# Questions tagged [vector-fields]

In vector calculus, a vector field is an assignment of a vector to each point in a subset of space. A vector field in the plane, for instance, can be visualized as a collection of arrows with a given magnitude and direction each attached to a point in the plane. Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout space.

2,879 questions
Filter by
Sorted by
Tagged with
28 views

• 219
31 views

### Norm on the space of vector fields

Let $M$ be a finite dimensional manifold. There exists the notion of the norm of a tangent vector field on M? In other words, the space of tangent vector fields is a normed space? Thank you in advance ...
• 159
26 views

### How do I find the absolute maximum and minimum values of the Lamb-Oseen Vortex?

I am researching alternative solutions to Stokes equations and I came across a problem with the Lamb-Oseen vortex I cannot solve that I hope will allow easier derivations of vortex functions with ...
117 views

### Application of Chain Rule in Proof of Stokes' Theorem

In the proof of Stokes' theorem in "Vector Calculus" by Marsden and Tromba, I noticed that the chain rule is applied selectively. Specifically, the chain rule is not used when expanding the ...
• 41
24 views

### Minimum conditions in order to make this integral equal zero

What is the minimum condition to impose in $F_{\bf B}$ and $G_{\bf B}$ in order to make this integral equal to zero? \int \left(\nabla\times F_{\bf B}\right)C({\bf x}) \left(\nabla\...
43 views

### An analogue of the de Rham complex for vector fields

Let $M$ be a smooth manifold and let $\chi$ be its tangent bundle and $\Omega^1$ be its bundle of $1$-forms. Using the exterior algebra we can extend the space of sections of $\Omega^1$ to a ...
29 views

• 33
82 views

### "field" vs. "vector field" [duplicate]

Is the "field" in the "vector field" as the same "field" in algebra: as the commutative ring with the multiplicative inverse? If yes, then the "vector field" ...
• 5,969
44 views

• 1,138
57 views

• 640
16 views

### Model probabilistic time evolution from vector field distribution

Given an axis-aligned grid${}^1$ $x_1 , \ldots , x_n \in \mathbb{R}^2$. Let $\mu \in \mathbb{R}^{2n}$ and $\Sigma \in \mathbb{R}^{2n\times 2n}$ be the means and covariance matrix and assume we have a ...
• 1,114
1 vote
33 views

• 352
116 views

• 1,697