Symmetry adapted Assur decompositions

Assur graphs are a tool originally developed by mechanical engineers to decompose mechanisms for simpler analysis and synthesis. Recent work has connected these graphs to strongly directed graphs, and decompositions of the pinned rigidity matrix. Many mechanisms have initial configurations which are symmetric, and other recent work has exploited the orbit matrix as a symmetry adapted form of the rigidity matrix. This paper explores how the decomposition and analysis of symmetric frameworks and their symmetric motions can be supported by the new symmetry adapted tools.Comment: 40 pages, 22 figure

Assur decompositions of direction-length frameworks

A bar-joint framework is a realisation of a graph consisting of stiff bars linked by universal joints. The framework is rigid if the only bar-length preserving continuous motions of the joints arise from isometries. A rigid framework is isostatic if deleting any single edge results in a flexible framework. Generically, rigidity depends only on the graph and we say an Assur graph is a pinned isostatic graph with no proper pinned isostatic subgraphs. Any pinned isostatic graph can be decomposed into Assur components which may be of use for mechanical engineers in decomposing mechanisms for simpler analysis and synthesis. A direction-length framework is a generalisation of bar-joint framework where some distance constraints are replaced by direction constraints. We initiate a theory of Assur graphs and Assur decompositions for direction-length frameworks using graph orientations and spanning trees and then analyse choices of pinning set

Rigidity through a Projective Lens

In this paper, we offer an overview of a number of results on the static rigidity and infinitesimal rigidity of discrete structures which are embedded in projective geometric reasoning, representations, and transformations. Part I considers the fundamental case of a bar−joint framework in projective d-space and places particular emphasis on the projective invariance of infinitesimal rigidity, coning between dimensions, transfer to the spherical metric, slide joints and pure conditions for singular configurations. Part II extends the results, tools and concepts from Part I to additional types of rigid structures including body-bar, body−hinge and rod-bar frameworks, all drawing on projective representations, transformations and insights. Part III widens the lens to include the closely related cofactor matroids arising from multivariate splines, which also exhibit the projective invariance. These are another fundamental example of abstract rigidity matroids with deep analogies to rigidity. We conclude in Part IV with commentary on some nearby areas

Case studies in estimating subsea systems’ readiness level

Copyright © The Author(s) 2020. Systems readiness level (SRL) is a metric defined for assessing progress in the development of systems. The methodologies to estimate SRLs are built on the technology readiness level (TRL), originally developed by NASA to assess the readiness of new technologies for insertion into a system. TRL was later adopted by governmental institutions and many industries, including the American Petroleum Institute (API). The TRL of each component is mathematically combined with another metric, integration readiness level (IRL), to estimate the overall level of readiness of a system. An averaging procedure is then used to estimate the composite level of systems readiness. The present paper builds on the previous paper by Yasseri (2013) and presents case examples to demonstrate the estimation of SRL using two approaches. The objective of the present paper is to show how the TRL, IRL, and SRL are combined mathematically. The performance of the methodology is also demonstrated in a parametric study by pushing the states of readiness to their extremes, namely very low and very high readiness. The present paper compares and contrasts the two major system readiness levels estimation methods: one proposed by Sauser et al. (2006) for defence acquisition based on NASA's TRL scale, and another based on API's TRL scale. The differences and similarities are demonstrated using a case study

Development of a positron emission tomograph for “in-vivo” dosimetry in hadrontherapy

