Zobrazeno 1 - 10
of 198
pro vyhledávání: '"DA SILVA, Luiz C."'
Context: Due to advances in synthesizing lower dimensional materials there is the challenge of finding the wave equation that effectively describes quantum particles moving on 1D and 2D domains. Jensen and Koppe and Da Costa independently introduced
Externí odkaz:
http://arxiv.org/abs/2406.03590
In the last two decades, much effort has been dedicated to studying curves and surfaces according to their angle with a given direction. However, most findings were obtained using a case-by-case approach, and it is often unclear what are consequences
Externí odkaz:
http://arxiv.org/abs/2403.10716
Autor:
da Silva, Luiz C. B., López, Rafael
The concept of catenary has been recently extended to the sphere and the hyperbolic plane by the second author [L\'opez, arXiv:2208.13694]. In this work, we define catenaries on any Riemannian surface. A catenary on a surface is a critical point of t
Externí odkaz:
http://arxiv.org/abs/2306.04013
Autor:
da Silva, Luiz C. B., López, Rafael
We introduce the concept of extrinsic catenary in the hyperbolic plane. Working in the hyperboloid model, we define an extrinsic catenary as the shape of a curve hanging under its weight as seen from the ambient space. In other words, an extrinsic ca
Externí odkaz:
http://arxiv.org/abs/2211.15297
Publikováno v:
Journal of Elasticity (2023)
The geometry and interactions between the constituents of a liquid crystal, which are responsible for inducing the partial order in the fluid, may locally favor an attempted phase that could not be realized in $\mathbb{R}^3$. While states that are in
Externí odkaz:
http://arxiv.org/abs/2211.08598
Autor:
da Silva, Luiz C. B., López, Rafael
This paper investigates the hanging chain problem in the simply isotropic plane as well as its 2-dimensional analog in the simply isotropic space. The simply isotropic plane and space are two- and three-dimensional geometries equipped with a degenera
Externí odkaz:
http://arxiv.org/abs/2209.01631
Publikováno v:
Sao Paulo J. Math. Sci. 2022
We investigate ruled surfaces in 3d Riemannian manifolds, i.e., surfaces foliated by geodesics. In 3d space forms, we find the striction curve, distribution parameter, and the first and second fundamental forms, from which we obtain the Gaussian and
Externí odkaz:
http://arxiv.org/abs/2106.10346
Autor:
da Silva, Luiz C. B., Efrati, Efi
The geometry and topology of the region in which a director field is embedded impose limitations on the kind of supported orientational order. These limitations manifest as compatibility conditions that relate the quantities describing the director f
Externí odkaz:
http://arxiv.org/abs/2102.07907
Autor:
da Silva, Luiz C. B.
Publikováno v:
J. Geom. 112 (2021) 35
It is known that minimal surfaces in Euclidean space can be represented in terms of holomorphic functions. For example, we have the well-known Weierstrass representation, where part of the holomorphic data is chosen to be the stereographic projection
Externí odkaz:
http://arxiv.org/abs/2101.11121
Autor:
da Silva, Luiz C. B., Efrati, Efi
Publikováno v:
Proc. R. Soc. A 477 (2021) 20200891
Minimal surfaces arise as energy minimizers for fluid membranes and are thus found in a variety of biological systems. The tight lamellar structures of the endoplasmic reticulum and plant thylakoids are composed of such minimal surfaces in which righ
Externí odkaz:
http://arxiv.org/abs/2011.06396