Kinetic model for the phase transition of the van der Waals fluid.

This is a continuation of previous works [S. Takata and T. Noguchi, J. Stat. Phys. 172, 880 (2018)JSTPBS0022-471510.1007/s10955-018-2068-z; S. Takata, T. Matsumoto, A. Hirahara, and M. Hattori, Phys. Rev. E 98, 052123 (2018)2470-004510.1103/PhysRevE.98.052123]. The simple model proposed in the previous works is extended to be free from the isothermal assumption. The new model conserves the total mass, momentum, and energy in the periodic domain. A monotone functional is found, assuring the H theorem for the new model. Different approaches are taken to tell apart the stable, the metastable, and the unstable uniform equilibrium state. Numerical simulations are also conducted for spatially one-dimensional cases to demonstrate various features occurring in the time evolution process. A prediction method for the profile at the stationary state is discussed as well.

Nanoscopic live electrooptic imaging.

A door to the nanoscopic domain is opened regarding real-time visualization of electric field distributions and dynamics. Through the use of a live electrooptic imaging system with an oil-immersion objective lens and a highly thinned electrooptic sensor film, a minimum linewidth of 330 nm and a minimum peak splitting of 650 nm in real-time electric field video images have been successfully demonstrated. In addition, room to improve the resolution is noted, while a few problems that need to be solved are discussed, including an effect caused by optical interference.

Vacuum formation behind the expansion wave in a piston motion problem.

Long time behavior of one-dimensional gas motion caused by pulling a piston with a high speed is numerically studied on the basis of the kinetic theory of gases. It is clarified that (i) if the piston speed is lower than a critical speed, the state of the gas time-asymptotically approaches the local equilibrium that corresponds to the isentropic solution in the conventional gas dynamics, namely, an expansion wave followed by a uniform state, and (ii) otherwise, there appears a highly nonequilibrium region with a very low pressure behind the expansion tail. In the latter case, the components of temperature parallel and perpendicular to the flow direction become highly different, and the density tends to vanish as time goes on, forming a vacuum region behind the tail at the infinite time.

Poiseuille-type flow of a rarefied gas between two parallel plates driven by a uniform external force.

A unidirectional flow of a rarefied gas between two parallel plates driven by a uniform external force is investigated on the basis of kinetic theory with special interest in the behavior in the near continuum regime. The Bhatnagar-Gross-Krook (BGK) model of the Boltzmann equation and the diffuse reflection boundary condition are employed as the basic system. First, a systematic asymptotic analysis of the basic system for small Knudsen numbers is carried out, and a system of fluid-dynamic-type equations and their boundary conditions are derived up to the second order in the Knudsen number. Then, an accurate numerical analysis of the original BGK system is performed for a wide range of the Knudsen number by means of a finite-difference method. The behavior of the gas, such as the non-Navier-Stokes effects in the near continuum regime, is clarified on the basis of the fluid-dynamic-type system as well as the numerical solution of the BGK system.