arXiv subjects

Atsushi Ikeda

Publications and source records attributed to Atsushi Ikeda.

At least 19 recordsLinked to original sources

arXiv2026

Hyperuniformity near jamming transition over a wide range of bidispersity

We numerically investigate hyperuniformity in two-dimensional frictionless jammed packings of bidisperse systems. Hyperuniformity is characterized by the suppression of density fluctuations at large length scales, and the structure factor asymptotically vanishes in the small-wavenumber limit as $S(q) \propto q^α$, where $α> 0$. It is well known that jammed configurations exhibit hyperuniformity over a wide range of wavenumbers windows, down to $q^{\ast}σ\approx 0.2$, where $σ$ is the particle diameter. In two dimensions, we find that the exponent $α$ is approximately $0.6\text{--}0.7$. This contrasts with the reported value of $α= 1$ for three-dimensional systems. We employ an advanced method recently introduced by Rissone \textit{et al.} \href{https://link.aps.org/doi/10.1103/PhysRevLett.127.038001}{[Phys. Rev. Lett. {\bf 127}, 038001 (2021)]}, originally developed for monodisperse and three-dimensional systems, to determine $α$ with high precision. This exponent is found to be unchanged for all size ratios between small and large particles, except in the monodisperse case, where the system crystallizes.

cond-mat.soft↗

arXiv2025

Prym loci of branched double coverings and generalized Andreotti-Mayer loci

The Andreotti-Mayer locus is a subset of the moduli space of principally polarized abelian varieties, defined by a condition on the dimension of the singular locus of the theta divisor. It is known that the Jacobian locus in the moduli space is an irreducible component of the Andreotti-Mayer locus. In this paper, we generalize the Andreotti-Mayer locus to the case of the moduli space of abelian varieties with non-principal polarization and prove that the Prym locus of branched double coverings is an irreducible component of the generalized Andreotti-Mayer locus.

math.AG↗

arXiv2025

Enhanced collective vibrations in granular materials

Granular materials are defined as collections of macroscopic dissipative particles. Although these systems are ubiquitous in our lives, the nature and the causes of their non-trivial collective dynamics still remain elusive and have attracted significant interest in non-equilibrium physics. Here, we focus on the vibrational dynamics of granular materials. While the vibrational dynamics of random packings have been examined concerning the jamming transition, previous research has overlooked the role of contact dissipations. We conducted numerical and analytical investigations into the vibrational dynamics of random packings influenced by the normal dissipative force, which is the simplest model for contact dissipations. Our findings reveal that the kinetic energy per mode diverges in the low-frequency range, following the scaling law $\mathcal{K}_l \propto ω^{-2}_l$ with the frequency $ω_l$, indicating that low-frequency modes experience strong excitation and that the equipartition of energy is violated. Additionally, the spatial structure factor of the velocity field displays the scaling law $S_v(q) \propto q^{-2}$ with the wavenumber $q$, which signifies that the velocity field has an infinitely long range. We demonstrate that these phenomena arise from the effects of weaker damping on softer modes, where the particle displacements parallel to the contacts are minimal in the low-frequency modes, rendering normal dissipation ineffective at dampening these modes.

cond-mat.soft↗

arXiv2024

Flow of supercooled liquids under dipolar force field

The viscosity of supercooled liquids notably increases with decreasing temperature, leading to solidification through a glass transition. This process is accompanied by dynamic heterogeneity, characterized by persistent dynamic spatial correlations. This study investigates how dynamic heterogeneity influences the applicability of the Navier-Stokes equations to the flow of supercooled liquids. Utilizing molecular dynamics simulations, we subjected a two-dimensional supercooled liquid to a localized dipolar force field and compared the resulting steady velocity field with the prediction from the Navier-Stokes equations. Our approach captures a significant breakdown of the Navier-Stokes equations in real space; specifically, supercooled liquids flow more rapidly near the external force than the prediction from the Navier-Stokes equations. Furthermore, this deviation is enhanced by the supercooling and is accompanied by the growth of dynamic heterogeneity.

