michio otsuki - Academia.edu (original) (raw)
Papers by michio otsuki
Journal of the Physical Society of Japan
Collective motion of caged particles is studied by calculating correlations of elongations (i.e. ... more Collective motion of caged particles is studied by calculating correlations of elongations (i.e. excess distances between two tagged particles) in a one-dimensional colloidal system, with the focus on the effect of overtaking events by which particles can hop out of the cage. It is shown analytically and verified numerically that the effect of overtaking is more prominent in shorter lengthscales, and also that the two-time elongation correlation exhibits ageing behavior due to overtaking.
Entropy
Subdiffusion is commonly observed in liquids with high density or in restricted geometries, as th... more Subdiffusion is commonly observed in liquids with high density or in restricted geometries, as the particles are constantly pushed back by their neighbors. Since this “cage effect” emerges from many-body dynamics involving spatiotemporally correlated motions, the slow diffusion should be understood not simply as a one-body problem but as a part of collective dynamics, described in terms of space–time correlations. Such collective dynamics are illustrated here by calculations of the two-particle displacement correlation in a system of repulsive Brownian particles confined in a (quasi-)one-dimensional channel, whose subdiffusive behavior is known as the single-file diffusion (SFD). The analytical calculation is formulated in terms of the Lagrangian correlation of density fluctuations. In addition, numerical solutions to the Langevin equation with large but finite interaction potential are studied to clarify the effect of overtaking. In the limiting case of the ideal SFD without overta...
AIP Conference Proceedings, 2008
The spatial correlation function of the momentum density in the three-dimensional dilute sheared ... more The spatial correlation function of the momentum density in the three-dimensional dilute sheared granular fluids is theoretically investigated. The existence of the long-range correlation is verified through both analytic calculation and numerical simulation.
Journal of Statistical Mechanics Theory and Experiment, Jul 30, 2009
The long-time behaviors of the velocity autocorrelation function (VACF) for sheared fluids are in... more The long-time behaviors of the velocity autocorrelation function (VACF) for sheared fluids are investigated theoretically and numerically. It is found the existence of the cross-overs of VACF from t −d/2 to t −d in sheared fluids of elastic particles without any thermostat, and from t −d/2 to t −(d+2)/2 in both sheared fluids of elastic particles with a thermostat and sheared granular fluids, where d is the spatial dimension. The validity of the predictions has been confirmed by our numerical simulations.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2009
Spatial correlations in sheared isothermal liquids for both elastic and granular cases are theore... more Spatial correlations in sheared isothermal liquids for both elastic and granular cases are theoretically investigated. Using the generalized fluctuating hydrodynamics, correlation functions for both the microscopic scale and the macroscopic scale are obtained. We find the existence of long-range correlations obeying power laws. The validity of our theoretical predictions has been verified from molecular-dynamics simulation.
A nonequilibrium liquid theory for uniformly sheared granular liquids is developed starting from ... more A nonequilibrium liquid theory for uniformly sheared granular liquids is developed starting from SLLOD equations. We derive a generalized Green-Kubo formula and demonstrate that it yields the nonequilibrium steady-state average which is essentially independent of the choice of the initial condition. It is also shown that the fluctuating hydrodynamics can be derived from Mori-type equations for density and current-density fluctuations if one considers a weak-shear and small-dissipation limit along with the Markovian approximation.
Progress of Theoretical Physics Supplement, 2012
The direct-interaction approximation, which is a self-consistent closure theory for calculating t... more The direct-interaction approximation, which is a self-consistent closure theory for calculating the correlation function of the velocity Fourier coefficients of turbulence, is applied to the nonlinear Langevin equation for glassy systems. We discuss the resultant closure equations in relation to the mode-coupling theory and the fluctuation-dissipation theorem.
