arXiv subjects

Hiizu Nakanishi

Publications and source records attributed to Hiizu Nakanishi.

At least 37 records · Page 2Linked to original sources

arXiv2008

Dynamical Analysis on Gene Activity in the Presence of Repressors and an Interfering Promoter

Transcription is regulated through interplay between transcription factors, an RNA polymerase(RNAP), and a promoter. Even for a simple repressive transcription factor that disturbs promoter activity at the initial binding of RNAP, its repression level is not determined solely by the dissociation constant of transcription factor but is sensitive to the time scales of processes in RNAP. We first analyse the promoter activity under strong repression by a slow binding repressor, in which case transcriptions occur in a burst, followed by a long quiescent period while a repressor binds to the operator; the number of transcriptions, the bursting and the quiescent times are estimated by reaction rates. We then examine interference effect from an opposing promoter, using the correlation function of transcription initiations for a single promoter. The interference is shown to de-repress the promoter because RNAP's from the opposing promoter most likely encounter the repressor and remove it in case of strong repression. This de-repression mechanism should be especially prominent for the promoters that facilitate fast formation of open complex with the repressor whose binding rate is slower than about 1/sec. Finally, we discuss possibility of this mechanism for high activity of promoter PR in the hyp-mutant of lambda phage.

q-bio.MN↗

arXiv2007

Anomalous fluctuations in sliding motion of cytoskeletal filament driven by molecular motors: Model simulations

It has been found in in vitro experiments that cytoskeletal filaments driven by molecular motors show finite diffusion in sliding motion even in the long filament limit [Y. Imafuku et al., Biophys. J. 70 (1996) 878-886; N. Noda et al., Biophys. 1 (2005) 45-53]. This anomalous fluctuation can be an evidence for cooperativity among the motors in action because fluctuation should be averaged out for a long filament if the action of each motor is independent. In order to understand the nature of the fluctuation in molecular motors, we perform numerical simulations and analyse velocity correlation in three existing models that are known to show some kind of cooperativity and/or large diffusion coefficient, i.e. Sekimoto-Tawada model [K. Sekimoto and K. Tawada, Phys. Rev. Lett. 75 (1995) 180], Prost model [J. Prost et al., Phys. Rev. Lett. 72 (1994) 2652], and Duke model [T. Duke, Proc. Natl. Acad. Sci. USA, 96 (1999) 2770]. It is shown that Prost model and Duke model do not give a finite diffusion in the long filament limit in spite of collective action of motors. On the other hand, Sekimoto-Tawada model has been shown to give the diffusion coefficient that is independent of filament length, but it comes from the long time correlation whose time scale is proportional to filament length, and our simulations show that such a long correlation time conflicts with the experimental time scales. We conclude that none of the three models do not represent experimental findings. In order to explain the observed anomalous diffusion, we have to seek for the mechanism that should allow both the amplitude and the time scale of the velocity correlation to be independent of the filament length.

q-bio.QM↗

arXiv2007

Velocity correlations in the dense granular shear flows: Effects on energy dissipation and normal stress

We study the effect of pre-collisional velocity correlations on granular shear flow by molecular dynamics simulations of the inelastic hard sphere system. Comparison of the simulations with the kinetic theory reveals that the theory overestimates both the energy dissipation rate and the normal stress in the dense flow region. We find that the relative normal velocity of colliding particles is smaller than that expected from random collisions, and the discrepancies in the dissipation and the normal stress can be adjusted by introducing the idea of the collisional temperature, from which we conclude that the velocity correlation neglected in the kinetic theory is responsible for the discrepancies. Our analysis of the distributions of the pre-collisional velocity suggests that the correlation grows through multiple inelastic collisions during the time scale of the inverse of the shear rate. As for the shear stress, the discrepancy is also found in the dense region, but it depends strongly on the particle inelasticity.

cond-mat.stat-mech↗

arXiv2006

Slow relaxation in the two dimensional electron plasma under the strong magnetic field

We study slow relaxation processes in the point vortex model for the two-dimensional pure electron plasma under the strong magnetic field. By numerical simulations, it is shown that, from an initial state, the system undergoes the fast relaxation to a quasi-stationary state, and then goes through the slow relaxation to reach a final state. From analysis of simulation data, we find (i) the time scale of the slow relaxation increases linearly to the number of electrons if it is measured by the unit of the bulk rotation time, (ii) during the slow relaxation process, each electron undergoes an superdiffusive motion, and (iii) the superdiffusive motion can be regarded as the Levy flight, whose step size distribution is of the power law. The time scale that each electron diffuses over the system size turns out to be much shorter than that of the slow relaxation, which suggests that the correlation among the superdiffusive trajectories is important in the slow relaxation process.

