One-loop quantization of rigid spinning strings in AdS3×S3×T4AdS_3 \times S^3 \times T^4 with mixed flux

We compute the one-loop correction to the classical dispersion relation of rigid closed spinning strings with two equal angular momenta in the $AdS_3 \times S^3 \times T^4$ background supported with a mixture of R-R and NS-NS three-form fluxes. This analysis is extended to the case of two arbitrary angular momenta in the pure NS-NS limit. We perform this computation by means of two different methods. The first method relies on the Euler-Lagrange equations for the quadratic fluctuations around the classical solution, while the second one exploits the underlying integrability of the problem through the finite-gap equations. We find that the one-loop correction vanishes in the pure NS-NS limit.Comment: 35 pages. v2: Minor changes and references updated. v3: Published versio

A thermodynamically consistent plastic-damage framework for localized failure in quasi-brittle solids: material model and strain localization analysis

Aiming for the modeling of localized failure in quasi-brittle solids, this paper addresses a thermodynamically consistent plastic-damage framework and the corresponding strain localization analysis. A unified elastoplastic damage model is first presented based on two alternative kinematic decompositions assuming infinitesimal deformations, with the evolution laws of involved internal variables characterized by a dissipative flow tensor. For the strong (or regularized) discontinuity to form in such inelastic quasi-brittle solids and to evolve eventually into a fully softened one, a novel strain localization analysis is then suggested. A kinematic constraint more demanding than the classical discontinuous bifurcation condition is derived by accounting for the traction continuity and the loading/unloading states consistent with the kinematics of a strong (or regularized) discontinuity. More specifically, the strain jumps characterized by Maxwell’s kinematic condition have to be completely inelastic (energy dissipative). Reproduction of this kinematics implies vanishing of the aforesaid dissipative flow tensorial components in the directions orthogonal to the discontinuity orientation. This property allows naturally developing a localized plastic-damage model for the discontinuity (band), with its orientation and the traction-based failure criterion consistently determined a posteriori from the given stress-based counterpart. The general results are then particularized to the 2D conditions of plane stress and plane strain. It is found that in the case of plane stress, strain localization into a strong (or regularized) discontinuity can occur at the onset of strain softening. Contrariwise, owing to an extra kinematic constraint, in the condition of plane strain some continuous inelastic deformations and substantial re-orientation of principal strain directions in general have to take place in the softening regime prior to strain localization. The classical Rankine, Mohr–Coulomb, von Mises (J2) and Drucker–Prager criteria are analyzed as illustrative examples. In particular, both the closed-form solutions for the discontinuity angles validated by numerical simulations and the corresponding traction-based failure criteria are obtained.Peer ReviewedPostprint (author's final draft

Regularization of spherical and axisymmetric evolution codes in numerical relativity

Several interesting astrophysical phenomena are symmetric with respect to the rotation axis, like the head-on collision of compact bodies, the collapse and/or accretion of fields with a large variety of geometries, or some forms of gravitational waves. Most current numerical relativity codes, however, can not take advantage of these symmetries due to the fact that singularities in the adapted coordinates, either at the origin or at the axis of symmetry, rapidly cause the simulation to crash. Because of this regularity problem it has become common practice to use full-blown Cartesian three-dimensional codes to simulate axi-symmetric systems. In this work we follow a recent idea idea of Rinne and Stewart and present a simple procedure to regularize the equations both in spherical and axi-symmetric spaces. We explicitly show the regularity of the evolution equations, describe the corresponding numerical code, and present several examples clearly showing the regularity of our evolutions.Comment: 11 pages, 9 figures. Several changes. Main corrections are in eqs. (2.12) and (5.14). Accepted in Gen. Rel. Gra

Non-negative matrix factorization for medical imaging

A non-negative matrix factorization approach to dimensionality reduction is proposed to aid classification of images. The original images can be stored as lower-dimensional columns of a matrix that hold degrees of belonging to feature components, so they can be used in the training phase of the classification at lower runtime and without loss in accuracy. The extracted features can be visually examined and images reconstructed with limited error. The proof of concept is performed on a benchmark of handwritten digits, followed by the application to histopathological colorectal cancer slides. Results are encouraging, though dealing with real-world medical data raises a number of issues.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec