On the analytic solution of the pairing problem: one pair in many levels

We search for approximate, but analytic solutions of the pairing problem for one pair of nucleons in many levels of a potential well. For the collective energy a general formula, independent of the details of the single particle spectrum, is given in both the strong and weak coupling regimes. Next the displacements of the solutions trapped in between the single particle levels with respect to the unperturbed energies are explored: their dependence upon a suitably defined quantum number is found to undergo a transition between two different regimes.Comment: 30 pages, AMS Latex, 8 figures. Submitted to Phys. Rev.

Two-functional seal for hose connection

Seal, machined from a plastic material, prevents liquid hydrogen leakage from hose connectors. It serves as a block-type seal supporting maximum loading of the poppet with slight elastic deflection or as a lip-type seal that is deformed elastically in bending, tension, or compression by the seated poppet

Solar array subsystems study

The effects on life cycle costs of a number of technology areas are examined for a LEO, 500 kW solar array. A baseline system conceptual design is developed and the life cycle costs estimated in detail. The baseline system requirements and design technologies are then varied and their relationships to life cycle costs quantified. For example, the thermal characteristics of the baseline design are determined by the array materials and masses. The thermal characteristics in turn determine configuration, performance and hence life cycle cost

Arc Phenomena in low-voltage current limiting circuit breakers

Circuit breakers are an important safety feature in most electrical circuits, and they act to prevent excessive currents caused by short circuits, for example. Low-voltage current limiting circuit breakers are activated by a trip solenoid when a critical current is exceeded. The solenoid moves two contacts apart to break the circuit. However, as soon as the contacts are separated an electric arc forms between them, ionising the air in the gap, increasing the electrical conductivity of air to that of the hot plasma that forms, and current continues to flow. The currents involved may be as large as 80,000 amperes. Critical to the success of the circuit breaker is that it is designed to cause the arc to move away from the contacts, into a widening wedge-shaped region. This lengthens the arc, and then moves it onto a series of separator plates called an arc divider or splitter. The arc divider raises the voltage required to sustain the arcs across it, above the voltage that is provided across the breaker, so that the circuit is broken and the arcing dies away. This entire process occurs in milliseconds, and is usually associated with a sound like an explosion and a bright ash from the arc. Parts of the contacts and the arc divider may melt and/or vapourise. The question to be addressed by the Study Group was to mathematically model the arc motion and extinction, with the overall aim of an improved understanding that would help the design of a better circuit breaker. Further discussion indicated that two key mechanisms are believed to contribute to the movement of the arc away from the contacts, one being self-magnetism (where the magnetic field associated with the arc and surrounding circuitry acts to push it towards the arc divider), and the other being air flow (where expansion of air combined with the design of the chamber enclosing the arc causes gas flow towards the arc divider). Further discussion also indicated that a key aspect of circuit breaker design was that it is desirable to have as fast a quenching of the arc as possible, that is, the faster the circuit breaker can act to stop current flow, the better. The relative importance of magnetic and air pressure effects on quenching speed is of central interest to circuit design

The many levels pairing Hamiltonian for two pairs

We address the problem of two pairs of fermions living on an arbitrary number of single particle levels of a potential well (mean field) and interacting through a pairing force. The associated solutions of the Richardson's equations are classified in terms of a number $v_l$, which reduces to the seniority $v$ in the limit of large values of the pairing strength $G$ and yields the number of pairs not developing a collective behaviour, their energy remaining finite in the $G\to\infty$ limit. We express analytically, through the moments of the single particle levels distribution, the collective mode energy and the two critical values $G_{\rm cr}^{+}$ and $G_{\rm cr}^{-}$ of the coupling which can exist on a single particle level with no pair degeneracy. Notably $G_{\rm cr}^{+}$ and $G_{\rm cr}^{-}$ merge when the number of single particle levels goes to infinity, where they coincide with the $G_{\rm cr}$ (when it exists) of a one pair system, not envisioned by the Richardson theory. In correspondence of $G_{\rm cr}$ the system undergoes a transition from a mean field to a pairing dominated regime. We finally explore the behaviour of the excitation energies, wave functions and pair transfer amplitudes finding out that the former, for $G>G_{\rm cr}^{-}$, come close to the BCS predictions, whereas the latter display a divergence at $G_{\rm cr}$, signaling the onset of a long range off-diagonal order in the system.Comment: 35 pages, 6 figures, 2 tables, to be published in EPJ

First record of an Odontaspidid shark in Ascension Island waters

The occurrence of the poorly understood shark species Odontapsis ferox is reported at an oceanic seamount in the central south Atlantic, within the Exclusive Economic Zone of Ascension Island. The presence of the species at this location is confirmed by the discovery of a tooth embedded in scientific equipment, and footage of at least one animal on autonomous underwater video. The new record of this shark species at this location demonstrates the knowledge gaps which still exist at many remote, oceanic structures and their candidacy for status as important conservation areas.info:eu-repo/semantics/publishedVersio

Simultaneous Inference of User Representations and Trust

Inferring trust relations between social media users is critical for a number of applications wherein users seek credible information. The fact that available trust relations are scarce and skewed makes trust prediction a challenging task. To the best of our knowledge, this is the first work on exploring representation learning for trust prediction. We propose an approach that uses only a small amount of binary user-user trust relations to simultaneously learn user embeddings and a model to predict trust between user pairs. We empirically demonstrate that for trust prediction, our approach outperforms classifier-based approaches which use state-of-the-art representation learning methods like DeepWalk and LINE as features. We also conduct experiments which use embeddings pre-trained with DeepWalk and LINE each as an input to our model, resulting in further performance improvement. Experiments with a dataset of $\sim$356K user pairs show that the proposed method can obtain an high F-score of 92.65%.Comment: To appear in the proceedings of ASONAM'17. Please cite that versio

Perturbation theorems for Hele-Shaw flows and their applications

In this work, we give a perturbation theorem for strong polynomial solutions to the zero surface tension Hele-Shaw equation driven by injection or suction, so called the Polubarinova-Galin equation. This theorem enables us to explore properties of solutions with initial functions close to but are not polynomial. Applications of this theorem are given in the suction or injection case. In the former case, we show that if the initial domain is close to a disk, most of fluid will be sucked before the strong solution blows up. In the later case, we obtain precise large-time rescaling behaviors for large data to Hele-Shaw flows in terms of invariant Richardson complex moments. This rescaling behavior result generalizes a recent result regarding large-time rescaling behavior for small data in terms of moments. As a byproduct of a theorem in this paper, a short proof of existence and uniqueness of strong solutions to the Polubarinova-Galin equation is given.Comment: 25 page

The case for a wet, warm climate on early Mars

Arguments are presented in support of the idea that Mars possessed a dense CO2 atmosphere and a wet, warm climate early in its history. The plausibility of a CO2 greenhouse is tested by formulating a simple model of the CO2 geochemical cycle on early Mars. By scaling the rate of silicate weathering on Earth, researchers estimated a weathering time constant of the order of several times 10 to the 7th power years for early Mars. Thus, a dense atmosphere could have existed for a geologically significant time period (approx. 10 to the 9th power years) only if atmospheric CO2 was being continuously resupplied. The most likely mechanism by which this could have been accomplished is the thermal decomposition of carbonate rocks induced directly or indirectly by intense, global scale volcanism