A mathematical and computational review of Hartree–Fock SCF methods in quantum chemistry

We present a review of the fundamental topics of Hartree–Fock theory in quantum chemistry. From the molecular Hamiltonian, using and discussing the Born–Oppenheimer approximation, we arrive at the Hartree and Hartree–Fock equations for the electronic problem. Special emphasis is placed on the most relevant mathematical aspects of the theoretical derivation of the final equations, and on the results regarding the existence and uniqueness of their solutions. All Hartree–Fock versions with different spin restrictions are systematically extracted from the general case, thus providing a unifying framework. The discretization of the one-electron orbital space is then reviewed and the Roothaan–Hall formalism introduced. This leads to an exposition of the basic underlying concepts related to the construction and selection of Gaussian basis sets, focusing on algorithmic efficiency issues. Finally, we close the review with a section in which the most relevant modern developments (especially those related to the design of linear-scaling methods) are commented on and linked to the issues discussed. The paper is intentionally introductory and rather self-contained, and may be useful for non-experts intending to use quantum chemical methods in interdisciplinary applications. Moreover, much material that can be found scattered in the literature has been put together to facilitate comprehension and to serve as a handy reference.     

Modelling of high-temperature dark current in multi-quantum well structures from MWIR to VLWIR

In this paper, a model to calculate the dark current of quantum well infrared photodetectors at high-temperature regime is presented. The model is derived from a positive-definite quantum probability-flux and considers thermionic emission and thermally-assisted tunnelling as mechanisms of dark current generation. Its main input data are the wave functions obtained by time-independent Schrodinger equation and it does not require empirical parameters related to the transport of carriers. By means of this model, the dark current of quantum well infrared photodetectors at high-temperature regime is investigated with respect to the temperature, the barrier width, the applied electric field and the position of the first excited state. The theoretical results are compared with experimental data obtained from lattice-matched InAlAs/InGaAs, InGaAsP/InP on InP substrate and AlGaAs/GaAs structures with rectangular wells and symmetric barriers, whose absorption peak wavelengths range from MWIR to VLWIR. The corresponding results are in a good agreement with experimental data at different temperatures and at a wide range of applied electric field.     

大型试件的X射线CT检测方法探讨

当对投影长度大于探测器长度的大型试件做平行光束CT时 ,可以认为投影被截断了。从数学上讲 ,这种情况下的解析法重建如滤波反投影法是不适宜的。然而从工程应用上来说 ,这又不是绝对的。就几种情况讨论了通过补充假数据 ,通过在 0～ 2π范围内对试件成像得到了完整的CT切片 ,获得了切片的精确重建     

Fast evaluation of Helmholtz potential on graphics processing units (GPUs)

This paper presents a parallel algorithm implemented on graphics processing units (GPUs) for rapidly evaluating spatial convolutions between the Helmholtz potential and a large-scale source distribution. The algorithm implements a non-uniform grid interpolation method (NGIM), which uses amplitude and phase compensation and spatial interpolation from a sparse grid to compute the field outside a source domain. NGIM reduces the computational time cost of the direct field evaluation at N observers due to N co-located sources from O(N²) to O(N) in the static and low-frequency regimes, to O(N log N) in the high-frequency regime, and between these costs in the mixed-frequency regime. Memory requirements scale as O(N) in all frequency regimes. Several important differences between CPU and GPU implementations of the NGIM are required to result in optimal performance on respective platforms. In particular, in the CPU implementations all operations, where possible, are pre-computed and stored in memory in a preprocessing stage. This reduces the computational time but significantly increases the memory consumption. In the GPU implementations, where handling memory often is a critical bottle neck, several special memory handling techniques are used to accelerate the computations. A significant latency of the GPU global memory access is hidden by implementing coalesced reading, which requires arranging many array elements in contiguous parts of memory. Contrary to the CPU version, most of the steps in the GPU implementations are executed on-fly and only necessary arrays are kept in memory. This results in significantly reduced memory consumption, increased problem size N that can be handled, and reduced computational time on GPUs. The obtained GPU–CPU speed-up ratios are from 150 to 400 depending on the required accuracy and problem size. The presented method and its CPU and GPU implementations can find important applications in various fields of physics and engineering.     

