Surface Percolation and Growth. An alternative scheme for breaking the diffraction limit in optical patterning

A nanopatterning scheme is presented by which the structure height can be controlled in the tens of nanometers range and the lateral resolution is a factor at least three times better than the point spread function of the writing beam. The method relies on the initiation of the polymerization mediated by a very inefficient energy transfer from a fluorescent dye molecule after single photon absorption. The mechanism has the following distinctive steps: the dye adsorbs on the substrate surface with a higher concentration than in the bulk, upon illumination it triggers the polymerization, then isolated islands develop and merge into a uniform structure (percolation), which subsequently grows until the illumination is interrupted. This percolation mechanism has a threshold that introduces the needed nonlinearity for the fabrication of structures beyond the diffraction limit.Comment: 10 pages, 8 figure

Lagrangian submanifolds and dynamics on Lie affgebroids

We introduce the notion of a symplectic Lie affgebroid and their Lagrangian submanifolds in order to describe the Lagrangian (Hamiltonian) dynamics on a Lie affgebroid in terms of this type of structures. Several examples are discussed.Comment: 50 pages. Several sections update

On the regularity of the covariance matrix of a discretized scalar field on the sphere

We present a comprehensive study of the regularity of the covariance matrix of a discretized field on the sphere. In a particular situation, the rank of the matrix depends on the number of pixels, the number of spherical harmonics, the symmetries of the pixelization scheme and the presence of a mask. Taking into account the above mentioned components, we provide analytical expressions that constrain the rank of the matrix. They are obtained by expanding the determinant of the covariance matrix as a sum of determinants of matrices made up of spherical harmonics. We investigate these constraints for five different pixelizations that have been used in the context of Cosmic Microwave Background (CMB) data analysis: Cube, Icosahedron, Igloo, GLESP and HEALPix, finding that, at least in the considered cases, the HEALPix pixelization tends to provide a covariance matrix with a rank closer to the maximum expected theoretical value than the other pixelizations. The effect of the propagation of numerical errors in the regularity of the covariance matrix is also studied for different computational precisions, as well as the effect of adding a certain level of noise in order to regularize the matrix. In addition, we investigate the application of the previous results to a particular example that requires the inversion of the covariance matrix: the estimation of the CMB temperature power spectrum through the Quadratic Maximum Likelihood algorithm. Finally, some general considerations in order to achieve a regular covariance matrix are also presented.Comment: 36 pages, 12 figures; minor changes in the text, matches published versio

Rational approximations in Analytic QCD

We consider the ``modified Minimal Analytic'' (mMA) coupling that involves an infrared cut to the standard MA coupling. The mMA coupling is a Stieltjes function and, as a consequence, the paradiagonal Pade approximants converge to the coupling in the entire $Q^2$-plane except on the time-like semiaxis below the cut. The equivalence between the narrow width approximation of the discontinuity function of the coupling, on the one hand, and this Pade (rational) approximation of the coupling, on the other hand, is shown. We approximate the analytic analogs of the higher powers of mMA coupling by rational functions in such a way that the singularity region is respected by the approximants.Several comparisons, for real and complex arguments $Q^2$, between the exact and approximate expressions are made and the speed of convergence is discussed. Motivated by the success of these approximants, an improvement of the mMA coupling is suggested, and possible uses in the reproduction of experimental data are discussed.Comment: 12 pages,9 figures (6 double figures); figs.6-8 corrected due to a programming error; analysis extended to two IR cutoffs; Introduction rewritten; to appear in J.Phys.

Three-body hadron systems with strangeness

Recently, many efforts are being put in studying three-hadron systems made of mesons and baryons and interesting results are being found. In this talk, I summarize the main features of the formalism used to study such three hadron systems with strangeness $S=-1,0$ within a framework built on the basis of unitary chiral theories and solution of the Faddeev equations. In particular, I present the results obtained for the $\pi\bar{K}N$, $K\bar{K}N$ and $KK\bar{K}$ systems and their respective coupled channels. In the first case, we find four $\Sigma$'s and two $\Lambda$'s with spin-parity $J^P=1/2^+$, in the 1500-1800 MeV region, as two meson-one baryon s-wave resonances. In the second case, a $1/2^+$ $N^*$ around 1900 MeV is found. For the last one a kaon close to 1420 MeV is formed, which can be identified with K(1460).Comment: Proceeding written for the HYP2012 conferenc

Complex Hybrid Inflation and Baryogenesis

We propose a hybrid inflation model with a complex waterfall field which contains an interaction term that breaks the U(1) global symmetry associated to the waterfall field charge. We show that the asymmetric evolution of the real and imaginary parts of the complex field during the phase transition at the end of inflation translates into a charge asymmetry. The latter strongly depends on the vev of the waterfall field, which is well constrained by diverse cosmological observations.Comment: 4 RevTex pages, no figures. Changes made in response to referee's comments; matches version published in Phys.Rev.Let

Searching for a dipole modulation in the large-scale structure of the Universe

Several statistical anomalies in the CMB temperature anisotropies seem to defy the assumption of a homogeneous and isotropic universe. In particular, a dipole modulation has been detected both in WMAP and Planck data. We adapt the methodology proposed by Eriksen et al. (2007) on CMB data to galaxy surveys, tracing the large-scale structure. We analyse the NRAO VLA Sky Survey (NVSS) data at a resolution of ~2 degrees for three different flux thresholds: 2.5, 5.0 and 10.0 mJy respectively. No evidence of a dipole modulation is found. This result suggests that the origin of the dipole asymmetry found in the CMB cannot be assigned to secondary anisotropies produced at redshifts around z = 1. However, it could still have been generated at redshifts higher or lower, such as the integrated Sachs-Wolfe effect produced by the local structures. Other all-sky surveys, like the infrared WISE catalogue, could help to explore with a high sensitivity a redshift interval closer than the one probed with NVSS.Comment: 6 pages, 2 figures. Some minor changes have been done from the original manuscript. This paper is accepted by MNRA

A general framework for nonholonomic mechanics: Nonholonomic Systems on Lie affgebroids

This paper presents a geometric description of Lagrangian and Hamiltonian systems on Lie affgebroids subject to affine nonholonomic constraints. We define the notion of nonholonomically constrained system, and characterize regularity conditions that guarantee that the dynamics of the system can be obtained as a suitable projection of the unconstrained dynamics. It is shown that one can define an almost aff-Poisson bracket on the constraint AV-bundle, which plays a prominent role in the description of nonholonomic dynamics. Moreover, these developments give a general description of nonholonomic systems and the unified treatment permits to study nonholonomic systems after or before reduction in the same framework. Also, it is not necessary to distinguish between linear or affine constraints and the methods are valid for explicitly time-dependent systems.Comment: 50 page

Conserved masses in GHS Einstein and string black holes

We analyze the relationship between quasilocal masses calculated for solutions of conformally related theories. We show that the ADM mass of a static, spherically symmetric solution is conformally invariant (up to a constant factor) only if the background action functional is conformally invariant. Thus, the requirement of conformal invariance places restrictions on the choice of reference spacetimes. We calculate the mass of the black hole solutions obtained by Garfinkle, Horowitz, and Strominger (GHS) for both the string and the Einstein metrics. In addition, the quasilocal thermodynamic quantities in the string metrics are computed and discussed.Comment: 16 pages REVTeX with packages amsfonts and amssym