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.

Flux-limited Keller-Segel (FLKS) model has been recently derived from kinetic transport models for bacterial chemotaxis and shown to represent better the collective movement observed experimentally. Recently, associated to the kinetic model, a new instability formalism has been discovered related to stiff chemotactic response. This motivates our study of traveling wave and aggregation in population dynamics of chemotactic cells based on the FLKS model with a population growth term. Our study includes both numerical and theoretical contributions. In the numerical part, we uncover a variety of solution types in the one-dimensional FLKS model additionally to standard Fisher/KPP type traveling wave. The remarkable result is a counter-intuitive backward traveling wave, where the population density initially saturated in a stable state transits toward an unstable state in the local population dynamics. Unexpectedly, we also find that the backward traveling wave solution transits to a localized spiky solution as increasing the stiffness of chemotactic response. In the theoretical part, we obtain a novel analytic formula for the minimum traveling speed which includes the counter-balancing effect of chemotactic drift vs. reproduction/diffusion in the propagating front. The front propagation speeds of numerical results only slightly deviate from the minimum traveling speeds, except for the localized spiky solutions, even for the backward traveling waves. We also discover an analytic solution of unimodal traveling wave in the large-stiffness limit, which is certainly unstable but exists in a certain range of parameters.

A Monte Carlo simulation of chemotactic bacteria is developed on the basis of the kinetic model and is applied to a one-dimensional traveling population wave in a microchannel. In this simulation, the Monte Carlo method, which calculates the run-and-tumble motions of bacteria, is coupled with a finite volume method to calculate the macroscopic transport of the chemical cues in the environment. The simulation method can successfully reproduce the traveling population wave of bacteria that was observed experimentally and reveal the microscopic dynamics of bacterium coupled with the macroscopic transports of the chemical cues and bacteria population density. The results obtained by the Monte Carlo method are also compared with the asymptotic solution derived from the kinetic chemotaxis equation in the continuum limit, where the Knudsen number, which is defined by the ratio of the mean free path of bacterium to the characteristic length of the system, vanishes. The validity of the Monte Carlo method in the asymptotic behaviors for small Knudsen numbers is numerically verified. (C) 2016 Elsevier Inc. All rights reserved.

The Synchronized Molecular-Dynamics simulation, which was recently proposed by authors (Yasuda and Yamamoto, 2014), is applied to the analysis of polymer lubrication between parallel plates. The changes in theological properties, conformational change of polymer chains, and temperature rise due to the viscous heating are investigated with varying values of thermal conductivity of the polymeric liquid. It is found that with a small applied shear stress on the plate, the temperature of the polymeric liquid only slightly increases in inverse proportion to the thermal conductivity; the apparent viscosity of the polymeric liquid is little affected by changing the thermal conductivity. However, at a large shear stress the transitional behaviors of the polymeric liquid are observed due to the interplay of the shear deformation and viscous heating by changing the thermal conductivity. This transition is characterized by the Nahme-Griffith number Na, which is defined as the ratio of the viscous heating to the thermal conduction at a characteristic temperature. When the Nahme-Griffith number exceeds unity, the temperature of the polymeric liquid increases rapidly and the apparent viscosity also exponentially decreases as the thermal conductivity decreases. The conformation of polymer chains is stretched and aligned by the shear flow when Na < 1, but the coherent structure becomes disturbed by the thermal motion of molecules when Na > 1. (C) 2015 Elsevier B.V. All rights reserved.

Thermo-hydrodynamic lubrication of a polymeric liquid composed of short chains between parallel plates is analysed by a multi-scale simulation, i.e. the synchronised molecular dynamics simulation via macroscopic heat and momentum transfer, which has been recently developed by us. The rheological properties and conformation of polymer chains coupled with the temperature rise caused by local viscous heating are investigated with a non-dimensional parameter, i.e. the Nahme-Griffith number, which is defined by the ratio of the viscous heating to the thermal conduction at the characteristic temperature required to sufficiently change the viscosity. The present simulation demonstrates that strong shear thinning and transitional behaviour of the conformation of the polymer chains occurs with a rapid temperature rise when the Nahme-Griffith number exceeds unity.

A synchronized molecular-dynamics simulation via macroscopic heat and momentum transfer is proposed to model the nonisothermal flow behaviors of complex fluids. In this method, the molecular-dynamics simulations are assigned to small fluid elements to calculate the local stresses and temperatures and are synchronized at certain time intervals to satisfy the macroscopic heat- and momentum-transport equations. This method is applied to the lubrication of a polymeric liquid composed of short chains of ten beads between parallel plates. The rheological properties and conformation of the polymer chains coupled with local viscous heating are investigated with a nondimensional parameter, the Nahme-Griffith number, which is defined as the ratio of the viscous heating to the thermal conduction at the characteristic temperature required to sufficiently change the viscosity. The present simulation demonstrates that strong shear thinning and a transitional behavior of the conformation of the polymer chains are exhibited with a rapid temperature rise when the Nahme-Griffith number exceeds unity. The results also clarify that the reentrant transition of the linear stress-optical relation occurs for large shear stresses due to the coupling of the conformation of polymer chains with heat generation under shear flows.

