arXiv subjects

Shugo Yasuda

Publications and source records attributed to Shugo Yasuda.

17 recordsLinked to original sources

arXiv2026

Synchronized molecular dynamics method for thin-layer flows of complex fluids

We propose a multiscale computational method for thin-layer flows of complex fluids, termed the synchronized molecular dynamics (SMD) method, which directly couples local molecular dynamics (MD) simulations with a macroscopic lubrication description. In thin layers, the flow can be decomposed into cross-sectional dynamics that are strongly influenced by interfacial effects, and streamwise transport along the channel. The SMD method exploits this separation of scales by sparsely distributing local MD cells along the channel and synchronizing them through macroscopic conservation laws. In this framework, the macroscopic continuity equation is enforced by iteratively updating the external forces applied to each MD cell, thereby allowing the cross-sectional velocity profiles and the streamwise pressure distribution to be obtained without prescribing constitutive relations or boundary conditions. The method is validated for pressure-driven and wall-driven flows of Lennard--Jones fluids in a wedge-shaped channel, demonstrating excellent agreement with a modified Reynolds equation that accounts for boundary slip. The SMD method is further applied to polymeric lubrication flows modeled by the Kremer--Grest chain model. At large pressure differences, the present approach naturally captures pronounced shear-thinning behavior coupled with microscopic polymer conformation dynamics. The results demonstrate that the SMD method provides an efficient and physically consistent framework for the multiscale simulation of complex fluid thin-layer flows.

physics.flu-dyn↗

arXiv2026

Multiscale analysis of a kinetic equation for mechanotaxis

We present a new kinetic equation for cell migration driven by mechanical interactions with the substrate, an effect not previously captured in kinetic models, and essential for explaining observed collective behaviors such as those in bacterial colonies. The model introduces an acceleration term that accounts for the dynamics of motile cells undergoing mechanotaxis, where extracellular signals modulate the forces arising from cell-substrate interactions. From this formulation, we derive a family of macroscopic limit equations and analyze their principal properties. In particular, we examine linear stability and pattern formation ability through theoretical analysis, supported by numerical simulations.

math.AP↗

arXiv2023

Effect of shear flow on the transverse thermal conductivity of polymer melts

The effect of shear flows on the thermal conductivity of polymer melts is investigated using a reversed nonequilibrium molecular dynamics (RNEMD) method. We extended the original RNEMD method to simultaneously produce spatial gradients of temperature and flow velocity in a single direction. This method enables accurate measurement of the thermal conductivity in the direction transverse to shear flow. The Weissenberg number defined with the shear rate and the relaxation time of the polymer conformation can uniformly differentiate the occurrence of shear rate dependence of the thermal conductivity across different chain lengths. The stress-thermal rule (STR) (i.e., the linear relationship between anisotropic parts of the stress tensor and the thermal conductivity tensor) holds for entangled polymer melts even under shear flows but not for unentangled polymer melts. Furthermore, once entanglements form in polymer chains, the stress-thermal coefficient in the STR remains independent of the polymer chain length. These observations align with the theoretical foundation of the STR, which focuses on energy transmission along the network structure of entangled polymer chains [Brule, Rheol. Acta 28, 257 (1989)]. However, under driven shear flows, the stress-thermal coefficient is notably smaller than that measured in the literature for a quasi-quiescent state without external forces. Although the mechanism of the STR in shear flows has yet to be fully elucidated, our study confirmed the validity of the STR in shear flows. This allows us to use the STR as a constitutive equation for computational thermo-fluid dynamics of polymer melts, thus having broad engineering applications.

cond-mat.soft↗

arXiv2022

Numerical study of the volcano e ect in chemotactic aggregation based on a kinetic transport equation with non-instantaneous tumbling

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.

math.AP↗

arXiv2021

Effects of internal dynamics on chemotactic aggregation of bacteria

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.

math.AP↗

arXiv2020

Numerical scheme for kinetic transport equation with internal state *

We investigate the numerical discretization of a two-stream kinetic system with an internal state, such system has been introduced to model the motion of cells by chemotaxis. This internal state models the intracellular methylation level. It adds a variable in the mathematical model, which makes it more challenging to simulate numerically. Moreover, it has been shown that the macroscopic or mesoscopic quantities computed from this system converge to the Keller-Segel system at diffusive scaling or to the velocity-jump kinetic system for chemotaxis at hyperbolic scaling. Then we pay attention to propose numerical schemes uniformly accurate with respect to the scaling parameter. We show that these schemes converge to some limiting schemes which are consistent with the limiting macroscopic or kinetic system. This study is illustrated with some numerical simulations and comparisons with Monte Carlo simulations.

math.AP↗

arXiv2019

Multiple asymptotics of Kinetic Equations with Internal States

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. The present study aims at deriving models at the macroscopic scale from assumptions on the microscopic scales. In particular we are interested in comparisons between the stiffness of the response and the adaptation time. 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.

math.AP↗

arXiv2019

Solidification of the Lennard-Jones fluid near the wall in thermohydrodynamic lubrication

We investigate the thermohydrodynamic lubrication of the Lennard-Jones (LJ) fluid in the parallel-plate channel composed of the LJ particles by using molecular dynamics (MD) simulation. We discover a counterintuitive solidification of the LJ fluid near the wall, i.e., \textit{viscous heating-induced solidification}, where solidification occurs only when the viscous heating of the LJ fluid is sufficiently large. The solidification mechanism is investigated from both macroscopic and microscopic points of view. It is found that the LJ molecules are densely confined in the vicinity of the wall via the thermohydrodynamic transport of the bulk fluid and that when the local density in the vicinity of the wall is close to the solidification line in the phase diagram, the LJ molecules are solidified due to the interaction with the crystallized wall molecules. Band formation is also observed in the highly confined regime when the channel width is sufficiently large.

