On the convergence of 2-dimensional markov chains in quadrants with boundary reflection

The aim of this paper is to prove a limit theorem on the weak convergence of a family of rescaled Markov chains in a quadrant with boundary reflection. The limiting process is specified in terms of solutions of a certain submartingale problem in the style used by Varadhan and Williams. The obtained result is then applied to the problem of approximating an arbitrary Brownian motion with oblique reflection in a wedge by a family of Markov chains.     

First-principles calculations to investigate structural,electronic, optical,and transport properties of half-Heusler VFeZ (Z = N and P) compounds

This research work investigates the structural, electronic, optical, and thermoelectric characteristics of VFeZ (Z = N and P) half-Heusler compounds. The study employs the full-potential linearized augmented plane wave (FP-LAPW) method integrated into the WIEN2K algorithm, serving as the underpinning framework for density functional theory (DFT) analysis. In the study, we use the PBE generalized gradient approximation (PBE-GGA) to identify numerous parameters associated with structural and elastic properties. Lattice parameter results are in agreement with previous outcomes. Moreover, computed elastic parameters satisfy the criterion for stability. In the cubic structure VFeZ (Z = N and P) is ductile, to enhance the computations of electronic characteristics, Tran and Blaha's modified Becke-Johnson potential (TB-mBJ) is used. Our simulations demonstrate that the materials exhibit semiconductor behavior, with a direct band gap for VFeZ (Z = N and P). Strong UV absorption is found via optical experiments suggest compounds are suitable for optical application. Furthermore, study of the thermoelectric properties suggests its application in the thermoelectric generators.     

光热偏转光谱法的研究

为了建立棱镜型光热偏转光谱法的理论框架,采用棱镜的光色散特性研究了激励光源对待测样品表面周期性照射情况下的探测光偏转角与光热信号之间的解析关系。得到了棱镜型样品表面周期性变化的偏转角表达式。实现结果表明,该方法比传统型光谱法具有理论模型简单、实验容易实现、分辨率高、灵敏度高等优点。     

Improving attosecond pulse reflection by large angle incidence for a periodic multilayer mirror in the extreme ultraviolet region

The improvement of attosecond pulse reflection by large angle incidence for a periodic multilayer mirror in the extreme ultraviolet region has been discussed. Numerical simulations of both spectral and temporal reflection characteristics of periodic multilayer mirrors under various incident angles have been analyzed and compared. It was found that the periodic multilayer mirror under a larger incidence angle can provide not only higher integrated reflectivity but also a broader reflection band with negligible dispersion, making it possible to obtain better a reflected pulse that has a higher pulse reflection efficiency and shorter pulse duration for attosecond pulse reflection. In addition, by increasing the incident angle, the promotion of attosecond pulse reflection capability has been proven for periodic multilayer mirrors with arbitrary layers.     

Quantitative evaluation of equatorial small-angle X-ray scattering for cylindrical fibers

Elongated microvoids, internal fibrillar structure, and edge scattering from both surface refraction cause an equatorial streak in small angle X-ray scattering. A model for analyzing the edge scattering of fibers is proposed. Simulation results indicate that the intensity of edge scattering from surface refraction of a cylindrical fiber is strong and makes an important contribution to the equatorial streak. Two factors influence edge scattering intensity. One is the sample-to-detector distance (D); edge scattering intensity increases with increasing D. The equatorial streak becomes weak when D is shortened. The other factor is the refraction index. Edge scattering intensity increases as the real component of the refraction index decreases. In experiment, weak or even no equatorial streaks were found for samples measured in a roughly index-matching fluid. Edge scattering can be eliminated or weakened, and it can be calculated by comparing the intensities of a cylindrical fiber when it is measured in air and in index-matching fluid. The simulation data are basically in agreement with the experimental data.     

Coulomb‐enhanced spin–orbit coupling and semiconductor to half‐metal transition under pressure in Sr2CrReO6

Ordered Sr₂CrReO₆ has been synthesized recently. It is measured to be ferrimagnetic semiconductor, in contrary to the previous reports of metallic properties. To solve the discrepancy, we have investigated the compound by using the density functional theory. The semiconducting behavior is reproduced by including the electron correlation and spin–orbit coupling simultaneously. The calculated band gap is 0.22 eV, close to the experimental value of 0.21 eV. A large orbital moment of 0.69µ_B is found for Re, which is caused by the Coulomb‐enhanced spin–orbit coupling. By applying pressure, a semiconductor to half‐metal transition is observed through 5% volume compression.

     

Effect of the chiral chain length on structural and phase properties of ferroelectric liquid crystals

Studies of structural and phase properties obtained on several ferroelectric liquid crystalline materials with 2-alkoxypropionate group used as a chiral centre and without any lateral substitution are presented. In dependence on the chiral chain length these compounds exhibit the cholesteric N* phase, the ferroelectric smectic C* and a low-temperature SmX phase. Values of the spontaneous polarization and spontaneous tilt angle have been determined within the whole range of the SmC* phase. A low-temperature SmX phase has been identified as the orthogonal hexatic SmB* phase. The molecular parameters, namely the layer spacing in the SmC* and SmB* phases and the average intermolecular distances (D) between neighbouring parallel molecules in all investigated phases have been determined using the results of the X-ray diffraction obtained on non-oriented samples. The effect of the chiral chain length on mesomorphic, structural and physical properties of the studied ferroelectric liquid crystalline materials is discussed.     

Dynamic characteristics of traffic flow with consideration of pedestrians’ road-crossing behavior

Pedestrians’ road-crossing behavior can often interrupt traffic flow and cause vehicle queueing. In this paper, we propose some moving rules for modeling the interaction of vehicles and pedestrians. The modified visual angle car-following model is presented for the movement of vehicles with consideration of the lateral effect of waiting pedestrians. The pedestrians’ behavior is summarized as consisting of three steps: pedestrian arrival, gap acceptance, and pedestrian crossing. Some characteristic parameters of pedestrians are introduced to characterize pedestrians’ behavior. Simulation results show that the interaction of vehicles and pedestrians lowers the traffic capacity and increases delays to both vehicles and pedestrians.     

On Finite 2‐Path‐Transitive Graphs

The class of graphs that are 2‐path‐transitive but not 2‐arc‐transitive is investigated. The amalgams for such graphs are determined, and structural information regarding the full automorphism groups is given. It is then proved that a graph is 2‐path‐transitive but not 2‐arc‐transitive if and only if its line graph is half‐arc‐transitive, thus providing a method for constructing new families of half‐arc‐transitive graphs. © 2012 Wiley Periodicals, Inc. J. Graph Theory 73: 225–237, 2013