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Register a new userConfiguration-tree Theoretical Calculation of the Mean-Squared Displacement of Particles in Glass Formers
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We report an analytical evaluation of the mean-squared displacement (MSD) of the particles in glasses based on their coarse grained trajectories. The calculation is conducted by means of a local random configuration-tree theory that was recently proposed by one of us [C.-H. Lam, J. Stat. Mech. textbf{2018}, 023301 (2018)]. Results are compared with the numerical simulations of a lattice glass model, and good quantitative agreement has been obtained over a wide range of temperatures in the entire region of time with virtually no free parameters. To the best of our knowledge, the calculation is the first in its kind.
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It was recently shown that the real part of the frequency-dependent fluidity for several glass-forming liquids of different chemistry conforms to the prediction of the random barrier model (RBM) devised for ac electrical conduction in disordered solids [S. P. Bierwirth textit{et al.}, Phys. Rev. Lett. {bf 119}, 248001 (2017)]. Inspired by these results we introduce a crystallization-resistant modification of the Kob-Andersen binary Lennard-Jones mixture for which the results of extensive graphics-processing unit (GPU)-based molecular-dynamics simulations are presented. We find that the low-temperature mean-square displacement is fitted well by the RBM prediction, which involves no shape parameters. This finding highlights the challenge of explaining why a simple model based on hopping of non-interacting particles in a fixed random energy landscape can reproduce the complex and highly cooperative dynamics of glass-forming liquids.
It is proposed that the rate of relaxation in a liquid is better described by the geometric mean of the van Hove distribution function, rather than the standard arithmetic mean used to obtain the mean squared displacement. The difference between the two means is shown to increase significantly with an increase in the non-Gaussian character of the displacement distribution. Preliminary results indicate that the geometric diffusion constant results in a substantial reduction of the deviation from Stokes-Einstein scaling.
In this study, we classify the COVID-19 anomalous diffusion in two categories of countries based on the mean squared displacement (MSD) of daily new cases, which includes the top four countries and four randomly selected countries in terms of the total cases. The COVID-19 diffusion is a stochastic process, and the daily new cases are regarded as the displacements of diffusive particles. The diffusion environment of COVID-19 in each country is heterogeneous, in which the underlying dynamic process is anomalous diffusion. The calculated MSD is a power law function of time, and the power law exponent is not a constant but varies with time. The power law exponents are estimated by using the bi-exponential model and the long short-term memory network (LSTM). The bi-exponential model frequently use in magnetic resonance imaging (MRI) can quantify the power law exponent and make an easy prediction. The LSTM network has much better accuracy than the bi-exponential model in predicting the power law exponent. The LSTM network is more flexible and preferred to predict the power law exponent, which is independent on the unique mathematical formula. The diffusion process of COVID-19 can be classified based on the power law exponent. More specific evaluation and suggestion can be proposed and submitted to the government in order to control the COVID-19 diffusion.
Using a distinguishable-particle lattice model based on void-induced dynamics, we successfully reproduce the well-known linear relation between heat capacity and temperature at very low temperatures. The heat capacity is dominated by two-level systems formed due to strong localization of voids to two neighboring sites, and can be exactly calculated in the limit of ultrastable glasses. Similar but weaker localization at higher temperatures accounts for the glass transition. Our approach provides an unified framework for relating microscopic dynamics of glasses at room and cryogenic temperatures.
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 relaxation on two length scales a. One length scale corresponds to structural relaxation at nearest neighbor distances and the other corresponds to relaxation of the tetrahedral structure. We find that the dynamic correlation length xi_4^{a} grows much slower with increasing relaxation time than for model fragile glass formers. We also find that chi_4^a ~ (xi_4^a)^z for a range of temperatures, but z < 3 at the lowest temperatures examined in this study. However, we do find evidence that the temperature where Stokes-Einstein violation begins marks a temperature where there is a change in the character of dynamically heterogeneous regions. Throughout the paper, we contrast the structure and dynamics of a strong glass former with that of a representative fragile glass former.
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