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.     

Topology optimization of composite hyperelastic material using SPIMFO-method

Meccanica - Fiber reinforced materials are used in assorted engineering application and for this reason, new additive manufacturing technologies have been developed for this type of materials. With...     

In vivo comprehensive multiphase NMR

Traditionally, due to different hardware requirements, nuclear magnetic resonance (NMR) has developed as two separate fields: one dealing with solids, and one with solutions. Comprehensive multiphase (CMP) NMR combines all electronics and hardware (magic angle spinning [MAS], gradients, high power Radio Frequency (RF) handling, lock, susceptibility matching) into a universal probe that permits a comprehensive study of all phases (i.e., liquid, gel-like, semisolid, and solid), in intact samples. When applied in vivo, it provides unique insight into the wide array of bonds in a living system from the most mobile liquids (blood, fluids) through gels (muscle, tissues) to the most rigid (exoskeleton, shell). In this tutorial, the practical aspects of in vivo CMP NMR are discussed including: handling the organisms, rotor preparation, sample spinning, water suppression, editing experiments, and finishes with a brief look at the potential of other heteronuclei (²H, ¹⁵N, ¹⁹F, ³¹P) for in vivo research. The tutorial is aimed as a general resource for researchers interested in developing and applying MAS-based approaches to living organisms. Although the focus here is CMP NMR, many of the approaches can be adapted (or directly applied) using conventional high-resolution magic angle spinning, and in some cases, even standard solid-state NMR probes.     

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.     

Soft X-ray resonant magnetic scattering studies on Fe/CoO exchange bias system

We have used soft X-ray resonant magnetic scattering (XRMS) to search for the presence of an effective ferromagnetic moment belonging to the antiferromagnetic (AF) layer which is in close contact with a ferromagnetic (F) layer. Taking advantage of the element specificity of the XRMS technique, we have measured hysteresis loops of both Fe and CoO layers of a CoO(40 Å)/Fe (150 Å) exchange bias bilayer. From these measurements we have concluded that the proximity of the F layer induces a magnetic moment in the AF layer. The F moment of the AF layer has two components: one is frozen and does not follow the applied magnetic field and the other one follows in phase the ferromagnetic magnetization of the F layer. The temperature dependence of the F components belonging to the AF layer is shown and discussed.     

Etorphine‐Related Ferrocenyl‐Substituted Morphinan Alkaloids

The two diastereoisomeric ferrocenyl‐substituted orvinols 2 and 3 were prepared. The modified alkaloids are still able to interact with opioid receptors (see Table). The ferrocene moiety allows highly selective and sensitive electrochemical detection. The X‐ray crystal structure of the major isomer 2 was determined. The combination of a metallocene and a morphinan alkaloid holds promise for useful antitumor activity.     

Quinazolines. VII. Synthesis of 1,3-Diamino-5,6-dihydrobenzo[f]quinazolines

Eighteen new 1,3-diamino-5,6-dihydrobenzo[f] quinazolines ( 6 , R. = alkyl, Cl, MeO) were synthesized via the condensation of appropriate 2-tetralones with cyanoguanidine under fusion conditions. Methods were developed for the preparation of a number of heretofore undescribed 2-tetralones as precursors. The final products can be viewed as conformationally rigid analogs of pyrimethamine ( 2 ), and are of interest as inhibitors of dihydrofolate reductase and as potential antimalarial and antitumor agents.     

Structure of small actin-containing liposomes probed by atomic force microscopy: effect of actin concentration & liposome size

Actin-containing liposomes were prepared via extrusion through 400 and 600 nm pore diameter membranes at different monomeric actin concentrations in low ionic strength buffer (G-buffer). After subjecting the liposome dispersions to high ionic strength polymerization buffer (F-buffer), topological changes in liposome structure were studied using atomic force microscopy (AFM). Paired dumbbell, horseshoelike, and disklike assemblies were observed for actin-containing liposomes extruded through 400 and 600 nm pore diameter membranes. The topology of actin-containing liposomes was found to be highly dependent on both liposome size and actin concentration. At 1 mg/mL actin, the actin-containing liposomes transformed into a disklike shape, whereas, at 5 mg/mL actin, the actin-containing liposomes retained a spherical shape. On the basis of these observations, we hypothesize that actin could either polymerize on the surface of the inner leaflet of the liposome membrane or polymerize in the aqueous core of the liposome. We explain the associated shape changes induced in actin-containing liposomes on the basis of the hypothesized mechanism of actin polymerization inside the liposomes. At higher actin concentrations (5 mg/mL), we observed membrane-induced actin self-assembly in G-buffer, which implies that G-actin is able to interact directly with lipid bilayers at sufficiently high concentrations.