arXiv subjects

Kuniyasu Saitoh

Publications and source records attributed to Kuniyasu Saitoh.

At least 19 recordsLinked to original sources

arXiv2026

Weakly Nonlinear Dynamics of Unstable Modes in Jammed Amorphous Solids

We investigate the structural evolution in jammed amorphous solids by analyzing the eigenmodes of a generalized Hessian matrix that incorporates spatial modulation via wave numbers. Unlike the conventional Hessian, this generalized formulation captures linearly unstable modes through a Fourier-based extension of the Hessian matrix, enabling us to study responses beyond the mechanically stable regime. We demonstrate that the excitation of unstable eigenmodes leads to structural rearrangements independent of the initial perturbation by the simulation. Furthermore, we derive a weakly nonlinear amplitude equation to describe the growth and saturation of these unstable modes, analogous to the Landau equation. Our framework provides a pathway to understand instability-driven configuration changes in disordered solids.

cond-mat.stat-mech↗

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

Relaxation dynamics and long-time tails explain shear-induced diffusion of soft athermal particles near jamming

We numerically study shear-induced diffusion of soft athermal particles in two dimensions. The Green-Kubo (GK) formula is applicable to the shear-induced diffusion coefficient, where both mean squared transverse velocity and relaxation time included in the GK formula are well described by critical scaling near jamming. We show that the auto-correlation function of transverse velocities is stretched exponential if the system is below jamming or shear rate is large enough. However, if the system is above jamming and the shear rate is sufficiently small, the auto-correlation function exhibits a long-time tail such that time integral in the GK formula diverges in two dimensions. We propose an empirical scaling relation for the critical exponents and show that the long-time tail is consistent with the divergence of the shear-induced diffusion coefficient.

cond-mat.soft↗

arXiv2025

Jamming transition and normal modes of polydispersed soft particle packing

The jamming transition of soft particles characterized by narrow size distributions has been well studied by physicists. However, polydispersed systems are more relevant to engineering, and the influence of polydispersity on jamming phenomena is still unexplored. Here, we numerically investigate jamming transitions of polydispersed soft particles in two dimensions. We find that polydispersity strongly influences contact forces, local coordination, and the jamming transition density. In contrast, the critical scaling of pressure and elastic moduli is not affected by the particle size distribution. Consistent with this observation, we find that the vibrational density of states is also insensitive to the polydispersity. Our results suggest that, regardless of particle size distributions, both mechanical and vibrational properties of soft particle packings near jamming are governed by the distance to jamming.

cond-mat.soft↗

arXiv2024

Unified study of viscoelasticity and sound damping in hard and soft amorphous solids

Recent research has made significant progress in understanding the non-phonon vibrational states present in amorphous materials. It has been established that their vibrational density of states follows non-Debye scaling laws. Here, we show that the non-Debye scaling laws play a crucial role in determining material properties of a broad range of amorphous solids, from ``hard" amorphous solids like structural glasses to ``soft" amorphous solids such as foams and emulsions. We propose a unified framework of viscoelasticity and sound damping for these materials. Although these properties differ significantly between hard and soft amorphous solids, they are determined by the non-Debye scaling laws. We also validate our framework using numerical simulations.

cond-mat.soft↗

arXiv2023

Scaling relations between viscosity and diffusivity in shear-thickening suspensions

Dense suspensions often exhibit a dramatic response to large external deformation. The recent body of work has related this behavior to transition from an unconstrained lubricated to a constrained frictional state. Here, we use numerical simulations to study the flow behavior and shear-induced diffusion of frictional non-Brownian spheres in two dimensions under simple shear flow. We first show that both viscosity $η$ and diffusivity $D/\dotγ$ of the particles increase at characteristic shear stress, which is associated with lubrication to frictional transition. Subsequently, we propose a one-to-one relation between viscosity and diffusivity using the length scale $ξ$ associated with the size of collective motions (rigid clusters) of the particles. We demonstrate that $η$ and $D/\dotγ$ are controlled by $ξ$ in two distinct flow regimes, i.e. in the frictionless and frictional states, where the one-to-one relation is described as a crossover from $D/\dotγ\simη$ ({frictionless}) to $η^{1/3}$ ({frictional}). We also confirm the proposed power laws are insensitive to the interparticle friction and system size.

cond-mat.soft↗

arXiv2023

Theory of rigidity and numerical analysis of density of states of two-dimensional amorphous solids with dispersed frictional grains in the linear response regime

