arXiv subjects

Fumiaki Nakai

Publications and source records attributed to Fumiaki Nakai.

12 recordsLinked to original sources

arXiv2026

Granular Rods Fall Faster in Denser Obstacle Fields

How does particle shape affect driven transport through obstacle fields? We simulate a dissipative rod falling under gravity through randomly placed fixed obstacles. For sufficiently slender rods, the mean descent speed before trapping decreases, increases, and then decreases again as obstacle density rises, opening a window of densities in which rods fall faster in denser fields. Scaling arguments based on collision rates and rod geometry explain the three regimes and their crossovers. Particle shape can thus reverse the expectation that crowding slows driven transport.

cond-mat.soft↗

arXiv2026

Steady shear rheology of a granular crystal containing a single dislocation

Monodisperse granular particles can form crystals whose yielding behavior is strongly affected by dislocations and differs markedly from that of conventional amorphous granular materials. Yet the rate dependence of their post-yield steady rheology remains unclear. We use the discrete element method to study steady shear in a granular crystal containing a single dislocation. We find that the steady shear-to-normal stress ratio $μ_b$ is organized by the scaled dislocation velocity $v_d/v_s$, rather than by the conventional inertial number $I$. Here, $v_d$ is related to the imposed shear rate through Orowan kinematics, and $v_s$ is a characteristic Hertzian elastic-wave speed. At low $v_d/v_s$, the stress ratio approaches a small plateau associated with the elastic lattice barrier and interparticle friction. At intermediate values of $v_d/v_s$, contact damping strongly affects the approximately linear increase of the stress ratio above the plateau. As $v_d/v_s$ approaches unity, the stress develops a stronger nonlinear velocity dependence. At still higher velocities, the coordination deficit rises sharply, marking the breakdown of crystalline order and the end of the single-dislocation description. These results identify the scaled dislocation velocity as the relevant rate variable for the steady rheology of dislocation-mediated granular flow and clarify the distinct roles of interparticle friction and contact damping in the low- and intermediate-velocity regimes, respectively.

cond-mat.soft↗

arXiv2026

Anomalous phonon dispersion near yielding in athermal crystals

Vibrational properties of ordered athermal solids near yielding remain poorly understood. We show that yielding in a sheared crystal is governed not by a single localized instability but by directionally extended multimode softening that forms a cross-shaped low-frequency region in wave number space. Near yielding, the acoustic dispersion $ω\sim k$ is replaced by $ω\sim k^2$ along the soft direction, and the vibrational density of states crosses over from Debye to non-Debye scaling, with a diverging length scale. We analytically derive these scaling laws.

cond-mat.mtrl-sci↗

arXiv2025

Dislocation Glides in Monolayered Granular Media: Effect of Lattice Constant

A recent study demonstrated that granular crystals containing a single dislocation exhibit dislocation glide analogous to that observed in atomic-scale crystals, resulting in plastic deformation at yield stresses several orders of magnitude lower than those of dislocation-free crystals. The yielding behavior strongly depends on the interparticle friction coefficient $μ$: dislocation glide occurs for friction coefficients below a critical value $μ_c$, while crystalline order deteriorates above $μ_c$. In this work, we use discrete element method simulations to systematically investigate how the lattice constant, which determines the interparticle spacing and is a fundamental parameter in microscopic crystalline solids, and the friction coefficient $μ$ influence the yielding behavior in monolayered granular crystals with dislocation. By decreasing the lattice constant, we find an increase in the critical friction coefficient $μ_c$, allowing dislocation glide to persist at higher friction values. Furthermore, we observe a linear scaling of yield stress with normal stress, except at extremely low friction coefficients.

cond-mat.soft↗

arXiv2024

Dislocation Glides in Granular Media

Atomic crystals with dislocations deform plastically at low stresses via dislocation glide. Whether dislocation glide occurs in macroscopic frictional granular media has remained unknown. The discrete element method is employed to simulate the structural and mechanical responses of a granular crystal with an edge dislocation. We find that dislocation glide occurs at low interparticle friction, resulting in significantly lower yield stresses than in dislocation-free crystals. Yield stress varies linearly with interparticle friction, attributed to both Peierls stress and frictional effect.

cond-mat.mtrl-sci↗

arXiv2024

Reducing segregation in vibrated binary-sized granular mixtures by excessive small particle introduction

We numerically examine binary-sized granular mixtures confined between two parallel walls subjected to vertical vibration using the discrete element method. For a size ratio of $3$ between large and small particles, we study the structure of large particles in moderately dense regimes where the combined two-dimensional packing fractions of both particle sizes exceed $1$. When the fraction of small particles is small, segregation of the large particles occurs. In contrast, as the fraction of small particles increases, an effective repulsion between the large particles emerges over distances greater than the large particle diameter, suppressing their segregation. The emergence of reduction in segregation is confirmed for another size ratio, vibrational acceleration, system size, and for a case of bidisperse size distribution. Additionally, at the size ratio of $3$, the effective repulsion induces a hexagonal phase of the large particles at packing fractions lower than in mono-component systems. This work will provide a fresh insight into granular physics, prompting further experimental and theoretical study.

