Hydrodynamical simulations of Galactic fountains - I. Evolution of single fountains

The ejection of the gas out of the disc in late-type galaxies is related to star formation and is due mainly to Type II supernovae. In this paper, we studied in detail the development of the Galactic fountains in order to understand their dynamical evolution and their influence on the redistribution of the freshly delivered metals over the disc. To this aim, we performed a number of 3D hydrodynamical radiative cooling simulations of the gas in the Milky Way where the whole Galaxy structure, the Galactic differential rotation and the supernova explosions generated by a single OB association are considered. A typical fountain powered by 100 Type II supernovae may eject material up to similar to 2 kpc which than collapses back mostly in the form of dense, cold clouds and filaments. The majority of the gas lifted up by the fountains falls back on the disc remaining within a radial distance Delta R = 0.5 kpc from the place where the fountain originated. This localized circulation of disc gas does not influence the radial chemical gradients on large scale, as required by the chemical models of the Milky Way which reproduce the metallicity distribution without invoking large fluxes of metals. Simulations of multiple fountains fuelled by Type II supernovae of different OB associations will be presented in a companion paper.

Modelling the secular evolution of migrating planet pairs

The subject of this paper is the secular behaviour of a pair of planets evolving under dissipative forces. In particular, we investigate the case when dissipative forces affect the planetary semimajor axes and the planets move inwards/outwards the central star, in a process known as planet migration. To perform this investigation, we introduce fundamental concepts of conservative and dissipative dynamics of the three-body problem. Based on these concepts, we develop a qualitative model of the secular evolution of the migrating planetary pair. Our approach is based on the analysis of the energy and the orbital angular momentum exchange between the two-planet system and an external medium; thus no specific kind of dissipative forces is invoked. We show that, under the assumption that dissipation is weak and slow, the evolutionary routes of the migrating planets are traced by the Mode I and Mode II stationary solutions of the conservative secular problem. The ultimate convergence and the evolution of the system along one of these secular modes of motion are determined uniquely by the condition that the dissipation rate is sufficiently smaller than the proper secular frequency of the system. We show that it is possible to reassemble the starting configurations and the migration history of the systems on the basis of their final states and consequently to constrain the parameters of the physical processes involved.

Hydrodynamical simulations of Galactic fountains - II. Evolution of multiple fountains

The ejection of gas out of the disc in late-type galaxies is related to star formation and is mainly due to the explosion of Type II supernovae (SN II). In a previous paper, we considered the evolution of a single Galactic fountain, that is, a fountain powered by a single SN cluster. Using three-dimensional hydrodynamical simulations, we studied in detail the fountain flow and its dependence with several factors, such as the Galactic rotation, the distance to the Galactic centre and the presence of a hot gaseous halo. As a natural followup, this paper investigates the dynamical evolution of multiple generations of fountains generated by similar to 100 OB associations. We have considered the observed size-frequency distribution of young stellar clusters within the Galaxy in order to appropriately fuel the multiple fountains in our simulations. Most of the results of the previous paper have been confirmed, like for example the formation of intermediate velocity clouds above the disc by the multiple fountains. Also, this work confirms the localized nature of the fountain flows: the freshly ejected metals tend to fall back close to the same Galactocentric region where they are delivered. Therefore, the fountains do not change significantly the radial profile of the disc chemical abundance. The multiple fountain simulations also allowed us to consistently calculate the feedback of the star formation on the halo gas. We found that the hot gas gains about 10 per cent of all the SN II energy produced in the disc. Thus, the SN feedback more than compensate for the halo radiative losses and allow for a quasi steady-state disc-halo circulation to exist. Finally, we have also considered the possibility of mass infall from the intergalactic medium and its interaction with the clouds that are formed by the fountains. Though our simulations are not suitable to reproduce the slow rotational pattern that is typically observed in the haloes around the disc galaxies, they indicate that the presence of an external gas infall may help to slow down the rotation of the gas in the clouds and thus the amount of angular momentum that they transfer to the coronal gas, as previously suggested in the literature.

Computer simulations of copper and gold nanowires and single-wall nanowires

Copper and gold nanowires under tension evolve to form linear atomic chains (LACs), and the study and understanding of this evolution is an important subject for the development of nanocontacts. Here we study the differences and similarities between copper and gold nanowires (NWs) under stress along the [111] crystallographic direction until their rupture using tight-binding molecular dynamics. In both metals, the first significant rearrangement occurs due to one inside atom that goes to the NW` surface. In an attempt to better understand this effect, for both metals we also consider hollow NW`s where the inside atoms were excluded after the initial relaxation to create single-wall NW`s (SWNWs). The dynamical evolution of these SWNWs provides insight on the formation of the constriction that evolves to form LACs. Studying the calculated forces supported by the NW`s we show that SWNWs can sustain larger forces before the first major rearrangement in the copper and gold when compared to the original NW`s.

