NIFTy 3 – Numerical Information Field Theory: A Python Framework for Multicomponent Signal Inference on HPC Clusters

NIFTy , “Numerical Information Field Theory,” is a software framework designed to ease the development and implementation of field inference algorithms. Field equations are formulated independently of the underlying spatial geometry allowing the user to focus on the algorithmic design. Under the hood, NIFTy ensures that the discretization of the implemented equations is consistent. This enables the user to prototype an algorithm rapidly in 1D and then apply it to high‐dimensional real‐world problems. This paper introduces NIFTy  3, a major upgrade to the original NIFTy  framework. NIFTy  3 allows the user to run inference algorithms on massively parallel high performance computing clusters without changing the implementation of the field equations. It supports n‐dimensional Cartesian spaces, spherical spaces, power spaces, and product spaces as well as transforms to their harmonic counterparts. Furthermore, NIFTy  3 is able to handle non‐scalar fields, such as vector or tensor fields. The functionality and performance of the software package is demonstrated with example code, which implements a mock inference inspired by a real‐world algorithm from the realm of information field theory. NIFTy  3 is open‐source software available under the GNU General Public License v3 (GPL‐3) at https://gitlab.mpcdf.mpg.de/ift/NIFTy/tree/NIFTy_3 .     

On the Relative Gain Array (RGA) with singular and rectangular matrices

This paper identifies a significant deficiency in the literature on the application of the Relative Gain Array (RGA) formalism in the case of singular matrices. Specifically, it is shown that the conventional use of the Moore–Penrose pseudoinverse is inappropriate because it fails to preserve critical properties that can be assumed in the nonsingular case. It is then shown that such properties can be rigorously preserved using an alternative generalized matrix inverse.     

零误差计算

研究采用有误差的数值计算来获得无误差的准确值具有重要的理论价值和应用价值.这种通过近似的数值方法获得准确结果的计算被称为零误差计算.本文首先指出,只有一致离散集合中的数才能够开展零误差计算,即有非零隔离界的数集,这也是"数"可以进行零误差计算的一个充要条件.以此为基本出发点,本文分析代数数零误差计算的最低理论精度,该精度对应于恢复近似代数数的准确值时必要的误差控制条件,但由于所采用恢复算法的局限性,这一理论精度往往不能保证成功恢复出代数数的准确值.为此,本文给出采用PSLQ (partial-sum-LQ-decomposition)算法进行代数数零误差计算所需的精度控制条件,与基于LLL (Lenstra-Lenstra-Lovász)算法相比,该精度控制条件关于代数数次数的依赖程度由二次降为拟线性,从而可降低相应算法的复杂度.最后探讨零误差计算未来的发展趋势.     

Lamb波频域逆散射全聚焦成像方法研究

Lamb波因其传播距离远、衰减小常被用于板状结构的无损检测中,在基于Lamb波损伤检测的诸多成像技术中,全聚焦方法(Total Focus Method,TFM)方法因其成像分辨率高、信噪比高而受青睐。然而Lamb波的频散效应导致时域延时量不能被准确计算,进而影响传统TFM方法对损伤定位及成像的精度;此外,既有的TFM方法仅以回波幅值作为成像指标,忽略了Lamb波与损伤的相互作用,故而不能通过损伤表面的物理参数增强成像质量。针对这两个问题,本文首先在时域TFM基础上发展了频域TFM,在计算中纳入频散关系以规避频散的影响;其次以包含明确的损伤特征参数--反射率为成像指标,结合频域TFM方法建立损伤逆散射模型,以实现对损伤的准确成像。仿真和实验结果表明:频域逆散射TFM成像方法能够实现对铝板结构中的损伤检测,在工程实践中具有应用价值。     

Nonlinear dynamical magnetosonic wave interactions and collisions in magnetized plasma

