Invariant manifolds of the Bonhoeffer-van der Pol oscillator

The stable and unstable manifolds of a saddle fixed point (SFP) of the Bonhoeffer-van der Pol oscillator are numerically studied. A correspondence between the existence of homoclinic tangencies (whic are related to the creation or destruction of Smale horseshoes) and the chaos observed in the bifurcation diagram is described. It is observed that in the non-chaotic zones of the bifurcation diagram, there may or may not be Smale horseshoes, but there are no homoclinic tangencies.Comment: 14 pages, 15 figure

Sharp-Interface Limit of a Fluctuating Phase-Field Model

We present a derivation of the sharp-interface limit of a generic fluctuating phase-field model for solidification. As a main result, we obtain a sharp-interface projection which presents noise terms in both the diffusion equation and in the moving boundary conditions. The presented procedure does not rely on the fluctuation-dissipation theorem, and can therefore be applied to account for both internal and external fluctuations in either variational or non-variational phase-field formulations. In particular, it can be used to introduce thermodynamical fluctuations in non-variational formulations of the phase-field model, which permit to reach better computational efficiency and provide more flexibility for describing some features of specific physical situations. This opens the possibility of performing quantitative phase-field simulations in crystal growth while accounting for the proper fluctuations of the system.Comment: 21 pages, 1 figure, submitted to Phys. Rev.

A probabilistic model for crystal growth applied to protein deposition at the microscale

A probabilistic discrete model for 2D protein crystal growth is presented. This model takes into account the available space and can describe growing processes of different nature due to the versatility of its parameters which gives the model great flexibility. The accuracy of the simulation is tested against a real protein (SbpA) crystallization experiment showing high agreement between the proposed model and the actual images of the nucleation process. Finally, it is also discussed how the regularity of the interface (i.e. the curve that separates the crystal from the substrate) affects to the evolution of the simulation.Comment: 13 pages, 12 figure

A wavelet-based tool for studying non-periodicity

This paper presents a new numerical approach to the study of non-periodicity in signals, which can complement the maximal Lyapunov exponent method for determining chaos transitions of a given dynamical system. The proposed technique is based on the continuous wavelet transform and the wavelet multiresolution analysis. A new parameter, the \textit{scale index}, is introduced and interpreted as a measure of the degree of the signal's non-periodicity. This methodology is successfully applied to three classical dynamical systems: the Bonhoeffer-van der Pol oscillator, the logistic map, and the Henon map.Comment: 14 pages, 6 figure

Beyond Invalidation: Unorthodox Forms of Judicial Review of Constitutional Amendments and Constitution-amending Case Law in Colombia

Judicial invalidation of constitutional amendments has garnered the attention of scholars in the last few years. Questions like whether and how a court should quash an amendment are at the forefront of contemporary comparative-constitutional-law and constitutional-theory inquiries. This excessive focus on annulment, however, has neglected some other nonconventional forms of judicial involvement regarding amendments. Taking Colombia as a case study, this article shows that the Constitutional Court has also had the power to initiate amendments, define their content, rewrite their text, and promulgate them. As these novel judicial interventions that go beyond invalidation resemble the prerogatives commonly vested on the amendment power, this research terms them ‘constitution-amending case law’, offers an in-depth exploration of them, and proposes a typology of such a jurisprudence. Lastly, the article ends with a cautionary note about the challenges this type of constitution-amending case law faces from the perspective of democracy and democratic backsliding.            

A simple formula to find the closest consistent matrix to a reciprocal matrix

Achieving consistency in pair-wise comparisons between decision elements given by experts or stakeholders is of paramount importance in decision-making based on the AHP methodology. Several alternatives to improve consistency have been proposed in the literature. The linearization method (Benitez et al., 2011 [10]), derives a consistent matrix based on an original matrix of comparisons through a suitable orthogonal projection expressed in terms of a Fourier-like expansion. We propose a formula that provides in a very simple manner the consistent matrix closest to a reciprocal (inconsistent) matrix. In addition, this formula is computationally efficient since it only uses sums to perform the calculations. A corollary of the main result shows that the normalized vector of the vector, whose components are the geometric means of the rows of a comparison matrix, gives the priority vector only for consistent matrices. (C) 2014 Elsevier Inc. All rights reserved.This work has been performed with the support of the project IDAWAS, DPI2009-11591 of the Direccion General de Investigacion del Ministerio de Ciencia e Innovacion (Spain), with the supplementary support of ACOMP/2010/146 of the Conselleria d'Educacio of the Generalitat Valenciana, and the support given to the first author by the Spanish project MTM2010-18539. The use of English in this paper was revised by John Rawlins; and the revision was funded by the Universitat Politecnica de Valencia, Spain.Benítez López, J.; Izquierdo Sebastián, J.; Pérez García, R.; Ramos Martínez, E. (2014). A simple formula to find the closest consistent matrix to a reciprocal matrix. Applied Mathematical Modelling. 38(15-16):3968-3974. https://doi.org/10.1016/j.apm.2014.01.007S396839743815-1

Properties of solutions for nonlinear Volterra integral equations

Some properties of non-locally bounded solutions for Abel integral equations are given. The case in which there exists two non-trivial solutions for such equations is also studied. Besides, some known results about existence, uniqueness and attractiveness of solutions for some Volterra equations are improved

A note on the uniqueness and attractive behavior of solutions for nonlinear Volterra equations

In this paper we prove that positive solutions of some nonlinear Volterra integral equations must be locally bounded and global attractors of positive functions. These results complete previous results about the existence and uniqueness of solutions and their attractive behavior

Influence of single-neutron stripping on near-barrier ⁶He+²⁰⁸Pb and ⁸He+²⁰⁸Pb elastic scattering

The influence of single-neutron stripping on the near-barrier elastic scattering angular distributions for the 6,8He+208Pb systems is investigated through coupled reaction channels (CRC) calculations fitting recently published data to explore the differences in the absorptive potential found in the scattering of these two neutron-rich nuclei. The inclusion of the coupling reduces the elastic cross section in the Coulomb-nuclear interference region for 8He scattering, whereas for 6He its major impact is on the large-angle elastic scattering. The real and imaginary dynamic polarization potentials are obtained by inverting the CRC elastic scattering S-matrix elements. These show that the main absorptive features occur between 11 and 12 fm for both projectiles, while the attractive features are separated by about 1 fm, with their main structures occurring at 10.5 fm for 6He and 11.5 fm for 8He