Supersymmetric methods in the traveling variable: inside neurons and at the brain scale

We apply the mathematical technique of factorization of differential operators to two different problems. First we review our results related to the supersymmetry of the Montroll kinks moving onto the microtubule walls as well as mentioning the sine-Gordon model for the microtubule nonlinear excitations. Second, we find analytic expressions for a class of one-parameter solutions of a sort of diffusion equation of Bessel type that is obtained by supersymmetry from the homogeneous form of a simple damped wave equations derived in the works of P.A. Robinson and collaborators for the corticothalamic system. We also present a possible interpretation of the diffusion equation in the brain contextComment: 14 pages, 1 figur

Optimal domain of qq-concave operators and vector measure representation of qq-concave Banach lattices

Given a Banach space valued $q$-concave linear operator $T$ defined on a $\sigma$-order continuous quasi-Banach function space, we provide a description of the optimal domain of $T$ preserving $q$-concavity, that is, the largest $\sigma$-order continuous quasi-Banach function space to which $T$ can be extended as a $q$-concave operator. We show in this way the existence of maximal extensions for $q$-concave operators. As an application, we show a representation theorem for $q$-concave Banach lattices through spaces of integrable functions with respect to a vector measure. This result culminates a series of representation theorems for Banach lattices using vector measures that have been obtained in the last twenty years

Solutions of the Perturbed KDV Equation for Convecting Fluids by Factorizations

In this paper, we obtain some new explicit travelling wave solutions of the perturbed KdV equation through recent factorization techniques that can be performed when the coefficients of the equation fulfill a certain condition. The solutions are obtained by using a two-step factorization procedure through which the perturbed KdV equation is reduced to a nonlinear second order differential equation, and to some Bernoulli and Abel type differential equations whose solutions are expressed in terms of the exponential and Weierstrass functionsComment: 4 pages, some changes in the text according to referees' suggestions, added one reference, accepted at Central Europ. J. Phy

Nonlinear second order ODE's: Factorizations and particular solutions

We present particular solutions for the following important nonlinear second order differential equations: modified Emden, generalized Lienard, convective Fisher, and generalized Burgers-Huxley. For the latter two equations these solutions are obtained in the travelling frame. All these particular solutions are the result of extending a simple and efficient factorization method that we developed in Phys. Rev. E 71 (2005) 046607Comment: 6 pages, v3=published versio

Intersection between class and gender and its effect on the quality of employment in Chile

Indexación: Web of Science; Scopus.En este artículo se analiza el efecto de la intersección entre clase y género sobre la calidad del empleo en Chile. La medida de posición de clase utilizada está basada en la propuesta de Erik O. Wright y la calidad del empleo en una medida multidimensional, que incluye un índice de condiciones objetivas de empleo y dos índices de condiciones subjetivas (motivación en el trabajo y percepción del control sobre el proceso de trabajo). Los resultados demuestran que la clase y el género determinan diferencias significativas en la calidad objetiva y subjetiva del empleo. Sin embargo, los datos también indican que el género (particularmente, el hecho de ser mujer) no actúa necesariamente como “amplificador” de las desigualdades de clase observadas en el mercado laboral. A partir de esto, al final del artículo se plantean algunas reflexiones sobre cómo opera la intersección entre clase y género en el mercado laboral chileno.This study explores the impact of the intersection between class and gender on the quality of employment in Chile. The method used to measure social class position is based on the work of Erik O. Wright, while, for the quality of employment, a multidimensional measurement was used, including one index for objective working conditions and two indices for subjective ones (motivation on the job and the perception of control over work processes). The results demonstrate that class and gender give rise to signifcant differences in objective and subjective job quality. However, the data also indicate that gender (more specifcally, the fact of being female) does not necessarily amplify the class-based inequalities observed in the labour market. Drawing on these fndings, a number of thoughts about how the class/gender intersection operates in the Chilean labour market are shared in the fnal section of this studyhttp://hdl.handle.net/11362/4079

Riccati nonhermiticity with application to the Morse potential

A supersymmetric one-dimensional matrix procedure similar to relationships of the same type between Dirac and Schrodinger equations in particle physics is described at the general level. By this means we are able to introduce a nonhermitic Hamiltonian having the imaginary part proportional to the solution of a Riccati equation of the Witten type. The procedure is applied to the exactly solvable Morse potential introducing in this way the corresponding nonhermitic Morse problem. A possible application is to molecular diffraction in evanescent waves over nanostructured surfacesComment: 8 pages, 4 figure

Clumpy Disc and Bulge Formation

We present a set of hydrodynamical/Nbody controlled simulations of isolated gas rich galaxies that self-consistently include SN feedback and a detailed chemical evolution model, both tested in cosmological simulations. The initial conditions are motivated by the observed star forming galaxies at z ~ 2-3. We find that the presence of a multiphase interstellar media in our models promotes the growth of disc instability favouring the formation of clumps which in general, are not easily disrupted on timescales compared to the migration time. We show that stellar clumps migrate towards the central region and contribute to form a classical-like bulge with a Sersic index, n > 2. Our physically-motivated Supernova feedback has a mild influence on clump survival and evolution, partially limiting the mass growth of clumps as the energy released per Supernova event is increased, with the consequent flattening of the bulge profile. This regulation does not prevent the building of a classical-like bulge even for the most energetic feedback tested. Our Supernova feedback model is able to establish a self-regulated star formation, producing mass-loaded outflows and stellar age spreads comparable to observations. We find that the bulge formation by clumps may coexit with other channels of bulge assembly such as bar and mergers. Our results suggest that galactic bulges could be interpreted as composite systems with structural components and stellar populations storing archaeological information of the dynamical history of their galaxy.Comment: Accepted for publication in MNRAS - Aug. 20, 201

Classical harmonic oscillator with Dirac-like parameters and possible applications

We obtain a class of parametric oscillation modes that we call K-modes with damping and absorption that are connected to the classical harmonic oscillator modes through the "supersymmetric" one-dimensional matrix procedure similar to relationships of the same type between Dirac and Schroedinger equations in particle physics. When a single coupling parameter, denoted by K, is used, it characterizes both the damping and the dissipative features of these modes. Generalizations to several K parameters are also possible and lead to analytical results. If the problem is passed to the physical optics (and/or acoustics) context by switching from the oscillator equation to the corresponding Helmholtz equation, one may hope to detect the K-modes as waveguide modes of specially designed waveguides and/or cavitiesComment: 14 pages, 9 figures, revised, accepted at J. Phys.