El computador en la clase de Matemáticas: desde lo dinámico y lo semiótico

En esta investigación se utilizó un enfoque que permitió explorar los conceptos propios del curso de ecuaciones diferenciales ordinarias, ofrecido para los estudiantes de la Facultad de Ingeniería de la Pontificia Universidad Javeriana, Cali, Colombia, considerando los modelos teóricos propuesto por Godino y Batanero; la propuesta de Vergnaud, y los esquemas de representación de Brown. Se utiliza el computador como “instrumento mediador” (soportado en las potencialidades del software MatLab) que favoreció trabajar con instancias de modelación de las ecuaciones diferenciales en contextos propios de la Ingeniería, desde una perspectiva dinámica de las ecuaciones y otra semiótica desde el diseño de actividades para los estudiantes

Curvature driven diffusion, Rayleigh-Plateau, and Gregory-Laflamme

It can be expected that the respective endpoints of the Gregory-Laflamme black brane instability and the Rayleigh-Plateau membrane instability are related because the bifurcation diagrams of the black hole-black string system and the liquid drop-liquid bridge system display many similarities. In this paper, we investigate the non-linear dynamics of the Rayleigh-Plateau instability in a range of dimensions, including the critical dimension at which the phase structure changes. We show that near the critical dimension and above, depending on a parameter in initial conditions an unstable cylinder will either pinch off or converge to an equilibrium state. The equilibrium state is apparently non-uniform but has a constant mean curvature everywhere. The results suggest that in the gravity side, near the critical dimension and above, the final state of an unstable black string (which is not too long) is a non-uniform black string. The equation of motion adopted to describe the dynamics is the surface diffusion equation, which was originally proposed to describe a grooving process of heated metal surfaces. An interesting correspondence between the diffusion dynamics and black hole (thermo)dynamics is discussed.Comment: 14 pages, 5 figures; v2: references added, typos fixe

NMR study of slowly exchanging protons in yeast tRNAAsp

We have monitored the exchange of imino and amino protons by NMR after quick transfer of yeast tRNAAsp in 2H2O solvent. When the concentration of exchange-catalyzing buffer is not too high, one imino proton exchanges considerably more slowly than any other (e.g., 100 hr versus 4 hr for the second-slowest imino proton at 18°C in 15 mM Mg). This provides excellent conditions for identification, by the nuclear Overhauser effect, of the slowest exchanging proton, which we show to be the imino proton of the U-8. A-14 reverse Hoogsteen tertiary-structure base pair; other slowly exchanging protons are identified as imino protons from A.U-11 and G.ψ-13. In preliminary experiments, we find that the exchange of these protons is catalyzed by cacodylate or Tris buffer. The lifetimes of two other imino protons, ca. 10 min at 28°C, are buffer independent. Slowly exchanging amino protons have also been observed. Correlation with the exchange of the uracil-8 imino proton suggests that they may be from adenine-14

Demonstration of the synchrotron-type spectrum of laser-produced Betatron radiation

Betatron X-ray radiation in laser-plasma accelerators is produced when electrons are accelerated and wiggled in the laser-wakefield cavity. This femtosecond source, producing intense X-ray beams in the multi kiloelectronvolt range has been observed at different interaction regime using high power laser from 10 to 100 TW. However, none of the spectral measurement performed were at sufficient resolution, bandwidth and signal to noise ratio to precisely determine the shape of spectra with a single laser shot in order to avoid shot to shot fluctuations. In this letter, the Betatron radiation produced using a 80 TW laser is characterized by using a single photon counting method. We measure in single shot spectra from 8 to 21 keV with a resolution better than 350 eV. The results obtained are in excellent agreement with theoretical predictions and demonstrate the synchrotron type nature of this radiation mechanism. The critical energy is found to be Ec = 5.6 \pm 1 keV for our experimental conditions. In addition, the features of the source at this energy range open novel perspectives for applications in time-resolved X-ray science.Comment: 5 pages, 4 figure

Wetting and Minimal Surfaces

We study minimal surfaces which arise in wetting and capillarity phenomena. Using conformal coordinates, we reduce the problem to a set of coupled boundary equations for the contact line of the fluid surface, and then derive simple diagrammatic rules to calculate the non-linear corrections to the Joanny-de Gennes energy. We argue that perturbation theory is quasi-local, i.e. that all geometric length scales of the fluid container decouple from the short-wavelength deformations of the contact line. This is illustrated by a calculation of the linearized interaction between contact lines on two opposite parallel walls. We present a simple algorithm to compute the minimal surface and its energy based on these ideas. We also point out the intriguing singularities that arise in the Legendre transformation from the pure Dirichlet to the mixed Dirichlet-Neumann problem.Comment: 22 page

Supersymmetric version of a Gaussian irrotational compressible fluid flow

The Lie point symmetries and corresponding invariant solutions are obtained for a Gaussian, irrotational, compressible fluid flow. A supersymmetric extension of this model is then formulated through the use of a superspace and superfield formalism. The Lie superalgebra of this extended model is determined and a classification of its subalgebras is performed. The method of symmetry reduction is systematically applied in order to derive special classes of invariant solutions of the supersymmetric model. Several new types of algebraic, hyperbolic, multi-solitonic and doubly periodic solutions are obtained in explicit form.Comment: Expanded introduction and added new section on classical Gaussian fluid flow. Included several additional reference

Pearling and Pinching: Propagation of Rayleigh Instabilities

A new category of front propagation problems is proposed in which a spreading instability evolves through a singular configuration before saturating. We examine the nature of this front for the viscous Rayleigh instability of a column of one fluid immersed in another, using the marginal stability criterion to estimate the front velocity, front width, and the selected wavelength in terms of the surface tension and viscosity contrast. Experiments are suggested on systems that may display this phenomenon, including droplets elongated in extensional flows, capillary bridges, liquid crystal tethers, and viscoelastic fluids. The related problem of propagation in Rayleigh-like systems that do not fission is also considered.Comment: Revtex, 7 pages, 4 ps figs, PR

Delayed Capillary Breakup of Falling Viscous Jets

Thin jets of viscous fluid like honey falling from capillary nozzles can attain lengths exceeding 10 m before breaking up into droplets via the Rayleigh-Plateau (surface tension) instability. Using a combination of laboratory experiments and WKB analysis of the growth of shape perturbations on a jet being stretched by gravity, we determine how the jet's intact length lb depends on the flow rate Q, the viscosity η, and the surface tension coefficient γ. In the asymptotic limit of a high-viscosity jet, lb∼(gQ2η4/γ4)1/3, where g is the gravitational acceleration. The agreement between theory and experiment is good, except for very long jets.</p

Peste porcine africaine Isolement et identification en France métropolitaine. Données épidémiologiques, cliniques, anatomopathologiques et de laboratoire

Gayot Georges, Carnero R., Costes Colette, Plateau F., Delclos G., Cazaubon P. Peste porcine africaine. In: Bulletin de l'Académie Vétérinaire de France tome 127 n°2, 1974. pp. 91-97