Dynamical self-stabilization of the Mott insulator: Time evolution of the density and entanglement entropy of out-of-equilibrium cold fermion gases

The time evolution of the out-of-equilibrium Mott insulator is investigated numerically through calculations of space-time-resolved density and entropy profiles resulting from the release of a gas of ultracold fermionic atoms from an optical trap. For adiabatic, moderate and sudden switching-off of the trapping potential, the out-of-equilibrium dynamics of the Mott insulator is found to differ profoundly from that of the band insulator and the metallic phase, displaying a self-induced stability that is robust within a wide range of densities, system sizes and interaction strengths. The connection between the entanglement entropy and changes of phase, known for equilibrium situations, is found to extend to the out-of-equilibrium regime. Finally, the relation between the system`s long time behavior and the thermalization limit is analyzed. Copyright (C) EPLA, 2011

Some Possible Dynamical Constraints for Life`s Origin

Oscillating biochemical reactions are common in cell dynamics and could be closely related to the emergence of the life phenomenon itself. In this work, we study the dynamical features of some classical chemical or biochemical oscillators where the effect of cell volume changes is explicitly considered. Such analysis enables us to find some general conditions about the cell membrane to preserve such oscillatory patterns, of possible relevance to hypothetical primitive cells in which these structures first appeared.

On the continuity of pullback attractors for evolution processes

In this paper we give general results on the continuity of pullback attractors for nonlinear evolution processes. We then revisit results of [D. Li, P.E. Kloeden, Equi-attraction and the continuous dependence of pullback attractors on parameters, Stoch. Dyn. 4 (3) (2004) 373-384] which show that, under certain conditions, continuity is equivalent to uniformity of attraction over a range of parameters (""equi-attraction""): we are able to simplify their proofs and weaken the conditions required for this equivalence to hold. Generalizing a classical autonomous result [A.V. Babin, M.I. Vishik, Attractors of Evolution Equations, North Holland, Amsterdam, 1992] we give bounds on the rate of convergence of attractors when the family is uniformly exponentially attracting. To apply these results in a more concrete situation we show that a non-autonomous regular perturbation of a gradient-like system produces a family of pullback attractors that are uniformly exponentially attracting: these attractors are therefore continuous, and we can give an explicit bound on the distance between members of this family. (C) 2009 Elsevier Ltd. All rights reserved.

A general treatment of geometric phases and dynamical invariants

Based only on the parallel-transport condition, we present a general method to compute Abelian or non-Abelian geometric phases acquired by the basis states of pure or mixed density operators, which also holds for nonadiabatic and noncyclic evolution. Two interesting features of the non-Abelian geometric phase obtained by our method stand out: i) it is a generalization of Wilczek and Zee`s non-Abelian holonomy, in that it describes nonadiabatic evolution where the basis states are parallelly transported between distinct degenerate subspaces, and ii) the non-Abelian character of our geometric phase relies on the transitional evolution of the basis states, even in the nondegenerate case. We apply our formalism to a two-level system evolving nonadiabatically under spontaneous decay to emphasize the non- Abelian nature of the geometric phase induced by the reservoir. We also show, through the generalized invariant theory, that our general approach encompasses previous results in the literature. Copyright (c) EPLA, 2008.

STABILITY ANALYSIS WITH APPLICATIONS OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM ARISING FROM A STOCHASTIC MODEL FOR AN ASSET MARKET

We analyze the stability properties of equilibrium solutions and periodicity of orbits in a two-dimensional dynamical system whose orbits mimic the evolution of the price of an asset and the excess demand for that asset. The construction of the system is grounded upon a heterogeneous interacting agent model for a single risky asset market. An advantage of this construction procedure is that the resulting dynamical system becomes a macroscopic market model which mirrors the market quantities and qualities that would typically be taken into account solely at the microscopic level of modeling. The system`s parameters correspond to: (a) the proportion of speculators in a market; (b) the traders` speculative trend; (c) the degree of heterogeneity of idiosyncratic evaluations of the market agents with respect to the asset`s fundamental value; and (d) the strength of the feedback of the population excess demand on the asset price update increment. This correspondence allows us to employ our results in order to infer plausible causes for the emergence of price and demand fluctuations in a real asset market. The employment of dynamical systems for studying evolution of stochastic models of socio-economic phenomena is quite usual in the area of heterogeneous interacting agent models. However, in the vast majority of the cases present in the literature, these dynamical systems are one-dimensional. Our work is among the few in the area that construct and study analytically a two-dimensional dynamical system and apply it for explanation of socio-economic phenomena.

CONTINUITY OF GLOBAL ATTRACTORS FOR A CLASS OF NON LOCAL EVOLUTION EQUATIONS

In this work we prove that the global attractors for the flow of the equation partial derivative m(r, t)/partial derivative t = -m(r, t) + g(beta J * m(r, t) + beta h), h, beta >= 0, are continuous with respect to the parameters h and beta if one assumes a property implying normal hyperbolicity for its (families of) equilibria.