cond-mat.soft↗

arXiv2018

Stiff-response-induced instability for chemotactic bacteria and flux-limited Keller-Segel equation

Collective motion of chemotactic bacteria as E. Coli relies, at the individual level, on a continuous reorientation by runs and tumbles. It has been established that the length of run is decided by a stiff response to a temporal sensingof chemical cues along the pathway.We describe a novel mechanism for pattern formation stemming from the stiffness of chemotactic response relying on a kinetic chemotaxis model which includes a recently discovered formalism for the bacterial chemotaxis. We prove instability both for amicroscopic description in the space-velocity space and for the macroscopic equation, a flux-limited Keller-Segel equation, which has attracted much attention recently.A remarkable property is that the unstable frequencies remain bounded, as it is the case in Turing instability. Numerical illustrations based on a powerful Monte Carlo method show that the stationary homogeneous state of population density isdestabilized and periodic patterns are generated in realistic ranges of parameters. These theoretical developments are in accordance with several biological observations.

math.AP↗

arXiv2017

Traveling Wave and Aggregation in a Flux-Limited Keller-Segel Model

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 counterbalancing 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.

math.AP↗

arXiv2017

A Monte Carlo simulation for kinetic chemotaxis models: an application to the traveling population wave

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.

physics.bio-ph↗

arXiv2014

Synchronized molecular dynamics simulation via macroscopic heat and momentum transfer: an application to polymer lubrication

The synchronized molecular dynamics simulation via macroscopic heat and momentum transfer is proposed for the non-isothermal 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 with ten beads between parallel plates. The rheological properties and conformation of polymer chains coupled with the 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 behavior of the conformation of the polymer chains occur 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 and heat generation under shear flows.

cond-mat.soft↗

arXiv2011

Dynamic rheology of a supercooled polymer melt in non-uniform oscillating flows in rapidly oscillating plates

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 rapidly oscillating plates, non-uniform 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. 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. Non-linear 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 non-slip boundary on the oscillating plate. We also find that the melt exhibits inter-cycle shear thinning between different positions but exhibits intra-cycle shear thickening at a fixed position in the vicinity of the plate.

cond-mat.soft↗

arXiv2011

Multiscale Simulations for Polymeric Flow

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 MD and CFD simulations is developed based on the local equilibrium assumption without memories of the flow history. (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.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 polymer-chain 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.

cond-mat.soft↗

arXiv2009

Multiscale modeling and simulation for polymer melt flows between parallel plates

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, visco-elastic liquid, and visco-elastic solid regimes, form over the oscillating plate according to the local Deborah numbers. The melt behaves as a viscous fluid in a region for $ωτ^R\lesssim 1$, and the crossover between the liquid-like and solid-like regime takes place around $ωτ^α\simeq 1$ (where $ω$ is the angular frequency of the plate and $τ^R$ and $τ^α$ are Rouse and $α$ relaxation time, respectively).

cond-mat.soft↗

arXiv2009

Rheology of a supercooled polymer melt near an oscillating plate: an application of multiscale modeling

The behavior of a supercooled polymer melt composed of short chains with ten beads near an oscillating plate are simulated by using a hybrid simulation of molecular dynamics (MD) and computational fluid dynamics (CFD). In the method, the macroscopic dynamics are solved by using CFD, but, instead of using any constitutive equations, a local stress is calculated by using a non-equilibrium MD simulation associated at each lattice node in the CFD calculation. It is seen that the local rheology of the melt varies considerably in a thin viscous diffusion layer that arises near an oscillating plate. It is also found that the local rheology of the melt is divided into the three different regimes, i.e., the viscous fluid, viscoelastic liquid, and viscoelastic solid regimes, according to the local Deborah number $De$, which is defined with the Rouse or $α$ relaxation time, $τ_R$ or $τ_α$, and the angular frequency of the plate $ω$ as $De^R$=$ωτ_R$ or $De^α$=$ωτ_α$. The melt behaves as a viscous fluid when $De^R\lesssim 1$, and the crossover between the liquid-like and solid-like regime takes place around $De^α\simeq 1$.

cond-mat.soft↗

arXiv2008

A Model for Hybrid Simulations of Molecular Dynamics and CFD

We propose a method for multi-scale hybrid simulations of molecular dynamics (MD) and computational fluid dynamics (CFD). In the method, usual lattice-mesh based simulations are applied for CFD level, but each lattice is associated with a small MD cell which generates a "local stress" according to a "local flow field" given from CFD instead of using any constitutive functions at CFD level. We carried out the hybrid simulations for some elemental flow problems of simple Lennard-Jones liquids and compared the results with those obtained by usual CFDs with a Newtonian constitutive relation in order to examine the validity of our hybrid simulation method. It is demonstrated that our hybrid simulations successfully reproduced the correct flow behavior obtained from usual CFDs as far as the mesh size $Δx$ and the time-step $Δt$ of CFD are not too large comparing to the system size $l_{\rm MD}$ and the sampling duration $t_{\rm MD}$ of MD simulations performed at each time step of CFDs. Otherwise, simulations are affected by large fluctuations due to poor statistical averages taken in the MD part. Properties of the fluctuations are analyzed in detail.

cond-mat.soft↗