Research

My research centres on granular rheology and particle diffusion, combining theory, numerical simulation, and tabletop experiments to study particle motion and mechanical response.

Granular Rheology

Granular materials consist of many discrete particles, typically tens of micrometres or larger. Familiar examples include soil, sand, volcanic ash, pollen, cosmetic and medicinal powders, flour, coffee beans, salt, and pachinko balls. I investigate their stiffness, flowability, fragility, mixing, and mobility through rheology—the study of how materials deform and flow.

Although granular materials are familiar and widely used, no unified physical framework yet captures their diverse behaviour. Conventional fluid mechanics and elasticity may fail because the constituent particles are discrete. Moreover, most granular systems are far from thermal equilibrium, making equilibrium statistical mechanics difficult to apply directly. I therefore use simple, well-controlled model systems to identify the physical mechanisms governing each phenomenon.

I choose methods to suit each research question. My theoretical work draws mainly on statistical mechanics and continuum mechanics. For numerical studies, I use the discrete element method (DEM), including large-scale simulations on supercomputers. I also build tabletop experimental setups using sensors and actuators.

Strength and Failure of Granular Media

Dislocation Glide in Granular Crystals

Simulation showing dislocation glide in a granular crystal — Dislocation glide in a two-dimensional granular crystal.

The mechanical response of a granular material depends strongly on particle arrangement. Ordered structures are often stronger than random packings, but lattice defects can alter their response. We found that a single edge dislocation in a granular crystal glides when interparticle friction is low, reducing the yield stress below that of a defect-free crystal. This result connects the strength of granular structures to the Peierls-stress framework developed for atomic crystals.

F. Nakai, T. Uneyama, Y. Sasaki, K. Yoshii, and H. Katsuragi, “Dislocation Glides in Granular Media,” Phys. Rev. Lett. 135, 048202 (2025). APS article
F. Nakai, T. Uneyama, Y. Sasaki, K. Yoshii, and H. Katsuragi, “Dislocation Glides in Monolayered Granular Media: Effect of Lattice Constant,” arXiv:2505.12042 (2025). arXiv preprint

Mixing and Segregation

Size Segregation in Binary Granular Mixtures

Simulation of a binary-sized granular mixture with large red and small brown particles — A vibrated mixture of large and small particles in a confined geometry.

Granular mixtures can segregate under flow when their particles differ in size, mass, or shape. In a confined, quasi-two-dimensional mixture of large and small particles, size segregation occurred when small particles were scarce. Adding enough small particles, however, eliminated the segregation. We are investigating the physical mechanism behind this transition.

F. Nakai and K. Yoshii, “Reducing segregation in vibrated binary-sized granular mixtures by excessive small particle introduction,” Granular Matter 27, 7 (2025). Springer article · arXiv preprint

Particle Diffusion

Microscopic particle motion governs material transport and influences macroscopic flow. Using deliberately simple model systems, I study how particle mass, shape, and environment affect diffusion.

Diffusion of Rod-Shaped Particles

Rod-shaped particle moving through fixed obstacles — A rod-shaped particle moving through fixed obstacles.

Particle mobility usually decreases as the surrounding obstacles become denser, but rod-shaped particles can show the opposite trend. Using a simple, mechanically consistent model, we showed that this increase in diffusivity can arise even in a Markov process and identified the mechanism responsible.

F. Nakai, M. Kröger, T. Ishida, T. Uneyama, Y. Doi, and Y. Masubuchi, “Increase in rod diffusivity emerges even in Markovian nature,” Phys. Rev. E 107, 044604 (2023). APS article · arXiv preprint

Fluctuating Diffusivity in Gases

Particle diffusion in a binary gas mixture.

Fluctuating diffusivity is commonly associated with internal molecular degrees of freedom or the spatiotemporal heterogeneity found in glasses. We showed that diffusivity can also fluctuate in a simple classical gas with neither feature, and used numerical analysis to identify the microscopic origin of the fluctuations.

F. Nakai, Y. Masubuchi, Y. Doi, T. Ishida, and T. Uneyama, “Fluctuating diffusivity emerges even in binary gas mixtures,” Phys. Rev. E 107, 014605 (2023). APS article · arXiv preprint
F. Nakai and T. Uneyama, “Brownian yet non-Gaussian diffusion of a light particle in heavy gas: Lorentz-gas-based analysis,” Phys. Rev. E 108, 044129 (2023). APS article · arXiv preprint

Molecular Diffusion in Cement Paste

Cement paste is heterogeneous at microscopic scales, so assuming constant molecular diffusivity may limit the accuracy of models for gas transport and long-term degradation. In collaboration with Takato Ishida, we developed a molecular-diffusion model with fluctuating diffusivity and analysed the resulting non-Gaussian transport in cement paste.

F. Nakai and T. Ishida, “Gas diffusion in cement pastes: An analysis using a fluctuating diffusivity model,” Constr. Build. Mater. 407, 133411 (2023). ScienceDirect article · arXiv preprint

Tracer Diffusion in an Ideal Gas

Even an ideal gas with no static structure can produce complex tracer dynamics. We identified parameter regimes in which the mean-square displacement develops a plateau and the tracer exhibits strongly non-Gaussian motion.

F. Nakai, Y. Masubuchi, and T. Uneyama, “Short-time dynamics of a tracer in an ideal gas,” Phys. Rev. E 102, 032104 (2020). APS article · arXiv preprint