Semi-Classical Quantization of Circular Strings in De Sitter and Anti De Sitter Spacetimes

We compute the {\it exact} equation of state of circular strings in the (2+1) dimensional de Sitter (dS) and anti de Sitter (AdS) spacetimes, and analyze its properties for the different (oscillating, contracting and expanding) strings. The string equation of state has the perfect fluid form $P=(\gamma-1)E,$ with the pressure and energy expressed closely and completely in terms of elliptic functions, the instantaneous coefficient $\gamma$ depending on the elliptic modulus. We semi-classically quantize the oscillating circular strings. The string mass is $m=\sqrt{C}/(\pi H\alpha'),\;C$ being the Casimir operator, $C=-L_{\mu\nu}L^{\mu\nu},$ of the $O(3,1)$-dS [$O(2,2)$-AdS] group, and $H$ is the Hubble constant. We find \alpha'm^2_{\mbox{dS}}\approx 5.9n,\;(n\in N_0), and a {\it finite} number of states N_{\mbox{dS}}\approx 0.17/(H^2\alpha') in de Sitter spacetime; m^2_{\mbox{AdS}}\approx 4H^2n^2 (large $n\in N_0$) and N_{\mbox{AdS}}=\infty in anti de Sitter spacetime. The level spacing grows with $n$ in AdS spacetime, while is approximately constant (although larger than in Minkowski spacetime) in dS spacetime. The massive states in dS spacetime decay through tunnel effect and the semi-classical decay probability is computed. The semi-classical quantization of {\it exact} (circular) strings and the canonical quantization of generic string perturbations around the string center of mass strongly agree.Comment: Latex, 26 pages + 2 tables and 5 figures that can be obtained from the authors on request. DEMIRM-Obs de Paris-9404

Knot Solitons

The existence of ring-like and knotted solitons in O(3) non-linear sigma model is analysed. The role of isotopy of knots/links in classifying such solitons is pointed out. Appearance of torus knot solitons is seen.Comment: Latex 9 pages + 2 eps figure

New vortex solution in SU(3) gauge-Higgs theory

Following a brief review of known vortex solutions in SU(N) gauge-adjoint Higgs theories we show the existence of a new ``minimal'' vortex solution in SU(3) gauge theory with two adjoint Higgs bosons. At a critical coupling the vortex decouples into two abelian vortices, satisfying Bogomol'nyi type, first order, field equations. The exact value of the vortex energy (per unit length) is found in terms of the topological charge that equals to the N=2 supersymmetric charge, at the critical coupling. The critical coupling signals the increase of the underlying supersymmetry.Comment: 15 page

Noncommutativity in (2+1)-dimensions and the Lorentz group

In this article we considered models of particles living in a three-dimensional space-time with a nonstandard noncommutativity induced by shifting canonical coordinates and momenta with generators of a unitary irreducible representation of the Lorentz group. The Hilbert space gets the structure of a direct product with the representation space, where we are able to construct operators which realize the algebra of Lorentz transformations. We study the modified Landau problem for both Schr\"odinger and Dirac particles, whose Hamiltonians are obtained through a kind of non-Abelian Bopp's shift of the dynamical variables from the ones of the usual problem in the normal space. The spectrum of these models are considered in perturbation theory, both for small and large noncommutativity parameters. We find no constraint between the parameters referring to no-commutativity in coordinates and momenta but they rather play similar roles. Since the representation space of the unitary irreducible representations SL(2,R) can be realized in terms of spaces of square-integrable functions, we conclude that these models are equivalent to quantum mechanical models of particles living in a space with an additional compact dimension.Comment: PACS: 03.65.-w; 11.30.Cp; 02.40.Gh, 19 pages, no figures. Version to appear in Physical Review

Reproductive capacity of the red cusk-eel genypterus chilensis (Guichenot, 1848) in captivity

