Universality of the self gravitational potential energy of any fundamental particle

Using the relation proposed by Weinberg in 1972, combining quantum and cosmological parameters, we prove that the self gravitational potential energy of any fundamental particle is a quantum, with physical properties independent of the mass of the particle. It is a universal quantum of gravitational energy, and its physical properties depend only on the cosmological scale factor R and the physical constants ℏ and c. We propose a modification of the Weinberg’s relation, keeping the same numerical value, but substituting the cosmological parameter H/c by 1/R.     

Galaxy–QSO correlation induced by weak gravitational lensing arising from large-scale structure

Observational evidence shows that gravitational lensing induces an angular correlation between the distribution of galaxies and much more distant QSOs. We use weak gravitational lensing theory to calculate this angular correlation, updating previous calculations and presenting new results exploring the dependence of the correlation on the large-scale structure. We study the dependence of the predictions on a variety of cosmological models, such as cold dark matter models, mixed dark matter models and models based on quintessence. We also study the dependence on the assumptions made about the nature of the primordial fluctuation spectrum: adiabatic, isocurvature and power spectra motivated by the cosmic string scenario are investigated. Special attention is paid to the issue of galaxy biasing, which is fully incorporated. We show that different mass power spectra imply distinct predictions for the angular correlation, and therefore the angular correlation provides an extra source of information about cosmological parameters and mechanisms of structure formation. We compare our results with observational data and discuss their potential uses. In particular, it is suggested that the observational determination of the galaxy–QSO correlation may be used to give an independent measurement of the mass power spectrum.     

The effects of Population III stars on the chemical and photometrical evolution of ellipticals

We have studied the effects of a hypothetical initial generation containing very massive stars [   M > 100 M_⊙  , pair-creation supernovae] on the chemical and photometric evolution of elliptical galaxies. To this purpose, we have computed the evolution of a typical elliptical galaxy with luminous mass of the order of  10¹¹ M_⊙  and adopted chemical evolution models already tested to reproduce the main features of ellipticals. We have tested several sets of yields for very massive zero-metallicity stars: these stars should produce quite different amounts of heavy elements than lower-mass stars. We found that the effects of Population III stars on the chemical enrichment is negligible if only one or two generations of such stars occurred, whereas they produce quite different results from the standard models if they continuously formed for a period not shorter than 0.1 Gyr. In this case, the results are at variance with the main observational constraints of ellipticals such as the average  [〈α/ Fe〉_*]  ratio in stars and the integrated colours. Therefore, we conclude that if Population III stars ever existed they must have been present for a very short period of time and their effects on the following evolution of the parent galaxy must have been negligible. This effect is minimum if a more realistic model with initial infall of gas rather than the classic monolithic model is adopted. Ultimately, we conclude that there is no need to invoke a generation of very massive stars in ellipticals to explain their chemical and photometric properties.     

Orbital Elements of 2004 Perseid Meteoroids Perturbed by Jupiter

Jupiter and Saturn produce important gravitational impulses on meteoroids released by comet 109P/Swift-Tuttle. The meteoroids from this comet once released follow retrograde orbits that during their periodic approaches to these planets (within 1.6 and 0.9 A.U., respectively) are impulsed gaining orbital energy. This perturbation effect is translated into a net inward shift in the node of the perturbed meteoroids. Such geometry with Jupiter occurred in 2004 over a meteoroid trail ejected by this comet during the 1862 A.D. return of the comet to perihelion. In order to study the predicted outburst produced by one-revolution meteoroids, the Spanish Photographic Meteor Network (SPMN) performed an extensive campaign. As a part of this observational effort here are presented 10 accurate meteoroid orbits. We discuss their origin by comparing them with the theoretical orbital elements of the dust trails intercepting the Earth during the 2004 Perseid return.     

Periodic Behavior and Stochastic Fluctuations of Solar Activity: Proper Orthogonal Decomposition Analysis

We use the Proper Orthogonal Decomposition (POD) to investigate the spatiotemporal features of the solar activity. Daily observation in the period 1949–1996 of the green coronal emission line at 530.3 nm are used as indicators of the activity behavior. We show that few POD modes suffice in describing both the space and time main periodicities. In particular, being affected by a strongly energetic stochastic behavior, daily data are described by five POD modes, while two POD modes are enough to describe the butterfly diagram in monthly averaged data. Apart from the basic period T₀ = 11 years, using daily data we found evidences for intercycle temporal periodicities.     

