We investigate the one-dimensional growth of a solid into a liquid bath, starting from a small crystal, using the Guyer-Krumhansl and Maxwell-Cattaneo models of heat conduction. By breaking the solidification process into the relevant time regimes we are able to reduce the problem to a system of two coupled ordinary differential equations describing the evolution of the solid-liquid interface and the heat flux. The reduced formulation is in good agreement with numerical simulations. In the case of silicon, differences between classical and non-classical solidification kinetics are relatively small, but larger deviations can be observed in the evolution in time of the heat flux through the growing solid. From this study we conclude that the heat flux provides more information about the presence of non-classical modes of heat transport during phase-change processes.
Anomalous conduction and second sound in the Fermi-Pasta-Ulam-Tsingou chain: wave-turbulence approach
一维粒子链是解释纳米管和纳米线等低维固体中反常热传导的基本模型。在这些系统中，热能由声子携带，即通过非线性共振相互作用的传播晶格振荡。声子之间的平均能量转移由直接从微观动力学导出的波动方程（WKE）描述。在这里，我们使用的空间非均匀WKE的原型$β-$费米-帕斯塔-乌拉姆-Tsingou（FPUT）模型，配备恒温器能够设置不同的温度在两端。我们的主要发现如下：（1）电导率与系统尺寸的异常标度，与已知的微观动力学结果密切一致，是由于高和低波数之间的非平凡的相互作用。(ii)高波数声子弛豫到局部热力学平衡，扩散地传输能量，{ \it à la Fourier}。(iii)低波数的声子几乎没有相互作用，并且以弹道的方式传递能量;后一种现象类似于第二声发射，例如在超流体中观察到的。
