arXiv subjects

Shigeru Takata

Publications and source records attributed to Shigeru Takata.

12 recordsLinked to original sources

arXiv2026

Heat transfer problem of a dense gas described by the Enskog equation with a modification of the Enskog factor

Heat transfer in a dense gas between two parallel plates is studied for assessing the quantitative difference of two variants of the Enskog equation, i.e., the original Enskog equation and the Enskog equation with a modified Enskog factor recently proposed in Phys. Rev. E \textbf{111}, 065108 (2025). The main advantage of the latter is that the H theorem, which is lacking in the former, has been established. The influence of the modification is assessed by comparing the macroscopic quantities in details. It is found that the influence of this modification is quite limited in the density, temperature, and heat flow vector. However, the influence on the stress tensor is visible in some severe setting of parameters.

math-ph↗

arXiv2026

Local H theorem for Enskog and Enskog-Vlasov equations with a modified Enskog factor

The local H theorem is shown to hold for the Enskog equation with a modified Enskog factor proposed by the authors [Phys. Rev. E 111, 065108 (2025)]. This is a stronger statement than the global one in the same paper and has been obtained along the lines of Mareschal et al. [Phys. Rev. Lett. 52, 1169-1172 (1984)] for the modified (or revised) Enskog equation. Furthermore, it is shown that the local H theorem also holds for the corresponding Enskog-Vlasov equation.

math.AP↗

arXiv2026

Numerical analysis of the thermal relaxation of the dense gas between two parallel plates: the free energy monotonicity for the Enskog equation

The thermal relaxation problem between two parallel plates with the same temperature is investigated, aiming to study the behavior of the free energy of the dense gas described by the Enskog equation. Two types of Enskog equation have been used: one is the Enskog equation with the original Enskog factor, while the other is that with a modified Enskog factor proposed recently in Takata & Takahashi, Phys. Rev. E 111, 065108 (2025). The evaluated free energy is a natural extension of the thermodynamic free energy to the non-equilibrium state. It is observed that this free energy monotonically decreases in time for the modified factor version, while it is not necessarily the case for the original version. Differences are also observed in other quantities in their time evolutions, most typically in the density profile.

cond-mat.mes-hall↗

arXiv2025

Fluid-dynamic limit of the Enskog equation with the guaranteed H-theorem

The fluid-dynamic limit of the Enskog equation with a slight modification is discussed on the basis of the Chapman-Enskog method. This modified version of the Enskog equation has been shown recently by the present authors to ensure the H-theorem. In the present paper, it is shown that the modified version recovers the same fluid-dynamic description of the dense gas as the original Enskog equation, at least up to the level of the Navier-Stokes-Fourier set of equations inclusive. Since the original Enskog equation is known to recover the fluid-dynamical transport properties well, this result implies that the modified version of the Enskog equation provides consistent descriptions both thermodynamically and fluid-dynamically.

physics.flu-dyn↗

arXiv2025

Enskog and Enskog-Vlasov equations with a slightly modified correlation factor and their H theorem

A novel modification of the original Enskog equation is proposed. The modification is much simpler than that is made in the modified (or revised) Enskog equation proposed by van Beijeren \& Ernst in 1973 and does not require a consideration of many-body configuration. The proposed modification is general enough to be adapted to various equations of states for non-ideal gases. It is shown that the H-theorem can be established for the Enskog and the Enskog--Vlasov equation with the proposed modification.

cond-mat.stat-mech↗

arXiv2023

Note on the summational invariant and corresponding local Maxwellian for the Enskog equation

The summational invariant and the corresponding local Maxwellian that are compatible with the Enskog equation are discussed, with special interest in the presence of a boundary. The local Maxwellian corresponding to the summational invariant is restrictive compared to the case of the Boltzmann equation in the sense that a radial flow and time-dependent temperature are forbidden. However, a rigid body rotation with a constant angular velocity is admitted as in the case of the Boltzmann equation. The influence of the presence of a boundary is also discussed in simple situations.

math-ph↗

arXiv2023

On the thermal relaxation of a dense gas described by the modified Enskog equation in a closed system in contact with a heat bath

