Search results for "Vector field"
showing 4 items of 164 documents
An explicit unconditionally stable numerical solution of the advection problem in irrotational flow fields
2004
[1] A new methodology for the Eulerian numerical solution of the advection problem is proposed. The methodology is based on the conservation of both the zero- and the first-order spatial moments inside each element of the computational domain and leads to the solution of several small systems of ordinary differential equations. Since the systems are solved sequentially (one element after the other), the method can be classified as explicit. The proposed methodology has the following properties: (1) it guarantees local and global mass conservation, (2) it is unconditionally stable, and (3) it applies second-order approximation of the concentration and its fluxes inside each element. Limitati…
Champs de vecteurs analytiques commutants, en dimension 3 ou 4: existence de zeros communs
1992
One proves the existence of a common zero for any two ℝ-analytic commuting vector fields on a 4-dimensional manifold with not zero Euler characteristic. A local version of this result remains true on 3-manifolds.
Visual understanding of divergence and curl: Visual cues promote better learning
2019
Prior research has shown that students struggle to indicate whether vector field plots have zero or non-zero curl or divergence. In an instruction-based eye-tracking study, we investigated whether visual cues (VC) provided in the vector field plot can foster students’ understanding of these concepts. The VC were only present during instruction and highlighted conceptual information about vector decomposition and partial derivatives. Thirty-two physics majors were assigned to two groups, one was instructed with VC about the problemsolving strategy, and one without. The results show that students in VC-condition performed better, responded with higher confidence, experienced less mental effor…
Relationship between volume and energy of vector fields
2001
Abstract A unified study of energy and volume functionals is presented here by determining the critical points of a functional that extends simultaneously energy and volume and that is defined on the product of the manifold of smooth maps C∞(M,N) times the manifold M of riemannian metrics on M. The restriction of this functional to different submanifolds of the space of vector fields X (M)× M is also considered, and used to study several functionals generalizing volume and energy or total bending of vector fields