Periodic Orbits of a Collinear Restricted Three-Body Problem

In this paper we study symmetric periodic orbits of a collinear restricted three-body problem, when the middle mass is the largest one. These symmetric periodic orbits are obtained from analytic continuation of symmetric periodic orbits of two collinear two-body problems.     

Equilibrium Points and Central Configurations for the Lennard-Jones 2- and 3-Body Problems

In this paper we study the relative equilibria and their stability for a system of three point particles moving under the action of a Lennard-Jones potential. A central configuration is a special position of the particles where the position and acceleration vectors of each particle are proportional, and the constant of proportionality is the same for all particles. Since the Lennard-Jones potential depends only on the mutual distances among the particles, it is invariant under rotations. In a rotating frame the orbits coming from central configurations become equilibrium points, the relative equilibria. Due to the form of the potential, the relative equilibria depend on the size of the system, that is, depend strongly of the momentum of inertia I. In this work we characterize the relative equilibria, we find the bifurcation values of I for which the number of relative equilibria is changing, we also analyze the stability of the relative equilibria. This revised version was published online in July 2006 with corrections to the Cover Date.     

Stochastic Modeling of the Residual Acceleration Field in a Microgravity Environment

We discuss fluid flows induced by thehigh-frequency components of the residual acceleration field onboard spacecraft (g-jitter) on representative experimental configurations.We study the statistics of g-jitter time series data from theNASA SL-J mission (SAMS-258), and discuss a recently introducedstochastic model of g-jitter. The examples studied are chosen to highlightintrinsically stochastic effects of g-jitter. They include free surfaceresonances, cavity flow, and inertial Brownian motion in suspensions. Thelatter is relevant for coarsening experiments in solid-liquid mixtures.     

The global flow of the parabolic restricted three-body problem

We have two mass points of equal masses m ₁=m ₂ > 0 moving under Newton’s law of attraction in a non-collision parabolic orbit while their center of mass is at rest. We consider a third mass point, of mass m ₃=0, moving on the straight line L perpendicular to the plane of motion of the first two mass points and passing through their center of mass. Since m ₃=0, the motion of m ₁ and m ₂ is not affected by the third and from the symmetry of the motion it is clear that m ₃ will remain on the line L. The parabolic restricted three-body problem describes the motion of m ₃. Our main result is the characterization of the global flow of this problem.     

Hip-hop solutions of the 2N-body problem

Hip-hop solutions of the 2N-body problem with equal masses are shown to exist using an analytic continuation argument. These solutions are close to planar regular 2N-gon relative equilibria with small vertical oscillations. For fixed N, an infinity of these solutions are three-dimensional choreographies, with all the bodies moving along the same closed curve in the inertial frame.     

GPR survey to confirm the location of ancient structures under the Valencian Cathedral (Spain)

This paper describes the ground-penetrating radar (GPR) survey performed inside the Cathedral of Valencia, Spain. It is part of historical studies performed in the Cathedral in order to add information to old maps and documents in the Cathedral Archives and also to analyze the extent and importance of potentially destructive moisture areas that were appearing on the floor. The construction of the Cathedral of Valencia occurred in three stages, all of which are well-documented in the Cathedral Archives with detailed drawings, maps, and charts. The radar data were successful in locating crypts, ossuaries, sepulchers, and graves, and the location of ancient walls that existed before the final Cathedral expansion. Three cultural layers corresponding to the three periods of construction were also identified corresponding to the Roman, Arabian and Middle Age Epochs. Measurements of relative sub-floor moisture were obtained by comparing dielectric permittivity changes and radar velocity differences between materials in humid and non-humid areas.     

Brane cosmology from observational surveys and its comparison with standard FRW cosmology

Several simple dark energy models on the brane are investigated. They are compared with corresponding models in the frame of 4d Friedmann-Robertson-Walker cosmology. For constraining the parameters of the models considered, recent observational data, including SNIa apparent magnitude measurements, baryon acoustic oscillation results, Hubble parameter evolution data and matter density perturbations are used. Also, explicit formulas of the so-called state-finder parameters in teleparallel theories are found that could be useful to test these models and compare Loop Quantum Cosmology and Brane Cosmology. The conclusion is reached that a joint analysis as the one developed here allows to estimate, in a very clear way, possible deviation of our cosmology from the standard Friedmann-Robertson-Walker one.     

Towards a quantum universe

In this short review we study the state of the art of the great problems in cosmology and their interrelationships. The reconciliation of these problems passes undoubtedly through the idea of a quantum universe.     

Insights in the exhumation history of the NW Zagros from bedrock and detrital apatite fission‐track analysis: evidence for a long‐lived orogeny

We present the first fission‐track (FT) thermochronology results for the NW Zagros Belt (SW Iran) in order to identify denudation episodes that occurred during the protracted Zagros orogeny. Samples were collected from the two main detrital successions of the NW Zagros foreland basin: the Palaeocene–early Eocene Amiran–Kashkan succession and the Miocene Agha Jari and Bakhtyari Formations. In situ bedrock samples were furthermore collected in the Sanandaj‐Sirjan Zone. Only apatite fission‐track (AFT) data have been successfully obtained, including 26 ages and 11 track‐length distributions. Five families of AFT ages have been documented from analyses of in situ bedrock and detrital samples: pre‐middle Jurassic at ～171 and ～225 Ma, early–late Cretaceous at ～91 Ma, Maastrichtian at ～66 Ma, middle–late Eocene at ～38 Ma and Oligocene–early Miocene at ～22 Ma. The most widespread middle–late Eocene cooling phase, around ～38 Ma, is documented by a predominant grain‐age population in Agha Jari sediments and by cooling ages of a granitic boulder sample. AFT ages document at least three cooling/denudation periods linked to major geodynamic events related to the Zagros orogeny, during the late Cretaceous oceanic obduction event, during the middle and late Eocene and during the early Miocene. Both late Cretaceous and early Miocene orogenic processes produced bending of the Arabian plate and concomitant foreland deposition. Between the two major flexural foreland episodes, the middle–late Eocene phase mostly produced a long‐lasting slow‐ or nondepositional episode in the inner part of the foreland basin, whereas deposition and tectonics migrated to the NE along the Sanandaj‐Sirjan domain and its Gaveh Rud fore‐arc basin. As evidenced in this study, the Zagros orogeny was long‐lived and multi‐episodic, implying that the timing of accretion of the different tectonic domains that form the Zagros Mountains requires cautious interpretation.     

On the families of periodic orbits which bifurcate from the circular Sitnikov motions

In this paper we deal with the circular Sitnikov problem as a subsystem of the three-dimensional circular restricted three-body problem. It has a first analytical part where by using elliptic functions we give the analytical expressions for the solutions of the circular Sitnikov problem and for the period function of its family of periodic orbits. We also analyze the qualitative and quantitative behavior of the period function. In the second numerical part, we study the linear stability of the family of periodic orbits of the Sitnikov problem, and of the families of periodic orbits of the three-dimensional circular restricted three-body problem which bifurcate from them; and we follow these bifurcated families until they end in families of periodic orbits of the planar circular restricted three-body problem. We compare our results with the previous ones of other authors on this problem. Finally, the characteristic curves of some bifurcated families obtained for the mass parameter close to 1/2 are also described.