Simple finite field method for calculation of static and dynamic vibrational hyperpolarizabilities: curvature contributions

In the static field limit, the vibrational hyperpolarizability consists of two contributions due to: (1) the shift in the equilibrium geometry (known as nuclear relaxation), and (2) the change in the shape of the potential energy surface (known as curvature). Simple finite field methods have previously been developed for evaluating these static field contributions and also for determining the effect of nuclear relaxation on dynamic vibrational hyperpolarizabilities in the infinite frequency approximation. In this paper the finite field approach is extended to include, within the infinite frequency approximation, the effect of curvature on the major dynamic nonlinear optical processes

Preparació de puntes de tungstè per a microscòpia d'efecte túnel (STM)

Es presenten els resultats experimentals obtinguts durant l’estudi sistemàtic realitzat de la preparació electroquímica de puntes de tungstè per al Microscopi d’Efecte Túnel (STM), fent servir dos electròlits: KOH i NaOH. L’estudi sobre la morfologia, longitud de la punta i radi de curvatura de la punta en funció del voltatge aplicat i les concentracions de l’electròlit es descriu al capítol 3. La caracterització de les puntes es va dur a terme, per una part, mitjançant un microscòpic electrònic de rastreig (SEM) i per l’altre banda, amb el ús de les puntes obtingudes al STM. En resumen, els resultats mostren que ambdós electròlits permeten obtenir puntes que es poden fer servir amb èxit per l’obtenció d’imatges amb l’STM. Les millors puntes són aquelles que s’obtenen dins de rangs de concentracions d’electròlit baixes, entre valor de 10 a 15% en pes pel NaOH i entre 10 i 20% pel KOH i rangs de voltatge entre 3 a 7 V pel NaOH i 4 a 8 V pel KOH. S’observa que es requereixen temps d’atac electroquímic menors fent servir com a electròlit NaOH. S’estudia, en el capítol 4, el tractament que requereix la punta per tal d’eliminar les impureses de la seva superfície. Es realitzen diferents proves amb tres mètodes de neteja: (1) tractament químic, (2) bombardeig iònic i (3) tractament tèrmic de recuit. En el capítol 5 del projecte s’analitzen les imatges d’una mostra d’or, Au(110), d’estructura coneguda, amb el microscopi d’efecte túnel STM) del laboratori fent servir les puntes obtingudes sota les condicions considerades òptimes. El resultat confirma el bon comportament de les puntes obtingudes sota les condicions descrites en els capítols anteriors i establert una pauta a seguir per obtenir puntes d’una manera senzilla i reproduïble.

Systematic weakly nonlinear analysis of interfacial instabilities in Hele-Shaw flows

We develop a systematic method to derive all orders of mode couplings in a weakly nonlinear approach to the dynamics of the interface between two immiscible viscous fluids in a Hele-Shaw cell. The method is completely general: it applies to arbitrary geometry and driving. Here we apply it to the channel geometry driven by gravity and pressure. The finite radius of convergence of the mode-coupling expansion is found. Calculation up to third-order couplings is done, which is necessary to account for the time-dependent Saffman-Taylor finger solution and the case of zero viscosity contrast. The explicit results provide relevant analytical information about the role that the viscosity contrast and the surface tension play in the dynamics of the system. We finally check the quantitative validity of different orders of approximation and a resummation scheme against a physically relevant, exact time-dependent solution. The agreement between the low-order approximations and the exact solution is excellent within the radius of convergence, and is even reasonably good beyond this radius.

Origin of the neutron skin thickness of 208Pb in nuclear mean-field models

We study whether the neutron skin thickness Δrnp of 208Pb originates from the bulk or from the surface of the nucleon density distributions, according to the mean-field models of nuclear structure, and find that it depends on the stiffness of the nuclear symmetry energy. The bulk contribution to Δrnp arises from an extended sharp radius of neutrons, whereas the surface contribution arises from different widths of the neutron and proton surfaces. Nuclear models where the symmetry energy is stiff, as typical of relativistic models, predict a bulk contribution in Δrnp of 208Pb about twice as large as the surface contribution. In contrast, models with a soft symmetry energy like common nonrelativistic models predict that Δrnp of 208Pb is divided similarly into bulk and surface parts. Indeed, if the symmetry energy is supersoft, the surface contribution becomes dominant. We note that the linear correlation of Δrnp of 208Pb with the density derivative of the nuclear symmetry energy arises from the bulk part of Δrnp. We also note that most models predict a mixed-type (between halo and skin) neutron distribution for 208Pb. Although the halo-type limit is actually found in the models with a supersoft symmetry energy, the skin-type limit is not supported by any mean-field model. Finally, we compute parity-violating electron scattering in the conditions of the 208Pb parity radius experiment (PREX) and obtain a pocket formula for the parity-violating asymmetry in terms of the parameters that characterize the shape of the 208Pb nucleon densities.