The thermal relaxation of a dense gas described by the modified Enskog equation is studied for a closed system in contact with a heat bath. As in the case of the Boltzmann equation, the Helmholtz free energy $\mathcal{F}$ that decreases monotonically in time is found under the conventional kinetic boundary condition that satisfies the Darrozes--Guiraud inequality. The extension to the modified Enskog--Vlasov equation is also presented.

math-ph↗

arXiv2022

On the entropic property of the Ellipsoidal Statistical model with the Prandtl number below 2/3

Entropic property of the Ellipsoidal Statistical model with the Prandtl number Pr below 2/3 is discussed. Although 2/3 is the lower bound of Pr for the H theorem to hold unconditionally, it is shown that the theorem still holds even for $\mathrm{Pr}<2/3$, provided that anisotropy of stress tensor satisfies a certain criterion. The practical tolerance of that criterion is assessed numerically by the strong normal shock wave and the Couette flow problems. A couple of moving plate tests are also conducted.

physics.flu-dyn↗

arXiv2021

Singular Behavior of the Macroscopic Quantity Near the Boundary for a Lorentz-Gas Model with the Infinite-Range Potential

Possibility of the diverging gradient of the macroscopic quantity near the boundary is investigated by a mono-speed Lorentz-gas model, with a special attention to the regularizing effect of the grazing collision for the infinite-range potential on the velocity distribution function (VDF) and its influence on the macroscopic quantity. By careful numerical analyses of the steady one-dimensional boundary-value problem, it is confirmed that the grazing collision suppresses the occurrence of a jump discontinuity of the VDF on the boundary. However, as the price for that regularization, the collision integral becomes no longer finite in the direction of the molecular velocity parallel to the boundary. Consequently, the gradient of the macroscopic quantity diverges, even stronger than the case of the finite-range potential. A conjecture about the diverging rate in approaching the boundary is made as well for a wide range of the infinite-range potentials, accompanied by the numerical evidence.

cond-mat.stat-mech↗

arXiv2018

Kinetic theory for a simple modeling of phase transition: Dynamics out of local equilibrium

This is a continuation of the previous work (Takata & Noguchi, J. Stat. Phys., 2018) that introduces the presumably simplest model of kinetic theory for phase transition. Here, main concern is to clarify the stability of uniform equilibrium states in the kinetic regime, rather than that in the continuum limit. It is found by the linear stability analysis that the linear neutral curve is invariant with respect to the Knudsen number, though the transition process is dependent on the Knudsen number. In addition, numerical computations of the (nonlinear) kinetic model are performed to investigate the transition processes in detail. Numerical results show that (unexpected) incomplete transitions may happen as well as clear phase transitions.

cond-mat.stat-mech↗

arXiv2018

A simple kinetic model for the phase transition of the van der Waals fluid

A simple kinetic model, which is presumably minimum, for the phase transition of the van der Waals fluid is presented. In the model, intermolecular collisions for a dense gas has not been treated faithfully. Instead, the expected interactions as the non-ideal gas effect are confined in a self-consistent force term. Collision term plays just a role of thermal bath. Accordingly, it conserves neither momentum nor energy, even globally. It is demonstrated that (i) by a natural separation of the mean-field self-consistent potential, the potential for the non-ideal gas effect is determined from the equation of state for the van der Waals fluid, with the aid of the balance equation of momentum, (ii) a functional which monotonically decreases in time is identified by the H theorem and is found to have a close relation to the Helmholtz free energy in thermodynamics, and (iii) the Cahn--Hilliard type equation is obtained in the continuum limit of the present kinetic model. Numerical simulations based on the Cahn--Hilliard type equation are also performed.

physics.flu-dyn↗

arXiv2012

On the second-order temperature jump coefficient of a dilute gas

We use LVDSMC simulations to calculate the second-order temperature jump coefficient for a dilute gas whose temperature is governed by the Poisson equation with a constant forcing term. Both the hard sphere gas and the BGK model of the Boltzmann equation are considered. Our results show that the temperature jump coefficient is different from the well known linear and steady case where the temperature is governed by the homogeneous heat conduction (Laplace) equation.

physics.flu-dyn↗