The Global Behavior of Finite Difference-Spatial Spectral Collocation Methods for a Partial Integro-Differential Equation with a Weakly Singular Kernel

The $z$-transform is introduced to analyze a full discretization method for a partial integro-differential equation (PIDE) with a weakly singular kernel. In this method, spectral collocation is used for the spatial discretization, and, for the time stepping, the finite difference method combined with the convolution quadrature rule is considered. The global stability and convergence properties of complete discretization are derived and numerical experiments are reported.     

MODIS植被指数监测农业干旱的适宜性评价

MODIS传感器提供的短波红外光谱波段为农业干旱遥感监测带来了新的机遇,因为它对植被水分十分敏感。本文选择中国东北松嫩平原为研究区,旱田为农业干旱的监测目标。基于2001—2010年的8天合成MODIS产品（MOD09A1）,分别计算了四种基于可见光和近红外光谱的植被绿度指数和四种基于近红外和短波红外光谱的植被水分指数,并以多尺度标准化降水指标(SPI)为判别植被指数农业干旱敏感性的标准,利用一种气象站点与象元配对关联的方法计算了不同植被指数与多尺度SPI的皮尔逊相关系数。研究表明,在农业干旱监测敏感性方面,MODIS植被水分指数（NDII6和NDII7）明显好于植被绿度指数。其中NDII7的表现最为出色,研究证实了MODIS短波红外光谱在监测农业干旱方面的潜力,为今后相关研究提供了新的见解。     

非富勒烯小分子有机太阳能电池电子受体材料的研究进展

富勒烯及其衍生物是一类重要的n-型电子受体材料,在有机太阳能电池器件中发挥了至关重要的作用. 但由于富勒烯材料吸光波长较窄、亲和能高、溶解性差等,严重限制了富勒烯作为有机太阳能电池n-型电子受体材料的更广泛应用和器件性能的进一步提升. 非富勒烯n-型电子受体材料具有能级可调、合成简便、加工成本低、溶解性能优异等特点,更重要的是,此类材料在可见太阳光光谱中比富勒烯及其衍生物材料有更加宽广的吸收范围;近年来,受到越来越多的关注和研究. 本文较为系统地阐述了非富勒烯小分子材料作为有机太阳能电池n-型电子受体材料的研究进展,并对其发展前景作了展望.     

Performance improvement of MEH-PPV:PCBM solar cells using bathocuproine and bathophenanthroline as the buffer layers

In this work, bathocuproine (BCP) and bathophenanthroline (Bphen), commonly used in small-molecule organic solar cells (OSCs), are adopted as the buffer layers to improve the performance of the polymer solar cells (PSCs) based on poly(2-methoxy-5-(2-ethylhexyloxy)-1,4-phenylenevinylene) (MEH-PPV): [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) bulk heterojunction. By inserting BCP or Bphen between the active layer and the top cathode, all the performance parameters are dramatically improved. The power conversion efficiency is increased by about 70% and 120% with 5-nm BCP and 12-nm Bphen layers, respectively, when compared with that of the devices without any buffer layer. The performance enhancement is attributed to BCP or Bphen (i) increasing the optical field, and hence the absorption in the active layer, (ii) effectively blocking the excitons generated in MEH-PPV from quenching at organic/aluminum (Al) interface due to the large band-gap of BCP or Bphen, which results in a significant reduction in series resistance (Rs), and (iii) preventing damage to the active layer during the metal deposition. Compared with the traditional device using LiF as the buffer layer, the BCP-based devices show a comparable efficiency, while the Bphen-based devices show a much larger efficiency. This is due to the higher electron mobility in Bphen than that in BCP, which facilitates the electron transport and extraction through the buffer layer to the cathode.     

