arXiv subjects

T. Arimitsu

Publications and source records attributed to T. Arimitsu.

14 recordsLinked to original sources

arXiv2011

Constitutive equations for granular flow with uniform mean shear and spin fields

Numerical simulations of two-dimensional granular flows under uniform shear and external body torque were performed in order to extract the constitutive equations for the system. The outcome of the numerical simulations is analyzed on the basis of the micropolar fluid model. Uniform mean shear field and mean spin field, which is not subordinate to the vorticity field, are realized in the simulations. The estimates of stresses based on kinetic theory by Lun [Lun, J. Fluid Mech., 1991, 233, 539] are in good agreement with the simulation results for a low area fraction $ν=0.1$ but the agreement becomes weaker as the area fraction gets higher. However, the estimates in the kinetic theory can be fitted to the simulation results up to $ν=0.7$ by renormalizing the coefficient of roughness. For a relatively dense granular flow ($ν=0.8$), the simulation results are also compared with Kanatani's theory [Kanatani, Int. J. Eng. Sci., 1979, 17, 419]. It is found that the dissipation function and its decomposition into the constitutive equations in Kanatani's theory are not consistent with the simulation results.

cond-mat.stat-mech↗

arXiv2005

Multifractal PDF analysis for intermittent systems

The formula for probability density functions (PDFs) has been extended to include PDF for energy dissipation rates in addition to other PDFs such as for velocity fluctuations, velocity derivatives, fluid particle accelerations, energy transfer rates, etc, and it is shown that the formula actually explains various PDFs extracted from direct numerical simulations and experiments performed in a wind tunnel. It is also shown that the formula with appropriate zooming increment corresponding to experimental situation gives a new route to obtain the scaling exponents of velocity structure function, including intermittency exponent, out of PDFs of velocity fluctuations.

cond-mat.stat-mech↗

arXiv2005

Boson and Fermion Brownian Motion

Dynamics of quantum systems which are perturbed by linear coupling to the reservoir stochastically can be studied in terms of quantum stochastic differential equations (for example, quantum stochastic Liouville equation and quantum Langevin equation). To work it out one needs definition of quantum Brownian motion. Since till very recent times only its boson version has been known, in present paper we demonstrate definition which makes possible consideration also for fermion Brownian motion.

math-ph↗

arXiv2003

An Aspect of Granulence in view of Multifractal Analysis

The probability density function of velocity fluctuations of {\em glanulence} observed by Radjai and Roux in their two-dimensional simulation of a slow granular flow under homogeneous quasistatic shearing is studied by the multifractal analysis for fluid turbulence proposed by the present authors.It is shown that the system of granulence and of turbulence have indeed common scaling characteristics.

cond-mat.soft↗

arXiv2003

Harmonious Representation of PDF's reflecting Large Deviations

The framework of multifractal analysis (MFA) is distilled to the most sophisticated one. Within this transparent framework, it is shown that the harmonious representation of MFA utilizing two distinct Tsallis distribution functions, one for the tail part of probability density function (PDF) and the other for its center part, explains the recently observed PDF's of turbulence in the highest accuracy superior to the analyses based on other models such as the log-normal model and the $p$ model.

cond-mat.stat-mech↗

arXiv2003

Multifractal analysis of fluid particle accelerations in turbulence

The probability density function (PDF) of accelerations in turbulence is derived analytically with the help of the multifractal analysis based on generalized entropy, i.e., the Tsallis or the Rényi entropy. It is shown that the derived PDF explains quite well the one obtained by Bodenschatz et al. in the measurement of fluid particle accelerations in the Lagrangian frame at $R_λ= 690$, and the one by Gotoh et al. in the DNS with the mesh size 1024$^3$ at $R_λ= 380$.

cond-mat.stat-mech↗

arXiv2003

Quantum stochastic differential equations for boson and fermion systems -- Method of Non-Equilibrium Thermo Field Dynamics

A unified canonical operator formalism for quantum stochastic differential equations, including the quantum stochastic Liouville equation and the quantum Langevin equation both of the Itô and the Stratonovich types, is presented within the framework of Non-Equilibrium Thermo Field Dynamics (NETFD). It is performed by introducing an appropriate martingale operator in the Schrödinger and the Heisenberg representations with fermionic and bosonic Brownian motions. In order to decide the double tilde conjugation rule and the thermal state conditions for fermions, a generalization of the system consisting of a vector field and Faddeev-Popov ghosts to dissipative open situations is carried out within NETFD.

math-ph↗

arXiv2002

Analysis of Shear-Thickening in Physical Gel. A Stochastic Theory for Polymer Networks

