溶液中的盐份富集在聚合物分子的带电基团附近，并形成盐浓度梯度分布。
Salts are enriched around electriferous groups of polymer molecules in solution, which formed a salt concentration gradient.
发现正则动量与空间相的梯度成正比。
It is found that the canonical momentum is directly proportional to the gradient of space phase.
采用高梯度磁选可将铁锂云母从尾矿中有效分离。
Zinnwaldite can be separated effectively by the high gradient magnetic separation from the tailing.
用▽表示,这就是梯度的符号。
You use this downward pointing triangle as the notation for the gradient.
维持啤酒泡沫稳定的是张力梯度。
垂直于梯度的方向上,方向导数为零。
The directional derivative in a direction that's perpendicular to the gradient is basically zero.
梯度向量应该垂直于等值线。
The gradient vector would be going perpendicular to the level.
指定精细的颜色梯度和模式。
现在，梯度向量是什么呢？
如果有一个梯度场，它也是一个保守场。
So, if you have a gradient field, it's what's called conservative.
很多向量场都不是梯度。
问题是a为多少时,这才可能是个梯度场？
The question is for which value of a is this going to be possibly a gradient?
一个是向量场,在给定平面区域内是梯度场。
One is to say that the vector field is a gradient in a certain region of a plane.
指向和梯度向量相反。
对这个函数取梯度，你应该又得到这个向量场。
If you take the gradient of this, you should get again this vector field over there.
这告诉我们，流动是和浓度的负梯度成比例的。
And that told us that the flow is proportional to a negative gradient of a concentration.
气压梯度与天气图上等压线的间隔大小成反比。
The atmosphere pressure gradient is an inverse measure of the spacing of the isobars on a weather map.
加1并不改变梯度。
再强调一下，这是梯度函数在u方向上的分量。
And, maybe I should also say in words, this is the component of the gradient in the direction of u.
我们说，当一个二元函数存在时，就有梯度向量。
So, we said when we have a function of two variables, we have the gradient vector.
也就是说f的梯度向量,应该与g的水平集垂直。
That means that the gradient of f is perpendicular to the level set of g.
但在2d的细胞培养基中，这样的梯度就不存在了。
我们也知道了，如何将各个偏导组合成一个梯度向量。
And we have learned how to package partial derivatives into a vector, the gradient vector.
实际上，找出一个函数，其梯度是这个向量场并不难。
Well, actually here it is not very hard to find a function whose gradient is this vector field.
确定一点，那么对我来说，这点的梯度向量就是确定的。
If I fix a point, then the gradient vector at that point is given to me.
健康方面的社会梯度从社会经济状况的顶端延伸到底部。
There is a social gradient in health that runs from top to bottom of the socioeconomic spectrum.
如果说函数的梯度是向量，那么向量场的散度就是函数。
So, if the gradient of a function is a vector, the divergence of a vector field is a function.
所以现在我们再回头看看梯度，看看它告诉了我们什么。
So now, let's go back to the gradient and see what this tells us about the gradient.
梯度向量方向是,在给定点处指向函数增加得最快的方向。
The gradient is the direction in which the function increases the most quickly at that point.
但它们不一定是，某个以该向量场为梯度的函数的等值线。
But they won't be the level curves of a function for which this is the gradient.
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