Progress of Theoretical Physics Supplement, 2012
We investigate the rheology of sheared granular materials near the jamming transition point. We n... more We investigate the rheology of sheared granular materials near the jamming transition point. We numerically determine the values of the critical fraction and the exponents for the jamming transition using a finite size scaling and the nonlinear minimization method known as the Levenberg-Marquardt algorithm. The exponents are close to our previous theoretical prediction, but there is a small discrepancy, if the critical point is independently determined. §1. Introduction Athermal disordered materials such as colloidal suspensions, 1) foams, 2) and granular materials 3) behave as dense liquids when the density is lower than a critical value, while they behave as amorphous solids when the density exceeds the critical value. This rigidity transition is known as the jamming transition, which could be a key concept to characterize disorder materials even for glassy materials. 4) Near the jamming transition point, such materials show critical behavior, where the pressure, the elastic moduli, and the characteristic frequency of the density of state exhibit power law dependences on the distance from the transition point. 5), 6), 7) In particular, the critical scaling law characterized by a set of critical exponents, similar to those in thermal critical phenomena, is observed in the rheology of athermal disordered materials, 8), 9), 10), 11), 12), 13), 14), 15), 16), 17) though the transition becomes discontinuous under the existence of friction for granular materials. 18) The precise values of the critical exponents, however, are still controversial because the values of them are inconsistent among the researchers. 8), 9), 10), 11), 12), 13), 14), 15), 16), 17), 18) In this paper, we try to numerically determine the critical exponents near the jamming transition for granular materials under the plane shear using a nonlinear minimization procedure and a finite size scaling for the critical fraction. The contents of this paper are organized as follows. Previous results for the critical rheology of athermal disordered materials are summarized in the next section. In § 3, the details of our numerical results are presented, where we explain models and their setup in § 3.1, and the critical fraction and the exponents are respectively determined in § 3.2 and § 3.3. In § 4, we discuss and conclude our results. §2. Review of scaling properties near the jamming transition Let us consider a sheared athermal system characterized by the packing fraction φ and the shear rateγ. We restrict our interest to systems consisting of repulsive particles in which the normal interaction force between contacting particles is pro
Physical Review E, 2013
Dynamics of a one-dimensional system of Brownian particles with short-range repulsive interaction... more Dynamics of a one-dimensional system of Brownian particles with short-range repulsive interaction (diameter σ) is studied with a liquid-theoretical approach. The mean square displacement, the two-particle displacement correlation, and the overlap-density-based generalized susceptibility are calculated analytically by way of the Lagrangian correlation of the interparticulate space, instead of the Eulerian correlation of density that is commonly used in the standard mode-coupling theory. In regard to the mean square displacement, the linear analysis reproduces the established result on the asymptotic subdiffusive behavior of the system. A finite-time correction is given by incorporating the effect of entropic nonlinearity with a Lagrangian version of mode-coupling theory. The notorious difficulty in derivation of the mode-coupling theory concerning violation of the fluctuation-dissipation theorem is found to disappear by virtue of the Lagrangian description. The Lagrangian description also facilitates analytical calculation of four-point correlations in the space-time, such as the twoparticle displacement correlation. The two-particle displacement correlation, which is asymptotically self-similar in the space-time, illustrates how the cage effect confines each particle within a short radius on one hand and creates collective motion of numerous particles on the other hand. As the time elapses, the correlation length grows unlimitedly, and the generalized susceptibility based on the overlap density converges to a finite value which is an increasing function of the density. The distribution function behind these dynamical four-point correlations and its extension to threedimensional cases, respecting the tensorial character of the two-particle displacement correlation, are also discussed.
Journal of the Physical Society of Japan, 2011
ABSTRACT The problem of one-dimensional diffusion is studied for Brownian particles with short-ra... more ABSTRACT The problem of one-dimensional diffusion is studied for Brownian particles with short-range repulsive interaction. The adoption of the continuous label variable as the spatial coordinate, inspired by the Lagrangian description in fluid mechanics, is shown to be effective in correct prediction of the anomalous diffusion, in which the mean square displacement of the particle grows in proportion to \sqrt{t}. The method is also applicable to the cases in which an external field is present. This suggests potential usefulness of the label variable formulation in describing the slow dynamics of glassy systems.
Journal of the Physical Society of Japan, 2008
We perform molecular dynamics simulations in order to examine the rheological transition of fluid... more We perform molecular dynamics simulations in order to examine the rheological transition of fluids confined in a small space. By performing finite-size scaling analysis, we demonstrate that this rheological transition results from the competition between the system size and the length scale of cooperative particle motion.
The European Physical Journal E, 2011
Arxiv preprint arXiv:0906.1930, 2009
We derive the generalized Green-Kubo relation and an integral form of the fluctuation theorem tha... more We derive the generalized Green-Kubo relation and an integral form of the fluctuation theorem that apply to uniformly sheared granular systems in which microscopic time-reversal symmetry is broken. The former relation provides an exact representation of nonequilibrium steady-...
