Memory effects are a key feature in the description of the dynamical systems governed by the generalized Langevin equation, which presents an exact reformulation of the equation of motion. A simple measure for the estimation of memory effects is introduced within the framework of this description. Numerical calculations of the suggested measure and the analysis of memory effects are also applied for various model physical systems as well as for the phenomena of “long time tails” and anomalous diffusion.

The influence of a stationary shear flow on the crystallization in a glassy system is studied by means of molecular dynamics simulations and subsequent cluster analysis. The results reveal two opposite effects of the shear flow on the processes of topological ordering in the system. Shear promotes the formation of separated crystallites and suppresses the appearance of the large clusters. The shear-induced ordering proceeds in two stages, where the first stage is related mainly to the growth of crystallites and the second stage is due to an adjustment of the created clusters and a progressive alignment of their lattice directions. The influence of strain and shear rate on the crystallization is also investigated. In particular, we find two plausible phenomenological relations between the shear rate and the characteristic time scale needed for ordering of the amorphous system under shear.

Collective excitations in liquids are important for understanding liquid dynamical and thermodynamic properties. Gapped momentum states (GMS) are a notable feature of liquid dynamics predicted to operate in the transverse collective excitations. Here, we combine inelastic neutron scattering experiments, theory, and molecular dynamics modeling to study collective excitations and GMS in liquid Ga in a wide range of temperature and $k$ points. We find that all three lines of enquiry agree for the longitudinal liquid collective dynamics. In the transverse collective dynamics, the experiments agree with theory, modeling, as well as earlier x-ray experiments at larger $k$, whereas theory and modeling agree in a wide range of temperature and $k$ points. We observe the emergence and development of the $k$ gap in the transverse dispersion relation which increases with temperature and inverse of relaxation time as predicted theoretically.

Nucleation is an out-of-equilibrium process that can be strongly affected by the presence of external fields. In this paper, we report a simple extension of classical nucleation theory to systems submitted to an homogeneous shear flow. The theory involves accounting for the anisotropy of the critical nucleus formation and introduces a shear-rate-dependent effective temperature. This extended theory is used to analyze the results of extensive molecular dynamics simulations that explore a broad range of shear rates and undercoolings. At fixed temperature, a maximum in the nucleation rate is observed, when the relaxation time of the system is comparable to the inverse shear rate. In contrast to previous studies, our approach does not require a modification of the thermodynamic description, as the effect of shear is mainly embodied into a modification of the kinetic prefactor and of the temperature.

We report results of nonequilibrium molecular dynamics simulations of a one-component glassy system under the influence of a shear flow, with the aim of investigating shear-induced ordering of this system. In spite of the very low temperature, the system transforms into a strained crystalline state through well defined nucleation events. Various characteristics of the observed ordering at different strain rates and temperatures are discussed. We also define and discuss the transition rates.