This thesis is related to the DoPET project, which aims to evaluate the feasibility of a dedicated Positron Emission Tomograph (PET) for measuring, monitoring, and verifying the radiation dose that is being delivered to the patient during hadrontherapy. Radiation therapy with protons and heavier ions is becoming a more common treatment option, with many new centers under construction or at planning stage worldwide. The main physical advantage of these new treatment modalities is the high selectivity in the dose delivery: very little dose is deposited in healthy tissues beyond the particles’ range. However, in clinical practice the beam path in the patient is not exactly known. This affects the quality of the treatment planning, and may compromise the translation of the physical advantage into a clinical benefit. The use of a PET system immediately after the therapeutical irradiation (“in-beam”) for in-vivo imaging of the tissue + activation produced by nuclear reactions of the ion beam with the target, could help to have a better control of the treatment delivery. The DoPET project, based on an Italian INFN collaboration, aims to explore one possible approach to the hadron-driven PET technique, through the development of a dedicated device. Such goal was reached through the validation of a PET prototype with proton irradiations on plastic phantoms at the CATANA proton therapy facility (LNS-INFN, Catania, Italy) and with carbon irradiations on plastic phantoms at the GSI synchrotron (Darmstadt, Germany). A preliminary comparison with an existing in-beam PET device was also performed. The candidate was involved with all aspects of this project, specifically the Monte Carlo simulations of the physical processes at the basis of phantom activation, the measurements for the characterization of the DoPET detector, the improvement of the image reconstruction algorithm, and the extensive measurements in plastic phantoms. The system and the methods described in this thesis have to be considered as a proof of principle, and the promising results justify a larger effort for the construction of a clinical system

The Material Theory of Induction

The fundamental burden of a theory of inductive inference is to determine which are the good inductive inferences or relations of inductive support and why it is that they are so. The traditional approach is modeled on that taken in accounts of deductive inference. It seeks universally applicable schemas or rules or a single formal device, such as the probability calculus. After millennia of halting efforts, none of these approaches has been unequivocally successful and debates between approaches persist. The Material Theory of Induction identifies the source of these enduring problems in the assumption taken at the outset: that inductive inference can be accommodated by a single formal account with universal applicability. Instead, it argues that that there is no single, universally applicable formal account. Rather, each domain has an inductive logic native to it.The content of that logic and where it can be applied are determined by the facts prevailing in that domain. Paying close attention to how inductive inference is conducted in science and copiously illustrated with real-world examples, The Material Theory of Induction will initiate a new tradition in the analysis of inductive inference

Development and application of a generalized Reynolds-stress model of turbulence

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Fourth NASA Langley Formal Methods Workshop

This publication consists of papers presented at NASA Langley Research Center's fourth workshop on the application of formal methods to the design and verification of life-critical systems. Topic considered include: Proving properties of accident; modeling and validating SAFER in VDM-SL; requirement analysis of real-time control systems using PVS; a tabular language for system design; automated deductive verification of parallel systems. Also included is a fundamental hardware design in PVS

OpenFPM: A scalable environment for particle and particle-mesh codes on parallel computers

Scalable and efficient numerical simulations continue to gain importance, as computation is firmly established tool of discovery, together with theory and experiment. Meanwhile, the performance of computing hardware grows with increasing heterogeneous hardware, enabling simulations of ever more complex models. However, efficiently implementing scalable codes on heterogeneous, distributed hardware systems becomes the bottleneck. This bottleneck can be alleviated by intermediate software layers that provide higher-level abstractions closer to the problem domain, hence allowing the computational scientist to focus on the simulation. Here, we present OpenFPM, an open and scalable framework that provides an abstraction layer for numerical simulations using particles and/or meshes. OpenFPM provides transparent and scalable infrastructure for shared-memory and distributed-memory implementations of particles-only and hybrid particle-mesh simulations of both discrete and continuous models, as well as non-simulation codes. This infrastructure is complemented with frequently used numerical routines, as well as interfaces to third-party libraries. This thesis will present the architecture and design of OpenFPM, detail the underlying abstractions, and benchmark the framework in applications ranging from Smoothed-Particle Hydrodynamics (SPH) to Molecular Dynamics (MD), Discrete Element Methods (DEM), Vortex Methods, stencil codes, high-dimensional Monte Carlo sampling (CMA-ES), and Reaction-Diffusion solvers, comparing it to the current state of the art and existing software frameworks