Spectral properties of a tight binding Hamiltonian with period doubling potential

We study a one dimensional tight binding hamiltonian with a potential given by the period doubling sequence. We prove that its spectrum is purely singular continuous and supported on a Cantor set of zero Lebesgue measure, for all nonzero values of the potential strength. Moreover, we obtain the exact labelling of all spectral gaps and compute their widths asymptotically for small potential strength.     

Convergence to equilibrium of critical branching particle systems and superprocesses,and related nonlinear partial differential equations

We consider a class of multitype particle systems in ^d undergoing spatial diffusion and critical stable multitype branching, and their limits known as critical stable multitype Dawson-Watanabe processes, or superprocesses. We show that for large classes of initial states, the particle process and the superprocess converge in distribution towards known equilibrium states as time tends to infinity. As an application we obtain the asymptotic behavior of a system of nonlinear partial differential equations whose solution is related to the distribution of both the particle process and the superprocess.Research partially supported by CONACyT (Mexico), CNRS (France) and BMfWuF (Austria).     

The Sample Average Approximation Method Applied to Stochastic Routing Problems: A Computational Study

The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. The resulting sample average approximating problem is then solved by deterministic optimization techniques. The process is repeated with different samples to obtain candidate solutions along with statistical estimates of their optimality gaps.We present a detailed computational study of the application of the SAA method to solve three classes of stochastic routing problems. These stochastic problems involve an extremely large number of scenarios and first-stage integer variables. For each of the three problem classes, we use decomposition and branch-and-cut to solve the approximating problem within the SAA scheme. Our computational results indicate that the proposed method is successful in solving problems with up to 2¹⁶⁹⁴ scenarios to within an estimated 1.0% of optimality. Furthermore, a surprising observation is that the number of optimality cuts required to solve the approximating problem to optimality does not significantly increase with the size of the sample. Therefore, the observed computation times needed to find optimal solutions to the approximating problems grow only linearly with the sample size. As a result, we are able to find provably near-optimal solutions to these difficult stochastic programs using only a moderate amount of computation time.     

Positive pion photoproduction from hydrogen at photon energies between 500 MeV and 1,400 MeV in forward direction

The differential cross section of the reactionγ+p→π ⁺ was measured at pion CM-angles of 20° and 30° for photon energies between 500 MeV and 1,400 MeV. The pions were detected in a magnetic spectrometer. By measuring each pion trajectory and by offline calculation of the initial pion parameters an energy resolution of about 2.5% FWHM was achieved. The results complete a set of data which were measured in recent years at the Bonn 2.5 GeV synchrotron. In comparison to photoproduction analyses two effects were revealed: The η cusp appears in the energy dependence of the cross section as a sharp drop atK _γ=710 MeV. In the region of the third resonance the data show a greater enhancement than predicted by most of the analyses.     

On transmittance and localization of the electromagnetic wave in two-dimensional graphene-based photonic crystals

Two-dimensional graphene-based photonic crystal (GPC) formed by a periodic array of the homogeneous dielectric cylinders etched in the alternating graphene and dielectric layers and its inverse counterpart are considered. The transmittance of the photonic crystal is obtained. The waveguide due to the localization of the electromagnetic wave on the lattice defect that breaks the translational symmetry of the GPC of two different topologies is studied. The different topologies of GPC are characterized by different photonic band structures with different widths of photonic band gaps (PBG) and provide different frequencies for the localized electromagnetic wave due to the defect. The frequencies of the localized mode for both type of the GPC, located inside the lowest PBG, are in the range of THz or tens of THz depending on the topology of the GPC. It is shown that the photonic band gap always can be tuned by changing the chemical potential of graphene to provide formation of the localized photonic mode due to the defect. The technological advantages of the GPC, as well as the opportunity to tune the PBG and the frequency of the localized electromagnetic wave in the terahertz region of spectrum for the GPC are discussed.     

CORSICA: correction of structured noise in fMRI by automatic identification of ICA components

When applied to functional magnetic resonance imaging (fMRI) data, spatial independent component analysis (sICA), a data-driven technique that addresses the blind source separation problem, seems able to extract components specifically related to physiological noise and brain movements. These components should be removed from the data to achieve structured noise reduction and improve any subsequent detection and analysis of signal fluctuations related to neural activity. We propose a new automatic method called CORSICA (CORrection of Structured noise using spatial Independent Component Analysis) to identify the components related to physiological noise, using prior information on the spatial localization of the main physiological fluctuations in fMRI data. As opposed to existing spectral priors, which may be subject to aliasing effects for long-TR data sets (typically acquired with TR >1 s), such spatial priors can be applied to fMRI data, regardless of the TR of the acquisitions. By comparing the proposed automatic selection to a manual selection performed visually by a human operator, we first show that CORSICA is able to identify the noise-related components for long-TR data with a high sensitivity and a specificity of 1. On short-TR data sets, we validate that the proposed method of noise reduction allows a substantial improvement of the signal-to-noise ratio evaluated at the cardiac and respiratory frequencies, even in the gray matter, while preserving the main fluctuations related to neural activity.     

Superbase‐catalyzed domino 3H‐pyrroles synthesis from ketoximes and acetylene: DFT study vs experiment

Elimination of vinyl alcohol from 5‐vinyloxypyrrolines in the presence of superbases (final step of domino 3H‐pyrroles synthesis from ketoximes and acetylene) is studied computationally at different levels of theory in DMSO solution (PCM). The sequences of transformations starting from nucleophilic addition of hydroxide ion to carbon‐carbon or carbon‐nitrogen double bonds are proposed as possible mechanisms. Unusual reactivity of 2,5‐dimethylphenyl substituted 5‐vinyloxypyrroline is explained within these mechanisms.     

Angle-resolved desorption and removal of surface nitrogen in deNOx

This paper reports on recent progress on angle-resolved desorption leading to structure-sensitive desorption dynamics. The sensitivity is exemplified in NO and N₂O reduction on Pd and Rh surfaces. The energy partitioning in the repulsive desorption of hyper-thermal products into their rotational and translational modes is an indispensable concept to examine the structure of a reaction site from desorbing molecules because it connects the structure of a transition state with each energy of desorbed products. The extent of the energy partitioning will be derived from the desorption-angle dependences of both the rotational and translational energies at each vibrational state. Such energy analysis has never been completed for any thermal reactive desorption. A new type of measurement is thus proposed. Additionally, we discuss the inadequate use of the detailed balance principle in desorption dynamics, which has prevented desorption dynamics from being sensitive to surface structures.     

基于石墨烯的光学控制窄带太赫兹开关

本文提出了一种光控太赫兹开关,该开关采用覆盖单层石墨烯的十字金属谐振器超表面。利用石墨烯表面电导率模型和有限元法计算了这种复合结构的光谱特性。模拟结果表明,在0.2 W/mm²的光泵浦后,传输谱（调制深度为36.8%,Q-因子为250）出现了窄带共振衰减现象。另外,这种衰减的调制深度可以通过改变泵浦强度微调节。因此,光学可调谐太赫兹开关的设计将有助于太赫兹通信应用的功能组件开发。