Projective moduli space of semistable principal sheaves for a reductive group

Let X be a smooth projective complex variety, and let G be an algebraic reductive complex group. We define the notion of principal G-sheaf, that generalises the notion of principal G-bundle. Then we define a notion of semistability, and construct the projective moduli space of semistable principal G-sheaves on X. This is a natural compactification of the moduli space of principal G-bundles. This is the announcement note presented by the second author in the conference held at Catania (11-13 April 2001), dedicated to the 60th birthday of Silvio Greco. Detailed proofs will appear elsewhere.Comment: 10 pages, LaTeX2e. Submitted to the conference proceedings of "Commutative Algebra and Algebraic Geometry", Catania, April 200

The micropolar Navier-Stokes equations: A priori error analysis

The unsteady Micropolar Navier-Stokes Equations (MNSE) are a system of parabolic partial differential equations coupling linear velocity and pressure with angular velocity: material particles have both translational and rotational degrees of freedom. We propose and analyze a first order semi-implicit fully-discrete scheme for the MNSE, which decouples the computation of the linear and angular velocities, is unconditionally stable and delivers optimal convergence rates under assumptions analogous to those used for the Navier-Stokes equations. With the help of our scheme we explore some qualitative properties of the MNSE related to ferrofluid manipulation and pumping. Finally, we propose a second order scheme and show that it is almost unconditionally stable

Modeling of magnetoelectric composite structures

Novel models to predict magnetoelectric (ME) properties of composites made of piezoelectric (PE) and piezomagnetic (PM) phases is proposed. Two different composite arrangements are used: laminate and particulate. ME properties for laminate arrangement are obtained by applying the multiphysics equations for all four possible laminate configurations (TT, LT, TL, and LL), with appropriate boundary conditions. Closed form, explicit formulas are derived for the calculation of the ME charge and voltage coefficients as a function of material properties of both phases and PM volume fraction. A new coefficient, the ME coupling factor, is proposed in order to assess the conversion of magnetic work into electric work. The predicted ME voltage coefficient is in agreement with previous work and experimental data. A new approach is proposed to take into account the conductivity of the PM phase, resulting in calculated ME charge coefficients within 30\% of experimental data. The voltage, current, and electric power generated by unit of magnetic field applied to the composite define the intrinsic voltage, current, and power conversion factors. Since the PM phase of the composite has a higher magnetic permeability than the surrounding medium, a far filed magnetic field is not fully utilized due to demagnetization. Thus, novel explicit equations are developed here to calculate the extrinsic voltage, current, and power conversion factors accounting for demagnetization. The proposed formulation is applied to various materials and geometries to illustrate the process of material and device-geometry selection leading to an optimum design. The magnetoelectric (ME) properties of particulate composites are calculated using Eshelby theory and two homogenization techniques: dilute approximation and Mori-Tanaka mean field theory. A method that allows the calculation of all ME properties under any boundary conditions is proposed. These boundary conditions are dictated by the experimental configuration, e.g. films on a substrate, free-standing composites, etc. Predictions are compared with calculations reported by Harshe et al. and Nan et al., and good correlation is obtained with those, but to achieve good correlation with experimental data, the conductivity of the piezomagnetic (PM) phase must be taken into account, and a method is proposed to that effect. Percolated composites do not have any piezoelectric (PE) or ME properties because the charge leaks through the conductive PM phase. The experimental parameters that influence the percolation threshold are discussed and the best particulate composite design is proposed. Unlike previous models that did not account for conductivity, correlation between the proposed model and experimental data is much better

Neighbourhood Consensus Networks

We address the problem of finding reliable dense correspondences between a pair of images. This is a challenging task due to strong appearance differences between the corresponding scene elements and ambiguities generated by repetitive patterns. The contributions of this work are threefold. First, inspired by the classic idea of disambiguating feature matches using semi-local constraints, we develop an end-to-end trainable convolutional neural network architecture that identifies sets of spatially consistent matches by analyzing neighbourhood consensus patterns in the 4D space of all possible correspondences between a pair of images without the need for a global geometric model. Second, we demonstrate that the model can be trained effectively from weak supervision in the form of matching and non-matching image pairs without the need for costly manual annotation of point to point correspondences. Third, we show the proposed neighbourhood consensus network can be applied to a range of matching tasks including both category- and instance-level matching, obtaining the state-of-the-art results on the PF Pascal dataset and the InLoc indoor visual localization benchmark.Comment: In Proceedings of the 32nd Conference on Neural Information Processing Systems (NeurIPS 2018