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We examine the anisotropy of a four-point correlation function $G_4(\vec{k},\vec{r};t)$ and it's associated structure factor $S_4(\vec{k},\vec{q};t)$ calculated using Brownian Dynamics computer simulations of a model glass forming system.…

Soft Condensed Matter · Physics 2015-05-13 Elijah Flenner , Grzegorz Szamel

We investigate the growth of dynamic heterogeneity in a glassy hard-sphere mixture for volume fractions up to and including the mode-coupling transition. We use an 80 000 particle system to test a new procedure to evaluate a dynamic…

Soft Condensed Matter · Physics 2015-05-19 Elijah Flenner , Grzegorz Szamel

There is a growing evidence that relaxation in glassy materials, both spontaneous and externally driven, is mediated by localized soft spots. Recent progress made it possible to identify the soft spots inside glassy structures and to…

Soft Condensed Matter · Physics 2019-06-19 Zohar Schwartzman-Nowik , Edan Lerner , Eran Bouchbinder

Molecular-dynamics simulations are presented for two correlation functions formed with the partial density fluctuations of binary hard-sphere mixtures in order to explore the effects of mixing on the evolution of glassy dynamics upon…

Soft Condensed Matter · Physics 2007-05-23 G. Foffi , W. Gotze , F. Sciortino , P. Tartaglia , Th. Voigtmann

We compute analytically and numerically the four-point correlation function that characterizes non-trivial cooperative dynamics in glassy systems within several models of glasses: elasto-plastic deformations, mode-coupling theory (MCT),…

Disordered Systems and Neural Networks · Physics 2015-06-24 Cristina Toninelli , Matthieu Wyart , Ludovic Berthier , Giulio Biroli , Jean-Philippe Bouchaud

The Shintani-Tanaka model is a glass-forming system whose constituents interact via anisotropic potential depending on the angle of a unit vector carried by each particle. The decay of time-correlation functions of the unit vectors exhibits…

Statistical Mechanics · Physics 2009-11-13 Edan Lerner , Itamar Procaccia , Ido Regev

Large scale simulations of two-dimensional bidisperse granular fluids allow us to determine spatial correlations of slow particles via the four-point structure factor $S_4(q,t)$. Both cases, elastic ($\varepsilon=1$) as well as inelastic…

Statistical Mechanics · Physics 2014-07-16 Karina E. Avila , Horacio E. Castillo , Andrea Fiege , Katharina Vollmayr-Lee , Annette Zippelius

We examine dynamic heterogeneities in a model glass-forming fluid, a binary harmonic sphere mixture, above and below the mode-coupling temperature T_c. We calculate the ensemble independent susceptibility chi_4(tau_alpha) and the dynamic…

Statistical Mechanics · Physics 2015-06-12 Elijah Flenner , Grzegorz Szamel

The effects of randomly pinning particles in a model glass-forming fluid are studied, with a focus on the dynamically heterogeneous relaxation in the presence of pinning. We show how four-point dynamical correlations can be analysed in real…

Statistical Mechanics · Physics 2013-10-30 Robert L. Jack , Christopher J. Fullerton

We report an extensive and systematic investigation of the multi-point and multi-time correlation functions to reveal the spatio-temporal structures of dynamic heterogeneities in glass-forming liquids. Molecular dynamics simulations are…

Soft Condensed Matter · Physics 2013-01-04 Kang Kim , Shinji Saito

We examined dynamic heterogeneity in a model tetrahedral network glass-forming liquid. We used four-point correlation functions to extract dynamic correlation lengths xi_4^a(t) and susceptibilities chi_4^a(t) corresponding to structural…

Soft Condensed Matter · Physics 2016-01-20 Hannah Staley , Elijah Flenner , Grzegorz Szamel

We use recently introduced three-point dynamic susceptibilities to obtain an experimental determination of the temperature evolution of the number of molecules, N_corr, that are dynamically correlated during the structural relaxation of…

We compute the moments of the nonlinear binary collision integral in the ultrarelativistic hard-sphere approximation for an arbitrary anisotropic distribution function in the local rest frame. This anisotropic distribution function has an…

Nuclear Theory · Physics 2025-07-03 Etele Molnár

We examine the structural relaxation of glassy materials at finite temperatures, considering the effect of activated rearrangements and long-range elastic interactions. Our three-dimensional mesoscopic relaxation model shows how the…

Soft Condensed Matter · Physics 2023-12-20 Gieberth Rodriguez-Lopez , Kirsten Martens , Ezequiel E. Ferrero

The interactions between the dielectric polarization and the fluctuations of the strain (stress) tensor in relaxor ferroelectrics are shown to give rise to the anisotropy of the anharmonic P4-term in the Landau-type free energy, however,…

Disordered Systems and Neural Networks · Physics 2015-06-11 R. Pirc , Z. Kutnjak , N. Novak

Dynamical four-point susceptibilities measure the extent of spatial correlations in the dynamics of glass forming systems. We show how these susceptibilities depend on the length scales that necessarily form part of their definition. The…

Statistical Mechanics · Physics 2007-05-23 David Chandler , Juan P. Garrahan , Robert L. Jack , Lutz Maibaum , Albert C. Pan

The super-cooled $N3$ model exhibits an increasingly slow dynamics as density approaches the model's random closest packing density. Here, we present a direct measurement of the dynamical correlation function $G_4(r,t)$, showing the…

Statistical Mechanics · Physics 2010-12-21 Ziv Rotman , Eli Eisenberg

We investigate the dynamic heterogeneities of glassy particle systems in the theoretical schemes of bond breakage and four-point correlation functions. In the bond-breakage scheme, we introduce the structure factor S_b(q,t) and the…

Soft Condensed Matter · Physics 2012-10-11 Hayato Shiba , Takeshi Kawasaki , Akira Onuki

Liquids near the glass transition exhibit dynamical heterogeneity, i.e. local relaxation rates fluctuate strongly over space and time. Here we introduce a simple continuum model that allows for quantitative predictions for the correlators…

Soft Condensed Matter · Physics 2024-03-20 Rajib K. Pandit , Horacio E. Castillo

We examine a length scale that characterizes the spatial extent of heterogeneous dynamics in a glass-forming binary hard-sphere mixture up to the mode-coupling volume fraction phi_c. First, we characterize the system's dynamics. Then, we…

Soft Condensed Matter · Physics 2015-05-27 Elijah Flenner , Min Zhang , Grzegorz Szamel
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