arXiv subjects

Hisao Hayakawa

Publications and source records attributed to Hisao Hayakawa.

At least 73 records · Page 4Linked to original sources

arXiv2016

Granular rotor as a probe for a non-equilibrium bath

This study numerically and analytically investigates the dynamics of a rotor under viscous or dry friction as a non-equilibrium probe of a granular gas. In order to demonstrate the role of the rotor as a probe for a non-equilibrium bath, the molecular dynamics (MD) simulation of the rotor is performed under viscous or dry friction surrounded by a steady granular gas under gravity. A one- to-one map between the velocity distribution function (VDF) of the granular gas and the angular distribution function for the rotor is theoretically derived. The MD simulation demonstrates that the one-to-one map accurately infers the local VDF of the granular gas from the angular VDF of the rotor, and vice versa.

cond-mat.stat-mech↗

arXiv2016

Efficiency at maximum power output for an engine with a passive piston

Efficiency at maximum power (MP) output for an engine with a passive piston without mechanical controls between two reservoirs is theoretically studied. We enclose a hard core gas partitioned by a massive piston in a temperature-controlled container and analyze the efficiency at MP under a heating and cooling protocol without controlling the pressure acting on the piston from outside. We find the following three results: (i) The efficiency at MP for a dilute gas is close to the Chambadal-Novikov-Curzon-Ahlborn (CNCA) efficiency if we can ignore the side wall friction and the loss of energy between a gas particle and the piston, while (ii) the efficiency for a moderately dense gas becomes smaller than the CNCA efficiency even when the temperature difference of reservoirs is small. (iii) Introducing the Onsager matrix for an engine with a passive piston, we verify that the tight coupling condition for the matrix of the dilute gas is satisfied, while that of the moderately dense gas is not satisfied because of the inevitable heat leak. We confirm the validity of these results using the molecular dynamics simulation and introducing an effective mean-field-like model which we call stochastic mean field model.

cond-mat.stat-mech↗

arXiv2016

Active cage model of glassy dynamics

We build up a phenomenological picture in terms of the effective dynamics of a tracer confined in a cage experiencing random hops to capture somec haracteristics of glassy systems. This minimal description exhibits scale invariance properties for the small-displacement distribution that echo experimental observations. We predict the existence of exponential tails as a cross-over between two Gaussian regimes. Moreover, we demonstrate that the onset of glassy behavior is controlled only by two dimensionless numbers: the number of hops occurring during the relaxation of the particle within a local cage, and the ratio of the hopping length to the cage size.

cond-mat.soft↗

arXiv2016

Kinetic theory for dilute cohesive granular gases with a square well potential

We develop the kinetic theory of dilute cohesive granular gases in which the attractive part is described by a square well potential. We derive the hydrodynamic equations from the kinetic theory with the microscopic expressions for the dissipation rate and the transport coefficients. We check the validity of our theory by performing the direct simulation Monte Carlo.

cond-mat.stat-mech↗

arXiv2016

Fulde-Ferrell-Larkin-Ovchinnikov states in a superconducting ring with magnetic fields: Phase diagram and the first-order phase transitions

We find the angular Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states (or the twisted kink crystals) in which a phase and an amplitude of a pair potential modulate simultaneously in a quasi-onedimensional superconducting ring with a static Zeeman magnetic field applied on the ring and static Aharonov-Bohm magnetic flux penetrating the ring. The superconducting ring with magnetic flux produces a persistent current, whereas the Zeeman split of Fermi energy results in the spatial modulation of the pair potential. We show that these two magnetic fields stabilize the FFLO phase in a large parameter region of the magnetic fields. We further draw the phase diagram with the two kinds of first-order phase transitions; one corresponds to phase slips separating the Aharonov-Bohm magnetic flux, and the other separates the number of peaks of the pair amplitude for the Zeeman magnetic field.

cond-mat.supr-con↗

arXiv2015

Drag Law of Two Dimensional Granular Fluids

The drag force law acting on a moving circular disk in a two-dimensional granular medium is analyzed based on the discrete element method (DEM). It is remarkable that the drag force on the moving disk in moderate dense and pure two-dimensional granular medium can be well reproduced by a perfect fluid with separation from the surface of the tracer. A yield force, being independent of the moving speed of the disk, appears if a dry friction between the granular disks and the bottom plate exists. The perfect fluidity is violated in this case. The yield force and the drag force diverge at the jamming point.

