The evolution of the Sun's birth cluster and the search for the solar siblings with Gaia

We use self-consistent numerical simulations of the evolution and disruption of the Sun's birth cluster in the Milky Way potential to investigate the present-day phase space distribution of the Sun's siblings. The simulations include the gravitational N-body forces within the cluster and the effects of stellar evolution on the cluster population. In addition the gravitational forces due to the Milky Way potential are accounted for in a self-consistent manner. Our aim is to understand how the astrometric and radial velocity data from the Gaia mission can be used to pre-select solar sibling candidates. We vary the initial conditions of the Sun's birth cluster, as well as the parameters of the Galactic potential. We show that the disruption time-scales of the cluster are insensitive to the details of the non-axisymmetric components of the Milky Way model and we make predictions, averaged over the different simulated possibilities, about the number of solar siblings that should appear in surveys such as Gaia or GALAH. We find a large variety of present-day phase space distributions of solar siblings, which depend on the cluster initial conditions and the Milky Way model parameters. We show that nevertheless robust predictions can be made about the location of the solar siblings in the space of parallaxes ($\varpi$), proper motions ($\mu$) and radial velocities ($V_\mathrm{r}$). By calculating the ratio of the number of simulated solar siblings to that of the number of stars in a model Galactic disk, we find that this ratio is above 0.5 in the region given by: $\varpi \geq 5$mas, $4 \leq \mu \leq 6$masyr$^{-1}$, and $-2\leq V_\mathrm{r} \leq 0$kms$^{-1}$. Selecting stars from this region should increase the probability of success in identifying solar siblings through follow up observations [Abridged].Comment: 13 pages, 7 figures. Accepted for publication in MNRA

Linearization of nonlinear connections on vector and affine bundles, and some applications

A linear connection is associated to a nonlinear connection on a vector bundle by a linearization procedure. Our definition is intrinsic in terms of vector fields on the bundle. For a connection on an affine bundle our procedure can be applied after homogenization and restriction. Several applications in Classical Mechanics are provided

Lithium, sodium, and potassium magnesiate chemistry : a structural overview

Until recently, deprotonative metalation reactions have been performed using organometallic compounds that contain only a single metal (eg, organolithium reagents). Since the turn of the millennium, bimetallic compounds such as alkali metal magnesiates have begun to emerge as a new class of complementary metalating reagents. These have many benefits over traditional lithium compounds, including their enhanced stability at ambient temperatures, their tolerance of reactive functional groups and their stability in common reaction solvents. In recent years, lots of attention has been focused on understanding the structure of alkali metal magnesiates in an effort to maximize synthetic efficiency and thus shed insight into approaches for future rational design. In this chapter, the diverse structural chemistry of alkali metal magnesiate compounds reported since 2007 will be summarized

Chemical weathering of the volcanic soils of Isla Santa Cruz (Galápagos Islands, Ecuador)

We present a study on weathering of volcanic soils using 43 profiles (131 horizons) sampled in Santa Cruz Island (Galapagos Islands). Several weathering indices, based on chemical composition, are used. Since the geological material is highly homogeneous the intensity of weathering is mostly related to climatic conditions controlled by topography. There is a gradient of increasing weathering from the arid conditions predominant in the coast to elevations of 400-500 m a.s.l. where much more humid conditions prevail

A non self-referential expression of Tsallis' probability distribution function

The canonical probability distribution function (pdf) obtained by optimizing the Tsallis entropy under the linear mean energy constraint (first formalism) or the escort mean energy constraint (third formalism) suffer self-referentiality. In a recent paper [Phys. Lett. A {\bf335} (2005) 351-362] the authors have shown that the pdfs obtained in the two formalisms are equivalent to the pdf in non self-referential form. Based on this result we derive an alternative expression, which is non self-referential, for the Tsallis distributions in both first and third formalisms.Comment: 3 page

Cellular automaton supercolliders

Gliders in one-dimensional cellular automata are compact groups of non-quiescent and non-ether patterns (ether represents a periodic background) translating along automaton lattice. They are cellular-automaton analogous of localizations or quasi-local collective excitations travelling in a spatially extended non-linear medium. They can be considered as binary strings or symbols travelling along a one-dimensional ring, interacting with each other and changing their states, or symbolic values, as a result of interactions. We analyse what types of interaction occur between gliders travelling on a cellular automaton `cyclotron' and build a catalog of the most common reactions. We demonstrate that collisions between gliders emulate the basic types of interaction that occur between localizations in non-linear media: fusion, elastic collision, and soliton-like collision. Computational outcomes of a swarm of gliders circling on a one-dimensional torus are analysed via implementation of cyclic tag systems

A Computation in a Cellular Automaton Collider Rule 110

A cellular automaton collider is a finite state machine build of rings of one-dimensional cellular automata. We show how a computation can be performed on the collider by exploiting interactions between gliders (particles, localisations). The constructions proposed are based on universality of elementary cellular automaton rule 110, cyclic tag systems, supercolliders, and computing on rings.Comment: 39 pages, 32 figures, 3 table

Chaotic scattering with direct processes: A generalization of Poisson's kernel for non-unitary scattering matrices

The problem of chaotic scattering in presence of direct processes or prompt responses is mapped via a transformation to the case of scattering in absence of such processes for non-unitary scattering matrices, \tilde S. In the absence of prompt responses, \tilde S is uniformly distributed according to its invariant measure in the space of \tilde S matrices with zero average, < \tilde S > =0. In the presence of direct processes, the distribution of \tilde S is non-uniform and it is characterized by the average (\neq 0). In contrast to the case of unitary matrices S, where the invariant measures of S for chaotic scattering with and without direct processes are related through the well known Poisson kernel, here we show that for non-unitary scattering matrices the invariant measures are related by the Poisson kernel squared. Our results are relevant to situations where flux conservation is not satisfied. For example, transport experiments in chaotic systems, where gains or losses are present, like microwave chaotic cavities or graphs, and acoustic or elastic resonators.Comment: Added two appendices and references. Corrected typo