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Atsushi Ikeda

Publications and source records attributed to Atsushi Ikeda.

At least 73 records · Page 4Linked to original sources
arXiv2016

Mean-field dynamic criticality and geometric transition in the Gaussian core model

We use molecular dynamics simulations to investigate dynamic heterogeneities and the potential energy landscape of the Gaussian core model (GCM). Despite the nearly Gaussian statistics of particles' displacements, the GCM exhibits giant dynamic heterogeneities close to the dynamic transition temperature. The divergence of the four-point susceptibility is quantitatively well described by the inhomogeneous version of the Mode-Coupling theory. Furthermore, the potential energy landscape of the GCM is characterized by a geometric transition and large energy barriers, as expected from the lack of activated, hopping dynamics. These observations demonstrate that all major features of mean-field dynamic criticality can be observed in a physically sound, three-dimensional model.

cond-mat.stat-mech↗
arXiv2015

Thermal fluctuations, mechanical response, and hyperuniformity in jammed solids

Jamming is a geometric phase transition occurring in dense particle systems in the absence of temperature. We use computer simulations to analyse the effect of thermal fluctuations on several signatures of the transition. We show that scaling laws for bulk and shear moduli only become relevant when thermal fluctuations are extremely small, and propose their relative ratio as a quantitative signature of jamming criticality. Despite the nonequilibrium nature of the transition, we find that thermally induced fluctuations and mechanical responses obey equilibrium fluctuation-dissipation relations near jamming, provided the appropriate fluctuating component of the particle displacements is analysed. This shows that mechanical moduli can be directly measured from particle positions in mechanically unperturbed packings, and suggests that the definition of a "nonequilibrium index" is unnecessary for amorphous materials. We find that fluctuations of particle displacements are spatially correlated, and define a transverse and a longitudinal correlation lengthscales which both diverge as the jamming transition is approached. We analyse the frozen component of density fluctuations and find that it displays signatures of nearly-hyperuniform behaviour at large lengthscales. This demonstrates that hyperuniformity in jammed packings is unrelated to a vanishing compressibility and explains why it appears remarkably robust against temperature and density variations. Differently from jamming criticality, obstacles preventing the observation of hyperuniformity in colloidal systems do not originate from thermal fluctuations.

cond-mat.stat-mech↗
arXiv2015

Equilibrium phase diagram of a randomly pinned glass-former

We use computer simulations to study the thermodynamic properties of a glass former in which a fraction $c$ of the particles has been permanently frozen. By thermodynamic integration, we determine the Kauzmann, or ideal glass transition, temperature $T_K(c)$ at which the configurational entropy vanishes. This is done without resorting to any kind of extrapolation, {\it i.e.}, $T_K(c)$ is indeed an equilibrium property of the system. We also measure the distribution function of the overlap, {\it i.e.}, the order parameter that signals the glass state. We find that the transition line obtained from the overlap coincides with that obtained from the thermodynamic integration, thus showing that the two approaches give the same transition line. Finally we determine the geometrical properties of the potential energy landscape, notably the $T-$and $c-$dependence of the saddle index and use these properties to obtain the dynamic transition temperature $T_d(c)$. The two temperatures $T_K(c)$ and $T_d(c)$ cross at a finite value of $c$ and indicate the point at which the glass transition line ends. These findings are qualitatively consistent with the scenario proposed by the random first order transition theory.

cond-mat.soft↗
arXiv2015

One-dimensional Kac model of dense amorphous hard spheres

We introduce a new model of hard spheres under confinement for the study of the glass and jamming transitions. The model is an one-dimensional chain of the $d$-dimensional boxes each of which contains the same number of hard spheres, and the particles in the boxes of the ends of the chain are quenched at their equilibrium positions. We focus on the infinite dimensional limit ($d \to \infty$) of the model and analytically compute the glass transition densities using the replica liquid theory. From the chain length dependence of the transition densities, we extract the characteristic length scales at the glass transition. The divergence of the lengths are characterized by the two exponents, $-1/4$ for the dynamical transition and $-1$ for the ideal glass transition, which are consistent with those of the $p$-spin mean-field spin glass model. We also show that the model is useful for the study of the growing length scale at the jamming transition.

