亲爱的学霸们 这里是由Károly Zsolnai-Fehér带来的两分钟论文
Dear Fellow Scholars, this is Two Minute Papers with Károly Zsolnai-Fehér.
这一集是关于模拟一种美丽的自然现象——蜂蜜的
This episode is about simulating a beautiful phenomenon in nature, the buckling and coiling
屈曲和卷绕效果
effect of honey.
嗯！
Mmm!
这种效果来自于像蜂蜜一样的高粘性材料 这意味着它们
This effect is due to the high viscosity of materials like honey, which means that they
能高度抵抗形变
are highly resistant against deformation.
然而 水的粘稠性却低得多 通过较弱的分子间作用力结合在一起
Water, however, is much less viscous as it is held together by weaker intermolecular
因此水更容易变形 使其很容易倒入玻璃杯中
forces, therefore it is easier to deform, making it so easy to pour it into a glass.
我们早期的节目中有一集是关于蜂蜜的屈曲性 如同每个经验丰富的学霸知道的
We had an earlier episode on honey buckling, and as every seasoned Fellow Scholar already
它的链接在视频描述中可用
knows, the link is available in the video description.
这项工作的一个主要不同点是 旧的方法是建立在拉格朗日方法的基础上
One key difference of this work is that the older solution was built upon a Lagrangian
这意味着模拟方法包括计算速度和
approach, which means that the simulation consists of computing the velocities and the
作用于这些粒子的压力
pressure that acts on these particles.
它是一个基于粒子的模拟方法
It is a particle-based simulation.
在这里 提出了一个基于欧拉方法的方案 这意味着我们不去计算
Here, a solution is proposed for the Eulerian approach, which means that we do not compute
这些遍布连续空间里的量 但我们使用一个精细的三维网格
these quantities everywhere in the continuum of space, but we use a fine 3D grid, and we
我们仅在这些网格点中计算这些量
compute these quantities only in these gridpoints.
不再有随处可见的粒子
No particles to be seen anywhere.
这里用到了一种数学技巧 可以尝试猜测这些独立的网格点之间发生的事件
There are mathematical techniques to try to guess what happens between these individual
这个过程被称为 插值
gridpoints, and this process is referred to as interpolation.
通常情况下 在这种基于网格的方法中 如果我们想模拟这样的屈曲效果
So normally, in this grid-based approach, if we wish to simulate such a buckling effect,
我们会非常失望 因为我们将看到的 就是那些
we’ll be sorely disappointed because what we will see is that the surface details rapidly
由于模拟中的不准确而迅速消失的表面细节
disappear due to the inaccuracies in the simulation.
这是由于经典的基于网格的模拟器利用了一种
The reason for this is that the classical grid-based simulators utilize a technique
数学家喜欢称之为算子分裂的技术
that mathematicians like to call operator splitting.
这意味着我们解决这些流体方程时 是将对流 压力
This means that we solve these fluid equations by taking care of advection, pressure, and
和粘度分开进行处理的
viscosity separately.
分开的数量 分开的解决方案
Separate quantities, separate solutions.
这很好 因为它降低了问题的计算复杂性 不过 我们
This is great, because it eases the computational complexity of the problem, however, we have
为此付出的代价就是引入了新的不准确性
to pay a price for it in the form of newly introduced inaccuracies.
例如 一些动力学和切变力的量被显著抑制
For instance, some kinetic and shear forces are significantly dampened, which leads to
导致传统技术中屈曲效应的细节损失
a loss of detail for buckling effects with traditional techniques.
这篇论文介绍了一种有效的新方法 能在保留模拟中的耦合效应的情况下
This paper introduces a new way of efficiently solving these operators together in a way
一起解决这些算子
that these coupling effects are retained in the simulation.
最终的解决方案不仅看起来很稳定 同时对于各种情况
The final solution not only looks stable, but is mathematically proven to work well
在数学上也被证明是有效的 这其中也考虑到了与其它固体对象
for a variety of cases, and it also takes into consideration collisions with other solid
碰撞情形下的正确性
objects correctly.
我超喜欢这个 任何人在创作电影过程中
I absolutely love this, and anyone who is in the middle of creating a new movie with
只要使用了流体运动 都应该使用这项新技术
some fluid action going on has to be all over this new technique.
而且 这篇文章是绝对一流的
And, the paper is absolutely amazing.
它包含极其清晰的写作 许多段落非常紧凑 我甚至觉得几乎不可能
It contains crystal clear writing, many paragraphs are so tight that I’d find it almost impossible
从它们中删去一个字 但它仍然易于理解
to cut even one word from them, yet it is still digestible and absolutely beautifully
且写得非常漂亮
written.
一定要看看 一如既往的 链接在视频描述中
Make sure to have a look, as always, the link is available in the video description.
这些一流的论文 每篇都是该让所有人知道的故事
These amazing papers are stories that need to be told to everyone.
而这不仅仅只是针对专家而言
Not only to experts.
而是针对所有人
To everyone.
在创建这些视频之前 我总是尽我所能与这些作品的
And before creating these videos, I always try my best to be in contact with the authors
作者联系
of these works.
而现在 很多作者都告诉我 他们真的惊讶于那些
And nowadays, many of them are telling me that they were really surprised by the influx
在节目中展示后涌入的观点感到非常惊讶
of views they got after they were showcased in the series.
撰写那些两分钟论文里提到的论文 需要耗费大量的辛勤工作
Writing papers that are featured in Two Minute Papers takes a ridiculous amount of hard work,
完成后 研究人员会将成果免费开放给所有人
and after that, the researchers make them available for everyone free of charge.
现在 我很高兴看到他们的辛勤工作得到越来越多的认可
And now, I am so glad to see them get more and more recognition for their hard work.
非常棒
Absolutely amazing.
感谢您的观看和慷慨支持 我们下次再见！
Thanks for watching and for your generous support, and I’ll see you next time!