The deformation and breakup processes of a particle-cluster aggregate under shear flows are numerically investigated by the two-phase lattice Boltzmann method. The van der Waals attraction is considered to be the force between particles. Simulations are performed for various fluid forces acting on particles and various inter-particle forces. It is found that the ratio of the fluid force to the maximum inter-particle force, Y, is a key factor in dispersion, and the aggregate of non-Brownian particles is dispersed when Y is over 0.001. The Péclet number, which is the ratio of the diffusion rate due to shear flow to that due to the Brownian motion, is also considered. By comparing the calculated result of the dispersion of Brownian particles with that of non-Brownian particles, it is found that the Brownian motion impedes dispersion and the effect of the Brownian motion is remarkable when the Péclet number is under 105. © 2013.

Multiscale simulation methods have been developed based on the local stress sampling strategy and applied to three flow problems with different difficulty levels: (a) general flow problems of simple fluids, (b) parallel (one-dimensional) flow problems of polymeric liquids, and (c) general (two- or three-dimensional) flow problems of polymeric liquids. In our multiscale methods, the local stress of each fluid element is calculated directly by performing microscopic or mesoscopic simulations according to the local flow quantities instead of using any constitutive relations. For simple fluids (a), such as the Lenard-Jones liquid, a multiscale method combining molecular dynamics (MD) and computational fluid dynamics (CFD) simulations is developed rather straightforwardly based on the local stationarity assumption without memories of the flow history. For polymeric liquids in parallel flows (b), the multiscale method is extended to take into account the memory effects that arise in hydrodynamic stress due to the slow relaxation of polymer-chain conformations. The memory of polymer dynamics on each fluid element is thus resolved by performing MD simulations in which cells are fixed at the mesh nodes of the CFD simulations. The complicated viscoelastic flow behaviors of a polymeric liquid confined between oscillating plates are simulated using the multiscale method. For general (two- or three-dimensional) flow problems of polymeric liquids (c), it is necessary to trace the history of microscopic information such as polymer-chain conformation, which carries the memories of past flow history, along the streamline of each fluid element. A Lagrangian-based CFD is thus implemented to correctly advect the polymerchain conformation consistently with the flow. On each fluid element, coarse-grained polymer simulations are carried out to consider the dynamics of entangled polymer chains that show extremely slow relaxation compared to microscopic time scales. This method is successfully applied to simulate a flow around a cylindrical obstacle. © 2013 The Physical Society of Japan.

The dynamic rheology of a polymer melt composed of short chains with ten beads between rapidly oscillating plates is investigated for various oscillation frequencies by using the hybrid simulation of the molecular dynamics and computational fluid dynamics. In the quiescent state, the melt is in a supercooled state, and the stress relaxation function G(t) exhibits a stretched exponential relaxation on the time scale of the a relaxation time tau(alpha) (the structural relaxation of beads) and then follows the Rouse relaxation function characterized by the Rouse relaxation time tau(R) (the conformational relaxation of polymer chains). In the rapidly oscillating plates, nonuniform boundary layer flows are generated over the plate due to inertia of the fluid, and the local rheological properties of the melt are spatially varied according to the local flow fields. The local strain and local strain rate of the melt monotonically decrease with the distance from the plate at each oscillation frequency of the plate, but their dependencies on the oscillation frequency at a fixed distance from the plate vary with the distance. Far from the plate, the local strain decreases as the oscillation frequency increases such that the dynamic rheology deviates from the linear moduli at the low oscillation frequencies rather than high oscillation frequencies. On the contrary, near the plate, the local strain rate increases with the oscillation frequency such that the shear thinning is enhanced at high oscillation frequencies. In close vicinity to the plate, the dynamic viscosity is mostly independent of the oscillation frequency, and the shear thinning behavior becomes similar to that observed in steady shear flows. We show the diagram of the loss tangent of the melt for different oscillation frequencies and local strain rates. It is seen that the melt generates three different rheological regimes, i.e., the viscous fluid regime, liquidlike viscoelastic regime, and solidlike viscoelastic regime, according to the oscillation frequency and local strain rate. Nonlinear rheological properties are also investigated by the spectrum analysis and the Lissajous-Bowditch curve. It is found that the fractional amplitude of the higher harmonics to the linear harmonics is suppressed within the boundary layer due to the nonslip boundary on the oscillating plate. We also find that the melt exhibits intercycle shear thinning between different positions but exhibits intracycle shear thickening at a fixed position in the vicinity of the plate.