Using the Jacobian matrix, we obtain theoretical expression of rigidity and the density of states of two-dimensional amorphous solids consisting of frictional grains in the linear response to an infinitesimal strain, in which we ignore the dynamical friction caused by the slip processes of contact points. The theoretical rigidity agrees with that obtained by molecular dynamics simulations. We confirm that the rigidity is smoothly connected to the value in the frictionless limit. For the density of states, we find that there are two modes in the density of states for sufficiently small $k_{T}/k_{N}$, which is the ratio of the tangential to normal stiffness. Rotational modes exist at low frequencies or small eigenvalues, whereas translational modes exist at high frequencies or large eigenvalues. The location of the rotational band shifts to the high-frequency region with an increase in $k_{T}/k_{N}$ and becomes indistinguishable from the translational band for large $k_{T}/k_{N}$. The rigidity determined by the translational modes agrees with that obtained by the molecular dynamics simulations, whereas the contribution of the rotational modes is almost zero for small $k_{T}/k_{N}$.

cond-mat.soft↗

arXiv2023

The role of microscopic friction in statistics and scaling laws of avalanches

We investigate statistics and scaling laws of avalanches in two-dimensional frictional particles by numerical simulations. We find that the critical exponent for avalanche size distributions is governed by microscopic friction between the particles in contact, where the exponent is larger and closer to mean-field predictions if the friction coefficient is finite. We reveal that microscopic ``slips" between frictional particles induce numerous small avalanches which increase the slope, as well as the power-law exponent, of avalanche size distributions. We also analyze statistics and scaling laws of the avalanche duration and maximum stress drop rates, and examine power spectra of stress drop rates. Our numerical results suggest that the microscopic friction is a key ingredient of mean-field descriptions and plays a crucial role in avalanches observed in real materials.

cond-mat.soft↗

arXiv2023

Avalanche Interpretation of the Power-Law Energy Spectrum in Three-Dimensional Dense Granular Flow

Turbulence is ubiquitous in nonequilibrium systems, and it has been noted that even dense granular flows exhibit characteristics that are typical of turbulent flow, such as the power-law energy spectrum. However, studies on the turbulent-like behavior of granular flows are limited to two-dimensional (2D) flow. We demonstrate that the statistics in three-dimensional (3D) flow are qualitatively different from those in 2D flow. We also elucidate that avalanche dynamics can explain this dimensionality dependence. Moreover, we define clusters of collectively moving particles that are equivalent to vortex filaments. The clusters unveil complicated structures in 3D flows that are absent in 2D flows.

cond-mat.soft↗

arXiv2023

Eigenvalue analysis of stress-strain curve of two-dimensional amorphous solids of dispersed frictional grains with finite shear strain

The stress-strain curve of two-dimensional frictional dispersed grains interacting with a harmonic potential without considering the dynamical slip under a finite strain is determined by using eigenvalue analysis of the Hessian matrix. After the configuration of grains is obtained, the stress-strain curve based on the eigenvalue analysis is in almost perfect agreement with that obtained by the simulation, even if there are plastic deformations caused by stress avalanches. Unlike the naive expectation, the eigenvalues in our model do not indicate any precursors to the stress-drop events.

cond-mat.soft↗

arXiv2021

Localized and extended dynamical correlation lengths in jammed packings of soft athermal disks under slow shear

Dynamics of jammed packings of soft athermal disks under finite-rate shear are studied by means of molecular dynamics simulations. Particularly, we investigate the spatial structures of stress drop events, which are expected to provide information about plasticity. Investigating the displacement fields during stress drop events, we show that there are qualitatively different two types of events in the low rate limit: localized ones and extended ones. We further investigate the time evolution of events and clarify that both types of events are due to oscillatory motion of the stress, which is unique for systems under finite-rate shear. The difference between two types of events is the regime that events reside in: while localized events take place during plastic events, extended ones occur in the elastic branch.

cond-mat.soft↗

arXiv2021

Dynamic susceptibilities in dense soft athermal spheres under a finite-rate shear

The mechanical responses of dense packings of soft athermal spheres under a finite-rate shear are studied by means of molecular dynamics simulations. We investigate the volume fraction and shear rate dependence of the fluctuations in the shear stress and the interparticle contact number. In particular, we quantify them by defining the susceptibility as the ratio of the global to local fluctuations. The obtained susceptibilities form ridges on the volume fraction-shear rate plane, which are reminiscent of the Widom lines around the critical point in an equilibrium phase transition.

cond-mat.soft↗

arXiv2020

Sound damping in frictionless granular materials: The interplay between configurational disorder and inelasticity

