Milnor open books and Milnor fillable contact 3-manifolds

We say that a contact manifold is Milnor fillable if it is contactomorphic to the contact boundary of an isolated complex-analytic singularity (X,x). Generalizing results of Milnor and Giroux, we associate to each holomorphic function f defined on X, with isolated singularity at x, an open book which supports the contact structure. Moreover, we prove that any 3-dimensional oriented manifold admits at most one Milnor fillable contact structure up to contactomorphism. * * * * * * * * In the first version of the paper, we showed that the open book associated to f carries the contact structure only up to an isotopy. Here we drop this restriction. Following a suggestion of Janos Kollar, we also give a simplified proof of the algebro-geometrical theorem 4.1, central for the uniqueness result.Comment: 17 page

Diffusive spreading and mixing of fluid monolayers

The use of ultra-thin, i.e., monolayer films plays an important role for the emerging field of nano-fluidics. Since the dynamics of such films is governed by the interplay between substrate-fluid and fluid-fluid interactions, the transport of matter in nanoscale devices may be eventually efficiently controlled by substrate engineering. For such films, the dynamics is expected to be captured by two-dimensional lattice-gas models with interacting particles. Using a lattice gas model and the non-linear diffusion equation derived from the microscopic dynamics in the continuum limit, we study two problems of relevance in the context of nano-fluidics. The first one is the case in which along the spreading direction of a monolayer a mesoscopic-sized obstacle is present, with a particular focus on the relaxation of the fluid density profile upon encountering and passing the obstacle. The second one is the mixing of two monolayers of different particle species which spread side by side following the merger of two chemical lanes, here defined as domains of high affinity for fluid adsorption surrounded by domains of low affinity for fluid adsorption.Comment: 12 pages, 3 figure

Spectral properties of the largest asteroids associated with Taurid Complex

We obtained spectra of six of the largest asteroids (2201, 4183, 4486, 5143, 6063, and 269690) associated with Taurid complex. The observations were made with the IRTF telescope equipped with the spectro-imager SpeX. Their taxonomic classification is made using Bus-DeMeo taxonomy. The asteroid spectra are compared with the meteorite spectra from the Relab database. Mineralogical models were applied to determine their surface composition. All the spectral analysis is made in the context of the already published physical data. Five of the objects studied in this paper present spectral characteristics similar to the S taxonomic complex. The spectra of ordinary chondrites (spanning H, L, and LL subtypes) are the best matches for these asteroid spectra. {\bf The asteroid} (269690) 1996 RG3 presents a flat featureless spectrum which could be associated to a primitive C-type object. The increased reflectance above 2.1 microns constrains its geometrical albedo to a value around 0.03. While there is an important dynamical grouping among the Taurid Complex asteroids, the spectral data of the largest objects do not support a common cometary origin. Furthermore, there are significant variations between the spectra acquired until now.Comment: Accepted for publication in A&

Quantum Thermalization With Couplings

We study the role of the system-bath coupling for the generalized canonical thermalization [S. Popescu, et al., Nature Physics 2,754(2006) and S. Goldstein et al., Phys. Rev. Lett. 96, 050403(2006)] that reduces almost all the pure states of the "universe" [formed by a system S plus its surrounding heat bath $B$] to a canonical equilibrium state of S. We present an exactly solvable, but universal model for this kinematic thermalization with an explicit consideration about the energy shell deformation due to the interaction between S and B. By calculating the state numbers of the "universe" and its subsystems S and B in various deformed energy shells, it is found that, for the overwhelming majority of the "universe" states (they are entangled at least), the diagonal canonical typicality remains robust with respect to finite interactions between S and B. Particularly, the kinematic decoherence is utilized here to account for the vanishing of the off-diagonal elements of the reduced density matrix of S. It is pointed out that the non-vanishing off-diagonal elements due to the finiteness of bath and the stronger system-bath interaction might offer more novelties of the quantum thermalization.Comment: 4 pages, 2 figure

Compositional characterisation of the Themis family

Context. It has recently been proposed that the surface composition of icy main-belt asteroids (B-,C-,Cb-,Cg-,P-,and D-types) may be consistent with that of chondritic porous interplanetary dust particles (CPIDPs). Aims. In the light of this new association, we re-examine the surface composition of a sample of asteroids belonging to the Themis family in order to place new constraints on the formation and evolution of its parent body. Methods. We acquired NIR spectral data for 15 members of the Themis family and complemented this dataset with existing spectra in the visible and mid-infrared ranges to perform a thorough analysis of the composition of the family. Assuming end-member minerals and particle sizes (<2\mum) similar to those found in CPIDPs, we used a radiative transfer code adapted for light scattering by small particles to model the spectral properties of these asteroids. Results. Our best-matching models indicate that most objects in our sample possess a surface composition that is consistent with the composition of CP IDPs.We find ultra-fine grained Fe-bearing olivine glasses to be among the dominant constituents. We further detect the presence of minor fractions of Mg-rich crystalline silicates. The few unsuccessfully matched asteroids may indicate the presence of interlopers in the family or objects sampling a distinct compositional layer of the parent body. Conclusions. The composition inferred for the Themis family members suggests that the parent body accreted from a mixture of ice and anhydrous silicates (mainly amorphous) and subsequently underwent limited heating. By comparison with existing thermal models that assume a 400km diameter progenitor, the accretion process of the Themis parent body must have occurred relatively late (>4Myr after CAIs) so that only moderate internal heating occurred in its interior, preventing aqueous alteration of the outer shell.Comment: 9 pages, 5 figures, accepted for publication in A&

Scalar and tensorial topological matter coupled to (2+1)-dimensional gravity:A.Classical theory and global charges

We consider the coupling of scalar topological matter to (2+1)-dimensional gravity. The matter fields consist of a 0-form scalar field and a 2-form tensor field. We carry out a canonical analysis of the classical theory, investigating its sectors and solutions. We show that the model admits both BTZ-like black-hole solutions and homogeneous/inhomogeneous FRW cosmological solutions.We also investigate the global charges associated with the model and show that the algebra of charges is the extension of the Kac-Moody algebra for the field-rigid gauge charges, and the Virasoro algebrafor the diffeomorphism charges. Finally, we show that the model can be written as a generalized Chern-Simons theory, opening the perspective for its formulation as a generalized higher gauge theory.Comment: 40 page