7 citations · 16 across the 7 of their papers we have counts for
8 papers
Double groupoids of composites: applications to uniformity
V. M. Jiménez, M. De León, M. Epstein
In this paper we present a geometrical framework to study the uniformity of a composite material by means of double groupoid theory. The notions of vertical and horizontal uniformi…
New notions of uniformity and homogeneity of Cosserat media
V. M. Jiménez, M. De León
In this paper, we study internal properties of a Cosserat media. In fact, by using groupoids and smooth distributions, we obtain a three canonical equations. The \textit{non-holono…
A geometric model for non-uniform processes of morphogenesis
V. M. Jiménez, M. de León
In this paper we present an application of the groupoid theory to the study of relevant case of material evolution phenomena, the \textit{process of morphogenesis}. Our theory is i…
The evolution equation: an application of groupoids to material evolution
V. M. Jiménez, M. De León
The aim of this paper is to study the evolution of a material point of a body by itself, and not the body as a whole. To do this, we construct a groupoid encoding all the intrinsic…
Characteristic foliations of material evolution: from remodeling to aging
V. M. Jiménez, M. de León y M. Esptein
For any body-time manifold there exists a groupoid, called material groupoid, encoding all the material properties of the evolution material. A smoo…
Reduction of a Hamilton-Jacobi equation for nonholonomic systems
Oğul Esen, Manuel de León, Víctor Manuel Jiménez Morales +1
Nonholonomic mechanical systems have been attracting more interest in recent years because of their rich geometric properties and their applications in Engineering. In all generali…
Characteristic distribution: An application to material bodies
V. M. Jiménez, M. de León, M. Epstein
Associated to each material body there exists a groupoid consisting of all the material isomorphisms connecting the points of $\mathcal{…
Lie groupoids and algebroids applied to the study of uniformity and homogeneity of Cosserat media
V. M. Jiménez, M. de León, M. Esptein
A Lie groupoid, called \textit{second-order non-holonomic material Lie groupoid}, is associated in a natural way to any Cosserat media. This groupoid is used to give a new definiti…