Starting step size for an ODE solver

AbstractOne of the more critical issues in solving ordinary differential equations by a step-by-step process occurs in the starting phase. Somehow the procedure must be supplied with an initial step size that is on scale for the problem at hand. It must be small enough to yield a reliable solution by the process, but not so small as to significantly affect the efficiency of solution. In this paper, we discuss an algorithm for obtaining a good starting step size and present a subroutine which can be readily used in most ODE solvers

International Evidence on the Determinants of Organizational Ethical Vulnerability

© 2018 British Academy of Management This paper proposes a model to explain what makes organizations ethically vulnerable. Drawing upon legitimacy, institutional, agency and individual moral reasoning theories we consider three sets of explanatory factors and examine their association with organizational ethical vulnerability. The three sets comprise external institutional context, internal corporate governance mechanisms and organizational ethical infrastructure. We combine these three sets of factors and develop an analytical framework for classifying ethical issues and propose a new model of organizational ethical vulnerability. We test our model on a sample of 253 firms that were involved in ethical misconduct and compare them with a matched sample of the same number of firms from 28 different countries. The results suggest that weak regulatory environment and internal corporate governance, combined with profitability warnings or losses in the preceding year, increase organizational ethical vulnerability. We find counterintuitive evidence suggesting that firms’ involvement in bribery and corruption prevention training programmes is positively associated with the likelihood of ethical vulnerability. By synthesizing insights about individual and corporate behaviour from multiple theories, this study extends existing analytical literature on business ethics. Our findings have implications for firms’ external regulatory settings, corporate governance mechanisms and organizational ethical infrastructure

A problem-solving environment for the numerical solution of boundary value problems

Boundary value problems (BVPs) are systems of ordinary differential equations (ODEs) with boundary conditions imposed at two or more distinct points. Such problems arise within mathematical models in a wide variety of applications. Numerically solving BVPs for ODEs generally requires the use of a series of complex numerical algorithms. Fortunately, when users are required to solve a BVP, they have a variety of BVP software packages from which to choose. However, all BVP software packages currently available implement a specific set of numerical algorithms and therefore function quite differently from each other. Users must often try multiple software packages on a BVP to find the one that solves their problem most effectively. This creates two problems for users. First, they must learn how to specify the BVP for each software package. Second, because each package solves a BVP with specific numerical algorithms, it becomes difficult to determine why one BVP package outperforms another. With that in mind, this thesis offers two contributions. First, this thesis describes the development of the BVP component to the fully featured problem-solving environment (PSE) for the numerical solution of ODEs called pythODE. This software allows users to select between multiple numerical algorithms to solve BVPs. As a consequence, they are able to determine the numerical algorithms that are effective at each step of the solution process. Users are also able to easily add new numerical algorithms to the PSE. The effect of adding a new algorithm can be measured by making use of an automated test suite. