On the Solution of Markov-switching Rational Expectations Models

This paper describes a method for solving a class of forward-looking Markov-switching Rational Expectations models under noisy measurement, by specifying the unobservable expectations component as a general-measurable function of the observable states of the system, to be determined optimally via stochastic control and filtering theory. Solution existence is proved by setting this function to the regime-dependent feedback control minimizing the mean-square deviation of the equilibrium path from the corresponding perfect-foresight autoregressive Markov jump state motion. As the exact expression of the conditional (rational) expectations term is derived both in finite and infinite horizon model formulations, no (asymptotic) stationarity assumptions are needed to solve forward the system, for only initial values knowledge is required. A simple sufficient condition for the mean-square stability of the obtained rational expectations equilibrium is also provided.Rational Expectations, Markov-switching dynamic systems, Dynamic programming, Time-varying Kalman filter

Energy transfer from the freshwater to the wastewater network using a PAT-equipped turbopump

A new strategy to increase the energy efficiency in a water network exists using turbo pumps, which are systems consisting of a pump and a turbine directly coupled on a same shaft. In a turbo pump, the pump is fed by a turbine that exploits a surplus head in a freshwater network in order to produce energy for one system (wastewater) and reduce the excess pressure in another (drinking water). A pump as turbine (PAT) may be preferred over a classic turbine here due to its lower cost. The result of such a coupling is a PAT-pump turbocharger (P&P). In this research, the theoretical performance of a P&P plant is employed using data from a real water distribution network to exploit the excess pressure of a freshwater stream and to feed a pump conveying wastewater toward a treatment plant. Therefore, the P&P plant is a mixed PAT-pump turbocharger, operating with both fresh and wastewater. A new method to perform a preliminary geometric selection of the machines constituting the P&P plant has been developed. Furthermore, the plant operation has been described by means of a new mathematical model under different boundary conditions. Moreover, the economic viability of the plant has been assessed by comparison with a conventional wastewater pumping system working in ON/OFF mode. Therefore, the net present value (NPV) of the investment has been evaluated in both situations for different time periods. According to the economical comparison, the PAT-pump turbocharger represents the most economically advantageous configuration, at least until the useful life of the plant. Such convenience amounts to 175% up to a time period equal to 20 years

Hydropower Potential inWater Distribution Networks: Pressure Control by PATs

Pressure control is one of the main techniques to control leakages in Water Distribution Networks (WDNs) and to prevent pipe damage, improving the delivery standards of a water supply systems. Pressure reducing stations (PRSs) equipped by either pressure reducing valves or motor driven regulating valves are commonly used to dissipate excess hydraulic head in WDNs. An integrated new technical solution with economic and system flexibility benefits is presented which replaces PRSs with pumps used as turbines (PATs). Optimal PAT performance is obtained by a Variable Operating Strategy (VOS), recently developed for the design of small hydropower plants on the basis of valve time operation, and net return determined by both energy production and savings through minimizing leakage. The literature values of both leakages costs and energy tariffs are used to develop a buisness plan model and evaluate the economic benefit of small hydropower plants equipped with PATs. The study shows that the hydropower installation produces interesting economic benefits, even in presence of small available power, that could encourage the leakage reduction even if water savings are not economically relevant, with consequent environmental benefits

Experimental results on the physical model of an USBR type II stilling basin

The present paper describes the experimental campaign carried on the physical model of the spillway of Lower Diamphwe Dam (Malawi), which is provided with a USBR type II stilling basin. Stilling basins are used in order to reduce the excessive kinetic energy of flowing water downstream of spillways. Specifically, a USBR type II basin is provided with blocks at the end of the chute and with a confining dentated sill; these appurtenances allow to dissipate excess energy with high efficiency. The study focuses on the hydraulic behavior of the stilling basin; tests were carried on for different values of incoming discharge and downstream water depth. Results show the dissipation efficiency of the stilling basin in terms of pressure fluctuation and the variability of the jump type with the hydraulic characteristics of the incoming and the downstream flow depths

Sustainable Water-Energy Nexus towards Developing Countries’ Water Sector Efficiency