Effects of adult dysthyroidism on the morphology of hippocampal neurons.

This study investigates the effect of thyroid hormones on the morphology of hippocampal neurons in adult rats. Hypo- and hyperthyroidism were induced by adding 0.02% methimazole and 1% l-thyroxine, in drinking water from 40 days of age, respectively. When the rats were 89 days old their brains were removed and stained by a modified Golgi method and blood samples were collected in order to measure T4 serum levels. Neurons were selected and drawn using a camera lucida. Our results show that methimazole administration reduces the dendritic branching of the apical shafts of CA3 and CA1 pyramidal neurons mainly by increasing the distance to the first branch point in both types of neurons, and reducing branch points in the radius of 50 μm from the soma in CA1 neurons. Nevertheless, it was observed an increase of apical spine density in CA3 neurons from this group. Thyroxine reduces apical and basal tree of CA3 pyramidal neurons increasing the distance to the first branch point, reducing branch points in the radius of 50 μm from the soma and increases their apical and basal spine density. In CA1 field, thyroxine reduces the number of basal branch points. Both treatments seems to provoke alterations in the same direction reducing the dendritic branching and increasing spine density, although no significances appeared in some of the parameters analyzed. The effects are more evident in thyroxine than methimazole group; and in CA3 neurons than in CA1 neurons. In discussion it is pointed that the increase of spine density could be a mechanism to compensate the functionality reduction that can be provoke by the treatment effect on dendritic branching.

The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center

We prove that if f is a partially hyperbolic diffeomorphism on the compact manifold M with one dimensional center bundle, then the logarithm of the spectral radius of the map induced by f on the real homology groups of M is smaller or equal to the topological entropy of f. This is a particular case of the Shub's entropy conjecture, which claims that the same conclusion should be true for any C1 map on any compact manifold.

Integral formulae for a Riemannian manifold with a distribution

We obtain a new series of integral formulae for symmetric functions of curvature of a distribution of arbitrary codimension (an its orthogonal complement) given on a compact Riemannian manifold, which start from known formula by P.Walczak (1990) and generalize ones for foliations by several authors: Asimov (1978), Brito, Langevin and Rosenberg (1981), Brito and Naveira (2000), Andrzejewski and Walczak (2010), etc. Our integral formulae involve the co-nullity tensor, certain component of the curvature tensor and their products. The formulae also deal with a number of arbitrary functions depending on the scalar invariants of the co-nullity tensor. For foliated manifolds of constant curvature the obtained formulae give us the classical type formulae. For a special choice of functions our formulae reduce to ones with Newton transformations of the co-nullity tensor.

On Lundh's percolation diffusion

A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable configurations are generated with positive probability Lundh calls this percolation diffusion. An integral condition for percolation diffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles.

On Lundh's percolation diffusion

A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable con gurations are generated with positive probability Lundh calls this percolation di usion. An integral condition for percolation di ffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles.

Vertically coupled double quantum rings at zero magnetic field

Within local-spin-density functional theory, we have investigated the ¿dissociation¿ of few-electron circular vertical semiconductor double quantum ring artificial molecules at zero magnetic field as a function of interring distance. In a first step, the molecules are constituted by two identical quantum rings. When the rings are quantum mechanically strongly coupled, the electronic states are substantially delocalized, and the addition energy spectra of the artificial molecule resemble those of a single quantum ring in the few-electron limit. When the rings are quantum mechanically weakly coupled, the electronic states in the molecule are substantially localized in one ring or the other, although the rings can be electrostatically coupled. The effect of a slight mismatch introduced in the molecules from nominally identical quantum wells, or from changes in the inner radius of the constituent rings, induces localization by offsetting the energy levels in the quantum rings. This plays a crucial role in the appearance of the addition spectra as a function of coupling strength particularly in the weak coupling limit.

Experiments in a rotating Hele-Shaw cell

We introduce a modification to Hele-Shaw flows consisting of a rotating cell. A viscous fluid (oil) is injected at the rotation axis of the cell, which is open to air. The morphological instability of the oil-air interface is thus driven by centrifugal force and is controlled by the density (not viscosity) difference. We derive the linear dispersion relation and verify the maximum growth rate selection of initial patterns within experimental uncertainty. The nonlinear growth regime is studied in the case of vanishing injection rate. Several characteristic lengths are studied to quantify the patterns obtained. Experimental data exhibit good collapse for two characteristic lengths, namely, the radius of gyration and the radial finger length, which in the nonlinear regime appear to grow linearly in time.