cond-mat.stat-mech↗

arXiv2006

Boundary Dynamics of Sweeping Interface

A new type of boundary dynamics is proposed to describe the interface that sweeps space to collect distributed material. Based upon geometrical consideration on a simple physical process representing a certain experiment, the dynamics is formulated as the small diffusion limit of Mullins-Sekerka problem of crystal growth. It is demonstrated that a steadily extending finger solution exists for a finite range of propagation speed, but numerical simulations suggest they are unstable and the interface shows a complex time development.

cond-mat.soft↗

arXiv2006

Lattice Model of Sweeping Interface for Drying Process in Water-Granule Mixture

Based on the invasion percolation model, a lattice model for the sweeping interface dynamics is constructed to describe the pattern forming process by a sweeping interface upon drying the water-granule mixture. The model is shown to produce labyrinthine patterns similar to those found in the experiment[Yamazaki and Mizuguchi, J. Phys. Soc. Jpn. \textbf{69} (2000) 2387]. Upon changing the initial granular density, resulting patterns undergo the percolation transition, but estimated critical exponents are different from those of the conventional percolation. Loopless structure of clusters in the patterns produced by the sweeping dynamics seems to influence the nature of the transition.

cond-mat.stat-mech↗

arXiv2006

Quasi-stationary States of Two-Dimensional Electron Plasma Trapped in Magnetic Field

We have performed numerical simulations on a pure electron plasma system under a strong magnetic field, in order to examine quasi-stationary states that the system eventually evolves into. We use ring states as the initial states, changing the width, and find that the system evolves into a vortex crystal state from a thinner-ring state while a state with a single-peaked density distribution is obtained from a thicker-ring initial state. For those quasi-stationary states, density distribution and macroscopic observables are defined on the basis of a coarse-grained density field. We compare our results with experiments and some statistical theories, which include the Gibbs-Boltzmann statistics, Tsallis statistics, the fluid entropy theory, and the minimum enstrophy state. From some of those initial states, we obtain the quasi-stationary states which are close to the minimum enstrophy state, but we also find that the quasi-stationary states depend upon initial states, even if the initial states have the same energy and angular momentum, which means the ergodicity does not hold.

cond-mat.stat-mech↗

arXiv2005

Phase Field Model for Dynamics of Sweeping Interface

Motivated by the drying pattern experiment by Yamazaki and Mizuguchi[J. Phys. Soc. Jpn. {\bf 69} (2000) 2387], we propose the dynamics of sweeping interface, in which material distributed over a region is swept by a moving interface. A model based on a phase field is constructed and results of numerical simulations are presented for one and two dimensions. Relevance of the present model to the drying experiment is discussed.

cond-mat.stat-mech↗

arXiv2005

Bagnold scaling, density plateau, and kinetic theory analysis of dense granular flow

We investigate the bulk rheology of dense granular flow down a rough slope, where the density profile has been found to show a plateau except for the boundary layers in simulations [Silbert {\it et al.}, Phys. Rev. E {\bf 64}, 051302 (2001)]. It is demonstrated that both the Bagnold scaling and the framework of kinetic theory are applicable in the bulk, which allows us to extract the constitutive relations from simulation data. The detailed comparison of our data with the kinetic theory shows quantitative agreement for the normal and shear stresses, but there exists slight discrepancy in the energy dissipation, which causes rather large disagreement in the kinetic theory analysis of the flow.

cond-mat.stat-mech↗

arXiv2004

Isostaticity and Mechanical Response of Two-Dimensional Granular Piles

We numerically study the static structure and the mechanical response of two-dimensional granular piles. The piles consist of polydisperse disks with and without friction. Special attention is paid for the rigid grain limit by examining the systems with various disk elasticities. It is shown that the static pile structure of frictionless disks becomes isostatic in the rigid limit, while the isostaticity of frictional pile depends on the pile forming procedure, but in the case of the infinite friction is effective, the structure becomes very close to isostatic in the rigid limit. The mechanical response of the piles are studied by infinitesimally displacing one of the disks at the bottom. It is shown that the total amount of the displacement in the pile caused by the perturbation diverges in the case of frictionless pile as it becomes isostatic, while the response remains finite for the frictional pile. In the frictionless isostatic pile, the displacement response in each sample behaves rather complicated way, but its average shows wave like propagation.

cond-mat.soft↗

arXiv2003

Isostaticity in two dimensional pile of rigid disks

We study the static structure of piles made of polydisperse disks in the rigid limit with and without friction using molecular dynamic simulations for various elasticities of the disks and pile preparation procedures. The coordination numbers are calculated to examine the isostaticity of the pile structure. For the frictionless pile, it is demonstrated that the coordination number converges to 4 in the rigid limit, which implies that the structure of rigid disk pile is isostatic. On the other hand, for the frictional case with the infinite friction constant, the coordination number depends on the preparation procedure of the pile, but we find that the structure becomes very close to isostatic with the coordination number close to 3 in the rigid limit when the pile is formed through the process that tends to make a pile of random configuration.

