On the relationship between instability and Lyapunov times for the three-body problem

In this study we consider the relationship between the survival time and the Lyapunov time for three-body systems. It is shown that the Sitnikov problem exhibits a two-part power-law relationship as demonstrated by Mikkola & Tanikawa for the general three-body problem. Using an approximate Poincaré map on an appropriate surface of section, we delineate escape regions in a domain of initial conditions and use these regions to analytically obtain a new functional relationship between the Lyapunov time and the survival time for the three-body problem. The marginal probability distributions of the Lyapunov and survival times are discussed and we show that the probability density function of Lyapunov times for the Sitnikov problem is similar to that for the general three-body problem.     

On the Relationship Between Fast Lyapunov Indicator and Periodic Orbits for Continuous Flows

It is already known (Froeschlé et al., 1997a) that the fast Lyapunov indicator (hereafter FLI), i.e. the computation on a relatively short time of a quantity related to the largest Lyapunov indicator, allows us to discriminate between ordered and weak chaotic motion. Using the FLI many results have been obtained on the standard map taken as a model problem. On this model we are not only able to discriminate between a short time weak chaotic motion and an ordered one, but also among regular motion between non resonant and resonant orbits. Moreover, periodic orbits are characterised by constant FLI values which appear to be related to the order of periodic orbits (Lega and Froeschlé, 2001). In the present paper we extend all these results to the case of continuous dynamical systems (the Hénon and Heiles system and the restricted three-body problem). Especially for the periodic orbits we need to introduce a new value: the orthogonal FLI in order to fully recover the results obtained for mappings.     

on the relationship between fast lyapunov indicator and periodic orbits for symplectic mappings

The computation on a relatively short time of a quantity, related to the largest Lyapunov Characteristic Exponent, called Fast Lyapunov Indicator allows to discriminate between ordered and weak chaotic motion and also, under certain conditions, between resonant and non resonant regular orbits. The aim of this paper is to study numerically the relationship between the Fast Lyapunov Indicator values and the order of periodic orbits. Using the two-dimensional standard map as a model problem we have found that the Fast Lyapunov Indicator increases as the logarithm of the order of periodic orbits up to a given order. For higher order the Fast Lyapunov Indicator grows linearly with the order of the periodic orbits. We provide a simple model to explain the relationship that we have found between the values of the Fast Lyapunov Indicator, the order of the periodic orbits and also the minimum number of iterations needed to obtain the Fast Lyapunov Indicator values.     

On the relationship between pulsars and supernova remnants

We propose that single stars in the mass range 4–6·5M _⊙, that explode as Supernovae of Type I, are totally disrupted by the explosion and form shell-type remnants. More massive single stars which explode as Supernovae of Type II also give rise to shell-type remnants, but in this case a neutron star or a black hole is left behind. The first supernova explosion in a close binary also gives rise to a shell-type supernova remnant. The Crab-like filled-centre supernova remnants are formed by the second supernova explosion in a close binary. The hybrid supernova remnants, consisting of a filled centre surrounded by a shell, are formed if there is an active neutron star inside the shell.     

On the relationship between ground temperature histories and meteorological records: a report on the Pomquet station

An experimental air–ground climate station is operating in Pomquet, Nova Scotia, monitoring meteorological (surface air temperatures at three heights, wind velocity and direction, incoming solar radiation, precipitation, snow depth and relative humidity) and ground thermal variables (soil temperatures at depths of 0, 5, 10, 20, 50 and 100 cm). Readings are taken every 30 s and 5 min averages are stored, in order to characterize the energy exchanges at the air ground interface. Here, I report on the first year of operation. For spring, summer and fall, we find that soil temperatures track surface air temperatures with amplitude attenuation and phase lag with depth confirming that heat conduction adequately describe the soil thermal field at the Pomquet site. For winter conditions, we find that heat transfer is dominated by latent heat released during soil freezing and to a lesser extent by the insulating affect of snow cover. A numerical model of heat conduction was used in order to estimate the magnitude of the heat released by freezing during the winter months. I also show that there is an inverse correlation for the difference between soil (100 cm) and air temperatures and the incoming solar radiation at the site.     

Groups of galaxies. IV. Effect of observational selection on the relationship between the characteristics and distance of groups and a comparison with the groups of Geller and Huchra

The effect of observational selection on the relationship between the characteristics of groups of galaxies and their distances is discussed in this paper. For our groups the dependence of the pairwise distance between the members on the distance of the group is just that. For the groups of Geller and Huchra, on the other hand, the analogous dependence is distorted by the effect of their selection criteria for groups of galaxies. The average dispersion of the radial velocities of the galaxies for our groups is less than half that for the groups of Geller and Huchra, while the mass-to-luminosity ratio is smaller, on the average, by more than an order of magnitude in our case. Geller-Huchra groups with mass-to-luminosity ratios greater than 1000 are most likely unreal. __________ Translated from Astrofizika, Vol. 50, No. 4, pp. 535–546 (November 2007).