cond-mat.soft↗
arXiv2015

Diverging viscosity and soft granular rheology in non-Brownian suspensions

We use large scale computer simulations and finite size scaling analysis to study the shear rheology of dense three-dimensional suspensions of frictionless non-Brownian particles in the vicinity of the jamming transition. We perform simulations of soft repulsive particles at constant shear rate, constant pressure, and finite system size, and study carefully the asymptotic limits of large system sizes and infinitely hard particle repulsion. Extending earlier analysis by about two orders of magnitude, we first study the asymptotic behavior of the shear viscosity in the hard particle limit. We confirm its asymptotic power law divergence at the jamming transition, but show that a precise determination of the critical density and critical exponent is difficult due to the `multiscaling' behavior of the viscosity. Additionally, finite-size scaling analysis suggests that this divergence is accompanied by a growing correlation length scale, which also diverges algebraically. We then study the effect of soft repulsion, and propose a natural extension of the standard granular rheology to account for softness effects, which we validate from simulations. Close to the jamming transition, this `soft granular rheology' offers a detailed description of the non-linear rheology of soft particles, which differs from earlier empirical scaling forms.

cond-mat.soft↗
arXiv2014

Correlation of Local Order with Particle Mobility in Supercooled Liquids is Highly System Dependent

We investigate the connection between local structure and dynamical heterogeneity in supercooled liquids. Through the study of four different models we show that the correlation between a particle's mobility and the degree of local order in nearby regions is highly system dependent. Our results suggest that the correlation between local structure and dynamics is weak or absent in systems that conform well to the mean-field picture of glassy dynamics and strong in those that deviate from this paradigm. Finally, we investigate the role of order-agnostic point-to-set correlations and reveal that they provide similar information content to local structure measures, at least in the system where local order is most pronounced.

cond-mat.stat-mech↗
arXiv2014

Thinning or thickening? Multiple rheological regimes in dense suspensions of soft particles

The shear rheology of dense colloidal and granular suspensions is strongly nonlinear, as these materials exhibit shear-thinning and shear-thickening, depending on multiple physical parameters. We numerically study the rheology of a simple model of soft repulsive particles at large densities, and show that nonlinear flow curves reminiscent of experiments on real suspensions can be obtained. By using dimensional analysis and basic elements of kinetic theory, we rationalize these multiple rheological regimes and disentangle the relative impact of thermal fluctuations, glass and jamming transitions, inertia and particle softness on the flow curves. We characterize more specifically the shear-thickening regime and show that both particle softness and the emergence of a yield stress at the jamming transition compete with the inertial effects responsible for the observed thickening behaviour. This allows us to construct a dynamic state diagram, which can be used to analyze experiments.

cond-mat.soft↗
arXiv2013

Yield stress in amorphous solids: A mode-coupling theory analysis

The yield stress is a defining feature of amorphous materials which is difficult to analyze theoretically, because it stems from the strongly non-linear response of an arrested solid to an applied deformation. Mode-coupling theory predicts the flow curves of materials undergoing a glass transition, and thus offers predictions for the yield stress of amorphous solids. We use this approach to analyse several classes of disordered solids, using simple models of hard sphere glasses, soft glasses, and metallic glasses for which the mode-coupling predictions can be directly compared to the outcome of numerical measurements. The theory correctly describes the emergence of a yield stress of entropic nature in hard sphere glasses, and its rapid growth as density approaches random close packing at qualitative level. By contrast, the emergence of solid behavior in soft and metallic glasses, which originates from direct particle interactions is not well described by the theory. We show that similar shortcomings arise in the description of the vibrational dynamics of the glass phase at rest. We discuss the range of applicability of mode-coupling theory to understand the yield stress and non-linear rheology of amorphous materials.

cond-mat.stat-mech↗
arXiv2013

Cluster and reentrant anomalies of nearly Gaussian core particles

We study through integral equation theory and numerical simulations the structure and dynamics of fluids composed of ultrasoft, nearly Gaussian particles. Namely, we explore the fluid phase diagram of a model in which particles interact via the generalized exponential potential u(r)=εexp[-(r/σ)^n], with a softness exponent n slightly larger than 2. In addition to the well-known anomaly associated to reentrant melting, the structure and dynamics of the fluid display two additional anomalies, which are visible in the isothermal variation of the structure factor and diffusivity. These features are correlated to the appearance of dimers in the fluid phase and to the subsequent modification of the cluster structure upon compression. We corroborate these results through an analysis of the local minima of the potential energy surface, in which clusters appear as much tighter conglomerates of particles. We find that reentrant melting and clustering coexist for softness exponents ranging from 2^+ up to values relevant for the description of amphiphilic dendrimers, i.e., n=3.