cond-mat.soft↗

arXiv2015

Divergence of Viscosity in Jammed Granular Materials: A Theoretical Approach

A theory for jammed granular materials is developed with the aid of a nonequilibrium steady-state distribution function. The approximate nonequilibrium steady-state distribution function is explicitly given in the weak dissipation regime by means of the relaxation time. The theory quantitatively agrees with the results of the molecular dynamics simulation on the critical behavior of the viscosity below the jamming point without introducing any fitting parameter.

cond-mat.soft↗

arXiv2015

Size distribution of particles in Saturn's rings from aggregation and fragmentation

Saturn's rings consist of a huge number of water ice particles, with a tiny addition of rocky material. They form a flat disk, as the result of an interplay of angular momentum conservation and the steady loss of energy in dissipative inter-particle collisions. For particles in the size range from a few centimeters to a few meters, a power-law distribution of radii, $\sim r^{-q}$ with $q \approx 3$, has been inferred; for larger sizes, the distribution has a steep cutoff. It has been suggested that this size distribution may arise from a balance between aggregation and fragmentation of ring particles, yet neither the power-law dependence nor the upper size cutoff have been established on theoretical grounds. Here we propose a model for the particle size distribution that quantitatively explains the observations. In accordance with data, our model predicts the exponent $q$ to be constrained to the interval $2.75 \le q \le 3.5$. Also an exponential cutoff for larger particle sizes establishes naturally with the cutoff-radius being set by the relative frequency of aggregating and disruptive collisions. This cutoff is much smaller than the typical scale of micro-structures seen in Saturn's rings.

astro-ph.EP↗

arXiv2015

Hydrodynamic instabilities in shear flows of cohesive granular particles

We extend the dynamic van der Waals model introduced by A. Onuki [Phys. Rev. Lett. 94, 054501 (2005)] to the description of cohesive granular flows under a plane shear to study their hydrodynamic instabilities. Numerically solving the dynamic van der Waals model, we observe various heterogeneous structures of the density in steady states, where the viscous heating is balanced with the energy dissipation caused by inelastic collisions. Based on the linear stability analysis, we find that the spatial structures are determined by the mean volume fraction, the applied shear rate, and the inelasticity, where the instability is triggered if the system is thermodynamically unstable, i.e. the pressure, $p$, and the volume fraction, $ϕ$, satisfy $\partial p/\partialϕ<0$.

cond-mat.soft↗

arXiv2015

Minimal Model of Stochastic Athermal Systems: Origin of Non-Gaussian Noise

For a wide class of stochastic athermal systems, we derive Langevin-like equations driven by non-Gaussian noise, starting from master equations and developing a new asymptotic expansion. We found an explicit condition whereby the non-Gaussian properties of the athermal noise become dominant for tracer particles associated with both thermal and athermal environments. Furthermore, we derive an inverse formula to infer microscopic properties of the athermal bath from the statistics of the tracer particle. We apply our formulation to a granular motor under viscous friction, and analytically obtain the angular velocity distribution function. Our theory demonstrates that the non-Gaussian Langevin equation is the minimal model of athermal systems.

cond-mat.stat-mech↗

arXiv2014

Non-divergent representation of non-Hermitian operator near the exceptional point with application to a quantum Lorentz gas

We propose a non-singular representation for a non-Hermitian operator even if the parameter space contains exceptional points (EPs), at which the operator cannot be diagonalized and the usual spectral representation ceases to exist. Our representation has a generalized Jordan block form and is written in terms of extended pseudo-eigenstates. Our method is free from a divergence in the spectral representation at EPs, at which multiple eigenvalues and eigenvectors coalesce and the eigenvectors cannot be normalized. Our representation improves the accuracy of numerical calculations of physical quantities near EPs. We also find that our method is applicable to various problems related to EPs in the parameter space of non-Hermitian operators. We demonstrate the usefulness of our representation by investigating Boltzmann's collision operator in a one-dimensional quantum Lorentz gas in the weak coupling approximation.

cond-mat.stat-mech↗

arXiv2014

Rheology of Dense Sheared Granular Liquids

The rheology of dense sheared granular liquids is investigated based on the mode-coupling theory (MCT). This extended MCT includes correlations for the density-current mode as well as the density-density correlation mode, and a self-consistent coupling equation for the energy balance condition. The extended MCT exhibits disappearance of the two-step relaxation of the density-density correlation function, and also successfully reproduces the density dependence of the shear viscosity for volume fractions between 0.50 and 0.60, if we shift the density. However, it predicts unphysical tendency for the granular temperature. The cause of this drawback and the possibilities of its amendment are discussed.

