安田 修悟

Aggregation of chemotactic bacteria under a unimodal distribution of chemical cues was investigated by Monte Carlo (MC) simulation based on a kinetic transport equation, which considers an internal adaptation dynamics as well as a finite tumbling duration. It was found that there exist two different regimes of the adaptation time, between which the effect of the adaptation time on the aggregation behavior is reversed; that is, when the adaptation time is as small as the running duration, the aggregation becomes increasingly steeper as the adaptation time increases, while, when the adaptation time is as large as the diffusion time of the population density, the aggregation becomes more diffusive as the adaptation time increases. Moreover, the aggregation profile becomes bimodal (volcano) at the large adaptation-time regime when the tumbling duration is sufficiently large while it is always unimodal at the small adaptation-time regime. A remarkable result of this study is the identification of the parameter regime and scaling for the volcano effect. That is, by comparing the results of MC simulations to the continuum-limit models obtained at each of the small and large adaptation-time scalings, it is clarified that the volcano effect arises due to the coupling of diffusion, adaptation, and finite tumbling duration, which occurs at the large adaptation-time scaling.

The effects of internal adaptation dynamics on the self-organized aggregation of chemotactic bacteria are investigated by Monte Carlo (MC) simulations based on a two-stream kinetic transport equation coupled with a reaction-diffusion equation of the chemoattractant that bacteria produce. A remarkable finding is a nonmonotonic behavior of the peak aggregation density with respect to the adaptation time; more specifically, aggregation is the most enhanced when the adaptation time is comparable to or moderately larger than the mean run time of bacteria. Another curious observation is the formation of a trapezoidal aggregation profile occurring at a very large adaptation time, where the biased motion of individual cells is rather hindered at the plateau regimes due to the boundedness of the tumbling frequency modulation. Asymptotic analysis of the kinetic transport system is also carried out, and a novel asymptotic equation is obtained at the large adaptation-time regime while the Keller-Segel type equations are obtained when the adaptation time is moderate. Numerical comparison of the asymptotic equations with MC results clarifies that trapezoidal aggregation is well described by the novel asymptotic equation, and the nonmonotonic behavior of the peak aggregation density is interpreted as the transient of the asymptotic solutions between different adaptation time regimes.

The run and tumble process is well established in order to describe the movement of bacteria in response to a chemical stimulus. However, the relation between the tumbling rate and the internal state of bacteria is poorly understood. This study aims at deriving macroscopic models as limits of the mesoscopic kinetic equation in different regimes. In particular, we are interested in the roles of the stiffness of the response and the adaptation time in the kinetic equation. Depending on the asymptotics chosen both the standard Keller–Segel equation and the flux-limited Keller–Segel (FLKS) equation can appear. An interesting mathematical issue arises with a new type of equilibrium equation leading to solution with singularities.

We investigate the thermohydrodynamic lubrication of the Lennard-Jones (LJ) fluid in plain wall channels by using a molecular-dynamics simulation. It is found that the LJ fluid solidifies near the wall when the viscous heating of the LJ fluid in the bulk regime is sufficiently large. The thickness of the solidified layer increases with the channel width. Thus, a long-range-ordered crystal-like structure forms near the wall in high-speed lubrication when the channel width is large. The mechanism of this counterintuitive solidification is investigated from both macroscopic and microscopic points of view. It is elucidated that the LJ molecules are densely confined in the vicinity of the wall due to the macroscopic mass and heat transport in the bulk regime. In this densely confined regime, the fluid molecules form a crystal-like structure, which is similar to that of the wall molecules, via direct molecular interaction. Band formation is also observed in the solidified region when the channel width is sufficiently large.

The thermal lubrication of an entangled polymeric liquid in wall-driven shear flows between parallel plates is investigated by using a multiscale hybrid method, coupling molecular dynamics and hydrodynamics (i.e., the synchronized molecular dynamics method). The temperature of the polymeric liquid rapidly increases due to viscous heating once the drive force exceeds a certain threshold value, and the rheological properties drastically change at around the critical drive force. In the weak viscous-heating regime, the conformation of polymer chains is dominated by the flow field so that the polymers are more elongated as the drive force increases. However, in the large viscous-heating regime, the conformation dynamics is dominated by the thermal agitation of polymer chains so that the conformation of polymers recovers more uniform and random structures as the drive force increases, even though the local shear flows are further enhanced. Remarkably, this counter-intuitive transitional behavior gives an interesting re-entrant transition in the stress⁻optical relation, where the linear stress⁻optical relation approximately holds even though each of the macroscopic quantities behaves nonlinearly. Furthermore, the shear thickening behavior is also observed in the large viscous-heating regime-this was not observed in a series of previous studies on an unentangled polymer fluid. This qualitative difference of the thermo-rheological property between the entangled and unentangled polymer fluids gives completely different velocity profiles in the thermal lubrication system.