A Method for Measuring the Three-Dimensional Refractive-Index Distribution of Single Cells Using Proximal Two-Beam Optical Tweezers and a Phase-Shifting Mach—Zehnder Interferometer

This paper describes a method for measuring the three-dimensional (3D) refractive-index distribution in a single cell. The method can be used to observe the distribution of cell components without fluorescence staining. The two-dimensional optical path length distributions from multiple directions are obtained by non-contact rotation of the cell. These optical path lengths are converted into the line integrals of the refractive index, and the 3D refractive-index distribution is reconstructed by means of computed tomography. The refractive-index distribution in a breast cancer cell can be measured using a phase-shifting Mach—Zehnder interferometer in conjunction with proximal two-beam optical tweezers.     

Fresnel entropic characterization of optical Laguerre-Gaussian beams

A novel approach, based on Fresnel tomography, to determine the entropy of two-dimensional optical Laguerre-Gaussian beams is presented and discussed. Numerical evaluations of the entropy distribution in the phase space associated with Laguerre-Gauss modes are presented. It is shown that the concept of Fresnel entropy provides a general criterion for studying and characterizing the vorticity of Laguerre-Gauss modes.     

Three dimensional accurate morphology measurements of polystyrene standard particles on silicon substrate by electron tomography

Polystyrene latex (PSL) nanoparticle (NP) sample is one of the most widely used standard materials. It is used for calibration of particle counters and particle size measurement tools. It has been reported that the measured NP sizes by various methods, such as Differential Mobility Analysis, dynamic light scattering (DLS), optical microscopy (OM), scanning electron microscopy (SEM) and atomic force microscopy (AFM), differ from each other. Deformation of PSL NPs on mica substrate has been reported in AFM measurements: the lateral width of PSL NPs is smaller than their vertical height. To provide a reliable calibration standard, the deformation must be measured by a method that can reliably visualize the entire three dimensional (3D) shape of the PSL NPs. Here we present a method for detailed measurement of PSL NP 3D shape by means of electron tomography in a transmission electron microscope. The observed shape of the PSL NPs with 100 nm and 50 nm diameter were not spherical, but squished in direction perpendicular to the support substrate by about 7.4% and 12.1%, respectively. The high difference in surface energy of the PSL NPs and that of substrate together with their low Young modulus appear to explain the squishing of the NPs without presence of water film.     

Characterizing turbulence in globally coupled maps with stochastic finite automata

We describe a method to discriminate between ordered and turbulent behavior in a general class of collective systems known as Globally Coupled Maps (GCM). Our method is able to discover an unknown small ordered region inside the turbulent phase of GCM parameter space. The computational nature of the method is the main novelty of our approach; it is another example of how measures based on computational notions of structure may provide new information in the study of dynamical systems.     

Depth information extraction with an aperture-rotating camera

This paper focuses on extracting depth information with an aperture-rotating camera. Compared with previous work, the proposed method is applicable for arbitrary rotation angle by making use of pixel registration to get pixel shift angle, and calculating the pixel shift along this angle. Besides, consumption time for shift angle is reduced by means of sampling. Compared with point-by-point method, the proposed method reduces the computation time from about 1 h to 1 min for a 15-megapixel image. Experimental results of a scene named “bottles” show that the depth value has a margin of error of 5%. Proposed method makes it possible to extract depth information with a single camera and expands the application of DSLR camera.     

时域荧光分子层析图像重建的线性特征数据法

通过扩展用于时域扩散光成像(Diffuse Optical Tomography, DOT)的广义脉冲谱技术,提出了一种用于时域荧光分子层析成像(Fluorescence Molecular Tomography, FMT)的线性特征数据图像重建算法.此算法能够同时重建荧光产率和荧光寿命,并且利用模拟数据对此方法进行验证,证明了算法的有效性.