We numerically investigate sound damping in a model of granular materials in two dimensions. We simulate evolution of standing waves in disordered frictionless disks and analyze their damped oscillations by velocity autocorrelation functions and power spectra. We control the strength of inelastic interactions between the disks in contact to examine the effect of energy dissipation on sound characteristics of disordered systems. Increasing the strength of inelastic interactions, we find that (i) sound softening vanishes and (ii) sound attenuation due to configurational disorder, i.e. the Rayleigh scattering at low frequencies and disorder-induced broadening at high frequencies, is completely dominated by the energy dissipation. Our findings suggest that sound damping in granular media is determined by the interplay between elastic heterogeneities and inelastic interactions.

cond-mat.soft↗

arXiv2020

Structural and mechanical characteristics of sphere packings near the jamming transition: From fully amorphous to quasi-ordered structures

Mechanically stable sphere packings are generated in three-dimensional space using the discrete element method, which span a wide range in structural order, ranging from fully amorphous to quasi-ordered structures, as characterized by the bond orientational order parameter. As the packing pressure, $p$, varies from the marginally rigid limit at the jamming transition ($p \approx 0$) to that of more robust systems ($p \gg 0$), the coordination number, $z$, follows a familiar scaling relation with pressure, namely, $Δz = z - z_c \sim p^{1/2}$, where $z_c = 2d = 6$ ($d=3$ is the spatial dimension). While it has previously been noted that $Δz$ does indeed remain the control parameter for determining the packing properties, here we show how the packing structure plays an influential role on the mechanical properties of the packings. Specifically, we find that the elastic (bulk $K$ and shear $G$) moduli, generically referred to as $M$, become functions of both $Δz$ and the structure, to the extent that $M-M_c \sim Δz$. Here, $M_c$ are values of the elastic moduli at the jamming transition, which depend on the structure of the packings. In particular, the zero shear modulus, $G_c=0$, is a special feature of fully amorphous packings, whereas more ordered packings take larger, positive values, $G_c > 0$.

cond-mat.soft↗

arXiv2020

Critical scaling of diffusion coefficients and size of rigid clusters of soft athermal particles under shear

We numerically investigate the self-diffusion coefficient and correlation length of the rigid clusters (i.e., the typical size of the collective motions) in sheared soft athermal particles. Here we find that the rheological flow curves on the self-diffusion coefficient are collapsed by the proximity to the jamming transition density. This feature is in common with the well-established critical scaling of flow curves on shear stress or viscosity. We furthermore reveal that the divergence of the correlation length governs the critical behavior of the diffusion coefficient, where the diffusion coefficient is proportional to the correlation length and the strain rate for a wide range of the strain rate and packing fraction across the jamming transition density.

cond-mat.soft↗

arXiv2019

Stress relaxation above and below the jamming transition

We numerically investigate stress relaxation in soft athermal disks to reveal critical slowing down when the system approaches the jamming point. The exponents describing the divergence of the relaxation time differ dramatically depending on whether the transition is approached from the jammed or unjammed phase. This contrasts sharply with conventional dynamic critical scaling scenarios, where a single exponent characterizes both sides. We explain this surprising difference in terms of the vibrational density of states (vDOS), which is a key ingredient of linear viscoelastic theory. The vDOS exhibits an extra slow mode that emerges below jamming, which we utilize to demonstrate the anomalous exponent below jamming.

cond-mat.soft↗

arXiv2019

Universal relaxation dynamics of sphere packings below jamming

We show that non-Brownian suspensions of repulsive spheres below jamming display a slow relaxational dynamics with a characteristic time scale that diverges at jamming. This slow time scale is fully encoded in the structure of the unjammed packing and can be readily measured via the vibrational density of states. We show that the corresponding dynamic critical exponent is the same for randomly generated and sheared packings. Our results show that a wide variety of physical situations, from suspension rheology to algorithmic studies of the jamming transition are controlled by a unique diverging timescale, with a universal critical exponent.

cond-mat.soft↗

arXiv2018

Transition rates for slip-avalanches in soft athermal disks under quasi-static simple shear deformations

We study slip-avalanches in two-dimensional soft athermal disks by quasi-static simulations of simple shear deformations. Sharp drops in shear stress, or slip-avalanches, are observed intermittently during steady state. Such the stress drop is caused by restructuring of the contact networks, accompanied by drastic changes of the interaction forces. The changes of the forces happen heterogeneously in space, indicating that collective non-affine motions of the disks are most pronounced when slip-avalanches occur. We analyze and predict statistics for the force changes, by transition rates of the force and contact angle, where slip-avalanches are characterized by their wide power-law tails. We find that the transition rates are described as a q-Gaussian distribution regardless of the area fraction of the disks. Because the transition rates quantify structural changes of the force-chains, our findings are an important step towards a microscopic theory of slip-avalanches in the experimentally accessible quasi-static regime.

cond-mat.soft↗