Action minimizing orbits in the n-body problem with simple choreography constraint

In 1999 Chenciner and Montgomery found a remarkably simple choreographic motion for the planar 3-body problem (see \cite{CM}). In this solution 3 equal masses travel on a eight shaped planar curve; this orbit is obtained minimizing the action integral on the set of simple planar choreographies with some special symmetry constraints. In this work our aim is to study the problem of $n$ masses moving in \RR^d under an attractive force generated by a potential of the kind $1/r^\alpha$, $\alpha >0$, with the only constraint to be a simple choreography: if $q_1(t),...,q_n(t)$ are the $n$ orbits then we impose the existence of x \in H^1_{2 \pi}(\RR,\RR^d) such that q_i(t)=x(t+(i-1) \tau), i=1,...,n, t \in \RR, where $\tau = 2\pi / n$. In this setting, we first prove that for every d,n \in \NN and $\alpha>0$, the lagrangian action attains its absolute minimum on the planar circle. Next we deal with the problem in a rotating frame and we show a reacher phenomenology: indeed while for some values of the angular velocity minimizers are still circles, for others the minima of the action are not anymore rigid motions.Comment: 24 pages; 4 figures; submitted to Nonlinearit

Gravitational wave forms for a three-body system in Lagrange's orbit: parameter determinations and a binary source test

Continuing work initiated in an earlier publication [Torigoe et al. Phys. Rev. Lett. {\bf 102}, 251101 (2009)], gravitational wave forms for a three-body system in Lagrange's orbit are considered especially in an analytic method. First, we derive an expression of the three-body wave forms at the mass quadrupole, octupole and current quadrupole orders. By using the expressions, we solve a gravitational-wave {\it inverse} problem of determining the source parameters to this particular configuration (three masses, a distance of the source to an observer, and the orbital inclination angle to the line of sight) through observations of the gravitational wave forms alone. For this purpose, the chirp mass to a three-body system in the particular configuration is expressed in terms of only the mass ratios by deleting initial angle positions. We discuss also whether and how a binary source can be distinguished from a three-body system in Lagrange's orbit or others.Comment: 21 pages, 3 figures, 1 table; text improved, typos corrected; accepted for publication in PR

Uniqueness of collinear solutions for the relativistic three-body problem

Continuing work initiated in an earlier publication [Yamada, Asada, Phys. Rev. D 82, 104019 (2010)], we investigate collinear solutions to the general relativistic three-body problem. We prove the uniqueness of the configuration for given system parameters (the masses and the end-to-end length). First, we show that the equation determining the distance ratio among the three masses, which has been obtained as a seventh-order polynomial in the previous paper, has at most three positive roots, which apparently provide three cases of the distance ratio. It is found, however, that, even for such cases, there exists one physically reasonable root and only one, because the remaining two positive roots do not satisfy the slow motion assumption in the post-Newtonian approximation and are thus discarded. This means that, especially for the restricted three-body problem, exactly three positions of a third body are true even at the post-Newtonian order. They are relativistic counterparts of the Newtonian Lagrange points L1, L2 and L3. We show also that, for the same masses and full length, the angular velocity of the post-Newtonian collinear configuration is smaller than that for the Newtonian case. Provided that the masses and angular rate are fixed, the relativistic end-to-end length is shorter than the Newtonian one.Comment: 18 pages, 1 figure; typos corrected, text improved; accepted by PR

Evidence for amorphous multilayered silicon obtained by deposition under modulated pressure of hydrogen

International audienc

Kinetics of thorium and particle cycling along the U.S. GEOTRACES North Atlantic Transect

