Non-averaged regularized formulations as an alternative to semi-analytical orbit propagation methods

This paper is concerned with the comparison of semi-analytical and non-averaged propagation methods for Earth satellite orbits. We analyse the total integration error for semi-analytical methods and propose a novel decomposition into dynamical, model truncation, short-periodic, and numerical error components. The first three are attributable to distinct approximations required by the method of averaging, which fundamentally limit the attainable accuracy. In contrast, numerical error, the only component present in non-averaged methods, can be significantly mitigated by employing adaptive numerical algorithms and regularized formulations of the equations of motion. We present a collection of non-averaged methods based on the integration of existing regularized formulations of the equations of motion through an adaptive solver. We implemented the collection in the orbit propagation code THALASSA, which we make publicly available, and we compared the non-averaged methods to the semi-analytical method implemented in the orbit propagation tool STELA through numerical tests involving long-term propagations (on the order of decades) of LEO, GTO, and high-altitude HEO orbits. For the test cases considered, regularized non-averaged methods were found to be up to two times slower than semi-analytical for the LEO orbit, to have comparable speed for the GTO, and to be ten times as fast for the HEO (for the same accuracy). We show for the first time that efficient implementations of non-averaged regularized formulations of the equations of motion, and especially of non-singular element methods, are attractive candidates for the long-term study of high-altitude and highly elliptical Earth satellite orbits.Comment: 33 pages, 10 figures, 7 tables. Part of the CMDA Topical Collection on "50 years of Celestial Mechanics and Dynamical Astronomy". Comments and feedback are encourage

Local Chern Marker for Periodic Systems

Topological invariants are global properties of the ground-state wave function, typically defined as winding numbers in reciprocal space. Over the years, a number of topological markers in real space have been introduced, allowing to map topological order in heterogeneous crystalline and disordered systems. Notably, even if these formulations can be expressed in terms of lattice-periodic quantities, they can actually be deployed in open boundary conditions only, as in practice they require computing the position operator $\mathbf{r}$ which is ill-defined in periodic boundary conditions. Here we derive a local Chern marker for infinite two-dimensional systems with periodic boundary conditions in the large supercell limit, where the electronic structure is sampled with one single point in reciprocal space. We validate our approach with tight-binding numerical simulations on the Haldane model, including trivial/topological superlattices made of pristine and disordered Chern insulators. The strategy introduced here is very general and could be applied to other topological invariants and geometrical quantities in any dimension.Comment: 6 pages, 3 figures + supplementary material (3 pages

Estimation of heterogeneous aquifer parameters using centralized and decentralized fusion of hydraulic tomography data

Characterization of spatial variability of hydraulic properties of groundwater systems at high resolution is essential to simulate flow and transport phenomena. This paper investigates two schemes to invert transient hydraulic head data resulting from multiple pumping tests for the purpose of estimating the spatial distributions of the hydraulic conductivity, K, and the specific storage, Ss, of an aquifer. The two methods are centralized fusion and decentralized fusion. The centralized fusion of transient data is achieved when data from all pumping tests are processed concurrently using a central inversion processor, whereas the decentralized fusion inverts data from each pumping test separately to obtain optimal local estimates of hydraulic parameters, which are consequently fused using the generalized Millman formula, an algorithm for merging multiple correlated or uncorrelated local estimates. For both data fusion schemes, the basic inversion processor employed is the ensemble Kalman filter, which is employed to assimilate the temporal moments of impulse response functions obtained from the transient hydraulic head measurements resulting from multiple pumping tests. Assimilating the temporal moments instead of the hydraulic head transient data themselves is shown to provide a significant improvement in computational efficiency. Additionally, different assimilation strategies to improve the estimation of Ss are investigated. Results show that estimation of the K and Ss distributions using temporal moment analysis is fairly good, and the centralized inversion scheme consistently outperforms the decentralized inversion scheme

Nonlinear Multi-Frequency Converter Array for Vibration Energy Harvesting in Autonomous Sensors☆

Abstract This work proposes and experimentally validates a vibration energy harvester which combines the multi-frequency and nonlinear approaches into a converter array. The converter array consists of four piezoelectric cantilevers composed of ferromagnetic substrates with screen-printed lead zirconate titanate (PZT) layers coupled with a single permanent magnet elastically suspended on the array base in order to create a nonlinear behaviour. The presence of a moving magnet and the possibility to realize cantilevers with different potential curves can be useful to obtain a collective nonlinear behaviour due to strong coupling irrespective of the amplitude of the mechanical excitation, therefore increasing the overall effectiveness of the converter array. The experimental results confirm that combining cantilevers with different potential curves can be useful to obtain a collective bistable behaviour, therefore increasing the overall effectiveness of the converter array

Sensors and energy harvesters based on piezoelectric thick films

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Il contratto di credito al consumo: evoluzione normativa

L'elaborato si concentra sull'evoluzione normativa che ha interessato il contratto di credito al consumo nel tempo. in particolare illustra la regolamentazione dei principali aspetti, si sofferma sulla disciplina inerente il costo complessivo del finanziamento e la determinazione dei TAEG e approfondisce l'obbligo di valutazione del merito del consumatoreope

Impact-Enhanced Multi-Beam Piezoelectric Converter for Energy Harvesting in Autonomous Sensors

AbstractThis work proposes and experimentally validates a piezoelectric vibration energy harvester, which exploits the impact of a central compliant driving beam onto two piezoelectric parallel bimorph beams on flexible steel. At suitable mechanical excitation conditions, the central driving beam impacts the piezo beams and triggers a nonlinear frequency-up conversion mechanism that improves the overall effectiveness, i.e. increases the overall rms output voltage and widens the equivalent bandwidth of the converter with respect to the condition of the noninteracting linear converters

Contactless electromagnetic switched interrogation of micromechanical cantilever resonators

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Piezoelectric Resonant Sensors with Contactless Interrogation for Mass-Sensitive and Acoustic-Load Detection

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Assessment of heat transfer and Mach number effects on high-speed turbulent boundary layers

High-speed vehicles experience a highly challenging environment in which the free-stream Mach number and surface temperature greatly influence aerodynamic drag and heat transfer. The interplay of these two parameters strongly affects the near-wall dynamics of high-speed turbulent boundary layers in a non-trivial way, breaking similarity arguments on velocity and temperature fields, typically derived for adiabatic cases. In this work, we present direct numerical simulations of flat-plate zero-pressure-gradient turbulent boundary layers spanning three free-stream Mach numbers [2,4,6] and four wall temperature conditions (from adiabatic to very cold walls), emphasising the choice of the diabatic parameter $\mathit{\Theta}$ (Zhang, Bi, Hussain & She, J. Fluid Mech., vol. 739, pp. 392-420) to recover a similar flow organisation at different Mach numbers. We link qualitative observations on flow patterns to first- and second-order statistics to explain the strong decoupling of temperature-velocity fluctuations that occurs at reduced wall temperatures and high Mach numbers. For these cases, we find that the mean temperature gradient in the near-wall region can reach such a strong intensity that it promotes the formation of a secondary peak of thermal production in the viscous sublayer, which is in direct contrast with the monotonic behaviour of adiabatic profiles. We propose different physical mechanisms induced by wall-cooling and compressibility that result in apparently similar flow features, such as a higher peak in the streamwise velocity turbulence intensity, and distinct ones, such as the separation of turbulent scales