New neighborhood based rough sets

Neighborhood based rough sets are important generalizations of the classical rough sets of Pawlak, as neighborhood operators generalize equivalence classes. In this article, we introduce nine neighborhood based operators and we study the partial order relations between twenty-two different neighborhood operators obtained from one covering. Seven neighborhood operators result in new rough set approximation operators. We study how these operators are related to the other fifteen neighborhood based approximation operators in terms of partial order relations, as well as to seven non-neighborhood-based rough set approximation operators

The Spin-Orbit Evolution of GJ 667C System: The Effect of Composition and Other Planet's Perturbations

Potentially habitable planets within the habitable zone of M-dwarfs are affected by tidal interaction. We studied the tidal evolution in GJ 667C using a numerical code we call TIDEV. We reviewed the problem of the dynamical evolution focusing on the effects that a rheological treatment, different compositions and the inclusion of orbital perturbations, have on the spin-down time and the probability to be trapped in a low spin-orbit resonance. Composition have a strong effect on the spin-down time, changing, in some cases, by almost a factor of 2 with respect to the value estimated for a reference Earth-like model. We calculated the time to reach a low resonance value (3:2) for the configuration of 6 planets. Capture probabilities are affected when assuming different compositions and eccentricities variations. We chose planets b and c to evaluate the probabilities of capture in resonances below 5:2 for two compositions: Earth-like and Waterworld planets. We found that perturbations, although having a secular effect on eccentricities, have a low impact on capture probabilities and noth- ing on spin-down times. The implications of the eccentricity variations and actual habitability of the GJ 667C system are discussed.Comment: 15 pages, 9 figures, 4 tables. Accepted for publication in MNRAS - V

Mass Exchange Dynamics of Surface and Subsurface Oil in Shallow-Water Transport

We formulate a model for the mass exchange between oil at and below the sea surface. This is a particularly important aspect of modeling oil spills. Surface and subsurface oil have different chemical and transport characteristics and lumping them together would compromise the accuracy of the resulting model. Without observational or computational constraints, it is thus not possible to quantitatively predict oil spills based upon partial field observations of surface and/or sub-surface oil. The primary challenge in capturing the mass exchange is that the principal mechanisms are on the microscale. This is a serious barrier to developing practical models for oil spills that are capable of addressing questions regarding the fate of oil at the large spatio-temporal scales, as demanded by environmental questions. We use upscaling to propose an environmental-scale model which incorporates the mass exchange between surface and subsurface oil due to oil droplet dynamics, buoyancy effects, and sea surface and subsurface mechanics. While the mass exchange mechanism detailed here is generally applicable to oil transport models, it addresses the modeling needs of a particular to an oil spill model [1]. This transport model is designed to capture oil spills at very large spatio-temporal scales. It accomplishes this goal by specializing to shallow-water environments, in which depth averaging is a perfectly good approximation for the flow, while at the same time retaining mass conservation of oil over the whole oceanic domain.Comment: 18 pages, 6 figure

Negative-Energy Perturbations in Circularly Cylindrical Equilibria within the Framework of Maxwell-Drift Kinetic Theory

The conditions for the existence of negative-energy perturbations (which could be nonlinearly unstable and cause anomalous transport) are investigated in the framework of linearized collisionless Maxwell-drift kinetic theory for the case of equilibria of magnetically confined, circularly cylindrical plasmas and vanishing initial field perturbations. For wave vectors with a non-vanishing component parallel to the magnetic field, the plane equilibrium conditions (derived by Throumoulopoulos and Pfirsch [Phys Rev. E {\bf 49}, 3290 (1994)]) are shown to remain valid, while the condition for perpendicular perturbations (which are found to be the most important modes) is modified. Consequently, besides the tokamak equilibrium regime in which the existence of negative-energy perturbations is related to the threshold value of 2/3 of the quantity $\eta_\nu = \frac {\partial \ln T_\nu} {\partial \ln N_\nu}$, a new regime appears, not present in plane equilibria, in which negative-energy perturbations exist for {\em any} value of $\eta_\nu$. For various analytic cold-ion tokamak equilibria a substantial fraction of thermal electrons are associated with negative-energy perturbations (active particles). In particular, for linearly stable equilibria of a paramagnetic plasma with flat electron temperature profile ($\eta_e=0$), the entire velocity space is occupied by active electrons. The part of the velocity space occupied by active particles increases from the center to the plasma edge and is larger in a paramagnetic plasma than in a diamagnetic plasma with the same pressure profile. It is also shown that, unlike in plane equilibria, negative-energy perturbations exist in force-free reversed-field pinch equilibria with a substantial fraction of active particles.Comment: 31 pages, late

Active galactic nuclei at z ~ 1.5: III. Accretion discs and black hole spin

This is the third paper in a series describing the spectroscopic properties of a sample of 39 AGN at $z \sim 1.5$, selected to cover a large range in black hole mass ($M_{BH}$) and Eddington ratio ($L/L_{Edd}$). In this paper, we continue the analysis of the VLT/X-shooter observations of our sample with the addition of 9 new sources. We use an improved Bayesian procedure, which takes into account intrinsic reddening, and improved $M_{BH}$ estimates, to fit thin accretion disc (AD) models to the observed spectra and constrain the spin parameter ($a_*$) of the central black holes. We can fit 37 out of 39 AGN with the thin AD model, and for those with satisfactory fits, we obtain constraints on the spin parameter of the BHs, with the constraints becoming generally less well defined with decreasing BH mass. Our spin parameter estimates range from $\sim$$-$0.6 to maximum spin for our sample, and our results are consistent with the "spin-up" scenario of BH spin evolution. We also discuss how the results of our analysis vary with the inclusion of non-simultaneous GALEX photometry in our thin AD fitting. Simultaneous spectra covering the rest-frame optical through far-UV are necessary to definitively test the thin AD theory and obtain the best constraints on the spin parameter.Comment: 17 pages, 10 figures, accepted for publication in MNRA

Collider signals of gravitino dark matter in bilinearly broken R-parity

In models with gauge mediated supersymmetry breaking the gravitino is the lightest supersymmetric particle. If R-parity is violated the gravitino decays, but with a half-live far exceeding the age of the universe and thus is, in principle, a candidate for the dark matter. We consider the decays of the next-to-lightest supersymmetric particle, assumed to be the neutralino. We show that in models where the breaking of R-parity is bilinear, the condition that R-parity violation explains correctly the measured neutrino masses fixes the branching ratio of the decay ${\tilde \chi}^0_1 \to {\tilde G}\gamma$ in the range $10^{-3}-10^{-2}$, if the gravitino mass is in the range required to solve the dark matter problem, i.e. of the order (few) 100 eV. This scenario is therefore directly testable at the next generation of colliders.Comment: 13 pages, 3 figure