Том 12 № 1

Постійне посилання зібрання

Зараз показуємо 1 - 2 з 2

On the integrability problem for systems of partial differential equations in one unknown function, II
(2019) Antonio Kumpera
We continue here our discussion of Part I, [18], by examining the local equivalence problem for partial differential equations and illustrating it with some examples, since almost any integration process or method is actually a local equivalence problem involving a suitable model. We terminate the discussion by inquiring on non-integrable Pfaffian systems and on their integral manifolds of maximal dimension.
A Physics-Based Estimation of Mean Curvature Normal Vector for Triangulated Surfaces
(2019) Sudip Kumar Das, Mirza Cenanovic, Junfeng Zhang
In this note, we derive an approximation for the mean curvature normal vector on vertices of triangulated surface meshes from the Young-Laplace equation and the force balance principle. We then demonstrate that the approximation expression from our physics-based derivation is equivalent to the discrete Laplace-Beltrami operator approach in the literature. This work, in addition to providing an alternative expression to calculate the mean curvature normal vector, can be further extended to other mesh structures, including non-triangular and heterogeneous meshes.