Indexación: Scopus.This work was supported by the FONDEF Project D06I 1024 “Development of technologies for the production of red cusk-eel fingerlings (Genypterus chilensis)”.Genypterus chilensis is a marine fish of high gastronomic demand, whose capture has declined in recent years due to overfishing. In the development of the farming technology, high mortalities were obtained during egg incubation. The objective of this study is to contribute to the knowledge of fecundity and eggs viability of G. chilensis in captivity. The spawns of G. chilensis were analyzed over a period of 2 years and 3 months. The total fecundity was estimated by counting the masses and eggs produced monthly throughout the period. The results confirm that G. chilensis is a partial spawner, since a female may more than two masses of eggs per day, due to a large amount of mass spawned per season (621 average). The total production of masses of the Farming Centre during the period was 2,290; of these, only 7% (166) corresponding to 15,330,517 eggs were incubated. Because of its high fecundity, G. chilensis produces numerous masses of eggs, of which only a small percentage reaches incubation, as well as it occurs in other marine fish. © 2018, Escuela de Ciencias del Mar. All rights reserved.https://scielo.conicyt.cl/scielo.php?script=sci_arttext&pid=S0718-560X201800020048

Circular String-Instabilities in Curved Spacetime

We investigate the connection between curved spacetime and the emergence of string-instabilities, following the approach developed by Loust\'{o} and S\'{a}nchez for de Sitter and black hole spacetimes. We analyse the linearised equations determining the comoving physical (transverse) perturbations on circular strings embedded in Schwarzschild, Reissner-Nordstr\"{o}m and de Sitter backgrounds. In all 3 cases we find that the "radial" perturbations grow infinitely for $r\rightarrow 0$ (ring-collapse), while the "angular" perturbations are bounded in this limit. For $r\rightarrow\infty$ we find that the perturbations in both physical directions (perpendicular to the string world-sheet in 4 dimensions) blow up in the case of de Sitter space. This confirms results recently obtained by Loust\'{o} and S\'{a}nchez who considered perturbations around the string center of mass.Comment: 24 pages Latex + 2 figures (not included). Observatoire de Paris, Meudon No. 9305

String dynamics in cosmological and black hole backgrounds: The null string expansion

We study the classical dynamics of a bosonic string in the $D$--dimensional flat Friedmann--Robertson--Walker and Schwarzschild backgrounds. We make a perturbative development in the string coordinates around a {\it null} string configuration; the background geometry is taken into account exactly. In the cosmological case we uncouple and solve the first order fluctuations; the string time evolution with the conformal gauge world-sheet $\tau$--coordinate is given by $X^0(\sigma, \tau)=q(\sigma)\tau^{1\over1+2\beta}+c^2B^0(\sigma, \tau)+\cdots$, $B^0(\sigma,\tau)=\sum_k b_k(\sigma)\tau^k$ where $b_k(\sigma)$ are given by Eqs.\ (3.15), and $\beta$ is the exponent of the conformal factor in the Friedmann--Robertson--Walker metric, i.e. $R\sim\eta^\beta$. The string proper size, at first order in the fluctuations, grows like the conformal factor $R(\eta)$ and the string energy--momentum tensor corresponds to that of a null fluid. For a string in the black hole background, we study the planar case, but keep the dimensionality of the spacetime $D$ generic. In the null string expansion, the radial, azimuthal, and time coordinates $(r,\phi,t)$ are $r=\sum_n A^1_{n}(\sigma)(-\tau)^{2n/(D+1)}~,$ $\phi=\sum_n A^3_{n}(\sigma)(-\tau)^{(D-5+2n)/(D+1)}~,$ and $t=\sum_n A^0_{n} (\sigma)(-\tau)^{1+2n(D-3)/(D+1)}~.$ The first terms of the series represent a {\it generic} approach to the Schwarzschild singularity at $r=0$. First and higher order string perturbations contribute with higher powers of $\tau$. The integrated string energy-momentum tensor corresponds to that of a null fluid in $D-1$ dimensions. As the string approaches the $r=0$ singularity its proper size grows indefinitely like $\sim(-\tau)^{-(D-3)/(D+1)}$. We end the paper giving three particular exact string solutions inside the black hole.Comment: 17 pages, REVTEX, no figure