cond-mat.soft↗

arXiv2024

Avalanche criticality emerges by thermal fluctuation in a quiescent glass

We report avalanche criticality of thermal relaxation in glassy systems after a rapid quench by molecular simulation. Our analysis of the energy landscape and the scaling reveals that particle rearrangement is critical. The critical phenomenon has the same origin as avalanches in sheared amorphous solids, but the critical exponent differs from previously observed. Our results suggest that by viewing a glass as a thermally driven elastoplastic material, we can understand dynamics below the glass transition point, such as aging.

cond-mat.soft↗

arXiv2024

Effective medium theory for viscoelasticity of soft jammed solids

The viscoelastic properties of soft jammed solids, such as foams, emulsions, and soft colloids, have been the subject of experiments, with particular interest in the anomalous viscous loss. However, a microscopic theory to explain these experimental results is still lacking. Here, we develop an effective medium theory that incorporates the effects of contact damping. The theory explains experimentally observed viscoelastic properties, particularly attributing the anomalous viscous loss to marginal stability in amorphous systems. This work establishes a microscopic theory for describing the impact of damping on soft jammed solids and their viscoelastic behaviors.

cond-mat.soft↗

arXiv2024

Structural fluctuations in active glasses

The glassy dynamics of dense active matter have recently become a topic of interest due to their importance in biological processes such as wound healing and tissue development. However, while the liquid-state properties of dense active matter have been studied in relation to the glass transition of active matter, the solid-state properties of active glasses have yet to be understood. In this work, we study the structural fluctuations in the active glasses composed of self-propelled particles. We develop a formalism to describe the solid-state properties of active glasses in the harmonic approximation limit and use it to analyze the displacement fields in the active glasses. Our findings reveal that the dynamics of high-frequency normal modes become quasi-static with respect to the active forces, and consequently, excitations of these modes are significantly suppressed. This leads to a violation of the equipartition law, suppression of particle displacements, and the apparent collective motion of active glasses. Overall, our results provide a fundamental understanding of the solid-state properties of active glasses.

cond-mat.soft↗

arXiv2024

Universal mechanism of shear thinning in supercooled liquids

Soft glassy materials experience a significant reduction in viscosity $η$ when subjected to shear flow, known as shear thinning. This phenomenon is characterized by a power-law scaling of $η$ with the shear rate $\dotγ$, $η\propto \dotγ^{-ν}$, where the exponent $ν$ is typically around $0.7$ to $0.8$ across different materials. Two decades ago, the mode coupling theory (MCT) suggested that shear thinning occurs due to the advection. However, it predicts too large $ν= 1$ (> $0.7$ to $0.8$) and overestimates the onset shear rate by orders of magnitude. Recently, it was claimed that a minute distortion of the particle configuration is responsible for shear thinning. Here we extend the MCT to include the distortion, and find that both advection and distortion contribute to shear thinning, but the latter is dominant. Our formulation works quantitatively for several different glass formers. We explain why shear thinning is universal for many glassy materials.

cond-mat.soft↗

arXiv2024

A replica theory for the dynamic glass transition of hardspheres with continuous polydispersity

Glassy soft matter is often continuously polydisperse, in which the sizes or various properties of the constituent particles are distributed continuously. However, most of the microscopic theories of the glass transition focus on the monodisperse particles. Here, we developed a replica theory for the dynamic glass transition of continuously polydisperse hardspheres. We focused on the limit of infinite spatial dimension, where replica theory becomes exact. In theory, the cage size $A$, which plays the role of an order parameter, appears to depend on the particle size $σ$, and thus, the effective free energy, the so-called Franz-Parisi potential, is a functional of $A(σ)$. We applied this theory to two fundamental systems: a nearly monodisperse system and an exponential distribution system. We found that dynamic decoupling occurs in both cases; the critical particle size $σ^{\ast}$ emerges, and larger particles with $σ\geq σ^{\ast}$ vitrify, while smaller particles $σ< σ^{\ast}$ remain mobile. Moreover, the cage size $A(σ)$ exhibits a critical behavior at $σ\simeq σ^{\ast}$, originating from spinodal instability of $σ^{\ast}$-sized particles. We discuss the implications of these results for finite dimensional systems.