The one-dimensional nonlinear dynamical wave interactions in a system of quasineutral two-fluid plasma in a constant magnetic field are investigated.The existence of the travelling wave solutions is discussed.The modulation stability of linear waves and the modulation instability of weakly nonlinear waves are presented.Both suggest that the Korteweg-de Vries(KdV) system is modulationally stable.Besides,the wave interactions including the periodic wave interaction and the solitary wave interaction are captured and presented.It is shown that these interacting waves alternately exchange their energy during propagation.The Fourier spectrum analysis is used to depict the energy transformation between the primary and harmonic waves.It is known that the wave interactions in magnetized plasma play an important role in various processes of heating and energy transportation in space and astrophysical plasma.However,few researchers have considered such magnetohydrodynamic(MHD) wave interactions in plasma.It is expected that this work can provide additional insight into understanding of behaviors of MHD wave interactions.     

Accurate correction of arbitrary spin fermion quantum tunneling from non-stationary Kerr-de Sitter black hole based on corrected Lorentz dispersion relation

According to a corrected dispersion relation proposed in the study on the string theory and quantum gravity theory, the Rarita-Schwinger equation was precisely modified, which resulted in the Rarita-Schwinger-Hamilton-Jacobi equation. Using this equation, the characteristics of arbitrary spin fermion quantum tunneling radiation from non-stationary Kerr-de Sitter black holes were determined. A number of accurately corrected physical quantities, such as surface gravity, chemical potential, tunneling probability, and Hawking temperature, which describe the properties of black holes, were derived. This research has enriched the research methods and enabled increased precision in black hole physics research.     

System-size effect on the friction at liquid-solid interfaces

The friction at the liquid-solid interfaces is widely involved in various phenomena ranging from nanometer to micrometer scales. By the molecular dynamic(MD)simulation, the friction properties of liquid-solid interfaces at the molecular level are calculated via the Green-Kubo relation. It is found that the system size will influence the value of the friction coefficient, especially for the solid surfaces with the larger polar charge. The value of the friction coefficient decreases with the increase in the system size and converges at large system sizes. The large polar charge will lead to a significant friction coefficient. However, the diffusion of water molecules on this surface is almost a constant, indicating that the diffusion coefficient seems to be independent of the system size and polar charge. This work provides insights for the selection of the system size in modeling the frictional properties of hydrophobic/hydrophilic surfaces.     

Synthesis and structure–property relationship of carbazole‐alt‐benzothiadiazole copolymers

A series of four π‐conjugated carbazole‐alt‐benzothiadiazole copolymers (PCBT) were prepared by Suzuki cross‐coupling reaction between synthesized dibromocarbazoles as electron‐rich subunits and 4,7‐bis(4,4,5,5‐tetramethyl‐1,3,2‐dioxaborolan‐2‐yl)?2,1,3‐benzothiadiazole as electron‐deficient subunits. The subunits were directly linked through 2,7‐ or 3,6‐ positions of the carbazole. In addition, the carbazole monomers have been N‐substituted by a branched or a linear side‐chain. The chemical structure of the copolymers and their precursors was confirmed by NMR and IR spectroscopies, and their molar masses were estimated by SEC. Thermal analysis under N₂ atmosphere showed no weight loss below 329°C, and no glass transition was observed in between 0 and 250°C. The band gaps of all PCBTs evaluated by optical spectroscopies and by cyclic voltammetry analysis were consistent with expectations and ranged between 2.2 and 2.3 eV. Finally, 2,7 and 3,6 linkages were shown to influence optical properties of PCBTs. © 2015 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 2059–2068     

On the Fundamental Polymer Chemistry of Inverse Vulcanization for Statistical and Segmented Copolymers from Elemental Sulfur

In this concept review, the fundamental and polymerization chemistry of inverse vulcanization for the preparation of statistical and segmented sulfur copolymers, which have been actively developed and advanced in various applications over the past decade is discussed. This concept review delves into a discussion of step-growth polymerization constructs to describe the inverse vulcanization process and discuss prepolymer approaches for the synthesis of segmented sulfur polyurethanes. Furthermore, this concept review discusses the advantages of inverse vulcanization in conjunction with dynamic covalent polymerization and post-polymerization modifications to prepare segmented block copolymers with enhanced thermomechanical and flame retardant properties of these materials.