Nuclear pairing from microscopic forces: singlet channels and higher-partial waves

Background: An accurate description of nuclear pairing gaps is extremely important for understanding static and dynamic properties of the inner crusts of neutron stars and to explain their cooling process. Purpose: We plan to study the behavior of the pairing gaps $\Delta_F$ as a function of the Fermi momentum $k_F$ for neutron and nuclear matter in all relevant angular momentum channels where superfluidity is believed to naturally emerge. The calculations will employ realistic chiral nucleon-nucleon potentials with the inclusion of three-body forces and self-energy effects. Methods: The superfluid states of neutron and nuclear matter are studied by solving the BCS gap equation for chiral nuclear potentials using the method suggested by Khodel et al., where the original gap equation is replaced by a coupled set of equations for the dimensionless gap function $\chi(p)$ defined by $\Delta(p) = \Delta_F \chi(p)$ and a non-linear algebraic equation for the gap magnitude $\Delta_F = \Delta(p_F)$ at the Fermi surface. This method is numerically stable even for small pairing gaps, such as that encountered in the coupled $^3PF_2$ partial wave. Results: We have successfully applied Khodel's method to singlet ($S$) and coupled channel ($SD$ and $PF$) cases in neutron and nuclear matter. Our calculations agree with other ab-initio approaches, where available, and provide crucial inputs for future applications in superfluid systems.Comment: 18 pages and 9 figure

Sum-Rate Analysis for High Altitude Platform (HAP) Drones with Tethered Balloon Relay

High altitude platform (HAP) drones can provide broadband wireless connectivity to ground users in rural areas by establishing line-of-sight (LoS) links and exploiting effective beamforming techniques. However, at high altitudes, acquiring the channel state information (CSI) for HAPs, which is a key component to perform beamforming, is challenging. In this paper, by exploiting an interference alignment (IA) technique, a novel method for achieving the maximum sum-rate in HAP-based communications without CSI is proposed. In particular, to realize IA, a multiple-antenna tethered balloon is used as a relay between multiple HAP drones and ground stations (GSs). Here, a multiple-input multiple-output X network system is considered. The capacity of the considered M*N X network with a tethered balloon relay is derived in closed-form. Simulation results corroborate the theoretical findings and show that the proposed approach yields the maximum sum-rate in multiple HAPs-GSs communications in absence of CSI. The results also show the existence of an optimal balloon's altitude for which the sum-rate is maximized.Comment: Accepted in IEEE Communications Letter

Fluvial dynamics and watermills location in Basilicata (Southern Italy)

Watermills (grain mills, waulk mills, olive mills, sawmills and threshing machines) operated in the Basilicata Region from the Roman Period until the early decades of the twentieth century, representing an important feature of waterways that is today almost totally forgotten. Using documentary sources, ancient maps and field survey it is possible to catalogue and identify the location of these ancient hydraulic structures. Watermills were usually placed far enough away from the river to avoid inundation during floods, and near natural knickpoints or artificial steps in the river long profile that were created by mill engineers. Mill construction often had significant impacts on a rivers morphology, because it was necessary to divert the river discharge towards the mill wheel, to drive the grain-grinding mechanism. Watermill typological variations have been examined in relation to variations in river pattern to assess the ways in which the hydrographic and hydrological settings of the Basilicata Region have affected mill siting and operation. Most Basilicata watermills were built with a horizontal water-wheel and a tower. The characteristics of the tower and the associated hydraulic structures varied according to the environmental setting. Finally, mill positions define also the locations on the river system that have already been used to exploit hydraulic power and thus could be useful for future use in the micro-hydroelectric secto

Preconditioning Kernel Matrices

The computational and storage complexity of kernel machines presents the primary barrier to their scaling to large, modern, datasets. A common way to tackle the scalability issue is to use the conjugate gradient algorithm, which relieves the constraints on both storage (the kernel matrix need not be stored) and computation (both stochastic gradients and parallelization can be used). Even so, conjugate gradient is not without its own issues: the conditioning of kernel matrices is often such that conjugate gradients will have poor convergence in practice. Preconditioning is a common approach to alleviating this issue. Here we propose preconditioned conjugate gradients for kernel machines, and develop a broad range of preconditioners particularly useful for kernel matrices. We describe a scalable approach to both solving kernel machines and learning their hyperparameters. We show this approach is exact in the limit of iterations and outperforms state-of-the-art approximations for a given computational budget

Dual-PEEC Modeling of a Two-Port TEM Cell for VHF Applications

Two-port TEM cells with rectangular cross section are commonly used to produce plane electromagnetic waves with high electric field. The non-uniform structure makes the use of numerical methods extremely useful in the design phase in order to achieve a very good behavior of the TEM cell over a wide frequency range of operation. In this paper an extended version of PEEC is used to study a real device and results are compared with experimental ones

Converting NAD83 GPS heights into NAVD88 elevations with LVGEOID, a hybrid geoid height model for the Long Valley volcanic region, California

A GPS survey of leveling benchmarks done in Long Valley Caldera in 1999 showed that the application of the National Geodetic Survey (NGS) geoid model GEOID99 to tie GPS heights to historical leveling measurements would significantly underestimate the caldera ground deformation (known from other geodetic measurements). The NGS geoid model was able to correctly reproduce the shape of the deformation, but required a local adjustment to give a realistic estimate of the magnitude of the uplift. In summer 2006, the U.S. Geological Survey conducted a new leveling survey along two major routes crossing the Long Valley region from north to south (Hwy 395) and from east to west (Hwy 203 – Benton Crossing). At the same time, 25 leveling bench marks were occupied with dual frequency GPS receivers to provide a measurement of the ellipsoid heights. Using the heights from these two surveys, we were able to compute a precise geoid height model (LVGEOID) for the Long Valley volcanic region. Our results show that although the LVGEOID and the latest NGS GEOID03 model practically coincide in areas outside the caldera, there is a difference of up to 0.2 m between the two models within the caldera. Accounting for this difference is critical when using the geoid height model to estimate the ground deformation due to magmatic or tectonic activity in the calder

The scale-free topology of market investments

We propose a network description of large market investments, where both stocks and shareholders are represented as vertices connected by weighted links corresponding to shareholdings. In this framework, the in-degree ($k_{in}$) and the sum of incoming link weights ($v$) of an investor correspond to the number of assets held (\emph{portfolio diversification}) and to the invested wealth (\emph{portfolio volume}) respectively. An empirical analysis of three different real markets reveals that the distributions of both $k_{in}$ and $v$ display power-law tails with exponents $\gamma$ and $\alpha$. Moreover, we find that $k_{in}$ scales as a power-law function of $v$ with an exponent $\beta$. Remarkably, despite the values of $\alpha$, $\beta$ and $\gamma$ differ across the three markets, they are always governed by the scaling relation $\beta=(1-\alpha)/(1-\gamma)$. We show that these empirical findings can be reproduced by a recent model relating the emergence of scale-free networks to an underlying Paretian distribution of `hidden' vertex properties.Comment: Final version accepted for publication on Physica