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Using the method of breaking of circular symmetry and of subsequent symmetry restoration via projection techiques, we present calculations for the ground-state energies and excitation spectra of N -electron parabolic quantum dots in strong magnetic fields in the medium-size range 10 ≤ N ≤ 30. The physical picture suggested by our calculations is that of finite rotating electron molecules (REMs) comprising multiple rings, with the rings rotating independently of each other. An analytic expression for the energetics of such non-rigid multi-ring REMs is derived; it is applicable to arbitrary sizes given the corresponding equilibrium configuration of classical point charges. We show that the rotating electron molecules have a non-rigid (non-classical) rotational inertia exhibiting simultaneous crystalline correlations and liquid-like (non-rigidity) characteristics. This mixed phase appears in high magnetic fields and contrasts with the picture of a classical rigid Wigner crystal in the lowest Landau level.

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In the present work, the measured cetane numbers (CN) of pure fatty acid methyl esters (FAME), as well as the FAME compositions and the reported CN of 59 kinds of biodiesels collected from literature were used to develop a simple model involving as more FAME component as possible for predicting CN of biodiesel from its FAME composition. Two different regression equations correlating the CN of pure FAME with the carbon number of fatty acid chain were obtained by regression analysis, which shows that the dependence of the CN on the carbon number varies with the unsaturated degree of fatty acid chain. The 59 biodiesels were divided into two categories and used, respectively to develop and test a multiple linear regression model (MLRM) correlating the CN of biodiesel with its FAME composition. A simple and convenient regression equation with a high accuracy and a good reproducibility (average absolute error of 0.49 CN for testing set and 1.52 CN for all data) were developed, showing excellent correlation (R 2 : 0.9904 for testing set). The model developed in the present work can be used conveniently to give a satisfactory predicted CN of biodiesel from the FAME composition.

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Giant magnetostrictive actuators (GMAs) have received considerable attention in recent years and are becoming increasingly important in the exploitation of a new type electrohydraulic servovalve. In this paper, a deflector-jet servovalve (DJSV) using a giant magnetostrictive material (GMM) is developed for the first time, and the servovalve is mechanically less complex than a conventional DJSV. Next, a mathematical model of the GMM-based DJSV is built, which involves five submodels: a dynamic model of the power amplifier; a dynamic magnetization model of the GMM rod; a magnetoelastic model of the GMM rod; a kinetic model of the GMA; and a deflector-jet amplifier model. The experimental platform used for measuring the performance of the GMM-based DJSV is established, the prototype valve is fabricated, and the related unknown parameters are identified by experimental data from the GMA. Finally, a simulation and experimental research are performed on the GMM-based DJSV; the results indicate that the present GMM-based DJSV has a large output-pressure range, a rapid response, and a high bandwidth, which provides a competitive way to develop a new type of high-frequency and high-flow-rate electrohydraulic servovalve. Additionally, the measured characteristics of the prototype valve are in good agreement with the predicted results and demonstrate that the operational concept is viable, and the present mathematical model is reliable.

Exact-diagonalization calculations for N = 3 electrons in anisotropic quantum dots, covering a broad range of confinement anisotropies and strength of inter-electron repulsion, are presented for zero and low magnetic fields. The excitation spectra are analyzed as a function of the strength of the magnetic field and for increasing quantum-dot anisotropy. Analysis of the intrinsic structure of the many-body wave functions through spin-resolved two-point correlations reveals that the electrons tend to localize forming Wigner molecules. For certain ranges of dot parameters (mainly at strong anisotropy), the Wigner molecules acquire a linear geometry, and the associated wave functions with a spin projection Sz = 1/2 are similar to the representative class of strongly entangled states referred to as W -states. For other ranges of parameters (mainly at intermediate anisotropy), the Wigner molecules exhibit a more complex structure consisting of two mirror isosceles triangles. This latter structure can be viewed as an embryonic unit of a zig-zag Wigner crystal in quantum wires. The degree of entanglement in three-electron quantum dots can be quantified through the use of the von Neumann entropy.

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