Analyzing the Fierz Rearrangement Freedom for Local Chiral Two-Nucleon Potentials

Chiral effective field theory is a framework to derive systematic nuclear interactions. It is based on the symmetries of quantum chromodynamics and includes long-range pion physics explicitly, while shorter-range physics is expanded in a general operator basis. The number of low-energy couplings at a particular order in the expansion can be reduced by exploiting the fact that nucleons are fermions and therefore obey the Pauli exclusion principle. The antisymmetry permits the selection of a subset of the allowed contact operators at a given order. When local regulators are used for these short-range interactions, however, this "Fierz rearrangement freedom" is violated. In this paper, we investigate the impact of this violation at leading order (LO) in the chiral expansion. We construct LO and next-to-leading order (NLO) potentials for all possible LO-operator pairs and study their reproduction of phase shifts, the ${}^4$He ground-state energy, and the neutron-matter energy at different densities. We demonstrate that the Fierz rearrangement freedom is partially restored at NLO where subleading contact interactions enter. We also discuss implications for local chiral three-nucleon interactions.Comment: 11 pages, 5 figure

Large-cutoff behavior of local chiral effective field theory interactions

Interactions from chiral effective field theory have been successfully employed in a broad range of \textit{ab initio} calculations of nuclei and nuclear matter, but it has been observed that most results of few- and many-body calculations experience a substantial residual regulator and cutoff dependence. In this work, we investigate the behavior of local chiral potentials at leading order under variation of the cutoff scale for different local regulators. When varying the cutoff, we require that the resulting interaction produces no spurious bound states in the deuteron channel. We find that, for a particular choice of leading-order operators, nucleon-nucleon phase shifts and the deuteron ground-state energy converge to cutoff-independent plateaus, for all regulator functions we investigate. This observation may enable improved calculations with chiral Hamiltonians that also include three-nucleon interactions.Comment: 10 pages, 6 figures, published versio

Spacecraft applications of advanced global positioning system technology

The purpose of this study was to evaluate potential uses of Global Positioning System (GPS) in spacecraft applications in the following areas: attitude control and tracking; structural control; traffic control; and time base definition (synchronization). Each of these functions are addressed. Also addressed are the hardware related issues concerning the application of GPS technology and comparisons are provided with alternative instrumentation methods for specific functions required for an advanced low earth orbit spacecraft

Towards usable generation and enforcement of trust evidence from programmers’ intent

Programmers develop code with a sense of purpose and with expectations on how units of code should interact with other units of code. But this intent of programmers is typically implicit and undocumented, goes beyond considerations of functional correctness, and may depend on trust assumptions that programmers make. At present, neither programming languages nor development environments offer a means of articulating such intent in a manner that could be used for controlling whether software executions meet such intentions and their associated expectations. We here study how extant research on trust can inform approaches to articulating programmers’ intent so that it may help with creating trust evidence for more trustworthy interaction of software units

Mathematics for the exploration of requirements

The exploration of requirements is as complex as it is important in ensuring a successful software production and software life cycle. Increasingly, tool-support is available for aiding such explorations. We use a toy example and a case study of modelling and analysing some requirements of the global assembly cache of .NET to illustrate the opportunities and challenges that mathematically founded exploration of requirements brings to the computer science and software engineering curricula

Objective Bayesian Edge Screening and Structure Selection for Ising Networks

The Ising model is one of the most widely analyzed graphical models in network psychometrics. However, popular approaches to parameter estimation and structure selection for the Ising model cannot naturally express uncertainty about the estimated parameters or selected structures. To address this issue, this paper offers an objective Bayesian approach to parameter estimation and structure selection for the Ising model. Our methods build on a continuous spike-and-slab approach. We show that our methods consistently select the correct structure and provide a new objective method to set the spike-and-slab hyperparameters. To circumvent the exploration of the complete structure space, which is too large in practical situations, we propose a novel approach that first screens for promising edges and then only explore the space instantiated by these edges. We apply our proposed methods to estimate the network of depression and alcohol use disorder symptoms from symptom scores of over 26,000 subjects. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s11336-022-09848-8

Influence of the substrate-induced strain and irradiation disorder on the Peierls transition in TTF-TCNQ microdomains

The influence of the combined effects of substrate-induced strain, finite size and electron irradiation-induced defects have been studied on individual micron-sized domains of the organic charge transfer compound tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) by temperature-dependent conductivity and current-voltage measurements. The individual domains have been isolated by focused ion beam etching and electrically contacted by focused ion and electron beam induced deposition of metallic contacts. The temperature-dependent conductivity follows a variable range hopping behavior which shows a crossover of the exponent as the Peierls transition is approached. The low temperature behavior is analyzed within the segmented rod model of Fogler, Teber and Shklowskii, as originally developed for a charge-ordered quasi one-dimensional electron crystal. The results are compared with data obtained on as-grown and electron irradiated epitaxial TTF-TCNQ thin films of the two-domain type