The coupled-cluster formalism – a mathematical perspective

ABSTRACT

The Coupled-Cluster (CC) theory is one of the most successful high precision methods used to solve the stationary Schrödinger equation. In this article, we address the mathematical foundation of this theory with focus on the advances made in the past decade. Rather than solely relying on spectral gap assumptions (non-degeneracy of the ground state), we highlight the importance of coercivity assumptions – Gårding type inequalities – for the local uniqueness of the CC solution. Based on local strong monotonicity, different sufficient conditions for a local unique solution are suggested. One of the criteria assumes the relative smallness of the total cluster amplitudes (after possibly removing the single amplitudes) compared to the Gårding constants. In the extended CC theory the Lagrange multipliers are wave function parameters and, by means of the bivariational principle, we here derive a connection between the exact cluster amplitudes and the Lagrange multipliers. This relation might prove useful when determining the quality of a CC solution. Furthermore, the use of an Aubin–Nitsche duality type method in different CC approaches is discussed and contrasted with the bivariational principle.     

径向井排引导水力压裂裂缝扩展机理研究

为探究径向井排系统对裂缝的影响，明确水力裂缝的扩展规律，利用扩展有限元理论建立了流固耦合三维裂缝扩展模型，模拟了受径向井排引导的水力裂缝扩展过程。重点分析了3种影响因素（径向井排方位角、水平地应力差、径向井孔径）对水力裂缝的引导机理。首次提出了"引导因子"的概念，并将其作为有效评价径向井排引导效果的量化参数。研究发现，径向井方位角、水平地应力差、径向井井径会对水力裂缝的引导效果产生影响：较小的径向井方位角、水平地应力差以及较大的井径都使径向井排具有较强的引导能力和较好的引导效果，反之亦然。同时，较大井径对增加水力裂缝宽度有明显作用。最后，利用大尺寸真三轴水力压裂模拟试验证实了数值模拟结果具有一定的准确性。     

The single-polarization filter composed of gold-coated photonic crystal fiber

A single-polarization filter comprising a gold-coated photonic crystal fiber based on surface plasmon resonance is designed and investigated. The pattern matching and coupled polarization characteristics analyzed by the full-vector finite element method (FEM) and losses at 1,540 nm are achieved to 1,016.01739 dB/cm (x-pol core mode) and 33.81917 dB/cm (y-pol core mode). The crosstalk (CT) value of the 1,540 nm band is ?853.12653 dB for fiber length $L=1,000\mathrm{\mu }\text{m}$ and the bandwidth is 850 nm. The working wavelength of the filter ranges from 1,280 nm to 1,540 nm by varying the diameter of outer air holes ($d_1$), the diameter of inner air holes ($d_4$), the metal film thickness (t), as well as the liquid refractive index (n).     

Enhancing signal-to-noise ratio and resolution in low-field NMR relaxation measurements using post-acquisition digital filters

The traditional way to enhance signal-to-noise ratio (SNR) of nuclear magnetic resonance (NMR) signals is to increase the number of scans. However, this procedure increases the measuring time that can be prohibitive for some applications. Therefore, we have tested the use of several post-acquisition digital filters to enhance SNR up to one order of magnitude in time domain NMR (TD-NMR) relaxation measurements. The procedures were studied using continuous wave free precession (CWFP-T₁) signals, acquired with very low flip angles that contain six times more noise than the Carr–Purcell–Meiboom–Gill (CPMG) signal of the same sample and experimental time. Linear (LI) and logarithmic (LO) data compression, low-pass infinity impulse response (LP), Savitzky–Golay (SG), and wavelet transform (WA) post-acquisition filters enhanced the SNR of the CWFP-T₁ signals by at least six times. The best filters were LO, SG, and WA that have high enhancement in SNR without significant distortions in the ILT relaxation distribution data. Therefore, it was demonstrated that these post-acquisition digital filters could be a useful way to denoise CWFP-T₁, as well as CPMG noisy signals, and consequently reducing the experimental time. It was also demonstrated that filtered CWFP-T₁ method has the potential to be a rapid and nondestructive method to measure fat content in beef and certainly in other meat samples.     

过滤机液位控制系统在洗煤厂的应用

介绍了过滤机液位控制系统的结构、功能及其在洗煤厂的应用情况，并根据其运行结果，指出了需改进的部分。     

燃料添加剂对柴油机烟粒燃烧的影响

考察了燃料添加剂对降低柴油机烟粒燃点温度的效应。含金属添加剂的柴油机烟粒被收集在金属纤维过滤器上,把原状烟粒样品移入实验室反应器,用模拟柴油机排气进行燃烧试验。实验结果表明,当烟粒中含有Pd或Cu时,烟粒的燃点温度可降至430℃左右(普通柴油机烟粒的燃点温度约600℃);Pd的添加还可大大降低烟粒一次燃烧产物中CO的分率。文中还对金属(催化剂)/烟粒接触程度和添加剂溶液中可燃性部分对烟粒燃烧的影响作了讨论。     

COMPACT COUPLED LINEAR TAPERED LINE BANDPASS FILTER WITH TWO TRANSMISSION ZEROS

A new compact bandpass filter composed of two coupled linear tapered line resonators (LTLRs) is designed. The two resonators are arranged in different layers. The filter has two transmission zeros on both sides of the passband. It has small size and steep response below its passband. It is also shown that this filter has 0.6 dB low insertion loss at the centre frequency and 10.5% 3dB bandwidth. This work was supported by the Development Foundation of Shanghai Educational Committee (217608) and Shanghai Leading Academic Discipline Project (T0102).     

推广x重新标度模型的重标度参数经验公式

给出了推广x重新标度模型的重标度参数经验公式,其中建立了重标度参数与原子核的平均结合能之间的联系,由该公式可以得出A≥12的所有核的重标度参数值,利用这些参数值可以计算有关核过程并做出预言.     

直流稳压电源波形演示器制作说明

直流稳压电源可以将交流电压变换为直流电压,并使之稳定,在我们现实生活中应用很广泛,在实验中我们利用的电学知识,设计制造了一种直流稳压电源。本文简要介绍了这种直流稳压电源波形演示器的设计目的和电路原理,重点阐述了它的制作流程、滤波和稳压原理以及性能测试输出波形。