Revisiting the implications of Liouville's theorem to the anisotropy of cosmic rays

We present a solution to Liouville's equation for an ensemble of charged particles propagating in magnetic fields. The solution is presented using an expansion in spherical harmonics of the phase space density, allowing a direct interpretation of the distribution of arrival directions of cosmic rays. The results are found for chosen conditions of variability and source distributions. We show there are two conditions for an initially isotropic flux of particles to remain isotropic while traveling through a magnetic field: isotropy and homogeneity of the sources. The formalism is used to analyze the data measured by the Pierre Auger Observatory, contributing to the understanding of the dependence of the dipole amplitude with energy and predicting the energy in which the quadrupole signal should be measured

Cosmic-Ray Anisotropies in Right Ascension Measured by the Pierre Auger Observatory

We present measurements of the large-scale cosmic-ray (CR) anisotropies in R.A., using data collected by the surface detector array of the Pierre Auger Observatory over more than 14 yr. We determine the equatorial dipole component, through a Fourier analysis in R.A. that includes weights for each event so as to account for the main detector-induced systematic effects. For the energies at which the trigger efficiency of the array is small, the east-west method is employed. Besides using the data from the array with detectors separated by 1500 m, we also include data from the smaller but denser subarray of detectors with 750 m separation, which allows us to extend the analysis down to ∼0.03 EeV. The most significant equatorial dipole amplitude obtained is that in the cumulative bin above 8 EeV, %, which is inconsistent with isotropy at the 6σ level. In the bins below 8 EeV, we obtain 99% CL upper bounds on d ⊥ at the level of 1%-3%. At energies below 1 EeV, even though the amplitudes are not significant, the phases determined in most of the bins are not far from the R.A. of the Galactic center, at GC =-94°, suggesting a predominantly Galactic origin for anisotropies at these energies. The reconstructed dipole phases in the energy bins above 4 EeV point instead to R.A. that are almost opposite to the Galactic center one, indicative of an extragalactic CR origin

An Integrated Approach to Life Cycle Analysis

Life Cycle Analysis (LCA) is the evaluation of the impacts that design decisions have on a system and provides a framework for identifying and evaluating design benefits and burdens associated with the life cycles of space transportation systems from a "cradle-to-grave" approach. Sometimes called life cycle assessment, life cycle approach, or "cradle to grave analysis", it represents a rapidly emerging family of tools and techniques designed to be a decision support methodology and aid in the development of sustainable systems. The implementation of a Life Cycle Analysis can vary and may take many forms; from global system-level uncertainty-centered analysis to the assessment of individualized discriminatory metrics. This paper will focus on a proven LCA methodology developed by the Systems Analysis and Concepts Directorate (SACD) at NASA Langley Research Center to quantify and assess key LCA discriminatory metrics, in particular affordability, reliability, maintainability, and operability. This paper will address issues inherent in Life Cycle Analysis including direct impacts, such as system development cost and crew safety, as well as indirect impacts, which often take the form of coupled metrics (i.e., the cost of system unreliability). Since LCA deals with the analysis of space vehicle system conceptual designs, it is imperative to stress that the goal of LCA is not to arrive at the answer but, rather, to provide important inputs to a broader strategic planning process, allowing the managers to make risk-informed decisions, and increase the likelihood of meeting mission success criteria

A review of friction models in interacting joints for durability design.

This paper presents a comprehensive review of friction modelling to provide an understanding of design for durability within interacting systems. Friction is a complex phenomenon and occurs at the interface of two components in relative motion. Over the last several decades, the effects of friction and its modelling techniques have been of significant interests in terms of industrial applications. There is however a need to develop a unified mathematical model for friction to inform design for durability within the context of varying operational conditions. Classical dynamic mechanisms model for the design of control systems has not incorporated friction phenomena due to non-linearity behaviour. Therefore, the tribological performance concurrently with the joint dynamics of a manipulator joint applied in hazardous environments needs to be fully analysed. Previously the dynamics and impact models used in mechanical joints with clearance have also been examined. The inclusion of reliability and durability during the design phase is very important for manipulators which are deployed in harsh environmental and operational conditions. The revolute joint is susceptible to failures such as in heavy manipulators these revolute joints can be represented by lubricated conformal sliding surfaces. The presence of pollutants such as debris and corrosive constituents has the potential to alter the contacting surfaces, would in turn affect the performance of revolute joints, and puts both reliability and durability of the systems at greater risks of failure. Key literature is identified and a review on the latest developments of the science of friction modelling is presented here. This review is based on a large volume of knowledge. Gaps in the relevant field have been identified to capitalise on for future developments. Therefore, this review will bring significant benefits to researchers, academics and industrial professionals