arXiv subjects

Hidetsugu Sakaguchi

Publications and source records attributed to Hidetsugu Sakaguchi.

At least 91 records · Page 5Linked to original sources

arXiv2009

Splitting instability of cellular structures in the Ginzburg-Landau model under the feedback control

We study numerically a Ginzburg-Landau type equation for micelles in two dimensions. The domain size and the interface length of a cellular structure are controlled by two feedback terms. The deformation and the successive splitting of the cellular structure are observed when the controlled interface length is increased. The splitting instability is further investigated using coupled mode equations to understand the bifurcation structure.

cond-mat.soft↗

arXiv2009

Ratio control in a cascade model of cell differentiation

We propose a kind of reaction-diffusion equations for cell differentiation, which exhibits the Turing instability. If the diffusivity of some variables is set to be infinity, we get coupled competitive reaction-diffusion equations with a global feedback term. The size ratio of each cell type is controlled by a system parameter in the model. Finally, we extend the model to a cascade model of cell differentiation. A hierarchical spatial structure appears as a result of the cell differentiation. The size ratio of each cell type is also controlled by the system parameter.

q-bio.CB↗

arXiv2009

Delocalization transition of a small number of particles in a box with periodic boundary conditions

We perform molecular dynamics simulation of a small number of particles in a box with periodic boundary conditions from a view point of chaotic dynamical systems. There is a transition at a critical energy E_c that each particle is confined in each unit cell for E E_c. We find an anomalous behavior of the jump frequency above the critical energy in a two-particle system, which is related with the infinitely alternating stability change of the straight motion passing through a saddle point. We find simultaneous jump motions just above the critical energy in a four-particle system and sixteen-particle system, which is also related with the motion passing through the saddle point.

cond-mat.stat-mech↗

arXiv2008

Scaling Relations of Viscous Fingers in Anisotropic Hele-Shaw Cells

Viscous fingers in a channel with surface tension anisotropy are numerically studied. Scaling relations between the tip velocity v, the tip radius and the pressure gradient are investigated for two kinds of boundary conditions of pressure, when v is sufficiently large. The power-law relations for the anisotropic viscous fingers are compared with two-dimensional dendritic growth. The exponents of the power-law relations are theoretically evaluated.

cond-mat.soft↗

arXiv2008

Creation and Reproduction of Model Cells with Semipermeable Membrane

A high activity of reactions can be confined in a model cell with a semipermeable membrane in the Schlögl model. It is interpreted as a model of primitive metabolism in a cell. We study two generalized models to understand the creation of primitive cell systems conceptually from the view point of the nonlinear-nonequilibrium physics. In the first model, a single-cell system with a highly active state confined by a semipermeable membrane is spontaneously created from an inactive homogeneous state by a stochastic jump process. In the second model, many cell structures are reproduced from a single cell, and a multicellular system is created.

nlin.AO↗

arXiv2008

Synchronization in coupled phase oscillators

We make a short review about the synchronization in coupled phase oscillator models. Next, we study the common-noise-induced synchronization among active rotators. At an intermediate noise strength, the noise-induced synchronization takes place most effectively, which is analogous to the stochastic resonance. Finally, we study the synchronization of coupled phase oscillators with nonvariational interaction on scale-free networks. We find a sharp transition and a weak hysteresis in the nonvariational systems. The sharp transition is found also in the mean-field approximation.

nlin.AO↗

arXiv2007

Soliton turbulences in the complex Ginzburg-Landau equation

We study spatio-temporal chaos in the complex Ginzburg-Landau equation in parameter regions of weak amplification and viscosity. Turbulent states involving many soliton-like pulses appear in the parameter range, because the complex Ginzburg-Landau equation is close to the nonlinear Schrödinger equation. We find that the distributions of amplitude and wavenumber of pulses depend only on the ratio of the two parameters of the amplification and the viscosity. This implies that a one-parameter family of soliton turbulence states characterized by different distributions of the soliton parameters exists continuously around the completely integrable system.

nlin.PS↗

arXiv2006

Generalized Einstein Relation for Brownian Motion in Tilted Periodic Potential

A generalized Einstein relation is studied for Brownian motion in a tilted potential. The exact form of the diffusion constant of the Brownian motion is compared with the generalized Einstein relation. The generalized Einstein relation is a good approximation in a parameter range where the Brownian motion exhibits stepwise motion.

cond-mat.stat-mech↗

arXiv2006

Two-dimensional dark soliton in the nonlinear Schroedinger equation

Two-dimensional gray solitons to the nonlinear Schroedinger equation are numerically created by two processes to show its robustness. One is transverse instability of a one-dimensional gray soliton, and another is a pair annihilation of a vortex and an antivortex. The two-dimensional dark solitons are anisotropic and propagate in a certain direction. The two-dimensional dark soliton is stable against the head-on collision. The effective mass of the two-dimensional dark soliton is evaluated from the motion in a harmonic potential.

nlin.PS↗

arXiv2006

Gap solitons in quasiperiodic optical lattices

Families of solitons in one- and two-dimensional (1D and 2D) Gross-Pitaevskii equations with the repulsive nonlinearity and a potential of the quasicrystallic type are constructed (in the 2D case, the potential corresponds to a five-fold optical lattice). Stable 1D solitons in the weak potential are explicitly found in three bandgaps. These solitons are mobile, and they collide elastically. Many species of tightly bound 1D solitons are found in the strong potential, both stable and unstable (unstable ones transform themselves into asymmetric breathers). In the 2D model, families of both fundamental and vortical solitons are found and are shown to be stable.

