论文标题
在声子传输方程中的实心界面处重建热声子传输系数
Reconstructing the thermal phonon transmission coefficient at solid interfaces in the phonon transport equation
论文作者
论文摘要
热传播的AB启动模型是声子传输方程，这是一种类似玻尔兹曼的动力学方程。当两种材料并排放置时，从一种材料到另一种材料传播的热量具有热边界电阻。从数学上讲，它由两种材料界面上的声子传输方程的反射系数表示。该系数在不同材料之间的不同声子频率下采用不同的值。在实验中，科学家测量了一种材料的表面温度，以推断出反射系数作为声子频率的函数。在本文中，我们在优化框架中制定了这个反问题，并应用随机梯度下降（SGD）方法来查找最佳解决方案。我们进一步证明了最大原理，并显示了Fréchet衍生物的Lipschitz连续性。这些属性使我们能够在此设置中证明SGD的应用是合理的。
The ab initio model for heat propagation is the phonon transport equation, a Boltzmann-like kinetic equation. When two materials are put side by side, the heat that propagates from one material to the other experiences thermal boundary resistance. Mathematically, it is represented by the reflection coefficient of the phonon transport equation on the interface of the two materials. This coefficient takes different values at different phonon frequencies, between different materials. In experiments scientists measure the surface temperature of one material to infer the reflection coefficient as a function of phonon frequency. In this article, we formulate this inverse problem in an optimization framework and apply the stochastic gradient descent (SGD) method for finding the optimal solution. We furthermore prove the maximum principle and show the Lipschitz continuity of the Fréchet derivative. These properties allow us to justify the application of SGD in this setup.