Sinh-Gordon, Cosh-Gordon and Liouville Equations for Strings and Multi-Strings in Constant Curvature Spacetimes

We find that the fundamental quadratic form of classical string propagation in $2+1$ dimensional constant curvature spacetimes solves the Sinh-Gordon equation, the Cosh-Gordon equation or the Liouville equation. We show that in both de Sitter and anti de Sitter spacetimes (as well as in the $2+1$ black hole anti de Sitter spacetime), {\it all} three equations must be included to cover the generic string dynamics. The generic properties of the string dynamics are directly extracted from the properties of these three equations and their associated potentials (irrespective of any solution). These results complete and generalize earlier discussions on this topic (until now, only the Sinh-Gordon sector in de Sitter spacetime was known). We also construct new classes of multi-string solutions, in terms of elliptic functions, to all three equations in both de Sitter and anti de Sitter spacetimes. Our results can be straightforwardly generalized to constant curvature spacetimes of arbitrary dimension, by replacing the Sinh-Gordon equation, the Cosh-Gordon equation and the Liouville equation by higher dimensional generalizations.Comment: Latex, 19 pages + 1 figure (not included

Globular Clusters: DNA of Early-Type galaxies?

This paper explores if the mean properties of Early-Type Galaxies (ETG) can be reconstructed from "genetic" information stored in their GCs (i.e., in their chemical abundances, spatial distributions and ages). This approach implies that the formation of each globular occurs in very massive stellar environments, as suggested by some models that aim at explaining the presence of multi-populations in these systems. The assumption that the relative number of globular clusters to diffuse stellar mass depends exponentially on chemical abundance, [Z/H], and the presence of two dominant GC sub-populations blue and red, allows the mapping of low metallicity halos and of higher metallicity (and more heterogeneous) bulges. In particular, the masses of the low-metallicity halos seem to scale up with dark matter mass through a constant. We also find a dependence of the globular cluster formation efficiency with the mean projected stellar mass density of the galaxies within their effective radii. The analysis is based on a selected sub-sample of galaxies observed within the ACS Virgo Cluster Survey of the {\it Hubble Space Telescope}. These systems were grouped, according to their absolute magnitudes, in order to define composite fiducial galaxies and look for a quantitative connection with their (also composite) globular clusters systems. The results strengthen the idea that globular clusters are good quantitative tracers of both baryonic and dark matter in ETGs.Comment: 20 pages, 28 figures and 5 table

Landslide Risk: Economic Valuation in the North-Eastern Zone of Medellin City

Natural disasters of a geodynamic nature can cause enormous economic and human losses. The economic costs of a landslide disaster include relocation of communities and physical repair of urban infrastructure. However, when performing a quantitative risk analysis, generally, the indirect economic consequences of such an event are not taken into account. A probabilistic approach methodology that considers several scenarios of hazard and vulnerability to measure the magnitude of the landslide and to quantify the economic costs is proposed. With this approach, it is possible to carry out a quantitative evaluation of the risk by landslides, allowing the calculation of the economic losses before a potential disaster in an objective, standardized and reproducible way, taking into account the uncertainty of the building costs in the study zone. The possibility of comparing different scenarios facilitates the urban planning process, the optimization of interventions to reduce risk to acceptable levels and an assessment of economic losses according to the magnitude of the damage. For the development and explanation of the proposed methodology, a simple case study is presented, located in north-eastern zone of the city of Medellín. This area has particular geomorphological characteristics, and it is also characterized by the presence of several buildings in bad structural conditions. The proposed methodology permits to obtain an estimative of the probable economic losses by earthquake-induced landslides, taking into account the uncertainty of the building costs in the study zone. The obtained estimative shows that the structural intervention of the buildings produces a reduction the order of 21 % in the total landslide risk. © Published under licence by IOP Publishing Ltd