cond-mat.soft↗
arXiv2013

Disentangling glass and jamming physics in the rheology of soft materials

The shear rheology of soft particles systems becomes complex at large density because crowding effects may induce a glass transition for Brownian particles, or a jamming transition for non-Brownian systems. Here we successfully explore the hypothesis that the shear stress contributions from glass and jamming physics are `additive'. We show that the experimental flow curves measured in a large variety of soft materials (colloidal hard spheres, microgel suspensions, emulsions, aqueous foams) as well as numerical flow curves obtained for soft repulsive particles in both thermal and athermal limits are well described by a simple model assuming that glass and jamming rheologies contribute linearly to the shear stress, provided that the relevant scales for time and stress are correctly identified in both sectors. Our analysis confirms that the dynamics of colloidal hard spheres is uniquely controlled by glass physics while aqueous foams are only sensitive to jamming effects. We show that for micron-sized emulsions both contributions are needed to successfully account for the flow curves, which reveal distinct signatures of both phenomena. Finally, for two systems of soft microgel particles we show that the flow curves are representative of the glass transition of colloidal systems, and deduce that microgel particles are not well suited to studying the jamming transition experimentally.

cond-mat.soft↗
arXiv2012

Jamming Transition and Inherent Structures of Hard Spheres and Discs

Recent studies show that volume fractions $\phiJ$ at the jamming transition of frictionless hard spheres and discs are not uniquely determined but exist over a continuous range. Motivated by this observation, we numerically investigate dependence of $\phiJ$ on the initial configurations of the parent fluids equilibrated at a fraction $\phiini$, before compressing to generate a jammed packing. We find that $\phiJ$ remains constant when $\phiini$ is small but sharply increases when $\phiini$ exceeds the dynamic transition point which the mode-coupling theory predicts. We carefully analyze configurational properties of both jammed packings and parent fluids and find that, while all jammed packings remain isostatic, the increase of $\phiJ$ is accompanied with subtle but distinct changes of (i) local orders, (ii) a static length scale, and (iii) an exponent of the finite size scaling. These results quantitatively support the scenario of the random first order transition theoryof the glass transition.

cond-mat.soft↗
arXiv2012

Dynamic criticality at the jamming transition

We characterize vibrational motion occurring at low temperatures in dense suspensions of soft repulsive spheres over a broad range of volume fractions encompassing the jamming transition at (T = 0, phi = phi_J). We find that characteristic time and length scales of thermal vibrations obey critical scaling in the vicinity of the jamming transition. We show in particular that the amplitude and the time scale of dynamic fluctuations diverge symmetrically on both sides of the transition, and directly reveal a diverging correlation length. The critical region near phi_J is divided in three different regimes separated by a characteristic temperature scale T*(phi) that vanishes quadratically with the distance to phi_J. While two of them, (T < T*(phi), phi > phi_J) and (T < T*(phi), phi < phi_J), are described by harmonic theories developed in the zero temperature limit, the third one for T > T*(phi) is inherently anharmonic and displays new critical properties. We find that the quadratic scaling of T*(phi) is due to nonperturbative anharmonic contributions, its amplitude being orders of magnitude smaller than the perturbative prediction based on the expansion to quartic order in the interactions. Our results show that thermal vibrations in colloidal assemblies directly reveal the critical nature of the jamming transition. The critical region, however, is very narrow and has not yet been attained experimentally, even in recent specifically-dedicated experiments.

cond-mat.stat-mech↗
arXiv2012

Dimensional Study of the Caging Order Parameter at the Glass Transition

The glass problem is notoriously hard and controversial. Even at the mean-field level, little is agreed about how a fluid turns sluggish while exhibiting but unremarkable structural changes. It is clear, however, that the process involves self-caging, which provides an order parameter for the transition. It is also broadly assumed that this cage should have a Gaussian shape in the mean-field limit. Here we show that this ansatz does not hold. By performing simulations as a function of spatial dimension, we find the cage to keep a non-trivial form. Quantitative mean-field descriptions of the glass transition, such as mode-coupling theory, density functional theory, and replica theory, all miss this crucial element. Although the mean-field random first-order transition scenario of the glass transition is here qualitatively supported and non-mean-field corrections are found to remain small on decreasing dimension, reconsideration of its implementation is needed for it to result in a coherent description of experimental observations.

