Long-term Geomechanical Observation in the Jeroným Mine

Geomechanical measurements have been carried out in the medieval Jeroným Mine since 2001. At first quarterly observation and later also continual monitoring by distributed measurement network were used. The network includes a number of different sensors that have been installed in selected places of underground spaces. There have not been any manifestations documenting dangerous changes of stability during the period of monitoring (2001–2015). The results of accomplished measurements from all convergence profiles confirm the total stability of all underground spaces. However, a number of places have been documented as potentially unstable. Measured values of selected parameters are presented in the paper, namely, movements along fractures, changes of stress tensor and fluctuations in the level of mine water table.     

Modelling magnetization processes in single-and multi-domain rock samples using the preisach diagram

Summary The paper presents the results of identifying a model of the Preisach type for haematite grains of the single-domain as well as multi-domain size. Due to the phenomenological conception of the model, the relations between the parameters of the model and actual parameters are very complex, however, impressive accuracy and stability of the modified model indicate the need to resume studies of this problem. The model parameters also confirm the adequate properties of the vibrating-sample magnetometr (VSM) used and developed in our laboratories.     

Some New Observed Properties of Elliptical Galaxies

We suggest that elliptical galaxies, as stellar systems in a stage of quasi-equilibrium, may have a specific entropy. We use the Sérsic law to describe the light profile. The specific entropy (the Boltzmann–Gibbs definition) is then calculated assuming that the galaxy behaves as a spherical, isotropic, one-component system. We predict a relation between the three parameters of the Sérsic law linked to the specific entropy, defining a surface in the parameter space, an ‘entropic plane’. We have analysed a sample of simulated merging elliptical galaxies (virtual) and a sample of galaxies belonging to the Coma Cluster (real). Both virtual and realgalaxies are: 1) located in their own ‘entropic plane‘ and 2) in this plane, they are located on a straight line, indicating constant entropy: another physical property A careful examination of the value of the specific entropy indicates a very small increase in the specific entropy with the generation after merging (virtual sample). Although one cannot distinguish between various generations for real galaxies, the distribution of specific entropy in this sample is very similar to that in the virtual sample. This revised version was published online in July 2006 with corrections to the Cover Date.     

Repeat Ground Track Orbits of the Earth Tesseral Problem as Bifurcations of the Equatorial Family of Periodic Orbits

Orbits repeating their ground track on the surface of the earth are found to be members of periodic-orbit families (in a synodic frame) of the tesseral problem of the Earth artificial satellite. Families of repeat ground track orbits appear as vertical bifurcations of the equatorial family of periodic orbits, and they evolve from retrograde to direct motion throughout the 180 degrees of inclination. These bifurcations are always close to the resonances of the Earth's rotation rate and the mean motion of the orbiter.     

On the Centre Manifold of Collinear Points in the Planar Three-Body Problem

We study the existence of invariant tori in a neighbourhood of the collinear equilibrium points of the planar three-body problem. To this end some properties of the normal form of the Hamiltonian reduced to the 4D central manifold are proved. Using this normal form, we show that the nondegeneracy conditions of KAM theorem are satisfied for all positive masses, including the 2:1 resonance case. The evaluation of the conditions is done numerically.