Persona: Jiménez Morales, Víctor Manuel
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Jiménez Morales
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Víctor Manuel
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Publicación Lie groupoids and algebroids applied to the study of uniformity and homogeneity of material bodies(American Institute of Mathematical Sciences, 2018) León, Manuel de; Epstein, Marcelo; Jiménez Morales, Víctor ManuelA Lie groupoid, called material Lie groupoid, is associated in a natural way to any elastic material. The corresponding Lie algebroid, called material algebroid, is used to characterize the uniformity and the homogeneity properties of the material. The relation to previous results in terms of G−structures is discussed in detail. An illustrative example is presented as an application of the theory.Publicación Reduction of a Hamilton — Jacobi Equation for Nonholonomic Systems(Springer, 2019) Esen, Oğul; León, Manuel de; Sardón, Cristina; Jiménez Morales, Víctor ManuelWe discuss, in all generality, the reduction of a Hamilton — Jacobi theory for systems subject to nonholonomic constraints and invariant under the action of a group of symmetries. We consider nonholonomic systems subject to both linear and nonlinear constraints and with different positioning of such constraints with respect to the symmetries.Publicación On the Homogeneity of Non-uniform Material Bodies(Springer, 2020) León, Manuel de; Epstein, Marcelo; Jiménez Morales, Víctor ManuelA groupoid (B) called material groupoid is naturally associated to any simple body B (see [11, 9, 10]). The material distribution is introduced due to the (possible) lack of differentiability of the material groupoid (see [13, 15]). Thus, the inclusion of these new objects in the theory of material bodies opens the possibility of studying non-uniform bodies. As an example, the material distribution and its associated singular foliation result in a rigorous and unique subdivision of the material body into strictly smoothly uniform sub-bodies, laminates, filaments and isolated points. Furthermore, the material distribution permits us to present a “measure" of uniformity of a simple body as well as more general definitions of homogeneity for non-uniform bodies.Publicación The evolution equation: an application of groupoids to material evolution(CSIC, 2021) León, Manuel de; Jiménez Morales, Víctor ManuelThe 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 material point and its characteristic foliations, which permits us to define the evolution equation. We also discuss phenomena like remodeling and aging.Publicación New notions of uniformity and homogeneity of Cosserat media(AIP Publising, 2023) León, Manuel de; Jiménez Morales, Víctor ManuelIn this paper, we study internal properties of Cosserat media. In fact, by using groupoids and smooth distributions, we obtain three canonical equations. The non-holonomic material equation for Cosserat media characterizes the uniformity of the material. The holonomic material equation for Cosserat media permits us to study when a Cosserat material is a second-grade material. It is remarkable that these two equations also provide us a unique and maximal division of the Cosserat medium into uniform and second-grade parts, respectively. Finally, we present a proper definition of homogeneity of the Cosserat medium, which does not need to assume uniformity. Thus, the homogeneity equation for Cosserat media characterizes this notion of homogeneity.Publicación Automorphisms for Connections on Lie Algebroids(Springer Link, 2018-06) Iglesias Ponte, David; Jiménez Morales, Víctor ManuelPublicación Material geometry(Springer, 2019) Epstein, Marcelo; León, Manuel de; Jiménez Morales, Víctor ManuelWalter Noll's trailblazing constitutive theory of material defects in smoothly uniform bodies is recast in the language of Lie groupoids and their associated Lie algebroids. From this vantage point the theory is extended to non-uniform bodies by introducing the notion of singular material distributions and the physically cognate idea of graded uniformity and homogeneity.Publicación Lie groupoids and algebroids applied to the study of uniformity and homogeneity of Cosserat media(World Scientific, 2018) León, Manuel de; Epstein, Marcelo; Jiménez Morales, Víctor ManuelA Lie groupoid, called second-order non-holonomic material Lie groupoid, is associated in a natural way to any Cosserat medium. This groupoid is used to give a new definition of homogeneity which does not depend on a material archetype. The corresponding Lie algebroid, called second-order non-holonomic material Lie algebroid, is used to characterize the homogeneity property of the material. We also relate these results with the previously obtained ones in terms of non-holonomic second-order G¯¯¯¯ -structures.Publicación Material distributions(SAGE, 2017) León, Manuel de; Epstein, Marcelo; Jiménez Morales, Víctor ManuelThe concept of material distribution is introduced as describing the geometric material structure of a general nonuniform body. Any smooth constitutive law is shown to give rise to a unique smooth integrable singular distribution. Ultimately, the material distribution and its associated singular foliation result in a rigorous and unique subdivision of the material body into strictly smoothly uniform components. Thus, the constitutive law induces a unique partition of the body into smoothly uniform sub-bodies, laminates, filaments and isolated points.Publicación A geometric model for non-uniform processes of morphogenesis(Elsevier, 2022-09-23) León, Manuel de; Jiménez Morales, Víctor ManuelIn this paper we present an application of the groupoid theory to the study of relevant case of material evolution phenomena, the process of morphogenesis. Our theory is inspired by Walter Noll’s theories of continuous distributions and provides a unifying and very simple framework of these phenomena. We present the explicit equation, the morphogenesis equation, to calculate the material distributions associated to this phenomenon.