Water management and energy recovery can improve a system’s sustainability and efficiency in a cost-effective solution. This research assesses the renewable energy sources used in the water sector, as well as the related water sector performance indicators within Portuguese water management systems. A deep analysis of 432 water entities in Portugal, based on ERSAR data base, was conducted in order to identify factors to be improved regarding the system efficiency. On the other hand, the potential energy recovery developed in the REDAWN project was also used as a reference for the application of micro hydropower (MHP) solutions in the water sector. A water and energy nexus model was then developed to improve the systems efficiency and sustainability. A real case study in Africa, the Nampula water supply system, located in Mozambique, was selected as a promising potential for energy recovery. The application of a pump-as-turbine (PAT) allows the reduction in system costs and environmental impacts while increasing its efficiency. The proposed MHP has a capacity to generate ~23 MWh/year, providing significant savings. The developed economic analysis indicates the project is profitable, with an IRR ~40% depending on the energy selling price. This project can avoid the emission of more than 12 tCO2 to the atmosphere, and it can help to reduce the system’s real losses by more than 10,000 m3/year. Consequently, it creates a total economic benefit of 7604 EUR/year

K-edge X-ray absorption spectra in transition metal oxides beyond the single particle approximation: shake-up many body effects

The near edge structure (XANES) in K-edge X-ray absorption spectroscopy (XAS) is a widely used tool for studying electronic and local structure in materials. The precise interpretation of these spectra with the help of calculations is hence of prime importance, especially for the study of correlated materials which have a complicated electronic structure per se. The single particle approach, for example, has generally limited itself to the dominant dipolar cross-section. It has long been known however that effects beyond this approach should be taken into account, both due to the inadequacy of such calculations when compared to experiment and the presence of shake-up many-body satellites in core-level photoemission spectra of correlated materials. This effect should manifest itself in XANES spectra and the question is firstly how to account for it theoretically and secondly how to verify it experimentally. By using state-of-the-art first principles electronic structure calculations and 1s photoemission measurements we demonstrate that shake-up many-body effects are present in K-edge XAS dipolar spectra of NiO, CoO and CuO at all energy scales. We show that shake-up effects can be included in K-edge XAS spectra in a simple way by convoluting the single-particle first-principles calculations including core-hole effects with the 1s photoemission spectra. We thus describe all features appearing in the XAS dipolar cross-section of NiO and CoO and obtain a dramatic improvement with respect to the single-particle calculation in CuO. These materials being prototype correlated magnetic oxides, our work points to the presence of shake-up effects in K-edge XANES of most correlated transition metal compounds and shows how to account for them, paving the way to a precise understanding of their electronic structure.Comment: 6 pages, 4 picture

¹⁴N overtone transition in double rotation solid-state NMR

Solid-state NMR transitions involving outer energy levels of the spin-1 14N nucleus are immune, to first order in perturbation theory, to the broadening caused by the nuclear quadrupole interaction. The corresponding overtone spectra, when acquired in conjunction with magic-angle sample spinning, result in lines, which are just a few kHz wide, permitting the direct detection of nitrogen compounds without the need for labeling. Despite the success of this technique, “overtone” resonances are still broadened due to indirect, second order effects arising from the large quadrupolar interaction. Here we demonstrate that another order of magnitude in spectral resolution may be gained by using double rotation. This brings the width of the 14N solid-state NMR lines much closer to the region commonly associated with high-resolution solid-state NMR spectroscopy of 15N and demonstrates the improvements in resolution that may be possible through the development of pulsed methodologies to suppress these second order effects

Infrared spectroscopy of small-molecule endofullerenes

Hydrogen is one of the few molecules which has been incarcerated in the molecular cage of C$_{60}$ and forms endohedral supramolecular complex H$_2$@C$_{60}$. In this confinement hydrogen acquires new properties. Its translational motion becomes quantized and is correlated with its rotations. We applied infrared spectroscopy to study the dynamics of hydrogen isotopologs H$_2$, D$_2$ and HD incarcerated in C$_{60}$. The translational and rotational modes appear as side bands to the hydrogen vibrational mode in the mid infrared part of the absorption spectrum. Because of the large mass difference of hydrogen and C$_{60}$ and the high symmetry of C$_{60}$ the problem is identical to a problem of a vibrating rotor moving in a three-dimensional spherical potential. The translational motion within the C$_{60}$ cavity breaks the inversion symmetry and induces optical activity of H$_2$. We derive potential, rotational, vibrational and dipole moment parameters from the analysis of the infrared absorption spectra. Our results were used to derive the parameters of a pairwise additive five-dimensional potential energy surface for H$_2$@C$_{60}$. The same parameters were used to predict H$_2$ energies inside C$_{70}$[Xu et al., J. Chem. Phys., {\bf 130}, 224306 (2009)]. We compare the predicted energies and the low temperature infrared absorption spectra of H$_2$@C$_{70}$.Comment: Updated author lis