A formula of steady shear viscosity is derived by introducing a model to describe the dynamics of physically cross-linked network (physical gel), and successfully analyzes the shear-thickening behavior observed in HEUR aqueous solutions by Jenkins, Sileibi and El-Aasser. We take into account the effects of looped chains at junctions which detach their one end from the junction as the shear rate increases due to the collisions with other chains. This process produces the weak and wide enhancement of the number of chains whose both ends stick to the separate junctions (active chains) leading to the weak increase in the shear viscosity. It is also shown that the nonlinear force sustained by active chains induces the strong and sharp enhancement of the steady shear viscosity.

cond-mat.soft↗

arXiv2002

Analysis of Velocity Derivatives in Turbulence based on Generalized Statistics

A theoretical formula for the probability density function (PDF) of velocity derivatives in a fully developed turbulent flow is derived with the multifractal aspect based on the generalized measures of entropy, i.e., the extensive Renyi entropy or the non-extensive Tsallis entropy, and is used, successfully, to analyze the PDF's observed in the direct numerical simulation (DNS) conducted by Gotoh et al.. The minimum length scale r_d/eta in the longitudinal (transverse) inertial range of the DNS is estimated to be r_d^L/eta = 1.716 (r_d^T/eta = 2.180) in the unit of the Kolmogorov scale eta.

cond-mat.stat-mech↗

arXiv2002

Can "quantumness" be an origin of dissipation?

In their constructions of system of quantum stochastic differential equations, mathematicians and/or several physicists interpret that the function of random force operator is to preserve the canonical commutation relation in time, i.e., to secure the unitarity of time evolution generator even for dissipative systems. If this is the case, it means physically that the origin of dissipation is attributed to quantum non-commutativity ({\it quantumness}). The mechanism that the mathematician's approaches rest on will be investigated from the unified view point of Non-Equilibrium Thermo Field Dynamics (NETFD) which is a canonical operator formalism of quantum systems in far-from-equilibrium state including the system of quantum {\it stochastic} equations.

quant-ph↗

arXiv2002

Quantum Stochastic Differential Equations in View of Non-Equlibrium Thermo Field Dynamics

Most of the mathematical approaches for quantum Langevin equation are based on the non-commutativity of the random force operators. Non-commutative random force operators are introduced in order to guarantee that the equal-time commutation relation for the stochastic annihilation and creation operators preserves in time. If it is true, it means that the origin of dissipation is of quantum mechanical. However, physically, it is hard to believe it. By making use of the unified canonical operator formalism for the system of the quantum stochastic differential equations within Non-Equilibrium Thermo Field Dynamics, it is shown that it is not true in general.

math-ph↗

arXiv2001

Analysis of Velocity Fluctuation in Turbulence based on Generalized Statistics

The numerical experiments of turbulence conducted by Gotoh et al. are analyzed precisely with the help of the formulae for the scaling exponents of velocity structure function and for the probability density function (PDF) of velocity fluctuations. These formulae are derived by the present authors with the multifractal aspect based on the statistics that are constructed on the generalized measures of entropy, i.e., the extensive Rényi's or the non-extensive Tsallis' entropy. It is revealed that there exist two scaling regions separated by a crossover length, i.e., a definite length approximately of the order of the Taylor microscale. It indicates that the multifractal distribution of singularities in velocity gradient in turbulent flow is robust enough to produce scaling behaviors even for the phenomena out side the inertial range.

cond-mat.stat-mech↗

arXiv2001

Multifractal Analysis of Turbulence by Statistics based on Non-Extensive Tsallis' or Extensive Rényi's Entropy

An analytical expression of probability density function (PDF) of velocity fluctuation is derived with the help of the statistics based on generalized entropy (the Tsallis entropy or the Rényi entropy). It is revealed that the derived PDF explains the detailed structure of experimentally observed PDF as well as the scaling exponents of velocity structure function. Every parameters appeared in the analysis, including the index proper to the Tsallis entropy or the Rényi entropy, are determined, self-consistently, by making use of observed value of intermittency exponent. The experiments conducted by Lewis and Swinney (1999) are analyzed.

cond-mat.stat-mech↗

arXiv1999

Thermo field hydrodynamic and kinetic equations of dense quantum nuclear systems

Basic equations of nonequilibrium thermo field dynamics of dense quantum systems are presented. A formulation of nonequilibrium thermo field dynamics has been performed using the nonequilibrium statistical operator method by D.N.Zubarev. Hydrodynamic equations have been obtained in thermo field representation. Two levels of the description of kinetics and hydrodynamics of a dense nuclear matter are considered. The first one is a quantum system with strongly coupled states, the second one is a quark-gluon plasma. Generalized transfer equations of a consistent description of kinetics and hydrodynamics have been obtained, as well as limiting cases are considered.

nucl-th↗