cond-mat.stat-mech↗

arXiv2014

Simulation of cohesive fine powders under a plane shear

Three dimensional molecular dynamics simulations of cohesive dissipative powders under a plane shear are performed. We find the various phases depending on the dimensionless shear rate and the dissipation rate as well as the density. We also find that the shape of clusters depends on the initial condition of velocities of particles when the dissipation is large. Our simple stochastic model reproduces the non-Gaussian velocity distribution function appearing in the coexistence phase of a gas and a plate.

cond-mat.soft↗

arXiv2014

Geometric pumping induced by shear flow in dilute liquid crystalline polymer solutions

We investigate nonlinear rheology of dilute liquid crystalline polymer solutions under time dependent two-directional shear flow. We analyze the Smoluchowski equation, which describes the dynamics of the orientation of a liquid crystalline polymer, by employing technique of the full counting statistics. In the adiabatic limit, we derive the expression for time integrated currents generated by a Berry-like curvature. Using this expression, it is shown that the expectation values of the time-integrated angular velocity of a liquid crystalline polymer and the time-integrated stress tensor are generally not zero even if the time average of the shear rate is zero. The validity of the theoretical calculations is confirmed by direct numerical simulations of the Smoluchowski equation. Nonadiabatic effects are also investigated by simulations and it is found that the time-integrated stress tensor depends on the speed of the modulation of the shear rate if we adopt the isotropic distribution as an initial state.

cond-mat.soft↗

arXiv2014

Asymptotic derivation of Langevin-like equation with non-Gaussian noise and its analytical solution

We asymptotically derive a non-linear Langevin-like equation with non-Gaussian white noise for a wide class of stochastic systems associated with multiple stochastic environments, by developing the expansion method in our previous paper [K. Kanazawa et al., arXiv: 1407.5267 (2014)]. We further obtain a full-order asymptotic formula of the steady distribution function in terms of a large friction coefficient for a non-Gaussian Langevin equation with an arbitrary non-linear frictional force. The first-order truncation of our formula leads to the independent-kick model and the higher-order correction terms directly correspond to the multiple-kicks effect during relaxation. We introduce a diagrammatic representation to illustrate the physical meaning of the high-order correction terms. As a demonstration, we apply our formula to a granular motor under Coulombic friction and get good agreement with our numerical simulations.

cond-mat.stat-mech↗

arXiv2014

Non-adiabatic effect in quantum pumping for a spin-boson system

We clarify the role of non-adiabatic effects in a quantum pumping for a spin-boson system. When we sinusoidally control the temperatures of two reservoirs with π/2 phase difference, we find that the pumping current strongly depends on the initial condition, and thus, the current deviates from that predicted by the adiabatic treatment. We also analytically obtain the contribution of non-adiabatic effects in the pumping current proportional to Ω^3 where Ωis the angular frequency of the temperature control. The validity of the analytic expression is verified by our numerical calculation. Moreover, we extend the steady heat fluctuation theorem to the case for slowly modulated temperatures and large transferred energies.

cond-mat.stat-mech↗

arXiv2014

Avalanche contribution to shear modulus of granular materials

Shear modulus of frictionless granular materials near the jamming transition under oscillatory shear is numerically investigated. It is found that the shear modulus $G$ satisfies a scaling law to interpolate between $G \sim (ϕ- ϕ_J)^{1/2}$ and $G \sim γ_0^{-1/2}(ϕ-ϕ_J)$ for a linear spring model of the elastic interaction between contacting grains, where $ϕ$, $ϕ_J$, and $γ_0$ are, respectively, the volume fraction of grains, the fraction at the jamming point, and the amplitude of the oscillatory shear. The linear relation between the shear modulus and $ϕ- ϕ_J$ can be understood by slip avalanches.

cond-mat.soft↗

arXiv2014

Energy pumping in electrical circuits under avalanche noise

We theoretically study energy pumping processes in an electrical circuit with avalanche diodes, where non-Gaussian athermal noise plays a crucial role. We show that a positive amount of energy (work) can be extracted by an external manipulation of the circuit in a cyclic way, even when the system is spatially symmetric. We discuss the properties of the energy pumping process for both quasi-static and fnite-time cases, and analytically obtain formulas for the amounts of the work and the power. Our results demonstrate the significance of the non-Gaussianity in energetics of electrical circuits.

cond-mat.stat-mech↗