Two novel classes of solvable many-body problems of goldfish type with constraints

Two novel classes of many-body models with nonlinear interactions "of goldfish type" are introduced. They are solvable provided the initial data satisfy a single constraint (in one case; in the other, two constraints): i. e., for such initial data the solution of their initial-value problem can be achieved via algebraic operations, such as finding the eigenvalues of given matrices or equivalently the zeros of known polynomials. Entirely isochronous versions of some of these models are also exhibited: i.e., versions of these models whose nonsingular solutions are all completely periodic with the same period.Comment: 30 pages, 2 figure

On a possible origin for the lack of old star clusters in the Small Magellanic Cloud

We model the dynamical interaction between the Small and Large Magellanic Clouds and their corresponding stellar cluster populations. Our goal is to explore whether the lack of old clusters ($\gtrsim 7$ Gyr) in the Small Magellanic Cloud (SMC) can be the result of the capture of clusters by the Large Magellanic Cloud (LMC), as well as their ejection due to the tidal interaction between the two galaxies. For this purpose we perform a suite of numerical simulations probing a wide range of parameters for the orbit of the SMC about the LMC. We find that, for orbital eccentricities $e \geq 0.4$, approximately 15 per cent of the SMC clusters are captured by the LMC. In addition, another 20 to 50 per cent of its clusters are ejected into the intergalactic medium. In general, the clusters lost by the SMC are the less tightly bound cluster population. The final LMC cluster distribution shows a spatial segregation between clusters that originally belonged to the LMC and those that were captured from the SMC. Clusters that originally belonged to the SMC are more likely to be found in the outskirts of the LMC. Within this scenario it is possible to interpret the difference observed between the star field and cluster SMC Age-Metallicity Relationships for ages $\gtrsim 7$ Gyr.Comment: 5 pages, 3 figures, accepted for publication in MNRAS Letter

Pion scattering poles and chiral symmetry restoration

Using unitarized Chiral Perturbation Theory methods, we perform a detailed analysis of the $\pi\pi$ scattering poles $f_0(600)$ and $\rho(770)$ behaviour when medium effects such as temperature or density drive the system towards Chiral Symmetry Restoration. In the analysis of real poles below threshold, we show that it is crucial to extend properly the unitarized amplitudes so that they match the perturbative Adler zeros. Our results do not show threshold enhancement effects at finite temperature in the $f_0(600)$ channel, which remains as a pole of broad nature. We also implement T=0 finite density effects related to chiral symmetry restoration, by varying the pole position with the pion decay constant. Although this approach takes into account only a limited class of contributions, we reproduce the expected finite density restoration behaviour, which drives the poles towards the real axis, producing threshold enhancement and $\pi\pi$ bound states. We compare our results with several model approaches and discuss the experimental consequences, both in Relativistic Heavy Ion Collisions and in $\pi\to \pi\pi$ and $\gamma\to \pi\pi$ reactions in nuclei.Comment: 17 pages, 9 figures, final version to appear in Phys.Rev.D, added comments and reference

Analytic estimates and topological properties of the weak stability boundary

The weak stability boundary (WSB) is the transition region of the phase space where the change from gravitational escape to ballistic capture occurs. Studies on this complicated region of chaotic motion aim to investigate its unique, fuel saving properties to enlarge the frontiers of low energy transfers. This “fuzzy stability” region is characterized by highly sensitive motion, and any analysis of it has been carried out almost exclusively using numerical methods. On the contrary this paper presents, for the planar circular restricted 3 body problem (PCR3BP), 1) an analytic definition of the WSB which is coherent with the known algorithmic definitions; 2) a precise description of the topology of the WSB; 3) analytic estimates on the “stable region” (nearby the smaller primary) whose boundary is, by definition, the WSB