The flow behaviors of polymer melt composed of short chains with ten beads between parallel plates are simulated by using a hybrid method of molecular dynamics and computational fluid dynamics. Three problems are solved: creep motion under a constant shear stress and its recovery motion after removing the stress, pressure-driven flows, and the flows in rapidly oscillating plates. In the creep/recovery problem, the delayed elastic deformation in the creep motion and evident elastic behavior in the recovery motion are demonstrated. The velocity profiles of the melt in pressure-driven flows are quite different from those of Newtonian fluid due to shear thinning. Velocity gradients of the melt become steeper near the plates and flatter at the middle between the plates as the pressure gradient increases and the temperature decreases. In the rapidly oscillating plates, the viscous boundary layer of the melt is much thinner than that of Newtonian fluid due to the shear thinning of the melt. Three different rheological regimes, i.e., the viscous fluid, viscoelastic liquid, and viscoelastic solid regimes, form over the oscillating plate according to the local Deborah numbers. The melt behaves as a viscous fluid in a region for omega tau(R)similar or equal to 1, and the crossover between the liquidlike and solidlike regime takes place around omega tau(alpha)similar or equal to 1 (where omega is the angular frequency of the plate and tau(R) and tau(alpha) are Rouse and alpha relaxation time, respectively).

The deformation and breakup processes of a particle-cluster aggregate under shear flows are investigated by the two-phase lattice Boltzmann method. In the simulation the particle is modeled by a hard droplet with large viscosity and strong surface tension. The van der Waals attraction force is taken into account for the interaction between the particles. Also, the Brownian motion is considered for nano-particles. Two important dimensionless parameters are introduced in order to classify calculated results. One is the ratio of fluid force to the maximum inter-particle force, Y, and the other is the Peclet number which is the ratio of the rate of diffusion by a shear flow to the rate of diffusion by Brownian motion. It is found that Y is the key factor in dispersion and that the Brownian motion retards the dispersion.

The behavior of supercooled polymer melt composed of short chains with 10 beads between rapidly oscillating plates is simulated by using a hybrid simulation of molecular dynamics and computational fluid dynamics. The flow profiles of polymer melt near an oscillating plate are quite different from those of Newtonian fluid. The viscous boundary layer of the melt is much thinner than that of the Newtonian fluid due to the shear thinning of the melt. Three different rheological regimes, i.e., the viscous fluid, viscoelastic liquid, and viscoelastic solid regimes, form over the oscillating plate according to the local Deborah numbers. The melt behaves as a viscous fluid when omega tau(R) less than or similar to 1, and the crossover between the liquid-like and solid-like regime takes place around omega tau(alpha) similar or equal to 1 (where omega is the angular frequency of the plate, and tau(R) and tau(alpha) are the Rouse and a relaxation times, respectively). Copyright (C) EPLA, 2009

We develop a method for multiscale hybrid simulations of molecular dynamics (MD) and computational fluid dynamics (CFD). In this method, the usual lattice-mesh based simulations are applied for the CFD level, but each lattice is associated with a small MD cell that generates a "local stress" according to a "local flow field" given from CFD instead of using any constitutive functions at the CFD level. We carried out hybrid simulations for some elemental flow problems involving simple Lennard-Jones liquids and compared the results with those obtained by usual CFD with a Newtonian constitutive relation in order to examine the validity of our hybrid simulation method. It is demonstrated that our hybrid simulations successfully reproduce the correct flow behavior obtained from usual CFD as long as the mesh size Delta x and the time step Delta t of CFD are not too large compared to the system size l(MD) and the sampling duration t(MD) of MD simulations performed at each time step of the CFD. Otherwise, the simulations are affected by large fluctuations due to poor statistical averages taken in the MD part. Properties of the fluctuations are analyzed in detail. (c) 2008 American Institute of Physics.

The steady-state simplified P-N approximation to the radiative transport equation has been successfully applied to many problems involving radiation. This paper presents the derivation of time-dependent simplified P-N (SPN) equations (up to N = 3) via two different approaches. First, we use an asymptotic analysis, similar to the asymptotic derivation of the steady-state SPN equations. Second, we use an approach similar to the original derivation of the steady-state SPN equations and we show that both approaches lead to similar results. Special focus is put on the well-posedness of the equations and the question whether it can be guaranteed that the solution satisfies the correct physical bounds. Several numerical test cases are shown, including an analytical benchmark due to Su and Olson [B. Su, G.L. Olson, An analytical benchmark for non-equilibrium radiative transfer in an isotropically scattering medium, Ann. Nucl. Energy 24 (1997) 1035-1055.]. (c) 2007 Elsevier Inc. All rights reserved.

