Person:
Oleaga Apadula, Gerardo Enrique

First Name

Gerardo Enrique

Last Name

Oleaga Apadula

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Ciencias Matemáticas

Department

Análisis Matemático Matemática Aplicada

Area

Matemática Aplicada

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Now showing 1 - 10 of 14

A proposed screening algorithm for bone remodeling
(Cambridge University Press, 2020-12-23) Arias, C. F.; Bertocchini, F.; Herrero, Miguel A.; Oleaga Apadula, Gerardo Enrique
One of the most remarkable aspects of human homeostasis is bone remodeling. This term denotes the continuous renewal of bone that takes place at a microscopic scale and ensures that our skeleton preserves its full mechanical compliance during our lives. We propose here that a renewal process of this type can be represented at an algorithmic level as the interplay of two different but related mechanisms. The first of them is a preliminary screening process, by means of which the whole skeleton is thoroughly and continuously explored. This is followed by a renovation process, whereby regions previously marked for renewal are first destroyed and then rebuilt, in such a way that global mechanical compliance is never compromised. In this work we pay attention to the first of these two stages. In particular we show that an efficient screening mechanism may arise out of simple local rules, which at the biological level are inspired by the possibility that individual bone cells compute signals from their nearest local neighbors. This is shown to be enough to put in place a process which thoroughly explores the region where such mechanism operates.
Planar cracks running along piecewise linear paths
(Royal Society of London, 2004-02-08) Oleaga Apadula, Gerardo Enrique; Herrero, Miguel A.; Velázquez, J.J. L.
Consider a crack propagating in a plane according to a loading that results in anti-plane shear deformation. We show here that if the crack path consists of two straight segments making an angle psi not equal 0 at their junction, examples can be provided for which the value of the stress-intensity factor (SIF) actually depends on the previous history of the motion. This is in sharp contrast with the rectilinear case (corresponding to psi = 0), where the SIF is known to have a local character, its value depending only on the position and velocity of the crack tip at any given time.
Early Stages of Bone Fracture Healing: Formation of a Fibrin–Collagen Scaffold in the Fracture Hematoma
(Springer, 2014-12) Herrero, Miguel A.; Oleaga Apadula, Gerardo Enrique; Echeverri, L.F.; López, J. M.
This work is concerned with the sequence of events taking place during the first stages of bone fracture healing, from bone breakup until the formation of early fibrous callus (EFC). The latter provides a scaffold over which subsequent remodeling processes will eventually result in successful bone repair. Specifically, some mathematical models are proposed to estimate the time required for (1) the formation immediately after fracture of a fibrin clot, described in terms of a phase transition in a polymerization process, and (2) the onset of EFC which is produced when fibroblasts arising from differentiation of chemotactically recruited mesenchymal stem cells remodel a previous fibrin clot by releasing a collagen matrix over it. An attempt has been made to keep models as simple as possible, so that a explicit dependence of the estimates obtained on relevant biochemical parameters involved is obtained.
On the dynamics of cracks in three dimensions
(Elsevier, 2003-01) Oleaga Apadula, Gerardo Enrique
We introduce a three-dimensional dynamic crack propagation law, which is derived from Hamilton's principle. The result is an extension of a previous one obtained, corresponding to the two-dimensional case. As a matter of fact, in an orthogonal plane to the crack front, the geometric condition to be satisfied over the path is the same as in two dimensions. The third mode enters only through the energy release rate. The fact that the physics of the problem is locally two dimensional is a consequence of the virtual motions allowed in the set of admissible crack configurations.
On the Eshelby-Kostrov property for the wave equation in the plane
(American Mathematical Society, 2006) Herrero, Miguel A.; Oleaga Apadula, Gerardo Enrique; Velázquez, J.J. L.
This work deals with the linear wave equation considered in the whole plane R2 except for a rectilinear moving slit, represented by a curve Γ (t) = {(x1, 0) : −∞ < x1 < λ(t)} with t ≥ 0. Along Γ (t) , either homogeneous Dirichlet or Neumann boundary conditions are imposed. We discuss existence and uniqueness for these problems, and derive explicit representation formulae for solutions. These last have a simple geometrical interpretation, and in particular allow to derive precise asymptotic expansions for solutions near the tip of the curve. In the Neumann case, we thus recover a classical result in fracture dynamics, namely the form of the stress intensity factor in crack propagation under antiplane shear conditions
Divergence of perturbation theory: Steps towards a convergent series
(American Physical Society, 1998-01-15) Oleaga Apadula, Gerardo Enrique; Pernice, Sergio A.
The mechanism underlying the divergence of perturbation theory is exposed. This is done through a detailed study of the violation of the hypothesis of Lebesgue's dominated convergence theorem using familiar techniques of quantum held theory. That theorem governs the validity (or lack of it) of the formal manipulations done to generate the perturbative series in the functional integral formalism. The aspects of the perturbative series that need to be modified to obtain a convergent series are presented. Useful tools for a practical implementation of these modifications are developed. Some resummation methods are analyzed in the light of the above mentioned mechanism.
On the Path of a Quasi-static Crack in Mode III
(Springer, 2004) Oleaga Apadula, Gerardo Enrique
A method for finding the path of a quasi-static crack growing in a brittle body is presented. The propagation process is modelled by a sequence of discrete steps optimizing the elastic energy released. An explicit relationship between the optimal growing direction and the parameters defining the local elastic field around the tip is obtained for an anti-plane field. This allows to describe a simple algorithm to compute the crack path.
The anti-symmetry principle for quasi-static crack propagation in Mode III
(Springer, 2007-09-01) Oleaga Apadula, Gerardo Enrique
In this note we study a basic propagation criterion for quasi-static crack evolution in Mode III. Using classical techniques of complex analysis, the assumption of stable growth is expressed in terms of the parameters defining the elastic field around the tip. We explore the consequences of the local condition obtained and analyse its role as a crack propagation law. In particular, we herein extend to bounded domains a number of results previously obtained for the whole plane.
The application of cliff degradation models for estimation of the initial height of rammed-earth walls (Por-Bajin Fortress, Southern Siberia, Russia)
(Wiley-Blackwell, 2013-10) Alfimov, G. L.; Nosyrev, G. V.; Panin, V.; Arzhantseva, A.; Oleaga Apadula, Gerardo Enrique
The main objective of this study is to recover the initial geometry of earthen walls from the shape of wall remains. The original parameters of the walls have been estimated by fitting the field-measured profiles with the theoretical shape predicted by the model. We estimate: (i) the initial wall height (between 2 and 3m); (ii) their shape (vertical or nearly vertical); and (iii) the time for complete degradation (between 250 and 400 years, depending on wall orientation). We show that this approach yields the best results when the main degradation factor is the temperature gradient, as it is for south-oriented wall faces.
The classical theory of univalent functions and quasistatic crack propagation
(Cambridge University Press, 2006) Oleaga Apadula, Gerardo Enrique
We study the propagation of a crack in critical equilibrium for a brittle material in a Mode III field. The energy variations for small virtual extensions of the crack are handled in a novel way: the amount of energy released is written as a functional over a family of univalent functions on the upper half plane. Classical techniques developed in connection to the Bieberbach Conjecture are used to quantify the energy-shape relationship. By means of a special family of trial paths generated by the so-called Löwner equation we impose a stability condition on the field which derives in a local crack propagation criterion. We called this the anti-symmetry principle, being closely related to the well known symmetry principle for the in-plane fields.