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pro vyhledávání: '"Jiménez, V. M."'
Autor:
Jiménez, V. M.
In Continuum Mechanic a simple material body $\mathcal{B}$ is represeted by a three-dimensional differentiable manifold and the configuration space is given by the space of embeddings $Emb \left( \mathcal{B} , \mathbb{R}^{n} \right)$. We use the topo
Externí odkaz:
http://arxiv.org/abs/2402.03039
Autor:
Jiménez, V. M., De León, M.
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-holonomic material equation for Cosserat media} characterizes the uniformity
Externí odkaz:
http://arxiv.org/abs/2305.14261
Autor:
Jiménez, V. M., de León, M.
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 inspired by Walter Noll's theories of continuous distributions and prov
Externí odkaz:
http://arxiv.org/abs/2207.03252
Autor:
Jiménez, V. M., De León, M.
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 properties of the particle and its characteristic foliations, which p
Externí odkaz:
http://arxiv.org/abs/2108.06766
For any body-time manifold $\mathbb{R} \times \mathcal{B}$ there exists a groupoid, called material groupoid, encoding all the material properties of the evolution material. A smooth distribution, the material distribution, is constructed to deal wit
Externí odkaz:
http://arxiv.org/abs/2108.02865
A groupoid $\Omega \left( \mathcal{B} \right)$ called material groupoid is naturally associated to any simple body $\mathcal{B}$. The material distribution is introduced due to the (possible) lack of differentiability of the material groupoid. Thus,
Externí odkaz:
http://arxiv.org/abs/1812.04970
Associated to each material body $\mathcal{B}$ there exists a groupoid $\Omega \left( \mathcal{B} \right)$ consisting of all the material isomorphisms connecting the points of $\mathcal{B}$. The uniformity character of $\mathcal{B}$ is reflected in t
Externí odkaz:
http://arxiv.org/abs/1711.09022
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 definition of homogeneity which does not depend on a reference crystal. The co
Externí odkaz:
http://arxiv.org/abs/1708.00337
A Lie groupoid, called \textit{material Lie groupoid}, is associated in a natural way to any elastic material. The corresponding Lie algebroid, called \textit{material algebroid}, is used to characterize the uniformity and the homogeneity properties
Externí odkaz:
http://arxiv.org/abs/1607.04043
Publikováno v:
Philosophical Transactions: Biological Sciences, 2016 Sep . 371(1704), 1-7.
Externí odkaz:
http://www.jstor.org/stable/24769377
