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关键词： 绝缘栅双极型晶体管   结温   格林函数  

摘要： 车用电驱动系统的逆变器通常工作于复杂工况,因此需要对其瞬态结温进行实时预测。基于格林函数方法,在形式上推导出逆变器的绝缘栅双极型晶体管(IGBT)瞬时温升的解析模型,并采用数值仿真的方法,拟合得到模型所需的单位温度冷却函数和单位阶跃响应函数。最后通过电驱动系统逆变器IGBT结温试验,验证了该模型的有效性。所提模型兼具数值仿真方法的精确度以及解析模型的计算效率,因此适用于逆变器IGBT实时温升预测和热管理。

关键词： parabolic PDEs   nonlinear Laplace-type systems   finite element methods   space-time discretization   p-heat equation  

摘要： We study the parabolic p-Laplacian system in a bounded domain. We deduce optimal convergence rates for the space-time discretization based on an implicit Euler scheme in time. Our estimates are expressed in terms of Nikolskiii spaces and therefore cover situations when the (gradient of the) solution has only fractional derivatives in space and time. The main novelty is that, different to all previous results, we do not assume any coupling condition between the space and time resolutions h and tau. For this we show that the L-2-projection is compatible with the quasi-norm. The theoretical error analysis is complemented by numerical experiments.

关键词： sublinear p-Laplacian Hamiltonian systems   infinitely many solutions   variational methods  

摘要： We give a general and weak sufficient condition that is very close to a necessary and sufficient condition for the existence of a sequence of solutions converging to zero for the partial differential equations known as the p-Laplacian Hamiltonian systems. An application is also given to illustrate our main theoretical result.

关键词： electron–   phonon interaction   optical signals   quantum coherence   Rabi oscillations   semiconductor quantum dots  

摘要： Semiconductor quantum dots are solid state few-level systems which can interact strongly with light. As such, they can be used as a single photon source or to perform solid-state quantum-optics experiments. A major difference to atoms is the interaction with the lattice vibrations, that is, the phonons, which strongly affect the optical signals from a quantum dot. In this paper, we calculate the time-resolved pump-probe signals from a continuously driven quantum dot accounting for detuned excitation and electron-phonon interaction. We provide analytical equations giving insight into the different phenomena observed in the spectra like an oscillation between absorptive and dispersive line shapes. For detuned excitation, the electron-phonon interaction can lead to phonon-assisted occupation of the exciton, giving rise to a strong asymmetry in the dynamical behavior depending on the sign of the detuning. The time-resolved spectra monitor this relaxation path, which helps understanding the effect of electron-phonon interaction in quantum dots.

摘要： For the discretization of the integral fractional Laplacian (-Delta)(s), 0 < s < 1, based on piecewise linear functions, we present and analyze a reliable weighted residual a posteriori error estimator. In order to compensate for the lack of L-2-regularity of the residual in the regime 3/4 < s < 1, this weighted residual error estimator includes as an additional weight a power of the distance from the mesh skeleton. We prove optimal convergence rates for an h-adaptive algorithm driven by this error estimator. Key to the analysis of the adaptive algorithm are local inverse estimates for the fractional Laplacian.

关键词： Positive solution   Fractional differential equation   Mixed derivative   Delay   p-Laplacian operator  

摘要： In this work, a class of fractional delay differential equations with four-point boundary condition and p-Laplacian operator is discussed. Based on the Avery-Peterson theorem, the existence of at least triple positive solutions is derived. A simple example is given to show the validity of the conditions of our main theorem. (C) 2021 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： differential inclusion   fractional p(x)-Laplacian   non-local differential operator   pseudomonotone mapping  

摘要： In this paper, we establish a new abstract functional space X-K,X-p(center dot)(Omega) where K is a uncertain weighted function and p is a variable exponent. Based on the properties of this space, we consider the existence and regularity of weak solutions for non-local fractional differential inclusion with homogeneous Dirichlet boundary conditions. Under a suplinear growth condition we obtain the existence of weak solutions, the compactness and Holder regularity of the solution set using set-valued analysis and the surjectivity principle of pseudomonotonicity. Furthermore, the existence of extremal solutions and a relaxation result is discussed.

关键词： Abyssal circulation   Meridional overturning circulation   Ocean dynamics  

摘要： Although the reconfiguration of the abyssal overturning circulation has been argued to be a salient feature of Earth's past climate changes, our understanding of the physical mechanisms controlling its strength remains limited. In particular, existing scaling theories disagree on the relative importance of the dynamics in the Southern Ocean versus the dynamics in the basins to the north. In this study, we systematically investigate these theories and compare them with a set of numerical simulations generated from an ocean general circulation model with idealized geometry, designed to capture only the basic ingredients considered by the theories. It is shown that the disagreement between existing theories can be partially explained by the fact that the overturning strengths measured in the channel and in the basin scale distinctly with the external parameters, including surface buoyancy loss, diapycnal diffusivity, wind stress, and eddy diffusivity. The overturning in the reentrant channel, which represents the Southern Ocean, is found to be sensitive to all these parameters, in addition to a strong dependence on bottom topography. By contrast, the basin overturning varies with the integrated surface buoyancy loss rate and diapycnal diffusivity but is mostly unaffected by winds and channel topography. The simulated parameter dependence of the basin overturning can be described by a scaling theory that is based only on basin dynamics.

摘要： This thesis details experimental measurements performed on III-V semiconductor quantum dots, with the main body of work on nanohole GaAs/AlGaAs quantum dots. Through the use of optically detected nuclear magnetic resonance (NMR) and micro-photoluminescence, the components of the gradient elastic tensor, an important material parameter, are deter- mined for GaAs. These values are S 11, 69 Ga = (−22.2 ± 1.1) × 10 21 V m −2, S 11, 75 As = (23.9 ± 1.1) × 10 21 V m −2, with S 44 S 11 75 As being in the range of 1.20 to 2.36 and S 44 S 11 69 Ga being in the range of −0.88 to −0.11. These values are significantly different to that of the previous work, however, the ratio of the first components for the two nuclei, S 11, 69 Ga S 11, 75 As, is in close agreement with the previous work, with other derived material parameters being in agreement with the accepted values. The second component of the gradient elastic tensor, S 44, is found to be in close agreement for one nuclei, with a factor of 2 difference for the other nuclei. We conclude that the previous work had unrecognised systematic errors that impacted their results. We study two GaAs/AlGaAs samples with different barrier thicknesses, using NMR and micro-photoluminescence, and observe unexpected up-conversion and dynamic nuclear po- larisation phenomena in both samples, one of which was measured with and without ex- ternally applied stress. One of the unexpected phenomena, up-conversion, has its origin isolated to three potential impurities / defects in two possible locations in the sample. The other unexpected phenomena, relating to nuclear polarisation, are discussed in depth with their potential origins being presented. In addition to this, the fabrication of Schottky diodes for charge control of InGaAs quan- tum dot samples is detailed with the initial characterisation, through photoluminescence spectroscopy, being performed to identify the quantum dot states and charge plateaus.

关键词： Solid State Physics   Spectroscopy/Spectrometry   Atoms and Molecules in Strong Fields   Laser Matter Interaction   Physical Chemistry   Organic Chemistry  

摘要： Series expansion of the two-spin correlation functions is obtained in the context of the hybrid quantum-classical method of simulation of high-temperature spin dynamics. The resulting series are compared with the corresponding series for the exact correlation functions obtained from purely quantum dynamics.