So, if you have a gradient field, it's what's called conservative.
如果有一个梯度场，它也是一个保守场。
And, of course, it is not a coincidence because this vector field is a gradient field.
当然这并非巧合，因为这个向量场是有势场。
It changes things quite a bit, however, when it comes to testing whether a field is a gradient field.
然而，当考虑到一个场是否是一个有势场时，它有极大的影响。
If you fail this test then you know for sure that you are not gradient field so you might as well do that.
如果通不过检验，那么可以肯定，它不是梯度场，你可能也会那样做。
In this study, a new magnetic resonance (MR) fast imaging method in the invariant gradient field is presented.
本研究提出了恒定梯度场下磁共振快速成像的方法。
And it is a gradient field in that part of the plane and conservative and so on. The answer for now is, in general, no.
在那部分平面上，梯度场，是保守的，目前来说结论一般是不对的。
Well, if we know that it's a gradient field, that we've seen that we get these properties out of the fundamental theorem.
如果我们知道它是一个梯度场，就可以由基本定理，得到上面那些性质。
And, basically, we say that these properties are equivalent being a gradient field or being path independent or being conservative.
根本上说，以下性质是等价的，一个向量场是梯度场，等价于积分与路径无关，也等价于向量场是保守的。
Ok, so just to reinforce my warning that not every field is a gradient field, let's look again at our favorite vector field from yesterday.
好的，为了强调，不是所有场都是梯度场，我们再来看看昨天那个向量场。
The size of current path, resistivity, power density are main factors that effect the temperature field and temperature gradient field at crack tip.
试件的通流尺寸、电阻率、导入电流密度是影响裂纹尖端温度场和温度梯度场的主要因素。
Points are moved onto the iso-surface by an iterative clustering along gradient field, where the noise and outliers are removed and defective data are repaired.
原始点云经梯度方向迭代移动后，过滤噪音和剔除离群点，并修补点云缺失数据。
The test that we saw last time saying, well, to check if something is a gradient field if it's conservative, 0 we just have to compute the curl and check whether it's zero.
由上次的测试可知，如果一个东西是保守的，要确定是不是梯度，我们只需要计算旋度，查看它是否是。
The invention is used for measuring the distribution of the space charges in the high-voltage direct current power equipment insulation in the temperature gradient field.
本发明用以测量温度梯度场下高压直流电力设备绝缘中的空间电荷的分布。
Well, we've seen this criterion that if a curl of the vector field is zero and it's defined in the entire plane, then the vector field is conservative, and it's a gradient field.
我们已经知道了一个准则，如果向量场的旋度为零，而且它在整个平面上有定义，那么这个向量场是保守的，而且它是个梯度场。
Well, if I have a gradient field, then if I try to compute this line integral, I know it will be the value of the function at the end point minus the value at the starting point.
如果有一个梯度场，然后想计算线积分，我知道积分值是,起点的函数值减去终点的函数值。
OK, so, we've seen that if we have a vector field defined in a simply connected region, and its curl is zero, then it's a gradient field, and the line integral is path independent.
一个向量场,如果定义在单连通区域并且旋度为零，那么它就是一个梯度场，并且其上的线积分与路径无关。
For the natural convection in enclosure under permanent magnetic gradient field, the way to generate different magnetic accelerations by different magnetic field arrangements is developed.
针对永磁梯度磁场作用下封闭腔内的自然对流换热，提出通过不同磁场布置产生不同磁加速度的方法。
If we have a vector field that cannot possibly be a gradient then we shouldn't try to look for a potential.
如果一个向量场不可能是梯度场，那我们就不应该尝试去找势函数。
So, if the gradient of a function is a vector, the divergence of a vector field is a function.
如果说函数的梯度是向量，那么向量场的散度就是函数。
One is to say that the vector field is a gradient in a certain region of a plane.
一个是向量场,在给定平面区域内是梯度场。
OK, so that's the general method of calculation, but we've seen a shortcut for work when we can show that the field is the gradient of potential.
这就是计算的一般方法，但求功的时候，如果向量场是某个势的梯度,是有捷径可走的。
Well, actually here it is not very hard to find a function whose gradient is this vector field.
实际上，找出一个函数，其梯度是这个向量场并不难。
So, actually on Tuesday we'll see how to decide whether a vector field is a gradient or not, and if it is a gradient, how to find the potential function.
周二我们就知道，怎样确定一个场是不是梯度，如果确实是梯度的话，怎样算出势函数。
For example, the electric field or gravitational field is given by the gradient of the gravitational or electric potential.
例如由重力势梯度给出的重力场，或由电势梯度给出的电场。
If you take the gradient of this, you should get again this vector field over there.
对这个函数取梯度，你应该又得到这个向量场。
So, it's a force field is the gradient of a potential so, I'll still keep my plus signs.
有一个力场，它是某种势的梯度，我们还是保持正号。
In this paper the transmission of paraxial light beams was analyzed based on the gradient vector potential of electromagnetic field.
本文运用电磁场的梯度矢势分析了一般情况下傍轴光束的衍射传输问题。
The design of a pulsed field gradient unit for USES on NMR spectrometers is discussed.
给出一种用于核磁共振谱仪的脉冲场梯度单元的详细设计。
The design of a pulsed field gradient unit for USES on NMR spectrometers is discussed.
给出一种用于核磁共振谱仪的脉冲场梯度单元的详细设计。
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