# 挑战以前的理解：物理学家提出了一种基于波的热传输理论 精选

“近年来，巧妙推广的电报方程有了新的应用:它也开始被用来描述与扩散或热传输有关的现象。这一事实促使我们提出了一个有趣的问题，”IFJ PAN的卡塔日娜·戈斯卡（Katarzyna Gorska）博士说。“在波动方程的解中，即无阻尼时，会出现多普勒效应。这是一个典型的波动现象。但是它是否也出现在与热传递相关的电报方程的解中呢?如果是这样，我们将有一个很好的迹象表明，至少从理论的角度来看，没有理由相信在有阻尼的系统中，例如在生物组织中，热流不能被视为波现象。”

IFJ PAN的安德烈泽·霍泽拉（Andrezej Horzela）教授解释说:“多普勒现象发生在波动方程中，我们说它是局部的。我们理解当地的情况，因为在行动和反应之间没有延迟。例如，力学原理是局部性的——作用在物体上的合力的变化会立即引起物体加速度的变化。然而，我们都知道，我们可以拿起一个热杯子，在我们感觉到它燃烧之前，一两秒钟过去了。这种现象具有一定的滞后性;我们说它是非局部的，换句话说，是在时间上被涂抹的。因此，我们是否在描述时间涂抹系统的广义电报方程中看到了多普勒效应?

From burns to the wave nature of heat – via the telegraph equation

Abstract

The paper is devoted to study the frequency shift in the solution of the generalized telegraph equation with a moving point-wise harmonic source. This equation contains the nonlocality in time derivatives which is expressed by the memory functions and, where smears the second time-derivative and the first one. Moreover, in the Laplace domain we have. The generalized telegraph equation with an external source is solved by using the integral decomposition which allows us to write this solution as a product of the solution of the telegrapher equation with harmonic source and which is a function of the Laplace transform of memory function. Such obtained solution manifests the frequency shift which is illustrated in three examples of the memory functions: the localized case, its mixture with power-law, and the power-law case only. We show that only the first two cases have the wave front and the Doppler-like shift. The third example, despite the lack of wave fronts, also manifests the frequency shift. Thus it turns out that the frequency shift occurs regardless of the existence of a wave front, but it is more visible when such a front exists.

https://blog.sciencenet.cn/blog-212210-1437458.html

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