Force dipoles and stable local defects on fluid vesicles

An exact description is provided of an almost spherical fluid vesicle with a fixed area and a fixed enclosed volume locally deformed by external normal forces bringing two nearby points on the surface together symmetrically. The conformal invariance of the two-dimensional bending energy is used to identify the distribution of energy as well as the stress established in the vesicle. While these states are local minima of the energy, this energy is degenerate; there is a zero mode in the energy fluctuation spectrum, associated with area and volume preserving conformal transformations, which breaks the symmetry between the two points. The volume constraint fixes the distance $S$, measured along the surface, between the two points; if it is relaxed, a second zero mode appears, reflecting the independence of the energy on $S$; in the absence of this constraint a pathway opens for the membrane to slip out of the defect. Logarithmic curvature singularities in the surface geometry at the points of contact signal the presence of external forces. The magnitude of these forces varies inversely with $S$ and so diverges as the points merge; the corresponding torques vanish in these defects. The geometry behaves near each of the singularities as a biharmonic monopole, in the region between them as a surface of constant mean curvature, and in distant regions as a biharmonic quadrupole. Comparison of the distribution of stress with the quadratic approximation in the height functions points to shortcomings of the latter representation. Radial tension is accompanied by lateral compression, both near the singularities and far away, with a crossover from tension to compression occurring in the region between them.Comment: 26 pages, 10 figure

Incorporating Public Insecurity Indicators: A New Approach to Measuring Social Welfare in Mexico

Social Welfare (SW) is a multidimensional and contextual concept. It is generally adjusted to reflect the prevailing social realities of a given context (Grasso & Canova, 2008). It consists of a material dimension, including economic indicators such as income, employment, level of schooling, and access to social security services (Di Pasquale, 2008; Mæstad & Norheim, 2012). The other dimension of social welfare is subjective and includes elements such as happiness and satisfaction with life (Diener, 1994, 2000).ITESO, A.C.Boston College, School of Social WorkUniversidad Iberoamericana Ciudad de Méxic

Porous medium equation with nonlocal pressure

We provide a rather complete description of the results obtained so far on the nonlinear diffusion equation $u_t=\nabla\cdot (u^{m-1}\nabla (-\Delta)^{-s}u)$, which describes a flow through a porous medium driven by a nonlocal pressure. We consider constant parameters $m>1$ and $0<s<1$, we assume that the solutions are non-negative, and the problem is posed in the whole space. We present a theory of existence of solutions, results on uniqueness, and relation to other models. As new results of this paper, we prove the existence of self-similar solutions in the range when $N=1$ and $m>2$, and the asymptotic behavior of solutions when $N=1$. The cases $m = 1$ and $m = 2$ were rather well known.Comment: 24 pages, 2 figure

Ischemia/reperfusion increases the oxidized state of specific cys residues in proteins from mitochondrial supopulation from rat miocardium that are protected by ischemia preconditioning

Comunicaciones a congreso

Femtosecond infrared intrastromal ablation and backscattering-mode adaptive-optics multiphoton microscopy in chicken corneas

The performance of femtosecond (fs) laser intrastromal ablation was evaluated with backscattering-mode adaptive-optics multiphoton microscopy in ex vivo chicken corneas. The pulse energy of the fs source used for ablation was set to generate two different ablation patterns within the corneal stroma at a certain depth. Intrastromal patterns were imaged with a custom adaptive-optics multiphoton microscope to determine the accuracy of the procedure and verify the outcomes. This study demonstrates the potential of using fs pulses as surgical and monitoring techniques to systematically investigate intratissue ablation. Further refinement of the experimental system by combining both functions into a single fs laser system would be the basis to establish new techniques capable of monitoring corneal surgery without labeling in real-time. Since the backscattering configuration has also been optimized, future in vivo implementations would also be of interest in clinical environments involving corneal ablation procedures

Spinor representation of surfaces and complex stresses on membranes and interfaces

Variational principles are developed within the framework of a spinor representation of the surface geometry to examine the equilibrium properties of a membrane or interface. This is a far-reaching generalization of the Weierstrass-Enneper representation for minimal surfaces, introduced by mathematicians in the nineties, permitting the relaxation of the vanishing mean curvature constraint. In this representation the surface geometry is described by a spinor field, satisfying a two-dimensional Dirac equation, coupled through a potential associated with the mean curvature. As an application, the mesoscopic model for a fluid membrane as a surface described by the Canham-Helfrich energy quadratic in the mean curvature is examined. An explicit construction is provided of the conserved complex-valued stress tensor characterizing this surface.Comment: 17 page

On the asymptotic behaviour of solutions to the fractional porous medium equation with variable density

We are concerned with the long time behaviour of solutions to the fractional porous medium equation with a variable spatial density. We prove that if the density decays slowly at infinity, then the solution approaches the Barenblatt-type solution of a proper singular fractional problem. If, on the contrary, the density decays rapidly at infinity, we show that the minimal solution multiplied by a suitable power of the time variable converges to the minimal solution of a certain fractional sublinear elliptic equation.Comment: To appear in DCDS-

El precondicionamiento isquémico produce cambios en las proteínas de las fosforilación oxidativa y atenúa el daño oxidativo durante la isquemia-reperfusión por mecanismos independientes de la señalización citosólica

Comunicaciones a congreso