© The Author(s), 2017. This is the author's version of the work. It is posted here under a nonexclusive, irrevocable, paid-up, worldwide license granted to WHOI. It is made available for personal use, not for redistribution. The definitive version was published in Deep Sea Research Part I: Oceanographic Research Papers 125 (2017): 106-128, doi:10.1016/j.dsr.2017.05.003.The high particle reactivity of thorium has resulted in its widespread use in tracing processes impacting marine particles and their chemical constituents. The use of thorium isotopes as tracers of particle dynamics, however, largely relies on our understanding of how the element scavenges onto particles. Here, we estimate apparent rate constants of Th adsorption (k1), Th desorption (k−1), bulk particle degradation (β-1), and bulk particle sinking speed (w) along the water column at 11 open-ocean stations occupied during the GEOTRACES North Atlantic Section (GA03). First, we provide evidence that the budgets of Th isotopes and particles at these stations appear to be generally dominated by radioactive production and decay sorption reactions, particle degradation, and particle sinking. Rate parameters are then estimated by fitting a Th and particle cycling model to data of dissolved and particulate 228,230,234Th, 228Ra, particle concentrations, and 234,238U estimates based on salinity, using a nonlinear programming technique. We find that the adsorption rate constant (k1) generally decreases with depth across the section: broadly, the time scale 1/k1 averages 1.0 yr in the upper 1000 m and (1.4–1.5) yr below. A positive relationship between k1 and particle concentration (P) is found, i.e., , k1 ∝ Pb where b ≥ 1, consistent with the notion that k1 increases with the number of surface sites available for adsorption. The rate constant ratio, K = k1/(k-1 + β-1), which measures the collective influence of rate parameters on Th scavenging, averages 0.2 for most stations and most depths. We clarify the conditions under which K/P is equivalent to the distribution coefficient, KD, test that the conditions are met at the stations, and find that decreases with P, in line with a particle concentration effect (dKD/dP < 0). In contrast to the influence of colloids as envisioned by the Brownian pumping hypothesis, we provide evidence that the particle concentration effect arises from the joint effect of P on the rate constants for thorium attachment to, and detachment from, particles.We acknowledge the U.S. National Science Foundation for providing funding for this study (grant OCE-1232578) and for U.S. GEOTRACES North Atlantic section ship time, sampling, and data analysis. The U.S. NSF also supported the generation of 230Th data (OCE-0927064 to LDEO, OCE-O092860 to WHOI, and OCE-0927754 to UMN) and 228,234Th data (OCE-0925158 to WHOI)

Caracterización racial del palomo Buchón Jienense

La Colombicultura, como especialidad dentro de la Avicultura Artística, es un arte muy antiguo pero el tratamiento de esta disciplina por parte de los aficionados, criadores y especialistas desde un punto de vista científico y técnico es muy reciente. En España, y especialmente en Andalucía, contamos con gran diversidad de razas dentro del grupo de las buchonas, como legado directo de la cultura e influencia árabe. En este trabajo desarrollamos un estudio sobre el palomo Buchón Jienense, raza autóctona de mayores censos y más amplia distribución geográfica en Andalucía. Se realiza un análisis de su posible origen y formación como raza así como una revisión de su patrón racial: características morfológicas, características fanerópticas y características funcionales

The SFXC software correlator for Very Long Baseline Interferometry: Algorithms and Implementation

In this paper a description is given of the SFXC software correlator, developed and maintained at the Joint Institute for VLBI in Europe (JIVE). The software is designed to run on generic Linux-based computing clusters. The correlation algorithm is explained in detail, as are some of the novel modes that software correlation has enabled, such as wide-field VLBI imaging through the use of multiple phase centres and pulsar gating and binning. This is followed by an overview of the software architecture. Finally, the performance of the correlator as a function of number of CPU cores, telescopes and spectral channels is shown.Comment: Accepted by Experimental Astronom

Repair of a Reinforced Earth Wall

The facing of a Reinforced Earth retaining wall, built at an altitude of 1200 m, was damaged during the winter 1981. The repair was achieved quickly and under traffic. The instrumentation carried out on the repairs and the tests run on the backfill material have revealed the action of the frost and its increase in the fortuitous presence of water

Collinear solution to the general relativistic three-body problem

The three-body problem is reexamined in the framework of general relativity. The Newtonian three-body problem admits Euler's collinear solution, where three bodies move around the common center of mass with the same orbital period and always line up. The solution is unstable. Hence it is unlikely that such a simple configuration would exist owing to general relativistic forces dependent not only on the masses but also on the velocity of each body. However, we show that the collinear solution remains true with a correction to the spatial separation between masses. Relativistic corrections to the Sun-Jupiter Lagrange points L1, L2 and L3 are also evaluated.Comment: 12 pages, 2 figures, accepted for publication in PR