Magneto-optics of zero-dimensional electron systems

Photoluminescence spectroscopy has been used to probe the occupied electron states below the Fermi energy of zero-dimensional electron systems (0DESs) in both zero and finite magnetic fields. The arrays of modulation-doped quantum dots investigated were fabricated by both reactive-ion etching and strain-confining GaAs heterojunctions with a -layer of Be present in the GaAs, in order to improve luminescence efficiency. For the etched quantum dots we show that the low magnetic field dispersion T) of the acceptor recombination line is directly related to the magnetic field dependence of the total ground-state energy of interacting electrons in the quantum dots. For the strain-confined 0DESs we have mapped the magneto-dispersion of the quantum confined electron states to reveal 15 electrons per dot.     

Rashba spin-splitting in narrow gap III–V semiconductor quantum wells

Using Kane's 8-band k·p theory and the envelope function approximation we derive a tight binding Hamiltonian for III–V semiconductor quantum well structures, which accurately models band structure and spin–orbit coupling. By applying a potential difference across the well we have calculated the Rashba spin-splitting in the lowest conduction subband. For identical well widths the Rashba splitting in InSb is shown to be approximately twice that of InAs and, in all cases, passes through a weak maximum with increasing quasimomentum.     

Asymptotics for logical limit laws: When the growth of the components is in an RT class

Compton's method of proving monadic second-order limit laws is based on analyzing the generating function of a class of finite structures. For applications of his deeper results we previously relied on asymptotics obtained using Cauchy's integral formula. In this paper we develop elementary techniques, based on a Tauberian theorem of Schur, that significantly extend the classes of structures for which we know that Compton's theory can be applied.

     

Economic Fluctuations and Statistical Physics: The Puzzle of Large Fluctuations

We present an overview of recent research applying ideas of statistical physics to try to better understand puzzles regarding economic fluctuations. One of these puzzles is how to describe outliers, phenomena that lie outside of patterns of statistical regularity. We review evidence consistent with the possibility that such outliers may not exist. This possibility is supported by recent analysis of a database containing the bid, ask, and sale price of each trade of every stock. Further, the data support the picture of economic fluctuations, due to Plerou et al., in which a financial market alternates between being in an “equilibrium phase” where market behavior is split roughly equally between buying and selling, and an “out-of-equilibrium phase” where the market is mainly either buying or selling.     

Understanding the Variability in Graph Data Sets through Statistical Modeling on the Stiefel Manifold

Network analysis provides a rich framework to model complex phenomena, such as human brain connectivity. It has proven efficient to understand their natural properties and design predictive models. In this paper, we study the variability within groups of networks, i.e., the structure of connection similarities and differences across a set of networks. We propose a statistical framework to model these variations based on manifold-valued latent factors. Each network adjacency matrix is decomposed as a weighted sum of matrix patterns with rank one. Each pattern is described as a random perturbation of a dictionary element. As a hierarchical statistical model, it enables the analysis of heterogeneous populations of adjacency matrices using mixtures. Our framework can also be used to infer the weight of missing edges. We estimate the parameters of the model using an Expectation-Maximization-based algorithm. Experimenting on synthetic data, we show that the algorithm is able to accurately estimate the latent structure in both low and high dimensions. We apply our model on a large data set of functional brain connectivity matrices from the UK Biobank. Our results suggest that the proposed model accurately describes the complex variability in the data set with a small number of degrees of freedom.     

A new auxiliary variable formulation of high-order local radiation boundary conditions: corner compatibility conditions and extensions to first-order systems

We present a new auxiliary variable formulation of high-order radiation boundary conditions for the numerical simulation of waves on unbounded domains. Retaining the flexibility of Higdon’s wave-product conditions, our approach allows arbitrary-order implementations. When applied to the scalar wave equation, the proposed method leads to balanced, symmetrizable systems of wave equations on the boundary. It can also be extended to first-order systems. Corner compatibility conditions are derived for the auxiliary variable equations. They are shown experimentally to lead to stable, accurate results.     

Regularity of Intermittent Bursts in BriggsRauscher Oscillating Systems with Phenol

The intermittency or intermittent bursting as the type of dynamic state when two qualitatively different behaviors replace one another randomly during the course of the reaction, although all the control parameters remain constant, is found in the Briggs? Rauscher oscillating system moderated by a very small amount of phenol. Within a range of phenol concentrations, the oscillation amplitude is diminished considerably, and after oscillations cease, they repeat intermittently, giving several bursts of oscillations. For the concentrations used here, the range of phenol concentrations where intermittent bursting oscillations occur in a closed reactor is ca. 1.8×10^?5 to 3.6×10^?5 M . Bursting also occurs in an open reactor and can be sustained indefinitely at 5.53×10^?5 M concentration. The intermittent bursting behavior is robust, and can be achieved at a variety of conditions.     

Catalytic,Stereoselective Dihalogenation of Alkenes: Challenges and Opportunities

Although recent years have witnessed significant advances in the development of catalytic, enantioselective halofunctionalizations of alkenes, the related dihalogenation of olefins to afford enantioenriched vicinal dihalide products remains comparatively underdeveloped. However, the growing number of complex natural products bearing halogen atoms at stereogenic centers has underscored this critical gap in the synthetic chemist’s arsenal. This Review highlights the selectivity challenges inherent in the design of enantioselective dihalogenation processes, and formulates a mechanism‐based classification of alkene dihalogenations, including those that may circumvent the “classical” haliranium (or alkene‐dihalogen π‐complex) intermediates. A variety of metal and main group halide reagents that have been used for the dichlorination or dibromination of alkenes are discussed, and the proposed mechanisms of these transformations are critically evaluated.     

Analysis of erbium-doped fiber amplifiers pumped at 800 nm

The performance and efficiency of erbium-doped fibers pumped in the 800-nm band has been analyzed using a quantitative amplifier model. Both a silica and a fluorophosphate host were investigated. The analysis showed that under optimized conditions the fluorophosphate is superior to the silica with higher gain and up to 60% higher quantum conversion efficiency. Only with respect to noise figure is the fluorophosphate poorer because of the shorter lifetime of the metastable state.