Journal of the Physical Society of Japan
Collective motion of caged particles is studied by calculating correlations of elongations (i.e. ... more Collective motion of caged particles is studied by calculating correlations of elongations (i.e. excess distances between two tagged particles) in a one-dimensional colloidal system, with the focus on the effect of overtaking events by which particles can hop out of the cage. It is shown analytically and verified numerically that the effect of overtaking is more prominent in shorter lengthscales, and also that the two-time elongation correlation exhibits ageing behavior due to overtaking.
Entropy
Subdiffusion is commonly observed in liquids with high density or in restricted geometries, as th... more Subdiffusion is commonly observed in liquids with high density or in restricted geometries, as the particles are constantly pushed back by their neighbors. Since this “cage effect” emerges from many-body dynamics involving spatiotemporally correlated motions, the slow diffusion should be understood not simply as a one-body problem but as a part of collective dynamics, described in terms of space–time correlations. Such collective dynamics are illustrated here by calculations of the two-particle displacement correlation in a system of repulsive Brownian particles confined in a (quasi-)one-dimensional channel, whose subdiffusive behavior is known as the single-file diffusion (SFD). The analytical calculation is formulated in terms of the Lagrangian correlation of density fluctuations. In addition, numerical solutions to the Langevin equation with large but finite interaction potential are studied to clarify the effect of overtaking. In the limiting case of the ideal SFD without overta...
AIP Conference Proceedings, 2008
The spatial correlation function of the momentum density in the three-dimensional dilute sheared ... more The spatial correlation function of the momentum density in the three-dimensional dilute sheared granular fluids is theoretically investigated. The existence of the long-range correlation is verified through both analytic calculation and numerical simulation.
Journal of Statistical Mechanics Theory and Experiment, Jul 30, 2009
The long-time behaviors of the velocity autocorrelation function (VACF) for sheared fluids are in... more The long-time behaviors of the velocity autocorrelation function (VACF) for sheared fluids are investigated theoretically and numerically. It is found the existence of the cross-overs of VACF from t −d/2 to t −d in sheared fluids of elastic particles without any thermostat, and from t −d/2 to t −(d+2)/2 in both sheared fluids of elastic particles with a thermostat and sheared granular fluids, where d is the spatial dimension. The validity of the predictions has been confirmed by our numerical simulations.
Physical review. E, Statistical, nonlinear, and soft matter physics, 2009
Spatial correlations in sheared isothermal liquids for both elastic and granular cases are theore... more Spatial correlations in sheared isothermal liquids for both elastic and granular cases are theoretically investigated. Using the generalized fluctuating hydrodynamics, correlation functions for both the microscopic scale and the macroscopic scale are obtained. We find the existence of long-range correlations obeying power laws. The validity of our theoretical predictions has been verified from molecular-dynamics simulation.
A nonequilibrium liquid theory for uniformly sheared granular liquids is developed starting from ... more A nonequilibrium liquid theory for uniformly sheared granular liquids is developed starting from SLLOD equations. We derive a generalized Green-Kubo formula and demonstrate that it yields the nonequilibrium steady-state average which is essentially independent of the choice of the initial condition. It is also shown that the fluctuating hydrodynamics can be derived from Mori-type equations for density and current-density fluctuations if one considers a weak-shear and small-dissipation limit along with the Markovian approximation.
Progress of Theoretical Physics Supplement, 2012
The direct-interaction approximation, which is a self-consistent closure theory for calculating t... more The direct-interaction approximation, which is a self-consistent closure theory for calculating the correlation function of the velocity Fourier coefficients of turbulence, is applied to the nonlinear Langevin equation for glassy systems. We discuss the resultant closure equations in relation to the mode-coupling theory and the fluctuation-dissipation theorem.
