Existence of periodic orbits near heteroclinic connections

We consider a potential $W:R^m\rightarrow R$ with two different global minima $a_-, a_+$ and, under a symmetry assumption, we use a variational approach to show that the Hamiltonian system \begin{equation} \ddot{u}=W_u(u), \hskip 2cm (1) \end{equation} has a family of $T$-periodic solutions $u^T$ which, along a sequence $T_j\rightarrow+\infty$, converges locally to a heteroclinic solution that connects $a_-$ to $a_+$. We then focus on the elliptic system \begin{equation} \Delta u=W_u(u),\;\; u:R^2\rightarrow R^m, \hskip 2cm (2) \end{equation} that we interpret as an infinite dimensional analogous of (1), where $x$ plays the role of time and $W$ is replaced by the action functional $$J_R(u)=\int_R\Bigl(\frac{1}{2}\vert u_y\vert^2+W(u)\Bigr)dy.$$ We assume that $J_R$ has two different global minimizers $\bar{u}_-, \bar{u}_+:R\rightarrow R^m$ in the set of maps that connect $a_-$ to $a_+$. We work in a symmetric context and prove, via a minimization procedure, that (2) has a family of solutions $u^L:R^2\rightarrow R^m$, which is $L$-periodic in $x$, converges to $a_\pm$ as $y\rightarrow\pm\infty$ and, along a sequence $L_j\rightarrow+\infty$, converges locally to a heteroclinic solution that connects $\bar{u}_-$ to $\bar{u}_+$.Comment: 36 pages, 4 figure

Geometry of flux attachment in anisotropic fractional quantum Hall states

Fractional quantum Hall (FQH) states are known to possess an internal metric degree of freedom that allows them to minimize their energy when contrasting geometries are present in the problem (e.g., electron band mass and dielectric tensor). We investigate the internal metric of several incompressible FQH states by probing its response to band mass anisotropy using infinite DMRG simulations on a cylinder geometry. We test and apply a method to extract the internal metric of a FQH state from its guiding center structure factor. We find that the response to band mass anisotropy is approximately the same for states in the same Jain sequence, but changes substantially between different sequences. We provide a theoretical explanation of the observed behavior of primary states at filling $\nu = 1/m$ in terms of a minimal microscopic model of flux attachment.Comment: 12 pages including references, 14 figure

Quantifying stellar radial migration in an N-body simulation: blurring, churning, and the outer regions of galaxy discs

Radial stellar migration in galactic discs has received much attention in studies of galactic dynamics and chemical evolution, but remains a dynamical phenomenon that needs to be fully quantified. In this work, using a Tree-SPH simulation of an Sb-type disc galaxy, we quantify the effects of blurring (epicyclic excursions) and churning (change of guiding radius). We quantify migration (either blurring or churning) both in terms of flux (the number of migrators passing at a given radius), and by estimating the population of migrators at a given radius at the end of the simulation compared to non-migrators, but also by giving the distance over which the migration is effective at all radii. We confirm that the corotation of the bar is the main source of migrators by churning in a bar-dominated galaxy, its intensity being directly linked to the episode of a strong bar, in the first 1-3 Gyr of the simulation. We show that within the outer Lindblad resonance (OLR), migration is strongly dominated by churning, while blurring gains progressively more importance towards the outer disc and at later times. Most importantly, we show that the OLR limits the exchange of angular momentum, separating the disc in two distinct parts with minimal or null exchange, except in the transition zone, which is delimited by the position of the OLR at the epoch of the formation of the bar, and at the final epoch. We discuss the consequences of these findings for our understanding of the structure of the Milky Way disc. Because the Sun is situated slightly outside the OLR, we suggest that the solar vicinity may have experienced very limited churning from the inner disc.Comment: Accepted for publication in Astronomy and Astrophysics (acceptance date: 27/04/15), 24 pages, 24 figure

On the Virtual Element Method for Topology Optimization on polygonal meshes: a numerical study