cond-mat.soft↗

arXiv2003

Effects of Velocity Correlation on Early Stage of Free Cooling Process of Inelastic Hard Sphere System

The free cooling process in the inelastic hard sphere system is studied by analysing the data from large scale molecular dynamics simulations on a three dimensional system. The initial energy decay, the velocity distribution function, and the velocity correlation functions are calculated to be compared with theoretical predictions. The energy decay rate in the homogeneous cooling state is slightly but distinctively smaller than that expected from the independent collision assumption. The form of the one particle velocity distribution is found not to be stationary. These contradict to the predictions of the kinetic theory based on the Enskog-Boltzmann equation and suggest that the velocity correlation is already important in the early stage of homogeneous cooling state. The energy decay rate is analysed in terms of the velocity correlation.

cond-mat.stat-mech↗

arXiv2003

Linear stability analysis of rapid granular flow on a slope and density wave formation

The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable against the long-wavelength perturbations longitudinal to the flow direction for certain parameter ranges to form the density wave, in contrast with the finite wavelength instability against the transverse perturbation (Forterre & Pouliquen 2002). It is shown that the instability can be understood as the the long-wave instability of the kinematic waves in a quasi-one dimensional system. The results are compared with our previous molecular dynamics simulations (Mitarai & Nakanishi 2001), where the spontaneous density wave formation has been found.

cond-mat.stat-mech↗

arXiv2003

Basin structure in the two-dimensional dissipative circle map

Fractal basin structure in the two-dimensional dissipative circle map is examined in detail. Numerically obtained basin appears to be riddling in the parameter region where two periodic orbits co-exist near a boundary crisis, but it is shown to consist of layers of thin bands.

nlin.CD↗

arXiv2003

Hard-sphere limit of soft-sphere model for granular materials: Stiffness dependence of steady granular flow

Dynamical behavior of steady granular flow is investigated numerically in the inelastic hard sphere limit of the soft sphere model. We find distinctively different limiting behaviors for the two flow regimes, i.e., the collisional flow and the frictional flow. In the collisional flow, the hard sphere limit is straightforward; the number of collisions per particle per unit time converges to a finite value and the total contact time fraction with other particles goes to zero. For the frictional flow, however, we demonstrate that the collision rate diverges as the power of the particle stiffness so that the time fraction of the multiple contacts remains finite even in the hard sphere limit although the contact time fraction for the binary collisions tends to zero.

cond-mat.stat-mech↗

arXiv2002

Velocity Distribution of Inelastic Granular Gas in Homogeneous Cooling State

The velocity distribution of inelastic granular gas is examined numerically on two dimensional hard disk system in nearly elastic regime using molecular dynamical simulations. The system is prepared initially in the equilibrium state with the Maxwell-Boltzmann distribution, then after a several inelastic collisions per particle, the system falls in the state that the Boltzmann equation predicts with the stationary form of velocity distribution. It turns out, however, that due to the velocity correlation the form of the distribution function does not stay time-independent, but is gradually returning to the Maxwellian immediately after the initial transient till the clustering instability sets in. It shows that, even in the homogeneous cooling state, the velocity correlation in the inelastic system invalidates the assumption of molecular chaos and the prediction by the Boltzmann equation fails.

cond-mat.stat-mech↗

arXiv2002

Riddled-like Basin in Two-Dimensional Map for Bouncing Motion of an Inelastic Particle on a Vibrating Board

Motivated by bouncing motion of an inelastic particle on a vibrating board, a simple two-dimensional map is constructed and its behavior is studied numerically. In addition to the typical route to chaos through a periodic doubling bifurcation, we found peculiar behavior in the parameter region where two stable periodic attractors coexist. A typical orbit in the region goes through chaotic motion for an extended transient period before it converges into one of the two periodic attractors. The basin structure in this parameter region is almost riddling and the fractal dimension of the basin boundary is close to two, {\it i.e.}, the dimension of the phase space.

nlin.CD↗

arXiv2002

Collisional Granular Flow as a Micropolar Fluid

We show that a micropolar fluid model successfully describes collisional granular flows on a slope. A micropolar fluid is the fluid with internal structures in which coupling between the spin of each particle and the macroscopic velocity field is taken into account. It is a hydrodynamical framework suitable for granular systems which consists of particles with macroscopic size. We demonstrate that the model equations can quantitatively reproduce the velocity and the angular velocity profiles obtained from the numerical simulation of the collisional granular flow on a slope using a simple estimate for the parameters in the theory.

cond-mat.stat-mech↗