Deuteron-equivalent and phase-equivalent interactions within light nuclei

Background: Phase-equivalent transformations (PETs) are well-known in quantum scattering and inverse scattering theory. PETs do not affect scattering phase shifts and bound state energies of two-body system but are conventionally supposed to modify two-body bound state observables such as the rms radius and electromagnetic moments. Purpose: In order to preserve all bound state observables, we propose a new particular case of PETs, a deuteron-equivalent transformation (DET-PET), which leaves unchanged not only scattering phase shifts and bound state (deuteron) binding energy but also the bound state wave function. Methods: The construction of DET-PET is discussed; equations defining the simplest DET-PETs are derived. We apply these simplest DET-PETs to the JISP16 $NN$ interaction and use the transformed $NN$ interactions in calculations of $^3$H and $^4$He binding energies in the No-core Full Configuration (NCFC) approach based on extrapolations of the No-core Shell Model (NCSM) basis space results to the infinite basis space. Results: We demonstrate the DET-PET modification of the $np$ scattering wave functions and study the DET-PET manifestation in the binding energies of $^3$H and $^4$He nuclei and their correlation (Tjon line). Conclusions: It is shown that some DET-PETs generate modifications of the central component while the others modify the tensor component of the $NN$ interaction. DET-PETs are able to modify significantly the $np$ scattering wave functions and hence the off-shell properties of the $NN$ interaction. DET-PETs give rise to significant changes in the binding energies of $^3$H (in the range of approximately 1.5 MeV) and $^4$He (in the range of more than 9 MeV) and are able to modify the correlation patterns of binding energies of these nuclei

Conceptual modelling: Towards detecting modelling errors in engineering applications

Rapid advancements of modern technologies put high demands on mathematical modelling of engineering systems. Typically, systems are no longer “simple” objects, but rather coupled systems involving multiphysics phenomena, the modelling of which involves coupling of models that describe different phenomena. After constructing a mathematical model, it is essential to analyse the correctness of the coupled models and to detect modelling errors compromising the final modelling result. Broadly, there are two classes of modelling errors: (a) errors related to abstract modelling, eg, conceptual errors concerning the coherence of a model as a whole and (b) errors related to concrete modelling or instance modelling, eg, questions of approximation quality and implementation. Instance modelling errors, on the one hand, are relatively well understood. Abstract modelling errors, on the other, are not appropriately addressed by modern modelling methodologies. The aim of this paper is to initiate a discussion on abstract approaches and their usability for mathematical modelling of engineering systems with the goal of making it possible to catch conceptual modelling errors early and automatically by computer assistant tools. To that end, we argue that it is necessary to identify and employ suitable mathematical abstractions to capture an accurate conceptual description of the process of modelling engineering systems

Influence of mean distance between fibers on the effective gas thermal conductivity in highly porous fibrous materials

This work was supported by the Russian Goverment Grant No. 14.Z50.31.0036.Peer reviewedPostprin

The Late Modernism of Cormac McCarthy (review)

David Holloway\u27s titular phrasing late modernism has an effective ring. It captures the theoretical underpinnings of his recent book, The Late Modernism of Cormac McCarthy, evoking Fredric Jameson\u27s work, on which Holloway heavily relies, while also situating McCarthy precisely where he wants him to be, historically and culturally. According to Holloway, McCarthy\u27s fiction constitutes an important redoubt against the diminishing of modernism\u27s once-valorous stance by forging a productive opposition to what he sees as a final stage in capitalist expansion. At the heart of Holloway\u27s project is his concern to restore an oppositional vitality to literary production, or what he terms a perspective of estrangement (2). Following certain poststructuralist accounts of language\u27s inherent instability and the related impossibilities of narrative, Holloway sees McCarthy as a writer whose singular prose at once foregrounds and incorporates the deathliness of language in his stories of an evacuated yet thoroughly commercialized American West—a topos and a space defined, Holloway suggests, by the ravages of globalization

Inelastic Neutron Scattering by Gaseous O2

The magnetic contributions to neutron diffraction by molecular oxygen have been studied both experimentally and theoretically. We extend the theoretical studies by performing a calculation of the magnetic interaction in the inelastic neutron cross section for gaseous O2. The magnetic inelastic cross section for O2 is significantly different from the nuclear inelastic cross section due to the lack of spherical symmetry in the magnetic‐moment distribution about each oxygen nucleus. It is expected from these results that the inelastic cross section for O2 will provide more information about the magnetic‐moment distribution than the angular distribution. We present representative calculations to indicate the size and nature of the magnetic contribution to the inelastic cross section.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71223/2/JCPSA6-49-2-890-1.pd