Zobrazeno 1 - 10
of 93
pro vyhledávání: '"Pozzi, Paola"'
In this article we study the anisotropic curve shortening flow for a planar network of three curves with fixed endpoints and which meet in a triple junction. We show that the anisotropic curvature energy fulfills a Lojasiewicz-Simon gradient inequali
Externí odkaz:
http://arxiv.org/abs/2310.05596
Autor:
Pozzi, Paola
Publikováno v:
Annali di Matematica Pura ed Applicata (1923 -)
In arXiv:2205.02920 a variant of the classical elastic flow for closed curves in $\mathbb{R}^{n}$ was introduced, that is more suitable for numerical purposes. Here we investigate the long-time properties of such evolution demonstrating that the flow
Externí odkaz:
http://arxiv.org/abs/2205.04178
Autor:
Pozzi, Paola, Stinner, Björn
Elastic flow for closed curves can involve significant deformations. Mesh-based approximation schemes require tangentially redistributing vertices for long-time computations. We present and analyze a method that uses the Dirichlet energy for this pur
Externí odkaz:
http://arxiv.org/abs/2205.02920
We consider motion by anisotropic curvature of a network of three curves immersed in the plane meeting at a triple junction and with the other ends fixed. We show existence, uniqueness and regularity of a maximal geometric solution and we prove that,
Externí odkaz:
http://arxiv.org/abs/2012.02490
Publikováno v:
Journal of Evolution Equations 2020 (for the improved version)
In this paper we study the $L^2$-gradient flow of the penalized elastic energy on networks of $q$-curves in $\R^{n}$ for $q \geq 3$. Each curve is fixed at one end-point and at the other is joint to the other curves at a movable $q$-junction. For thi
Externí odkaz:
http://arxiv.org/abs/1912.09626
Autor:
Pozzi, Paola, Stinner, Björn
A new semi-discrete finite element scheme for the evolution of three parametrized curves by curvature flow that are connected by a triple junction is presented and analyzed. In this triple junction, conditions are imposed on the angles at which the c
Externí odkaz:
http://arxiv.org/abs/1911.09636
Autor:
Novaga, Matteo, Pozzi, Paola
We consider a second order gradient flow of the p-elastic energy for a planar theta-network of three curves with fixed lengths. We construct a weak solution of the flow by means of an implicit variational scheme. We show long-time existence of the ev
Externí odkaz:
http://arxiv.org/abs/1905.06742
We provide a long-time existence and sub-convergence result for the elastic flow of a three network in $\mathbb{R}^{n}$ under some mild topological assumptions. The evolution is such that the sum of the elastic energies of the three curves plus their
Externí odkaz:
http://arxiv.org/abs/1812.11367
We study the evolution of closed inextensible planar curves under a second order flow that decreases the $p$-elastic energy. A short time existence result for $p \in (1,\infty)$ is obtained via a minimizing movements method. For $p = 2$, that is in t
Externí odkaz:
http://arxiv.org/abs/1811.06608
Autor:
Pozzi, Paola, Stinner, Björn
A finite element approach to the elastic flow of a curve coupled with a diffusion equation on the curve is analysed. Considering the graph case, the problem is weakly formulated and approximated with continuous linear finite elements, which is enable
Externí odkaz:
http://arxiv.org/abs/1707.08643