The half-space problem of the temperature, pressure, and concentration jumps for a binary mixture of vapors is investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules with the complete condensation condition. First, the problem is shown to be reduced to three elemental ones: the problem of the jumps caused by the net evaporation or condensation, that caused by the gradient of temperature, and that caused by the gradient of concentration. Then, the latter two are investigated numerically in the present contribution because the first problem has already been studied [Yasuda, Takata, and Aoki, Phys. Fluids 17, 047105 (2005)]. The numerical method is a finite-difference one, in which the complicated collision integrals are computed by the extension of the method proposed by Sone, Ohwada, and Aoki [Phys. Fluids A 1, 363 (1989)] to the case of a gas mixture. As a result, the behavior of the mixture is clarified not only at the level of the macroscopic quantities but also at the level of the velocity distribution function. In addition, accurate formulas of the temperature, pressure, and concentration jumps are constructed for arbitrary values of the concentration of the background reference state by the use of the Chebyshev polynomial approximation. The solution of the corresponding problem of a vapor-gas mixture and that of the temperature-jump problem on a simple solid wall are also obtained as special cases of the present problem.

Half-space problem of evaporation and condensation of a binary mixture of vapors is investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules with the complete condensation condition. The problem is analyzed numerically by a finite-difference method, in which the complicated collision integrals are computed by the extension of the method proposed by Y. Sone, T. Ohwada, and K. Aoki ["Temperature jump and Knudsen layer in a rarefied gas over a plane wall: Numerical analysis of the linearized Boltzmann equation for hard-sphere molecules," Phys. Fluids A 1, 363 (1989)] to the case of a gas mixture. As a result, the behavior of the mixture is clarified not only at the level of the macroscopic quantities but also at the level of the velocity distribution function. In addition, accurate formulas of the temperature, pressure, and concentration jumps caused by the evaporation and condensation are constructed for arbitrary values of the concentration of the background reference state by the use of the Chebyshev polynomial approximation. (C) 2005 American Institute of Physics.

The shear flow of a binary mixture of rarefied gases over a plane wall is investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules with the diffuse reflection boundary condition. This fundamental problem in rarefied gas dynamics is analyzed numerically by a finite-difference method, in which the complicated collision integrals are computed by the extension to the case of a gas mixture of the method proposed by Sone, Ohwada, and Aoki [Phys. Fluids A 1, 363 (1989)]. As a result, the behavior of the mixture is clarified not only at the level of the macroscopic variables but also at the level of the velocity distribution function. In addition, an accurate formula of the shear-slip (viscous-slip) coefficient for arbitrary values of the concentration of a component gas is constructed by the use of the Chebyshev polynomial approximation. (C) 2004 American Institute of Physics.

A steady state of a binary mixture of hard-sphere gases in the near continuum regime, where the Knudsen number is small, is considered in the case where the density and temperature variations are large, but the Mach number of the flow is as small as the Knudsen number. Thus, the flow vanishes in the continuum limit where the Knudsen number goes to zero. The set of fluid-dynamic-type equations in this case was derived by Takata and Aoki [Trunsp. Theor. Stat. Phys. 30, 205 (2001)] by means of a systematic asymptotic analysis of the Boltzmann equation. This set gives the correct behavior of the mixture in the continuum limit, i.e., it describes the ghost effect discovered by Sone et al. for a single-component gas [Phys. Fluids 8, 628 (1996)]. The set contains various transport coefficients that depend on the local properties of the gas. In particular, their dependence on the local concentration of one of the components cannot be obtained explicitly. In this paper, this unknown dependence is established numerically by a direct numerical analysis of the basic integral equations, and a database that provides the numerical values of the transport coefficients immediately for an arbitrarily specified local state of the mixture is constructed. The database makes the fluid-dynamic-type equations applicable to practical problems.

The thermal-slip (thermal-creep) and the diffusion-slip problems for a binary mixture of gases are investigated on the basis of the linearized Boltzmann equation for hard-sphere molecules with the diffuse reflection boundary condition. The problems are analyzed numerically by the finite-difference method incorporated with the numerical kernel method, which was first proposed by Sone, Ohwada, and Aoki [Phys. Fluids A 1, 363 (1989)] for a single-component gas. As a result, the behavior of the mixture is clarified accurately not only at the level of the macroscopic variables but also at the level of the velocity distribution function. In addition, accurate formulas of the thermal-slip and the diffusion-slip coefficients for arbitrary values of the concentration of a component gas are constructed by the use of the Chebyshev polynomial approximation. (C) 2003 American Institute of Physics.