TITLE

Systematic expansion in the order parameter for replica theory of the dynamical glass transition

AUTHOR(S)
Jacquin, Hugo; Zamponi, Francesco
PUB. DATE
March 2013
SOURCE
Journal of Chemical Physics;Mar2013, Vol. 138 Issue 12, p12A542
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
It has been shown recently that predictions from mode-coupling theory for the glass transition of hard-spheres become increasingly bad when dimensionality increases, whereas replica theory predicts a correct scaling. Nevertheless if one focuses on the regime around the dynamical transition in three dimensions, mode-coupling results are far more convincing than replica theory predictions. It seems thus necessary to reconcile the two theoretic approaches in order to obtain a theory that interpolates between low-dimensional, mode-coupling results, and 'mean-field' results from replica theory. Even though quantitative results for the dynamical transition issued from replica theory are not accurate in low dimensions, two different approximation schemes-small cage expansion and replicated hyper-netted-chain (RHNC)-provide the correct qualitative picture for the transition, namely, a discontinuous jump of a static order parameter from zero to a finite value. The purpose of this work is to develop a systematic expansion around the RHNC result in powers of the static order parameter, and to calculate the first correction in this expansion. Interestingly, this correction involves the static three-body correlations of the liquid. More importantly, we separately demonstrate that higher order terms in the expansion are quantitatively relevant at the transition, and that the usual mode-coupling kernel, involving two-body direct correlation functions of the liquid, cannot be recovered from static computations.
ACCESSION #
86446730

 

Related Articles

  • Anomalous nonlinear response of glassy liquids: General arguments and a mode-coupling approach. Tarzia, Marco; Biroli, Giulio; Lefèvre, Alexandre; Bouchaud, Jean-Philippe // Journal of Chemical Physics;2/7/2010, Vol. 132 Issue 5, p054501 

    We study theoretically the nonlinear response properties of glass formers. We establish several general results, which together with the assumption of time-temperature superposition, lead to a relation between the nonlinear response and the derivative of the linear response with respect to...

  • Multi-scale lattice Boltzmann and mode-coupling theory calculations of the flow of a glass-forming liquid. Papenkort, S.; Voigtmann, Th. // Journal of Chemical Physics;2015, Vol. 143 Issue 20, p1 

    We present a hybrid-lattice Boltzmann (LB) algorithm for calculating the flow of glass-forming fluids that are governed by integral constitutive equations with pronounced nonlinear, non-Markovian dependence of the stresses on the flow history. The LB simulation for the macroscopic flow fields is...

  • Jamming and glass transitions viewed from the mean field pictures. Ozawa, Misaki; Kuroiwa, Takeshi; Ikeda, Atsushi; Miyazaki, Kunimasa // AIP Conference Proceedings;Feb2013, Vol. 1518 Issue 1, p128 

    We present several theoretical and numerical results which bolster the mean-field scenario of the glass and jamming transitions. The results of the replica theory, the mode-coupling theory, and the simulation results are compared for the hard spheres in high dimensions, the ultrasoft potential...

  • On the Bauschinger effect in supercooled melts under shear: Results from mode coupling theory and molecular dynamics simulations. Frahsa, Fabian; Bhattacharjee, Amit Kumar; Horbach, Jürgen; Fuchs, Matthias; Voigtmann, Thomas // Journal of Chemical Physics;Mar2013, Vol. 138 Issue 12, p12A513 

    We study the nonlinear rheology of a glass-forming binary mixture under the reversal of shear flow using molecular dynamics simulations and a schematic model of the mode-coupling theory of the glass transition (MCT). Memory effects lead to a history-dependent response, as exemplified by the...

  • Microscopic models of mode-coupling theory: The F12 scenario. Arenzon, Jeferson J.; Sellitto, Mauro // Journal of Chemical Physics;8/28/2012, Vol. 137 Issue 8, p084501 

    We provide extended evidence that mode-coupling theory (MCT) of supercooled liquids for the F12 schematic model admits a microscopic realization based on facilitated spin models with tunable facilitation. Depending on the facilitation strength, one observes two distinct dynamical glass...

  • Geometrical frustration and static correlations in hard-sphere glass formers. Charbonneau, Benoit; Charbonneau, Patrick; Tarjus, Gilles // Journal of Chemical Physics;Mar2013, Vol. 138 Issue 12, p12A515 

    We analytically and numerically characterize the structure of hard-sphere fluids in order to review various geometrical frustration scenarios of the glass transition. We find generalized polytetrahedral order to be correlated with increasing fluid packing fraction, but to become increasingly...

  • A mode-selective circuit for TE01 gyrotron backward-wave oscillator with wide-tuning range. Chen, N. C.; Yu, C. F.; Yuan, C. P.; Chang, T. H. // Applied Physics Letters;3/9/2009, Vol. 94 Issue 10, pN.PAG 

    This study proposes a mode-selective circuit to suppress the competing modes in a TE01 gyrotron backward-wave oscillator (gyro-BWO). The circuit, also functioning as an interaction structure, comprises of several transverse slices. It eliminates the restrictions of the mode competitions and...

  • Non-monotonic size dependence of diffusion and levitation effect: A mode-coupling theory analysis. Nandi, Manoj Kumar; Banerjee, Atreyee; Bhattacharyya, Sarika Maitra // Journal of Chemical Physics;Mar2013, Vol. 138 Issue 12, p124505 

    We present a study of diffusion of small tagged particles in a solvent, using mode coupling theory (MCT) analysis and computer simulations. The study is carried out for various interaction potentials. For the first time, using MCT, it is shown that only for strongly attractive interaction...

  • Dynamic heterogeneities above and below the mode-coupling temperature: Evidence of a dynamic crossover. Flenner, Elijah; Szamel, Grzegorz // Journal of Chemical Physics;Mar2013, Vol. 138 Issue 12, p12A523 

    We examine dynamic heterogeneities in a model glass-forming fluid, a binary harmonic sphere mixture, above and below the mode-coupling temperature Tc. We calculate the ensemble independent susceptibility χ4(τα) and the dynamic correlation length ξ4(τα) at the α-relaxation...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics