Non-integrability of the Armbruster-Guckenheimer-Kim quartic Hamiltonian through Morales-Ramis theory

We show the non-integrability of the three-parameter Armburster-Guckenheimer-Kim quartic Hamiltonian using Morales-Ramis theory, with the exception of the three already known integrable cases. We use Poincar\'e sections to illustrate the breakdown of regular motion for some parameter values.Comment: Accepted for publication in SIAM Journal on Applied Dynamical Systems. Adapted version for arxiv with 19 pages and 11 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.

Flow equations in generalized braneworld scenarios

We discuss the flow equations in the context of general braneworld cosmologies with a modified Friedmann equation, for either an ordinary scalar field or a Dirac-Born-Infeld tachyon as inflaton candidates. The 4D, Randall-Sundrum, and Gauss-Bonnet cases are compared, using the patch formalism which provides a unified description of these models. The inflationary dynamics is described by a tower of flow parameters that can be evolved in time to select a particular subset of points in the space of cosmological observables. We analyze the stability of the fixed points in all the cosmologies (our results in the 4D case already extending those in the literature). Numerical integration of the flow equations shows that the predictions of the Gauss-Bonnet braneworld differ significantly as compared to the Randall-Sundrum and 4D scenarios, whereas tachyon inflation gives tensor perturbations smaller than those in the presence of a normal scalar field. These results are extended to the realization of a noncommutative space-time preserving maximal symmetry. In this case the tensor-to-scalar signal is unchanged, while blue-tilted spectra are favoured.Comment: 10 pages RevTeX4 with 3 figures included. Matches published version. Note change of title from original submissio

Las actitudes de los estudiantes frente al estudio de las matemáticas, en los programas de Administración de la Corporación Universitaria Minuto de Dios, Centro Regional Pasto

A continuación se describe la experiencia de los investigadores, quienes en su revisión bibliografía pertinente, encuentran que las creencias y actitudes de los estudiantes hacia las matemáticas tienen relación con el proceso de enseñanza de esta ciencia. Por lo cual, recurren a la herramienta Mapa de Empatía, conocida en el ámbito empresarial y articulada con el contexto pedagógico mediante el trabajo de Inés María Gómez Chacón, que se adapta y valida con el apoyo de profesionales de psicología del área de Bienestar Universitario de la institución. Este recurso se aplica a una muestra de estudiantes de tercer semestre de los tres programas de Administración y se identifican creencias, habilidades, aspectos culturales, motivacionales y de frustración con los que viven los estudiantes de Uniminuto, no solo en la etapa universitaria y en el rol de aprendices, sino también en etapas de formación previas y en los espacios propios de su cotidianidad