Low viscosity contrast fingering in a rotating Hele-Shaw cell

We study the fingering instability of a circular interface between two immiscible liquids in a radial Hele-Shaw cell. The cell rotates around its vertical symmetry axis, and the instability is driven by the density difference between the two fluids. This kind of driving allows studying the interfacial dynamics in the particularly interesting case of an interface separating two liquids of comparable viscosity. An accurate experimental study of the number of fingers emerging from the instability reveals a slight but systematic dependence of the linear dispersion relation on the gap spacing. We show that this result is related to a modification of the interface boundary condition which incorporates stresses originated from normal velocity gradients. The early nonlinear regime shows nearly no competition between the outgrowing fingers, characteristic of low viscosity contrast flows. We perform experiments in a wide range of experimental parameters, under conditions of mass conservation (no injection), and characterize the resulting patterns by data collapses of two characteristic lengths: the radius of gyration of the pattern and the interface stretching. Deep in the nonlinear regime, the fingers which grow radially outwards stretch and become gradually thinner, to a point that the fingers pinch and emit drops. We show that the amount of liquid emitted in the first generation of drops is a constant independent of the experimental parameters. Further on there is a sharp reduction of the amount of liquid centrifugated, punctuated by periods of no observable centrifugation.

Can extreme black Holes have (long) Abelian Higgs hair?

It has been argued that a black hole horizon can support the long-range fields of a Nielsen-Olesen string and that one can think of such a vortex as black hole "hair." In this paper, we examine the properties of an Abelian Higgs vortex in the presence of a charged black hole as we allow the hole to approach extremality. Using both analytical and numerical techniques, we show that the magnetic field lines (as well as the scalar field) of the vortex are completely expelled from the black hole in the extreme limit. This was to be expected, since extreme black holes in Einstein-Maxwell theory are known to exhibit such a "Meissner effect" in general. This would seem to imply that a vortex does not want to be attached to an extreme black hole. We calculate the total energy of the vortex fields in the presence of an extreme black hole. When the hole is small relative to the size of the vortex, it is energetically favored for the hole to remain inside the vortex region, contrary to the intuition that the hole should be expelled. However, as we allow the extreme horizon radius to become very large compared to the radius of the vortex, we do find evidence of an instability. This proves that it is energetically unfavorable for a thin vortex to interact with a large extreme black hole. This would seem to dispel the notion that a black hole can support "long" Abelian Higgs hair in the extreme limit. We show that these considerations do not go through in the near-extreme limit. Finally, we discuss the implications for strings that end at black holes, as in the processes where a string snaps by nucleating black holes.

On Lundh's percolation diffusion

A collection of spherical obstacles in the unit ball in Euclidean space is said to be avoidable for Brownian motion if there is a positive probability that Brownian motion diffusing from some point in the ball will avoid all the obstacles and reach the boundary of the ball. The centres of the spherical obstacles are generated according to a Poisson point process while the radius of an obstacle is a deterministic function. If avoidable configurations are generated with positive probability, Lundh calls this percolation diffusion. An integral condition for percolation diffusion is derived in terms of the intensity of the point process and the function that determines the radii of the obstacles.

El desenvolupament curricular del bloc d’activitats al medi natural per part dels professors d’Educació Física de la ciutat de Vic i les poblacions del voltant

L’estudi que es presenta a continuació té l’objectiu d’analitzar el desenvolupament curricular del bloc de continguts d’activitats al medi natural de l’assignatura d’Educació Física de la ciutat de Vic i de les poblacions situades en un radi de 10 kilòmetres. Per tal de dur-ho a terme, primerament s’ha realitzat un procés d’aproximació a les activitats al medi natural en l’educació, aprofundint en les característiques d’aquestes activitats en els centres, en la poca pràctica i els factors de limitació que tenen. A partir d’aquí, s’ha fet l’estudi amb una mostra formada de 29 professors d’Educació Física dels diferents cursos de la ESO. Per tal de realitzar la recerca i l’anàlisi, s’ha emprat una metodologia quantitativa de caràcter explicatiu, transversal i quasi experimental, i s’ha utilitzat l’instrument corresponent al qüestionari. Aquest, ha estat elaborat prenent com a referència el de l’estudi de Peñarrubia et al.(2011). Els resultats que s’han obtingut demostren que el bloc d’activitats al medi natural és el menys treballat per part del professors d’Educació Física, que un 14% del professorat no les treballa i dels que si ho fan un 68% les realitzen només una vegada a l’any. També destacar que aquests continguts no es treballen en el 33% dels cursos de la zona estudiada. Pel què fa els continguts més treballats destaquen l’orientació seguit del senderisme. Referent als factors de limitació destaquen la responsabilitat civil del professor i l’horari de classe com els més condicionants. Pel què fa a les activitats, l’escalada esdevé l’activitat on els factors de limitació influeixen més mentre que en l’orientació i el senderisme tenen poca importància. D’aquesta manera es pot veure una estreta relació entre els factors de limitació d’aquestes activitats i la poca pràctica d’aquestes en els centres educatius estudiats.