Ab initio study of anharmonicity in high pressure Cmca-4 metallic hydrogen

Hydrogen is the only atom for which the Schr odinger equation is solvable. Consisting only of a proton and an electron, hydrogen is the lightest element and, nevertheless, is far from being simple. Under ambient conditions, it forms diatomic molecules H2 in gas phase, but di erent temperature and pressures lead to a complex phase diagram, which is not completely known yet. Solid hydrogen was rst documented in 1899 [1] and was found to be isolating. At higher pressures, however, hydrogen can be metallized. In 1935 Wigner and Huntington predicted that the metallization pressure would be 25 GPa [2], where molecules would disociate to form a monoatomic metal, as alkali metals that lie below hydrogen in the periodic table. The prediction of the metallization pressure turned out to be wrong: metallic hydrogen has not been found yet, even under a pressure as high as 320 GPa. Nevertheless, extrapolations based on optical measurements suggest that a metallic phase may be attained at 450 GPa [3]. The interest of material scientist in metallic hydrogen can be attributed, at least to a great extent, to Ashcroft, who in 1968 suggested that such a system could be a hightemperature superconductor [4]. The temperature at which this material would exhibit a transition from a superconducting to a non-superconducting state (Tc) was estimated to be around room temperature. The implications of such a statement are very interesting in the eld of astrophysics: in planets that contain a big quantity of hydrogen and whose temperature is below Tc, superconducting hydrogen may be found, specially at the center, where the gravitational pressure is high. This might be the case of Jupiter, whose proportion of hydrogen is about 90%. There are also speculations suggesting that the high magnetic eld of Jupiter is due to persistent currents related to the superconducting phase [5]. Metallization and superconductivity of hydrogen has puzzled scientists for decades, and the community is trying to answer several questions. For instance, what is the structure of hydrogen at very high pressures? Or a more general one: what is the maximum Tc a phonon-mediated superconductor can have [6]? A great experimental e ort has been carried out pursuing metallic hydrogen and trying to answer the questions above; however, the characterization of solid phases of hydrogen is a hard task. Achieving the high pressures needed to get the sought phases requires advanced technologies. Diamond anvil cells (DAC) are commonly used devices. These devices consist of two diamonds with a tip of small area; for this reason, when a force is applied, the pressure exerted is very big. This pressure is uniaxial, but it can be turned into hydrostatic pressure using transmitting media. Nowadays, this method makes it possible to reach pressures higher than 300 GPa, but even at this pressure hydrogen does not show metallic properties. A recently developed technique that is an improvement of DAC can reach pressures as high as 600 GPa [7], so it is a promising step forward in high pressure physics. Another drawback is that the electronic density of the structures is so low that X-ray di raction patterns have low resolution. For these reasons, ab initio studies are an important source of knowledge in this eld, within their limitations. When treating hydrogen, there are many subtleties in the calculations: as the atoms are so light, the ions forming the crystalline lattice have signi cant displacements even when temperatures are very low, and even at T=0 K, due to Heisenberg's uncertainty principle. Thus, the energy corresponding to this zero-point (ZP) motion is signi cant and has to be included in an accurate determination of the most stable phase. This has been done including ZP vibrational energies within the harmonic approximation for a range of pressures and at T=0 K, giving rise to a series of structures that are stable in their respective pressure ranges [8]. Very recently, a treatment of the phases of hydrogen that includes anharmonicity in ZP energies has suggested that relative stability of the phases may change with respect to the calculations within the harmonic approximation [9]. Many of the proposed structures for solid hydrogen have been investigated. Particularly, the Cmca-4 structure, which was found to be the stable one from 385-490 GPa [8], is metallic. Calculations for this structure, within the harmonic approximation for the ionic motion, predict a Tc up to 242 K at 450 GPa [10]. Nonetheless, due to the big ionic displacements, the harmonic approximation may not su ce to describe correctly the system. The aim of this work is to apply a recently developed method to treat anharmonicity, the stochastic self-consistent harmonic approximation (SSCHA) [11], to Cmca-4 metallic hydrogen. This way, we will be able to study the e ects of anharmonicity in the phonon spectrum and to try to understand the changes it may provoque in the value of Tc. The work is structured as follows. First we present the theoretical basis of the calculations: Density Functional Theory (DFT) for the electronic calculations, phonons in the harmonic approximation and the SSCHA. Then we apply these methods to Cmca-4 hydrogen and we discuss the results obtained. In the last chapter we draw some conclusions and propose possible future work.

A Real-Time Sliding Mode Control for a Wind Energy System Based on a Doubly Fed Induction Generator

In this paper, a real time sliding mode control scheme for a variable speed wind turbine that incorporates a doubly feed induction generator is described. In this design, the so-called vector control theory is applied, in order to simplify the system electrical equations. The proposed control scheme involves a low computational cost and therefore can be implemented in real-time applications using a low cost Digital Signal Processor (DSP). The stability analysis of the proposed sliding mode controller under disturbances and parameter uncertainties is provided using the Lyapunov stability theory. A new experimental platform has been designed and constructed in order to analyze the real-time performance of the proposed controller in a real system. Finally, the experimental validation carried out in the experimental platform shows; on the one hand that the proposed controller provides high-performance dynamic characteristics, and on the other hand that this scheme is robust with respect to the uncertainties that usually appear in the real systems.

