Moduli spaces of bundles over non-projective K3 surfaces

We study moduli spaces of sheaves over non-projective K3 surfaces. More precisely, if $v=(r,\xi,a)$ is a Mukai vector on a K3 surface $S$ with $r$ prime to $\xi$ and $\omega$ is a "generic" K\"ahler class on $S$, we show that the moduli space $M$ of $\mu_{\omega}-$stable sheaves on $S$ with associated Mukai vector $v$ is an irreducible holomorphic symplectic manifold which is deformation equivalent to a Hilbert scheme of points on a K3 surface. If $M$ parametrizes only locally free sheaves, it is moreover hyperk\"ahler. Finally, we show that there is an isometry between $v^{\perp}$ and $H^{2}(M,\mathbb{Z})$ and that $M$ is projective if and only if $S$ is projective.Comment: 42 pages; major revisions; to appear in Kyoto J. Mat

Deformation of the O'Grady moduli spaces

In this paper we study moduli spaces of sheaves on an abelian or projective K3 surface. If $S$ is a K3, $v=2w$ is a Mukai vector on $S$, where $w$ is primitive and $w^{2}=2$, and $H$ is a $v-$generic polarization on $S$, then the moduli space $M_{v}$ of $H-$semistable sheaves on $S$ whose Mukai vector is $v$ admits a symplectic resolution $\widetilde{M}_{v}$. A particular case is the $10-$dimensional O'Grady example $\widetilde{M}_{10}$ of irreducible symplectic manifold. We show that $\widetilde{M}_{v}$ is an irreducible symplectic manifold which is deformation equivalent to $\widetilde{M}_{10}$ and that $H^{2}(M_{v},\mathbb{Z})$ is Hodge isometric to the sublattice $v^{\perp}$ of the Mukai lattice of $S$. Similar results are shown when $S$ is an abelian surface.Comment: 29 page

A thermodynamically consistent cohesive damage model for the simulation of mixed-mode delamination

This work is devoted to the formulation of a new cohesive model for mixed-mode delamination. The model is based on a thermodynamically consistent isotropic damage formulation, with consideration of an internal friction mechanism that governs the interaction between normal and shear opening modes

The moduli spaces of sheaves on K3 surfaces are irreducible symplectic varieties

We show that the moduli spaces of sheaves on a projective K3 surface are irreducible symplectic varieties, and that the same holds for the fibers of the Albanese map of moduli spaces of sheaves on an Abelian surface.Comment: 59 page

Linear and Nonlinear Bullets of the Bogoliubov-de Gennes Excitations

We report on the focalization of Bogoliubov–de Gennes excitations of the nonlinear Schrödinger equation in the defocusing regime (Gross-Pitaevskii equation for repulsive Bose-Einstein condensates) with a spatially modulated periodic potential. Exploiting the modification of the dispersion relation induced by the modulation, we demonstrate the existence of localized structures of the Bogoliubov–de Gennes excitations, in both the linear and nonlinear regimes (linear and nonlinear “bullets”). These traveling Bogoliubov–de Gennes bullets, localized both spatially and temporally in the comoving reference frame, are robust and propagate remaining stable, without spreading or filamentation. The phenomena reported in this Letter could be observed in atomic Bose-Einstein condensates in the presence of a spatially periodic potential induced by an optical lattice.Peer ReviewedPostprint (published version

Molecular Dynamics Simulations of Solutions at Constant Chemical Potential

Molecular Dynamics studies of chemical processes in solution are of great value in a wide spectrum of applications, which range from nano-technology to pharmaceutical chemistry. However, these calculations are affected by severe finite-size effects, such as the solution being depleted as the chemical process proceeds, which influence the outcome of the simulations. To overcome these limitations, one must allow the system to exchange molecules with a macroscopic reservoir, thus sampling a Grand-Canonical ensemble. Despite the fact that different remedies have been proposed, this still represents a key challenge in molecular simulations. In the present work we propose the Constant Chemical Potential Molecular Dynamics (C$\mu$MD) method, which introduces an external force that controls the environment of the chemical process of interest. This external force, drawing molecules from a finite reservoir, maintains the chemical potential constant in the region where the process takes place. We have applied the C$\mu$MD method to the paradigmatic case of urea crystallization in aqueous solution. As a result, we have been able to study crystal growth dynamics under constant supersaturation conditions, and to extract growth rates and free-energy barriers.Comment: 8 pages, 8 figures (Supplementary Information: 6 pages, 7 figures). Typos and labelling corrected Ver. 3: Minor comments added in Sec. 3. References 13,36,38 added. Minor text changes and typos correcte