修正荷载的Wilson-θ法的稳定性与精度分析

Wilson-θ法求得的位移、速度与加速度不满足t时刻的动力平衡方程。提出修正荷载的Wilson-θ法:增加一个荷载δF(t),使得t时刻的动力平衡方程得以满足;将-θ′δF(t)作为荷载加入t+Δt时刻的计算中,当θ′=0时,修正荷载的Wilson-θ法退化为Wilson-θ法。对应于不同的θ′值,在无条件稳定的前提下,θ的取值范围也不同。定义了逐步积分法中的计算误差。计算结果表明:计算误差与θ值成正相关,当θ′=0.6,无条件稳定的θ为最小值1.24,因而θ′=0.6,θ=1.24时,计算误差最小,建议在计算中采用。保持Wilson-θ法无条件稳定、几乎不增加计算量的条件下,修正荷载的Wilson-θ法可以提高计算精度。     

极坐标系下的Legendre谱元方法求解Poisson-型方程

r=0处的坐标奇异性是求解极坐标下Poisson-型方程的关键。本文提出一种极坐标系下基于Galerkin变分的Legendre谱元方法用于求解圆形区域内的Poisson-型方程,物理区域的径向和周向划分若干单元,计算单元均采用Legendre多项式展开;圆心所在单元的径向使用LGR(Legendre Gauss Radau)积分点,其他单元径向使用LGL(Legendre Gauss Lobatto)积分点,从而避免了极点处1/r坐标奇异性,周向单元均采用LGL积分点。利用区域分解技术,可以避免节点在极点附近聚集;最后求解了多个Dirichlet或Neumann边界条件下的Poisson-型方程算例。数值结果表明,谱元方法具有很高的精度。     

The Dissipative Spectral Methods for the First Order Linear Hyperbolic Equations

In this paper, we introduce the dissipative spectral methods (DSM) for the first order linear hyperbolic equations in one dimension. Specifically, we consider the Fourier DSM for periodic problems and the Legendre DSM for equations with the Dirichlet boundary condition. The error estimates of the methods are shown to be quasi-optimal for variable-coefficients equations. Numerical results are given to verify high accuracy of the DSM and to compare the proposed schemes with some high performance methods, showing some superiority in long-term integration for the periodic case and in dealing with limited smoothness near or at the boundary for the Dirichlet case.     

Discontinuity of dipole-moment matrix elements in ellipsoidally shaped nanoparticles and profiles of spectral lines

The behaviour of energy levels and optical spectra of a charged particle (electron or hole) confined within a potential well of ellipsoidal shape is investigated as a function of the shape-anisotropy parameter. If two energy levels of the same symmetry intersect in a perturbation-theory approximation, they move apart on direct diagonalization of the appropriate Hamiltonian. The intersection of the energy levels leads to a discontinuity of the corresponding dipole-moment matrix element. The discontinuity of matrix elements is not reflected in the behaviour of transition probabilities which are continuous functions of the shape-anisotropy parameter. The profiles of a spectral line emitted or absorbed by an ensemble of ellipsoidally shaped nanoparticles with a Gaussian distribution of size are calculated and discussed.     

A conservative,thermodynamically consistent numerical approach for low Mach number combustion. Part I: Single-level integration

We present a numerical approach for low Mach number combustion that conserves both mass and energy while remaining on the equation of state to a desired tolerance. We present both unconfined and confined cases, where in the latter the ambient pressure changes over time. Our overall scheme is a projection method for the velocity coupled to a multi-implicit spectral deferred corrections (SDC) approach to integrate the mass and energy equations. The iterative nature of SDC methods allows us to incorporate a series of pressure discrepancy corrections naturally that lead to additional mass and energy influx/outflux in each finite volume cell in order to satisfy the equation of state. The method is second order, and satisfies the equation of state to a desired tolerance with increasing iterations. Motivated by experimental results, we test our algorithm on hydrogen flames with detailed kinetics. We examine the morphology of thermodiffusively unstable cylindrical premixed flames in high-pressure environments for confined and unconfined cases. We also demonstrate that our algorithm maintains the equation of state for premixed methane flames and non-premixed dimethyl ether jet flames.     

Pervasive randomness in physics: an introduction to its modelling and spectral characterisation

An introduction to the modelling and spectral characterisation of random phenomena is detailed at a level consistent with a first exposure to the subject at an undergraduate level. A signal framework for defining a random process is provided and this underpins an introduction to common random processes including the Poisson point process, the random walk, the random telegraph signal, shot noise, information signalling random processes, jittered pulse trains, birth–death random processes and Markov chains. An introduction to the spectral characterisation of signals and random processes, via either an energy spectral density or a power spectral density, is detailed. The important case of defining a white noise random process concludes the paper.