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↗

arXiv2024

Non-Equilibrium Fluidization of Dense Active Suspension

We investigate dense suspensions of swimming bacteria prepared in a nutrient-exchange chamber. Near the pellet concentration, nonthermal fluctuations showed notable agreement between self and collective behaviors, a phenomenon not previously observed at equilibrium. The viscosity of active suspensions dramatically decreased compared to their inactive counterparts, where glassy features, such as non-Newtonian viscosity and dynamic heterogeneity, disappeared. Instead, the complex shear modulus showed a power-law rheology,$G^*(ω)\propto\left(-iω\right)^\frac{1}{2}$, indicating the role of bacterial activity in driving the system towards a critical jamming state.

cond-mat.soft↗

arXiv2024

A link between anomalous viscous loss and boson peak in soft jammed solids

Soft jammed solids exhibit intriguing mechanical properties, while their linear response is elusive. In particular, foams and emulsions generally reveal anomalous viscous loss with the loss and storage modulus following $G^{\prime \prime} \propto \sqrtω$ and $G^{\prime} \propto ω^0$. In this study, we offer a comprehensive microscopic understanding of this behavior. Using microrheology experiment, we measured $G^* = G^{\prime} + i G^{\prime \prime}$ of concentrated emulsions in a wide range of frequencies. In theory, we applied a linear response formalism for microrheology to a soft sphere model that undergoes the jamming transition. We find that the theory quantitatively explains the experiments without the need for parameter adjustments. Our analysis reveals that the anomalous viscous loss results from the boson peak, which is a universal vibrational property of amorphous solids and reflects the marginal stability in soft jammed solids. We discuss that the anomalous viscous loss is universal in systems with various interparticle interactions as it stems from the universal boson peak, and it even survives below the jamming density where thermal fluctuation is pronounced and the dynamics becomes inherently nonlinear.

cond-mat.soft↗

arXiv2024

Instantaneous normal modes of glass-forming liquids during the athermal relaxation process of the steepest descent algorithm

Understanding glass formation by quenching remains a challenge in soft condensed matter physics. Recent numerical studies on steepest descent dynamics, which is one of the simplest models of quenching, revealed that quenched liquids undergo slow relaxation with a power law towards mechanical equilibrium and that the late stage of this process is governed by local rearrangements of particles. These advances motivate the detailed study of instantaneous normal modes during the relaxation process because the glassy dynamics is considered to be governed by stationary points of the potential energy landscape. Here, we performed a normal mode analysis of configurations during the steepest descent dynamics and found that the dynamics is driven by almost flat directions of the potential energy landscape at long times. These directions correspond to localized modes and we characterized them in terms of their statistics and structure using methods developed in the study of local minima of the potential energy landscape.

cond-mat.soft↗

arXiv2023

Heterogeneity and Low-Frequency Vibrations in Bidisperse Sphere Packings

In the jamming transition of monodisperse packings, spatial heterogeneity is irrelevant as the transition is described by mean-field theories. Here, we show that this situation drastically changes if the particle-size dispersity is large enough. We use computer simulations to study the structural and vibrational properties of bidisperse sphere packings with a large size ratio. Near the critical point, the small particles tend to form clusters, leading to the emergence of large-scale structural heterogeneity. Concomitantly, the low-frequency vibrations are significantly enhanced compared to those in monodisperse packings, and their density of states follows a linear law with the frequency. We numerically and theoretically demonstrate that these behaviors of the structural heterogeneity and the low-frequency vibrations are intimately connected. The present work suggests that the nature of heterogeneous packings is markedly different from that of homogeneous packings.

cond-mat.soft↗

arXiv2023

Microrheology near jamming

The jamming transition is a nonequilibrium critical phenomenon, which governs characteristic mechanical properties of jammed soft materials, such as pastes, emulsions, and granular matters. Both experiments and theory of jammed soft materials have revealed that the complex modulus measured by conventional macrorheology exhibits a characteristic frequency dependence. Microrheology is a new type of method to obtain the complex modulus, which transforms the microscopic motion of probes to the complex modulus through the generalized Stokes relation (GSR). Although microrheology has been applied to jammed soft materials, its theoretical understanding is limited. In particular, the validity of the GSR near the jamming transition is far from obvious since there is a diverging length scale $l_c$, which characterizes the heterogeneous response of jammed particles. Here, we study the microrheology of jammed particles by theory and numerical simulation. First, we develop a linear response formalism to calculate the response function of the probe particle, which is transformed to the complex modulus via the GSR. Then, we apply our formalism to a numerical model of jammed particles and find that the storage and loss modulus follow characteristic scaling laws near the jamming transition. Importantly, the observed scaling law coincides with that in macrorheology, which indicates that the GSR holds even near the jamming transition. We rationalize this equivalence by asymptotic analysis of the obtained formalism and numerical analysis on the displacement field of jammed particles under a local perturbation.