cond-mat.soft↗

arXiv2006

Efficiency and Fluctuation in Tight-Coupling Model of Molecular Motor

A simple tight-coupling model of a molecular chemical engine is proposed. The efficiency of the chemical engine and its average velocity can be explicitly calculated. The diffusion constant is evaluated approximately using the fluctuation theorem. Langevin simulations with stochastic boundary conditions are performed and the numerical results are compared with theoretical calculations.

cond-mat.stat-mech↗

arXiv2006

Reaction-Diffusion System in a Vesicle with Semi-Permeable Membrane

We study the Schloegl model in a vesicle with semi-permeable membrane. The diffusion constant takes a smaller value in the membrane region, which prevents the outflow of self-catalytic product. A nonequilibrium state is stably maintained inside of the vesicle. Nutrients are absorbed and waste materials are exhausted through the membrane by diffusion. It is interpreted as a model of primitive metabolism in a cell.

cond-mat.stat-mech↗

arXiv2006

Instability of synchronized motion in nonlocally coupled neural oscillators

We study nonlocally coupled Hodgkin-Huxley equations with excitatory and inhibitory synaptic coupling. We investigate the linear stability of the synchronized solution, and find numerically various nonuniform oscillatory states such as chimera states, wavy states, clustering states, and spatiotemporal chaos as a result of the instability.

q-bio.NC↗

arXiv2006

Two-dimensional solitons in the Gross-Pitaevskii equation with spatially modulated nonlinearity

We introduce a dynamical model of a Bose-Einstein condensate based on the 2D Gross-Pitaevskii equation, in which the nonlinear coefficient is a function of radius. The model describes a situation with spatial modulation of the negative atomic scattering length, via the Feshbach resonance controlled by a properly shaped magnetic of optical field. We focus on the configuration with the nonlinear coefficient different from zero in a circle or annulus, including the case of a narrow ring. Two-dimensional axisymmetric solitons are found in a numerical form, and also by means of a variational approximation; for an infinitely narrow ring, the soliton is found in an exact form (in the latter case, exact solitons are also found in a two-component model). A stability region for the solitons is identified by means of numerical and analytical methods. In particular, if the nonlinearity is supported on the annulus, the upper stability border is determined by azimuthal perturbations; the stability region disappears if the ratio of the inner and outer radii of the annulus exceeds a critical value 0.47. The model gives rise to bistability, as the stationary solitons coexist with stable axisymmetric breathers, whose stability region extends to higher values of the norm than that of the static solitons. The collapse threshold strongly increases with the radius of the inner hole of the annulus. Vortex solitons are found too, but they are unstable.

cond-mat.supr-con↗

arXiv2005

Higher-order vortex solitons, multipoles, and supervortices on a square optical lattice

We predict new generic types of vorticity-carrying soliton complexes in a class of physical systems including an attractive Bose-Einstein condensate in a square optical lattice (OL) and photonic lattices in photorefractive media. The patterns include ring-shaped higher-order vortex solitons and supervortices. Stability diagrams for these patterns, based on direct simulations, are presented. The vortex ring solitons are stable if the phase difference Δϕbetween adjacent solitons in the ring is larger than π/2, while the supervortices are stable in the opposite case, Δϕ<π/2. A qualitative explanation to the stability is given.

cond-mat.other↗

arXiv2005

Dynamic Scaling of an Adsorption-Diffusion Process on Fractals

A dynamic scaling of a diffusion process involving the Langmuir type adsorption is studied. We find dynamic scaling functions in one and two dimensions and compare them with direct numerical simulations, and we further study the dynamic scaling law on fractal surfaces. The adsorption-diffusion process obeys the fracton dynamics on the fractal surfaces.

cond-mat.stat-mech↗

arXiv2004

Resonant nonlinearity management for nonlinear-Schrödinger solitons

We consider effects of a periodic modulation of the nonlinearity coefficient on fundamental and higher-order solitons in the one-dimensional NLS equation, which is an issue of direct interest to Bose-Einstein condensates in the context of the Feshbach-resonance control, and fiber-optic telecommunications as concerns periodic compensation of the nonlinearity. We find from simulations, and explain by means of a straightforward analysis, that the response of a fundamental soliton to the weak perturbation is resonant, if the modulation frequency $ω$ is close to the intrinsic frequency of the soliton. For higher-order $n$-solitons with $n=2$ and 3, the response to an extremely weak perturbation is also resonant, if $ω$ is close to the corresponding intrinsic frequency. More importantly, a slightly stronger drive splits the 2- or 3-soliton, respectively, into a set of two or three moving fundamental solitons. The dependence of the threshold perturbation amplitude, necessary for the splitting, on $ω$ has a resonant character too. Amplitudes and velocities of the emerging fundamental solitons are accurately predicted, using exact and approximate conservation laws of the perturbed NLS equation.

nlin.PS↗

arXiv2004

Scattering of Solitons and Dark Solitons by Potential Walls in the Nonlinear Schroedinger Equation

Scattering of solitons and dark solitons by potential walls is studied in the nonlinear Schroedinger equation under various conditions. We investigate the conditions under which solitons are split into two solitons at the potential wall. We find that a soliton can be trapped in an interspace between two potential walls. A dark soliton can also be scattered at the potential wall. Similarly to a bright soliton, a dark soliton can pass through more easily the potential wall, as the width of the dark soliton is larger. A dark soliton can run away spontaneously from an interspace between the two potential walls. We also study the motion of a two-dimensional soliton in a two-dimensional quintic nonlinear Schroedinger equation. We find the coherent tunneling through a potential wall, and the refraction corresponding to Newton's refraction theory.

nlin.PS↗