Progress of Theoretical Physics Supplement, 2012
We investigate the rheology of sheared granular materials near the jamming transition point. We n... more We investigate the rheology of sheared granular materials near the jamming transition point. We numerically determine the values of the critical fraction and the exponents for the jamming transition using a finite size scaling and the nonlinear minimization method known as the Levenberg-Marquardt algorithm. The exponents are close to our previous theoretical prediction, but there is a small discrepancy, if the critical point is independently determined. §1. Introduction Athermal disordered materials such as colloidal suspensions, 1) foams, 2) and granular materials 3) behave as dense liquids when the density is lower than a critical value, while they behave as amorphous solids when the density exceeds the critical value. This rigidity transition is known as the jamming transition, which could be a key concept to characterize disorder materials even for glassy materials. 4) Near the jamming transition point, such materials show critical behavior, where the pressure, the elastic moduli, and the characteristic frequency of the density of state exhibit power law dependences on the distance from the transition point. 5), 6), 7) In particular, the critical scaling law characterized by a set of critical exponents, similar to those in thermal critical phenomena, is observed in the rheology of athermal disordered materials, 8), 9), 10), 11), 12), 13), 14), 15), 16), 17) though the transition becomes discontinuous under the existence of friction for granular materials. 18) The precise values of the critical exponents, however, are still controversial because the values of them are inconsistent among the researchers. 8), 9), 10), 11), 12), 13), 14), 15), 16), 17), 18) In this paper, we try to numerically determine the critical exponents near the jamming transition for granular materials under the plane shear using a nonlinear minimization procedure and a finite size scaling for the critical fraction. The contents of this paper are organized as follows. Previous results for the critical rheology of athermal disordered materials are summarized in the next section. In § 3, the details of our numerical results are presented, where we explain models and their setup in § 3.1, and the critical fraction and the exponents are respectively determined in § 3.2 and § 3.3. In § 4, we discuss and conclude our results. §2. Review of scaling properties near the jamming transition Let us consider a sheared athermal system characterized by the packing fraction φ and the shear rateγ. We restrict our interest to systems consisting of repulsive particles in which the normal interaction force between contacting particles is pro
Physical Review E, 2013
Dynamics of a one-dimensional system of Brownian particles with short-range repulsive interaction... more Dynamics of a one-dimensional system of Brownian particles with short-range repulsive interaction (diameter σ) is studied with a liquid-theoretical approach. The mean square displacement, the two-particle displacement correlation, and the overlap-density-based generalized susceptibility are calculated analytically by way of the Lagrangian correlation of the interparticulate space, instead of the Eulerian correlation of density that is commonly used in the standard mode-coupling theory. In regard to the mean square displacement, the linear analysis reproduces the established result on the asymptotic subdiffusive behavior of the system. A finite-time correction is given by incorporating the effect of entropic nonlinearity with a Lagrangian version of mode-coupling theory. The notorious difficulty in derivation of the mode-coupling theory concerning violation of the fluctuation-dissipation theorem is found to disappear by virtue of the Lagrangian description. The Lagrangian description also facilitates analytical calculation of four-point correlations in the space-time, such as the twoparticle displacement correlation. The two-particle displacement correlation, which is asymptotically self-similar in the space-time, illustrates how the cage effect confines each particle within a short radius on one hand and creates collective motion of numerous particles on the other hand. As the time elapses, the correlation length grows unlimitedly, and the generalized susceptibility based on the overlap density converges to a finite value which is an increasing function of the density. The distribution function behind these dynamical four-point correlations and its extension to threedimensional cases, respecting the tensorial character of the two-particle displacement correlation, are also discussed.
Journal of the Physical Society of Japan, 2011
ABSTRACT The problem of one-dimensional diffusion is studied for Brownian particles with short-ra... more ABSTRACT The problem of one-dimensional diffusion is studied for Brownian particles with short-range repulsive interaction. The adoption of the continuous label variable as the spatial coordinate, inspired by the Lagrangian description in fluid mechanics, is shown to be effective in correct prediction of the anomalous diffusion, in which the mean square displacement of the particle grows in proportion to \sqrt{t}. The method is also applicable to the cases in which an external field is present. This suggests potential usefulness of the label variable formulation in describing the slow dynamics of glassy systems.
Journal of the Physical Society of Japan, 2008
We perform molecular dynamics simulations in order to examine the rheological transition of fluid... more We perform molecular dynamics simulations in order to examine the rheological transition of fluids confined in a small space. By performing finite-size scaling analysis, we demonstrate that this rheological transition results from the competition between the system size and the length scale of cooperative particle motion.
The European Physical Journal E, 2011
Arxiv preprint arXiv:0906.1930, 2009
We derive the generalized Green-Kubo relation and an integral form of the fluctuation theorem tha... more We derive the generalized Green-Kubo relation and an integral form of the fluctuation theorem that apply to uniformly sheared granular systems in which microscopic time-reversal symmetry is broken. The former relation provides an exact representation of nonequilibrium steady-...