface, J. Phys. Soc. Jpn., 10.1143/JPSJ.74.1657, 74, 6, 1657-1660, J. Phys. Soc. Jpn. 74 (2005) 1657-1660., 2005.01. |
| 25. |
N. Mitarai and H. Nakanishi, Bagnold Scaling, Density Plateau, and Kinetic Theory Analysis of Dense Granular Flow, Phys. Rev. Lett., 10.1103/PhysRevLett.94.128001, 94, 12, Phys. Rev. Lett. 94 (2005) 128001., 2005.01. |
| 26. |
T. Iwashita, Y. Hayase, and H. Nakanishi, Phase Field Model for Dynamics of Sweeping Interface, J. Phys. Soc. Jpn. 74 (2005) 1657-1660., 10.1143/JPSJ.74.1657, 74, 6, 1657-1660, 2005.01. |
| 27. |
N. Mitarai and H. Nakanishi, Linear stability analysis of rapid granular flow on a slope
and density wave formation, J. Fluid Mech. (2004), 10.1017/S002211200400881X, 507, 309-334, 2004.04. |
| 28. |
M.Fujita, H.Nakatsuka, H.Nakanishi, and M.Matsuoka, Backward Echo in Two-Level Systems, Phy. Rev. Lett., vol.42 pp. 974-977, 1979.01. |
| 29. |
N. Mitarai and H. Hayakawa, and H. Nakanishi, Collisional Granular Flow as a Micropolar Fluid, Phys. Rev. Lett., Phys. Rev. Lett. {f 88} (2002) 174301.. |
| 30. |
S. Fukano, Y. Hayase, and H. Nakanishi, Riddled-like Basin in Two-Dimensional Map for Bouncing Motion of an
Inelastic Particle on a Vibrating Board, J. Phys. Soc. Jpn. {f 71} (2002) 2075--2077. |
| 31. |
H. Nakanishi, Velocity distribution of inelastic granular gas in a homogeneous
cooling state, Phys. Rev. E, {f 67} (2003) 010301-1--010301-4. |
| 32. |
N. Mitarai and H. Nakanishi, Hard-sphere limit of soft-sphere model for granular materials:
Stiffness dependence of steady granular flow, Phys. Rev. E, {f 67}(2003) 021301 -1--8. |
| 33. |
Y. Hayase, S. Fukano, and H. Nakanishi, Basin Structure in the Two-Dimensional Dissipative Circle Map, J. Phys. Soc. Jpn. {f 72} (2003) 1943--1947. |
| 34. |
N. Mitarai and H. Nakanishi, Stability Analysis of Collisional Granular Flow on a Slope, Int. J. Mod. Phys. B, {f 17} (2003) 4290--4294. |
| 35. |
R. Kawahara and H. Nakanishi, Effects of Velocity Correlation on Early Stage of Free Cooling Process
of Inelastic Hard Sphere System, J. Phys. Soc. Jpn. 73 (2004) 68--75. |
| 36. |
A. Kasahara and H. Nakanishi, Isostaticity in Two-Dimensional Pile of Rigid Disks, J. Phys. Soc. Jpn. 74 (2004) No.4. |
| 37. |
R. Kawahara and H. Nakanishi, Simulation of stationary states of the two dimensional electron plasma trapped in magnetic field, Proceedings of CN-Kyoto, March 14-18, 2005. |
| 38. |
R. Kawahara and H. Nakanishi, Quasi-stationary States of Two-Dimensional Electron Plasma Trapped in Magnetic Field, J. Phys. Soc. Jpn. 75 (2006) 054001-1 -- 8.. |
| 39. |
H. Nakanishi, Boundary dynamics of the sweeping interface, Phys. Rev. E 73 (2006) 061603-1 -- 5. |
