SIAM Review, Volume 66, Issue 4, Page 751-777, November 2024.
Granular materials are everywhere, in the environment but also in our pantry. Their properties are different from those of any solid material, due to the possibility of sudden phenomena such as avalanches or landslides. Here we present a brief survey on their characteristics and on what can be found (from the past thirty years) in the recent mathematics literature in order to reproduce their behavior. We discuss, in particular, differential models proposed for the growth of a sandpile on a table and, when wind comes into play, for the formation and dynamics of sand dunes. This field of research is still of great interest since there is no consolidated general model for the dynamics of granular matter, but rather only standalone models adapted to specific situations.

中文翻译：

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沙堆和沙丘：颗粒物质的数学模型


SIAM 评论，第 66 卷，第 4 期，第 751-777 页，2024 年 11 月。

颗粒状材料无处不在，在环境中，在我们的食品储藏室中也是如此。它们的特性与任何固体材料的特性不同，因为可能会发生雪崩或山体滑坡等突发现象。在这里，我们简要介绍了它们的特征以及在最近的数学文献中可以找到的内容（过去 30 年），以便重现它们的行为。我们特别讨论了为桌子上沙堆的增长提出的微分模型，以及当风发挥作用时，沙丘的形成和动力学。这个研究领域仍然非常有趣，因为没有用于颗粒物质动力学的统一通用模型，而只是适应特定情况的独立模型。