Contrasting interactions of sodium and potassium with H<Subscript>2</Subscript>O in haplogranitic liquids and glasses at 200 MPa from hydration–diffusion experiments

This study examines hydration–diffusion in the metaluminous haplogranite system at 200 MPa H₂O and 800–300°C. At 800°C hydration is accompanied by melting and uphill diffusion of sodium from anhydrous glass toward the region of hydration and melting, whereas potassium diffuses away from the hydration front and into anhydrous glass. Silicon and aluminum are simply diluted upon hydration. There is no change in molecular Al/(Na + K) throughout the entire hydration-diffusion aureole and, therefore, (1) there is no loss of alkalis to the vapor, and (2) K migrates to replace Na in order to maintain local charge balance required by ^IVAl. Alkali diffusion occurs over a viscosity contrast from 10^4.1 Pa s in hydrous liquid to 10^11.8–10^13.5 Pa s in anhydrous glass. From these results, we interpret that: (1) Na is structurally or energetically favored over K as a charge-balancing cation for ^IVAl in hydrous granitic liquids, whereas the opposite behavior has been observed for anhydrous melts, and (2) the diffusion of alkalis through silicate melts is largely independent of viscosity. Results from 600°C are similar to those at 800°C, but hydration at 300°C involves a loss of Na and concomitant increase in molar Al/(Na + K) in the hydration zone due to hydrogen-alkali exchange between fluid and glass. Hydration behavior at 400°C is transitional between those at 300°C and 600°C, suggesting that the change in hydration mechanism occurs near the glass transition.     

Experiments on the kinetics of partial melting of a leucogranite at 200 MPa H<Subscript>2</Subscript>O and 690–800°C: compositional variability of melts during the onset of H<Subscript>2</Subscript>O-saturated crustal anatexis

We have experimentally investigated the kinetics of melting of an aplitic leucogranite (quartz+sodic plagioclase of ≈Ab₉₀+K-feldspar+traces of biotite) at 690, 740, and 800°C, all at 200 MPa H₂O. Leucogranite cylinders, 3.5 mm in diameter and 7 mm in length, were run in the presence of excess H₂O using cold-seal pressure vessels for 11–2,925 h. At 690 and 740°C and any experimental time, and 800°C and short run times, silicate glass (melt at run conditions) occurs as interconnected films along most of the mineral boundaries and in fractures, with the predominant volume occurring along quartz/feldspars boundaries and quartz/plagioclase/K-feldspar triple junctions. Glass film thickness is roughly constant throughout a given experimental charge and increases with experimental temperature and run duration. The results indicate that H₂O-saturated partial melting of a quartzo-feldspathic protolith will produce an interconnected melt phase even at very low degrees (<5 vol%) of partial melting. Crystal grain boundaries are therefore completely occluded with melt films even at the lowest degrees of partial melting, resulting in a change in the mechanism of mass transport through the rock from advection of aqueous vapor to diffusion through silicate melt. At 690 and 740°C the compositions of glasses are homogeneous and (at both temperatures) close to, but not on, the H₂O-saturated 200 MPa haplogranite eutectic; glass compositions do not change with run duration. At 800°C glasses are heterogeneous and plot away from the minimum, although their molar ratios ASI (=mol Al₂O₃/CaO+Na₂O+K₂O) and Al/Na are constant throughout the entire charge at any experimental time. Glass compositions within individual 800°C experiments form linear trends in (wt%) normative quartz–albite–orthoclase space. The linear trends are oriented perpendicular to the 200 MPa H₂O haplogranite cotectic line, reflecting nearly constant albite/orthoclase ratio versus variable quartz/feldspar ratio, and have endpoints between the 800°C isotherms on the quartz and feldspar liquidus surfaces. With increasing experimental duration the trends migrate from the potassic side of the minimum toward the bulk rock composition located on the sodic side, due to more rapid (and complete) dissolution of K-feldspar relative to plagioclase. The results indicate that partial melting at or slightly above the solidus (690–740°C) is interface reaction-controlled, and produces disequilibrium melts of near-minimum composition that persist metastably for up to at least 3 months. Relict feldspars show no change in composition or texture, and equilibration between melt and feldspars might take from a few to tens of millions of years. Partial melting at temperatures well above the solidus (800°C) produces heterogeneous, disequilibrium liquids whose compositions are determined by the diffusive transport properties of the melt and local equilibrium with neighboring mineral phases. Feldspars recrystallize and change composition rapidly. Partial melting and equilibration between liquids and feldspars might take from a few to tens of years (H₂O-saturated conditions) at these temperatures well above the solidus.     

Quantitative perturbation theory by successive elimination of harmonics

We revisit some results of perturbation theories by a method of successive elimination of harmonics inspired by some ideas of Delaunay. On the one hand, we give a connection between the KAM theorem and the Nekhoroshev theorem. On the other hand, we support in a quantitative fashion a semi-numerical method of analysis of a perturbed system recently introduced by one of the authors.     

Classical constructive methods in KAM theory

Two methods for constructing quasiperiodic solutions as expansion in a small parameter are discussed. The first one is the classical Lindstedt's method; the second one an algorithm based on Kolmogorov's paper (Kolmogorov, 1954). Besides a complete formulation of the algorithms, an overview of the main ideas leading to the proof of convergence of the expansions is given. Some comparison is also made, including in particular the analysis of the effectiveness of the algorithms.