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.     

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。     

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.     

Investigation of segmental reorganization within amphiphilic block polymer nanoparticles derived from shell crosslinked micelle templates: Shell crosslinked knedel-like inversion

The construction of nanoscopic materials by synthetic methodologies that iterate covalent and supramolecular interactions has been developed over the past three decades as a powerful method to afford complex functional materials. Indeed, the present study was nearly lost in the archives of dissertation research completed in 2001, which revealed nanoscale conformational dynamics in the segmental reorganization, and partial inversion, of topologically shell crosslinked knedel-like (SCK) nanoparticles. © 2019 Wiley Periodicals, Inc. J. Polym. Sci. 2020 , 58, 204–214     

High strength,acid-resistant composites from canola,sunflower, or linseed oils: Influence of triglyceride unsaturation on material properties

Here are reported composites made by crosslinking unsaturated units in canola, sunflower, or linseed oil with sulfur to yield CanS , SunS , and LinS , respectively. These plant oils were selected because the average number of crosslinkable unsaturated units per triglyceride vary from 1.3 for canola to 1.5 for sunflower and 1.8 for linseed oil. The remeltable composites show compressive strengths that increase with increasing unsaturation number from CanS (9.3 MPa) to SunS (17.9 MPa) to LinS (22.9 MPa). These values for SunS and LinS are competitive when compared with the value of 17 MPa required for residential building using traditional Portland cement. The plant oil composites are recyclable over many cycles and can retain up to 100% of strength after 24 hr in oxidizing acid under conditions where Portland cement is dissolved in under 30 min. Infusion of the composites into premade cement blocks affords them with significantly improved acid resistance as well. This work thus provides a simple, nearly 100% atom economical route to convert plant oils and waste sulfur to composites having enhanced performance over commercial structural materials.     

Simple Equations Method (SEsM): Algorithm,Connection with Hirota Method,Inverse Scattering Transform Method,and Several Other Methods

The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is connected to a particular case of SEsM for a specific form of the function from Step 2 of SEsM and for simple equations of the kinds of differential equations for exponential functions. We illustrate this particular case of SEsM by obtaining the three- soliton solution of the Korteweg-de Vries equation, two-soliton solution of the nonlinear Schrödinger equation, and the soliton solution of the Ishimori equation for the spin dynamics of ferromagnetic materials. Then we show that a particular case of SEsM can be used in order to reproduce the methodology of the inverse scattering transform method for the case of the Burgers equation and Korteweg-de Vries equation. This particular case is connected to use of a specific case of Step 2 of SEsM. This step is connected to: (i) representation of the solution of the solved nonlinear partial differential equation as expansion as power series containing powers of a “small” parameter ϵ; (ii) solving the differential equations arising from this representation by means of Fourier series, and (iii) transition from the obtained solution for small values of ϵ to solution for arbitrary finite values of ϵ. Finally, we show that the much-used homogeneous balance method, extended homogeneous balance method, auxiliary equation method, Jacobi elliptic function expansion method, F-expansion method, modified simple equation method, trial function method and first integral method are connected to particular cases of SEsM.     

Local inverse inelastic mean free path at interface

We calculated a local inverse inelastic mean free path (local-IIMFP) for electrons crossing a medium–medium interface, considering various incident electron energies, crossing angles and combinations of materials. We used an extension of a classical dielectric model developed by Li and co-workers for an electron crossing a surface (interface vacuum-medium). Moreover, the integration over the distance of the local-IIMFP allows to obtain the interface excitation parameter (or IEP) characterizing the change in excitation probability for an electron crossing an interface once caused by the presence of the interface in comparison with an electron for which only volume excitations are considered. We perform these calculations for angles between 0° and 80°, for electron energies between 500 and 2500 eV and for various pairs of materials, as Al/In for its academic interest or Au/Si and SiO₂/Si for their technological importance. Small but not negligible variations of the local-IIMFP and the IEP were observed for metal–metal or metal–semiconductor interfaces, while quite significant variations are obtained when one of the materials is a insulator.