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Introduction
Published in Srinivasan Chandrasekaran, Offshore Semi-Submersible Platform Engineering, 2020
The wind is usually separated into mean and dynamic components for analytical considerations. The mean wind velocity and associated dynamic components are always calculated over a particular period due to the variation of the wind velocity concerning space and time. From the spectral analysis of wind velocity time history over such an extended period, the energy spectrum of wind can be developed. The wind spectrum consists of short-period components due to gust, while the long-period component occurs due to the change in pressure. There is a spectral gap of about 360 s to 1.60 hours. It results from the lack of contribution from both wind gusts and pressure change. The pressure effect and the wind gusts change the wind velocity slowly and rapidly about the mean, respectively. An hour-average wind period is used for analysis, and the design wind speeds are usually specified by considering its return period. The commonly used wind spectra for offshore locations are the Kaimal spectrum and American Petroleum Institute (API) spectrum. The spectral density plot for a mean wind speed of 15 m/s and a period of 10 seconds is shown in Figure 1.6.
Quantum Algorithm for Sequence Clustering
Published in Siddhartha Bhattacharyya, Anirban Mukherjee, Indrajit Pan, Paramartha Dutta, Arup Kumar Bhaumik, Hybrid Intelligent Techniques for Pattern Analysis and Understanding, 2017
Arit Kumar Bishwas, Ashish Mani, Vasile Palade
In association with the process of adiabatic quantum computation, at first a ground state Hamiltonian is originated. The ground state of this Hamiltonian describes the solution to the problem in scope. Then a system with a simple Hamiltonian is prepared and initialized at ground state and allows this simple Hamiltonian to evolve, which results in a final required complicated Hamiltonian. And as per the adiabatic theorem, the system will remain in a ground state, and describes the solution to the problem in scope. The time complexity of the adiabatic quantum algorithms depends on the spectral gap in energy of the Hamiltonian. So to keep the system in ground state during evolution, the spectral gap gapmin should be very small. The run time of the quantum algorithm then can be considered to be bounded by O(1gapmin2).
Intersubband Transitions in GaP-AlP Heterostructures for Infrared Applications
Published in J Kono, J Léotin, Narrow Gap Semiconductors, 2006
M.P. Semtsiv, U. Müller, W.T. Masselink, N. Georgiev, T. Dekorsy, M. Helm
Mid- and far-infrared optoelectronic devices based on intersubband transitions in heterostructures can be made of wide-band-gap III-V materials, which often have better materials properties than narrow-gap semiconductors and have the advantage of being transparent outside of the transition region. Such intersubband devices (detectors, modulators, and lasers) have been demonstrated covering the 1-to-200 μm spectral range, where they compete successfully with narrow-gap semiconductor devices. In the case of the intersubband lasers, however, there is a “spectral gap” in the operation range between 30 and 60 μm. This gap is primarily due to difficulties emitting within the phonon absorption band in the widely-used InAs, InGaAs, and GaAs well materials. Lasers at these wavelengths need to be constructed of materials with higher-energy phonon bands. For instance, GaN-AlGaN intersubband laser designed for 34 and 38 μm were recently proposed [1] to be grown on a-plane and c-plane sapphire.
The coupled-cluster formalism – a mathematical perspective
Published in Molecular Physics, 2019
A. Laestadius, F. M. Faulstich
Mathematical analysis is a well-established part of many natural sciences. Plenty examples show how various fields benefit from mathematical rigor and that mathematical analysis can define a framework of the method's applicability. This work takes off from recent developments of local analyses of CC methods, including the single-reference CC, the extended CC, the tailored CC (TCC) and its special case the CC method tailored by tensor network states (TNS–TCC) [15–17,31,32]. In the spirit of Robert Parr's fundamental approach to quantum chemistry, which was honored during the 58th Sanibel Symposium, we here present some mathematical concepts used to analyse CC methods in a functional analytic framework. These yield rigorous analytical results that are independent of benchmarks and interpretations but rather based on mathematical assumptions. Adapting these assumptions to cover the computations performed in practice remains a challenge and is subject of future work. The local analysis puts as a sufficient – but not necessary – condition that the cluster amplitudes are small relative to other constants. We discuss a possible way out of this restriction motivated by the fact that CC calculations are known to work for large (single) amplitudes as well. We furthermore address the -diagnostic [33] and mathematically derive a more sophisticated strategy that includes all cluster amplitudes and offers a sufficient condition of a locally unique and quasi-optimal solution (after possibly rotating out the single amplitudes) rather than rejection based on just large single amplitudes. We furthermore complement the literature by a detailed discussion on spectral gap assumptions. In this context, spectrum refers to the point spectrum, i.e. the eigenvalues of relevant operators. Although a gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO–LUMO gap), or a spectral gap of the exact Hamiltonian (non-degenerate ground state), is crucial for the analysis, we highlight the importance of coercivity conditions, either for or the Fock operator . Additionally, we derive an optimal constant in the monotonicity proof of the CC function for the finite dimensional case, i.e. the projected CC theory. Comparing the CC Lagrangian with the extended CC formulation [31], we propose by means of the bivariational principle an alternative to measure the quality of the Lagrange multipliers, here interpreted as wave function parameters.