Estimating reflectivity values from wind turbines for analyzing the potential impact on weather radar services

Locate full-text(opens in a new window)|View at Publisher| Export | Download | More... Atmospheric Measurement Techniques Volume 8, Issue 5, 27 May 2015, Pages 2183-2193 Estimating reflectivity values from wind turbines for analyzing the potential impact on weather radar services (Article) Angulo, I.a, Grande, O.a, Jenn, D.b, Guerra, D.a, De La Vega, D.a a University of the Basque Country (UPV/EHU), Bilbao, Spain b Naval Postgraduate School, Monterey, United States View references (28) Abstract The World Meteorological Organization (WMO) has repeatedly expressed concern over the increasing number of impact cases of wind turbine farms on weather radars. Current signal processing techniques to mitigate wind turbine clutter (WTC) are scarce, so the most practical approach to this issue is the assessment of the potential interference from a wind farm before it is installed. To do so, and in order to obtain a WTC reflectivity model, it is crucial to estimate the radar cross section (RCS) of the wind turbines to be built, which represents the power percentage of the radar signal that is backscattered to the radar receiver.

For the proposed model, a representative scenario has been chosen in which both the weather radar and the wind farm are placed on clear areas; i.e., wind turbines are supposed to be illuminated only by the lowest elevation angles of the radar beam.

This paper first characterizes the RCS of wind turbines in the weather radar frequency bands by means of computer simulations based on the physical optics theory and then proposes a simplified model to estimate wind turbine RCS values. This model is of great help in the evaluation of the potential impact of a certain wind farm on the weather radar operation.

Pitch Based Wind Turbine Intelligent Speed Setpoint Adjustment Algorithms

This work is aimed at optimizing the wind turbine rotor speed setpoint algorithm. Several intelligent adjustment strategies have been investigated in order to improve a reward function that takes into account the power captured from the wind and the turbine speed error. After different approaches including Reinforcement Learning, the best results were obtained using a Particle Swarm Optimization (PSO)-based wind turbine speed setpoint algorithm. A reward improvement of up to 10.67% has been achieved using PSO compared to a constant approach and 0.48% compared to a conventional approach. We conclude that the pitch angle is the most adequate input variable for the turbine speed setpoint algorithm compared to others such as rotor speed, or rotor angular acceleration.

Valuation of Wind Energy Projects: A Real Options Approach

We address the valuation of an operating wind farm and the finite-lived option to invest in it under different reward/support schemes: a constant feed-in tariff, a premium on top of the electricity market price (either a fixed premium or a variable subsidy such as a renewable obligation certificate or ROC), and a transitory subsidy, among others. Futures contracts on electricity with ever longer maturities enable market-based valuations to be undertaken. The model considers up to three sources of uncertainty: the electricity price, the level of wind generation, and the certificate (ROC) price where appropriate. When analytical solutions are lacking, we resort to a trinomial lattice combined with Monte Carlo simulation; we also use a two-dimensional binomial lattice when uncertainty in the ROC price is considered. Our data set refers to the UK. The numerical results show the impact of several factors involved in the decision to invest: the subsidy per MWh generated, the initial lump-sum subsidy, the maturity of the investment option, and electricity price volatility. Different combinations of variables can help bring forward investments in wind generation. One-off policies, e.g., a transitory initial subsidy, seem to have a stronger effect than a fixed premium per MWh produced.

Simplified Formulae for the Estimation of Offshore Wind Turbines Clutter on Marine Radars

The potential impact that offshore wind farms may cause on nearby marine radars should be considered before the wind farm is installed. Strong radar echoes from the turbines may degrade radars' detection capability in the area around the wind farm. Although conventional computational methods provide accurate results of scattering by wind turbines, they are not directly implementable in software tools that can be used to conduct the impact studies. This paper proposes a simple model to assess the clutter that wind turbines may generate on marine radars. This method can be easily implemented in the system modeling software tools for the impact analysis of a wind farm in a real scenario.

Aspects of quality control of wind profiler measurements in complex topography

It is well known in the scientific community that some remote sensing instruments assume that sample volumes present homogeneous conditions within a defined meteorological profile. At complex topographic sites and under extreme meteorological conditions, this assumption may be fallible depending on the site, and it is more likely to fail in the lower layers of the atmosphere. This piece of work tests the homogeneity of the wind field over a boundary layer wind profiler radar located in complex terrain on the coast under different meteorological conditions. The results reveal the qualitative importance of being aware of deviations in this homogeneity assumption and evaluate its effect on the final product. Patterns of behavior in data have been identified in order to simplify the analysis of the complex signal registered. The quality information obtained from the homogeneity study under different meteorological conditions provides useful indicators for the best alternatives the system can offer to build wind profiles. Finally, the results are also to be considered in order to integrate them in a quality algorithm implemented at the product level.