Lluís Gil Espert

Quasi-homothetic transformation for comparing the mechanical performance of planar models in biological research

The potential of Finite Element Analysis (FEA) as an analytical technique in biological research has been widely highlighted in recent years. In spite of its great power, only in the best of circumstances one can compare the behaviour of models that differ in size and shape. Here, a new and easy procedure to scale FE models of plane elasticity is presented for several species of extant bovids that significantly differ in size and morphology. The method is based on the modification of the values of the forces applied by taking into account the particularities of the elasticity plane models (plane strain and plane stress equations) using quasi-homothetic transformations. This approach is shown to be extremely useful when exploring the effect of the shape in front of the strength and the stiffness of vertebrate bone structures. Thus, the quasi-homothetic concept is a new and interesting proposal to be used in plane elasticity models of biological, and specifically of vertebrate, structures which can be modelled as two-dimensional finite element models.

Accounting for differences in element size and homogeneity when comparing Finite Element models: Armadillos as a case study

Computing the average Von Mises stress of Finite Element Models to obtain a single measurement that represents the relative strength of vertebrate structures has been used recently in different works in palaeobiology. However, due to the nature of the Finite Element Analysis (FEA) data, which depends on the size of the elements of the mesh, this approach needs to be fully developed taking into account this influence of the size elements in the results. In this work, we proposed a Mesh-Weighted Arithmetic Mean as the adequate central tendency statistic for non-uniform meshes. On the other hand, when other statistical tools are used, we propose a Quasi-Ideal Mesh that takes into account the differences in size of the elements. Firstly, in order to analyse our proposed approach, one Cingulata mandible has been used generating different meshes. Afterwards, FEA has been applied in a case study in 20 different mandibles belonging to 14 species of Cingulata. Our results suggest that the proposed methodologies are suitable to compare different patterns of stress distribution. In particular, the methods proposed have been shown to be extremely useful when analysing the biomechanics of vertebrate bone structures that can be modelled as planar models in an interspecific comparative framework.

Coupling finite element analysis and multibody system dynamics for biological research

Flexible Multibody System Dynamics (FMSD) is a simulation technique that can be used to study the behavior of the mechanical systems that consists of one or more deformable bodies. A deformable body can be modeled using a number of approaches while the floating frame of reference formulation is a widely used approach. In that approach, flexibility within Multibody System Dynamics (MSD) is described by employing the Finite Element Analysis (FEA) with a modal reduction approach. The applicability of an FMSD in the feeding mechanism of vertebrate structures is tested in order to utilize the potential of the method in biological research. Flexible Multibody System Dynamics is explored studying the feeding mechanism in a skull of Edingerella madagascariensis. Firstly, a static structural analysis is done using FEA and secondly, dynamic solutions based on FMSD are obtained by varying the number of deformation modes used in the modal reduction analysis. The conclusion is that use of this approach is feasible and efficient for the study of feeding mechanisms in vertebrate structures when a dynamic response should be evaluated.

Impact damage identification in composite laminates using vibration testing

We study a class of models with long-range repulsive interactions of the generalized Coulomb form

Improving mesh generation in finite element analysis for functional morphology approaches

V(r)\sim 1/r^{\alpha}

Estudio de la interfaz hormigón-epoxi-frp de un ensayo de doble cortante por medio de la teoría de mezclas serie/paralelo

. We show that decreasing the interaction exponent in the regime

Comparison between TRM and FRP strengthening systems at preventing buckling failure of brick masonry walls

\alpha T_c

Computational and experimental approach of the phenomenology in the impact of a hen eggshell

, which is characterized by an unusual temperature dependence of all quantities. In contrast, the leading critical behavior very close to the charge-ordering temperature remains identical as in models with short-range interactions.We describe conditions on non-gradient drift diffusion Fokker-Planck equations for its solutions to converge to equilibrium with a uniform exponential rate in Wasserstein distance. This asymptotic behaviour is related to a functional inequality, which links the distance with its dissipation and ensures a spectral gap in Wasserstein distance. We give practical criteria for this inequality and compare it to classical ones. The key point is to quantify the contribution of the diffusion term to the rate of convergence, which to our knowledge is a novelty.Gait disturbances similar to those of human Parkinsons disease (PD) can be observed in animals after administration of neurotoxin 6-hydroxydopamine (6-OHDA) to induce unilateral nigrostriatal dopamine depletion. However, the relationship between gait disturbances and dopamine depletion following 6-OHDA infusion has not been determined. The present study investigated the longitudinal changes of spatiotemporal gait patterns using a walkway system to acquire footprints and lateral limb images over a 6-week period following unilateral 6-OHDA injection into the medial forebrain bundle of rats. Our results indicated that hemiparkinsonian rats exhibited changes in gait patterns, as compared to normal controls, and pre-lesion levels, including a significantly decreased walking speed and step/stride length as well as an increased base of support and foot angle. The relative percentage of the gait cycle was also altered, showing an increase in the stance to swing ratio, which was more evident in the affected hindlimb. Time-course observations showed that these gait disturbances occurred as early as 4 days post-lesion and gradually increased up to 42 days post-injury. The extents of gait disturbances were compared with conventional apomorphine-induced turning behavior and akinesia bar tests, which were also apparent at 4 days post-lesion but remained relatively unchanged after 28 days. Our time-course gait analysis of a unilateral 6-OHDA rodent model provides insight into the compensatory changes of motor functions during the 6-week development of a nigrostriatal lesion, which might be useful for future objective assessment of novel treatments for human PD subjects.Let d=(d_1,d_2,..., d_n) be a vector of non-negative integers. We study the number of symmetric 0-1 matrices whose row sum vector equals d. While previous work has focussed on the case of zero diagonal, we allow diagonal entries to equal 1. When forming the row sum, each diagonal entry is multiplied by a factor of D, where D is 1 or 2. The case D=1 corresponds to enumeration by the usual row sum of matrices. The case D=2 corresponds to enumeration by degree sequence of undirected graphs with loops but no repeated edges, due to the convention that a loop contributes 2 to the degree of its incident vertex. We obtain asymptotically precise formulae for the number of matrices in the sparse range (where, roughly, the maximum row sum is o(n^{1/2})), and in the dense range (where, roughly, the average row sum is proportional to n and the row sums do not vary greatly).We prove the existence of equiangular tight frames having n=2d-1 elements drawn from either C^d or C^(d-1) whenever n is either 2^k-1 for k in N, or a power of a prime such that n=3 mod 4. We also find a simple explicit expression for the prime power case by establishing a connection to a 2d-element equiangular tight frame based on quadratic residues.Ultra High Energy Cosmic Rays (UHECR) at GZK cut off energy (E \geq 55 EeV eV) may keep sharp or diffused directionality wherever their composition is made by nucleon or light nuclei. AUGER UHECR (2007-2010) did show a mild clustering mainly around Cen A. Two over three of the recent discovered AUGER multiplet (a dozen of events each) tail clustering at twenty EeV are pointing to primary sources very near the same UHECR crowded Cen A region. The Tens EeV tail is aligned with the same UHECR events. We foresaw such possibility as fragment tails of lightest UHECR nuclei. We discuss the relevance of this correlation within a model where UHECR are mostly lightest He like nuclei. UHECR fragment multiplet clustering aligned along higher Cen A events (at 55 EeV energy) probe and reinforce our interpretation with an a priori probability near 3 part over a hundred thousand.