We investigate numerically the relaxation dynamics of an elastic string in two-dimensional random media by thermal fluctuations starting from a flat configuration. Measuring spatial fluctuations of its mean position, we find that the correlation length grows in time asymptotically as $ξ\sim (\ln t)^{1/\tildeχ}$. This implies that the relaxation dynamics is driven by thermal activations over random energy barriers which scale as $E_B(\ell) \sim \ell^{\tildeχ}$ with a length scale $\ell$. Numerical data strongly suggest that the energy barrier exponent $\tildeχ$ is identical to the energy fluctuation exponent $χ=1/3$. We also find that there exists a long transient regime, where the correlation length follows a power-law dynamics as $ξ\sim t^{1/z}$ with a nonuniversal dynamic exponent $z$. The origin of the transient scaling behavior is discussed in the context of the relaxation dynamics on finite ramified clusters of disorder.
Spatio-temporal scaling for out-of-equilibrium relaxation dynamics of an elastic manifold in random media: crossover between the Larkin regime and thermally activated regime
The kinetic fragility of liquids as manifestation of the elastic softening
我们表明，脆性$m$，接近玻璃化的粘度和弛豫时间的陡度，增加与弹性软化的程度，即随着温度的升高，在普遍的方式的弹性模量的降低。这提供了一个新的热力学之间的联系，通过模量，和动力学。这一发现是证明了数值模拟和与实验数据的玻璃形成广泛不同的脆性（$33 \le m \le 115$），导致一个脆性独立的弹性主曲线延伸超过十八个十年的粘度和弛豫时间的比较。主曲线由空腔模型解释，指出可用自由体积和笼柔软度的作用。我们的研究结果的一个主要含义是，超低松弛，几乎没有实验表征，成为可预测的线性弹性。作为一个例子，过冷二氧化硅的粘度是在没有可调参数的情况下在大约15年内导出的。
Effects of Cooling Rate on Structural Relaxation in Amorphous Drugs: Elastically Collective Nonlinear Langevin Equation Theory and Machine Learning Study