cond-mat.stat-mech↗
arXiv2012

Unified study of glass and jamming rheology in soft particle systems

We explore numerically the shear rheology of soft repulsive particles at large volume fraction. The interplay between viscous dissipation and thermal motion results in multiple rheological regimes encompassing Newtonian, shear-thinning and yield stress regimes near the `colloidal' glass transition when thermal fluctuations are important, crossing over to qualitatively similar regimes near the `jamming' transition when dissipation dominates. In the crossover regime, glass and jamming sectors coexist and give complex flow curves. Although glass and jamming limits are characterized by similar macroscopic flow curves, we show that they occur over distinct time and stress scales and correspond to distinct microscopic dynamics. We propose a simple rheological model describing the glass to jamming crossover in the flow curves, and discuss the experimental implications of our results.

cond-mat.soft↗
arXiv2011

Glass transition and random close packing above three dimensions

Motivated by a recently identified severe discrepancy between a static and a dynamic theory of glasses, we numerically investigate the behavior of dense hard spheres in spatial dimensions 3 to 12. Our results are consistent with the static replica theory, but disagree with the dynamic mode-coupling theory, indicating that key ingredients of high-dimensional physics are missing from the latter. We also obtain numerical estimates of the random close packing density, which provides new insights into the mathematical problem of packing spheres in large dimension.

cond-mat.dis-nn↗
arXiv2011

Thermodynamics and Structural Properties of the High Density Gaussian Core Model

We numerically study thermodynamic and structural properties of the one-component Gaussian core model (GCM) at very high densities. The solid-fluid phase boundary is carefully determined. We find that the density dependence of both the freezing and melting temperatures obey the asymptotic relation, $\log T_f$, $\log T_m \propto -ρ^{2/3}$, where $ρ$ is the number density, which is consistent with Stillinger's conjecture. Thermodynamic quantities such as the energy and pressure and the structural functions such as the static structure factor are also investigated in the fluid phase for a wide range of temperature above the phase boundary. We compare the numerical results with the prediction of the liquid theory with the random phase approximation (RPA). At high temperatures, the results are in almost perfect agreement with RPA for a wide range of density, as it has been already shown in the previous studies. In the low temperature regime close to the phase boundary line, although RPA fails to describe the structure factors and the radial distribution functions at the length scales of the interparticle distance, it successfully predicts their behaviors at shorter length scales. RPA also predicts thermodynamic quantities such as the energy, pressure, and the temperature at which the thermal expansion coefficient becomes negative, almost perfectly. Striking ability of RPA to predict thermodynamic quantities even at high densities and low temperatures is understood in terms of the decoupling of the length scales which dictate thermodynamic quantities from the interparticle distance which dominates the peak structures of the static structure factor due to the softness of the Gaussian core potential.

cond-mat.soft↗
arXiv2011

Slow Dynamics of the High Density Gaussian Core Model

We numerically study crystal nucleation and glassy slow dynamics of the one-component Gaussian core model (GCM) at high densities. The nucleation rate at a fixed supersaturation is found to decrease as the density increases. At very high densities, the nucleation is not observed at all in the time window accessed by long molecular dynamics (MD) simulation. Concomitantly, the system exhibits typical slow dynamics of the supercooled fluids near the glass transition point. We compare the simulation results of the supercooled GCM with the predictions of mode-coupling theory (MCT) and find that the agreement between them is better than any other model glassformers studied numerically in the past. Furthermore, we find that a violation of the Stokes-Einstein relation is weaker and the non-Gaussian parameter is smaller than canonical glassformers. Analysis of the probability distribution of the particle displacement clearly reveals that the hopping effect is strongly suppressed in the high density GCM. We conclude from these observations that the GCM is more amenable to the mean-field picture of the glass transition than other models. This is attributed to the long-ranged nature of the interaction potential of the GCM in the high density regime. Finally, the intermediate scattering function at small wavevectors is found to decay much faster than its self part, indicating that dynamics of the large-scale density fluctuations decouples with the shorter-ranged caging motion.

cond-mat.soft↗