It is well known that the solution of topology optimization problems may be affected both by the geometric properties of the computational mesh, which can steer the minimization process towards local (and non-physical) minima, and by the accuracy of the method employed to discretize the underlying differential problem, which may not be able to correctly capture the physics of the problem. In light of the above remarks, in this paper we consider polygonal meshes and employ the virtual element method (VEM) to solve two classes of paradigmatic topology optimization problems, one governed by nearly-incompressible and compressible linear elasticity and the other by Stokes equations. Several numerical results show the virtues of our polygonal VEM based approach with respect to more standard methods

Star formation efficiency in galaxy interactions and mergers: a statistical study

We investigate the enhancement of star formation efficiency in galaxy interactions and mergers, by numerical simulations of several hundred galaxy collisions. All morphological types along the Hubble sequence are considered in the initial conditions of the two colliding galaxies, with varying bulge-to-disk ratios and gas mass fractions. Different types of orbits are simulated, direct and retrograde, according to the initial relative energy and impact parameter, and the resulting star formation history is compared to that occuring in the two galaxies when they are isolated. Our principal results are: (1) retrograde encounters have a larger star formation efficiency (SFE) than direct encounters; (2) the amount of gas available in the galaxy is not the main parameter governing the SFE in the burst phase; (3) there is an anticorrelation between the amplitude of the star forming burst and the tidal forces exerted per unit of time, which is due to the large amount of gas dragged outside the galaxy by tidal tails in strong interactions; (4) globally, the Kennicutt-Schmidt law is retrieved statistically for isolated galaxies, interacting pairs and mergers; (5) the enhanced star formation is essentially occurring in nuclear starbursts, triggered by inward gas flows driven by non-axisymmetries in the galaxy disks. Direct encounters develop more pronounced asymmetries than retrograde ones. Based on these statistical results, we derive general laws for the enhancement of star formation in galaxy interactions and mergers, as a function of the main parameters of the encounter.Comment: 22 pages, 37 figures, 4 tables. Accepted on Astronomy & Astrophysic

Multi-asset minority games

We study analytically and numerically Minority Games in which agents may invest in different assets (or markets), considering both the canonical and the grand-canonical versions. We find that the likelihood of agents trading in a given asset depends on the relative amount of information available in that market. More specifically, in the canonical game players play preferentially in the stock with less information. The same holds in the grand canonical game when agents have positive incentives to trade, whereas when agents payoff are solely related to their speculative ability they display a larger propensity to invest in the information-rich asset. Furthermore, in this model one finds a globally predictable phase with broken ergodicity

Effects of diversification among assets in an agent-based market model

We extend to the multi-asset case the framework of a discrete time model of a single asset financial market developed in Ghoulmie et al (2005). In particular, we focus on adaptive agents with threshold behavior allocating their resources among two assets. We explore numerically the effect of this diversification as an additional source of complexity in the financial market and we discuss its destabilizing role. We also point out the relevance of these studies for financial decision making.Comment: 12 pages, 5 figures, accepted for publication in the Proceedings of the Complex Systems II Conference at the Australian National University, 4-7 December 2007, Canberra, ACT Australi

Quantum Tomography

This is the draft version of a review paper which is going to appear in "Advances in Imaging and Electron Physics"Comment: To appear in "Advances in Imaging and Electron Physics". Some figs with low resolutio

Old stellar counter-rotating components in early-type galaxies from elliptical-spiral mergers

We investigate, by means of numerical simulations, the possibility of forming counter-rotating old stellar components by major mergers between an elliptical and a spiral galaxy. We show that counter-rotation can appear both in dissipative and dissipationless retrograde mergers, and it is mostly associated to the presence of a disk component, which preserves part of its initial spin. In turn, the external regions of the two interacting galaxies acquire part of the orbital angular momentum, due to the action of tidal forces exerted on each galaxy by the companion.Comment: 6 pages, 15 figures. Accepted on Astronomy & Astrophysic