cond-mat.soft↗

arXiv2024

Brownian Yet Non-Gaussian Diffusion of a Light Particle in Heavy Gas: Lorentz Gas Based Analysis

Non-Gaussian diffusion was recently observed in gas mixtures with mass and fraction contrast [F. Nakai et al, Phys. Rev. E 107, 014605 (2023)]. The mean square displacement of a minor gas particle with a small mass is linear in time, while the displacement distribution deviates from the Gaussian distribution, which is called the Brownian yet non-Gaussian diffusion. In this work, we theoretically analyze this case where the mass contrast is sufficiently large. Major heavy particles can be interpreted as immobile obstacles, and a minor light particle behaves like a Lorentz gas particle within an intermediate time scale. Despite the similarity between the gas mixture and the conventional Lorentz gas system, the Lorentz gas description cannot fully describe the Brownian yet non-Gaussian diffusion. A successful description can be achieved through an ensemble average of the statistical quantities of the Lorentz gas over the initial speed.

cond-mat.stat-mech↗

arXiv2023

Increase in rod diffusivity emerges even in Markovian nature

Rod-shaped particles embedded in certain matrices have been reported to exhibit an increase in their center of mass diffusivity upon increasing the matrix density. This increase has been considered to be caused by a kinetic constraint in analogy with tube models. We investigate a mobile rod-like particle in a sea of immobile point obstacles using a kinetic Monte Carlo scheme equipped with a Markovian process, that generates gas-like collision statistics, so that such kinetic constraints do essentially not exist. Even in such a system, provided the particle's aspect ratio exceeds a threshold value of about 24, the unusual increase in the rod diffusivity emerges. This result implies that the kinetic constraint is not a necessary condition for the increase in the diffusivity.

cond-mat.stat-mech↗

arXiv2023

Gas Diffusion in Cement Pastes: An Analysis using a Fluctuating Diffusivity Model

This work propose an application of the concept of fluctuating diffusivity to the diffusion of gas molecules in cementitious materials, particularly through a two-state fluctuating diffusivity (2SFD) model. The 2SFD model is utilized to investigate the diffusion of oxygen in cement pastes. The analysis provides a reasonable description of the diffusion coefficient of oxygen in cement pastes, and highlights the presence of non-Gaussian diffusion, which can be attributed to the heterogeneous microstructure. The presence of non-Gaussianity in the probability density of the molecule's displacement, characterized by heavier tails than those of the Gaussian distribution, may have a significant impact on the durability assessments of concrete structures.

cond-mat.soft↗

arXiv2023

Fluctuating Diffusivity Emerges even in Binary Gas Mixtures

Diffusivity in some soft matter and biological systems changes with time, called the fluctuating diffusivity. In this work, we propose a novel origin for fluctuating diffusivity based on stochastic simulations of binary gas mixtures. In this system, the fraction of one component is significantly small, and the mass of the minor component molecule is different from that of the major component. The minor component exhibits fluctuating diffusivity when its mass is sufficiently smaller than that of the major component. We elucidate that this fluctuating diffusivity is caused by the time scale separation between the relaxation of the velocity direction and the speed of the minor component molecule.

cond-mat.stat-mech↗

arXiv2020

Short time dynamics of tracer in ideal gas

A small tagged particle immersed in a fluid exhibits the Brownian motion and diffuses at the long-time scale. Meanwhile, at the short-time scale, the dynamics of the tagged particle cannot be simply described by the usual generalized Langevin equation with the Gaussian noise, since the number of collisions between the tagged particle and fluid particles is rather small. At such a time scale, we should explicitly consider individual collision events between the tagged particle and the surrounding fluid particles. In this study, we analyzed the short-time dynamics of the tagged particle in an ideal gas, where we do not have static nor hydrodynamic correlations between fluid particles. We performed event-driven hard sphere simulations and show that the short-time dynamics of the tagged particle is correlated even under such an idealized situation. Namely, the velocity autocorrelation function becomes negative when the tagged particle is relatively light and the fluid density is relatively high. This result can be attributed to the dynamical correlation between collision events. To investigate the physical mechanism, which causes the dynamical correlation, we analyzed the correlation between successive collision events. We found that the tagged particle can collide with the same ideal gas particle several times, and such collisions cause the strong dynamical correlation for the velocity.

cond-mat.stat-mech↗

arXiv2019

Effect of Inertia on Linear Viscoelasticity of Harmonic Dumbbell Model

The overdamped (inertialess) dumbbell model is widely utilized to study rheological properties of polymers or other soft matters. In most cases, the effect of inertia is merely neglected because the momentum relaxation is much faster than the bond relaxation. We theoretically analyze the effect of inertia on the linear viscoelasticity of the harmonic dumbbell model. We show that the momentum and bond relaxation modes are kinetically coupled and the inertia can affect the bond relaxation if the momentum relaxation is not sufficiently fast. We derive an overdamped Langevin equation for the dumbbell model, which incorporates the weak inertia effect. Our model predicts the bond relaxation dynamics with the weak inertia effect correctly. We discuss how the weak inertia affects the linear viscoelasticity of a simple harmonic dumbbell model and the Rouse model.

cond-mat.soft↗