好吧,我知道你们其实不喜欢,计算一个向量场中曲面的通量,所以你们可能不知道我为什么要这么做。
Now, I know that you guys are not necessarily fond of computing flux of vector fieldS for surfaces so maybe you don't really see the point.
一个是要取通量的向量场。
也可以是一个向量场的通量,等等。
需要建立向量场点乘nds的通量积分。
So, we need to set up the flux integral for a vector field dot ndS.
从另一方面来看,“通量”度量的是,沿着曲线前进时,大致会有多少向量场通过曲线。
Flux, on the other hand, measures, when I go along the curve, roughly how much the field is going to across the curve.
散度定理为我们提供了一种,计算向量场通过闭曲面的通量的方法。
So, the divergence theorem gives us a way to compute the flux of a vector field for a closed surface.
但通常的习惯是,把立体区域上的外法向量规定为其定向,因为这么做之后,当你观察通量时会发现,它是从区域内部向外流动的。
But the usually traditional settings would be to take your normal vector pointing maybe out of the solid region because then you will be looking at flux that is coming out of that region of space.
如果想用单位法向量来计算通量,还得先把它标准化到单位长度?
Now, if you wanted the unit normal vector to compute flux, then you would just scale this guy down to unit length, OK?
特别地,有一种简单的情况,是不用计算的,当向量场与曲面相切,没有通量。
In particular, an easy case where you know you can get away without computing anything is, of course, if your vector field is tangent to the surface because then you know that there is no flux.
的法向量似乎是指向外部。,And, the,normal, vector, to,s, seems, to, be, pointing, out wards, everywhere。,如果我们有一个法向量指向外部的封闭曲面,并且我们要求出它的一个通量积分,那么我们可以用一个三重积分来代替这个通量积分。
S if we have a closed surface with a normal vector pointing outwards, and we want to find a flux integral for it, well, we can replace that with a triple integral.
我将要证明,一个只有z分量的向量场的通量,等于一个三重积分,其中被积表达式为。
I'm going to prove that the flux of a vector field that has only a z component is actually equal to the triple integral of, RzdV well, the divergence of this is just R sub z dV.
预测结果表明,支持向量机用于交通量的预测是可行及有效的。
The prediction results show that the prediction of traffic using the support vector machine (SVM) is feasible and effective.
预测结果表明,支持向量机用于交通量的预测是可行及有效的。
The prediction results show that the prediction of traffic using the support vector machine (SVM) is feasible and effective.
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