cond-mat.soft↗

arXiv2023

Arrhenius temperature dependence of the crystallization time of deeply supercooled liquids

Usually, supercooled liquids and glasses are thermodynamically unstable against crystallization. Classical nucleation theory (CNT) has been used to describe the crystallization dynamics of supercooled liquids. However, recent studies on overcompressed hard spheres show that their crystallization dynamics are intermittent and mediated by avalanche-like rearrangements of particles, which largely differ from the CNT. These observations suggest that the crystallization times of deeply supercooled liquids or glasses cannot be described by the CNT, but this point has not yet been studied in detail. In this paper, we use molecular dynamics simulations to study the crystallization dynamics of soft spheres just after an instantaneous quench. We show that although the equilibrium relaxation time increases in a super-Arrhenius manner with decreasing temperature, the crystallization time shows an Arrhenius temperature dependence at very low temperatures. This is contrary to the conventional formula based on the CNT. Furthermore, the estimated energy barrier for the crystallization is surprisingly small compared to that for the equilibrium dynamics. By comparing the crystallization and aging dynamics quantitatively, we show that a coupling between aging and crystallization is the key for understanding the rapid crystallization of deeply supercooled liquids or glasses.

cond-mat.soft↗

arXiv2023

Non-phononic density of states of two-dimensional glasses revealed by random pinning

The vibrational density of states of glasses is considerably different from that of crystals. In particular, there exist spatially localized vibrational modes in glasses. The density of states of these non-phononic modes has been observed to follow $g(ω) \propto ω^4$, where $ω$ is the frequency. However, in two-dimensional systems, the abundance of phonons makes it difficult to accurately determine this non-phononic density of states because they are strongly coupled to non-phononic modes and yield strong system-size and preparation-protocol dependencies. In this article, we utilize the random pinning method to suppress phonons and disentangle their coupling with non-phononic modes and successfully calculate their density of states as $g(ω) \propto ω^4$. We also study their localization properties and confirm that low-frequency non-phononic modes in pinned systems are truly localized without far-field contributions. We finally discuss the excess density of states over the Debye value that results from the hybridization of phonons and non-phononic modes.

cond-mat.soft↗

arXiv2022

Johari-Goldstein $β$ relaxation in glassy dynamics originates from two-scale energy landscape

Supercooled liquids undergo complicated structural relaxation processes, which have been a long-standing problem in both experimental and theoretical aspects of condensed matter physics. In particular, past experiments universally observed for many types of molecular liquids that relaxation dynamics separated into two distinct processes at low temperatures. One of the possible interpretations is that this separation originates from the two-scale hierarchical topography of the potential energy landscape; however, it has never been verified. Molecular dynamics simulations are a promising approach to tackle this issue, but we must overcome laborious difficulties. First, we must handle a model of molecular liquids that is computationally demanding compared to simple spherical models, which have been intensively studied but show only a slower process: $α$ relaxation. Second, we must reach a sufficiently low-temperature regime where the two processes become well separated. Here, we handle an asymmetric dimer system that exhibits a faster process: Johari-Goldstein $β$ relaxation. Then, we employ the parallel tempering method to access the low-temperature regime. These laborious efforts enable us to investigate the potential energy landscape in detail and unveil the first direct evidence of the topographic hierarchy that induces the $β$ relaxation. We also successfully characterize the microscopic motions of particles during each relaxation process. Finally, we study the predictive power of low-frequency modes for two relaxation processes. Our results establish for the first time a fundamental and comprehensive understanding of experimentally observed relaxation dynamics in supercooled liquids.

cond-mat.soft↗