24 нояб. 2014 г. · The entire field should be able to be broken into a curl component and a divergence component and if both are zero, the field must be zero.

14 окт. 2017 г. · The vector field is curl free in U because it can be shown by direct calculation that it is zero everywhere for z≠0, not because U is not simply connected.

4 февр. 2018 г. · This vector field is curl-free, but not conservative because going around the center once (with an integral) does not yield zero. This happens ...

29 апр. 2014 г. · The existence of non-conservative vector fields with zero curl is a topological matter, ie it only depends on the topology of the space on which the vector ...

10 авг. 2015 г. · If the curl of a vector function is equal to zero, then the vector function is the gradient of some other scalar function, but is this a must?

3 авг. 2018 г. · The curl measures the infinitesimal rotation of a vector field around a point (in the domain). Yes, V is not defined where x=y=0 because the coefficients aren' ...

2 июн. 2020 г. · I'm trying to gain some intuition for what the possible trajectories for particles would look like in the cases that this vector field has zero divergence, ...

1 дек. 2018 г. · The curl operator applies to vector fields it doesn't make sense for individual vectors. the vector field you are interested is just a map.

7 сент. 2013 г. · I am trying to find a vector → F such that ∇× → F =0 ∇⋅ → F =0 The way I go about it is: Becasue curl is 0, we know that → F =∇f so the divergence ...

5 дек. 2016 г. · Given X⊂R2 not simply-connected. I want to get an example of a vector field that has zero curl, but is not the gradient of any smooth function ...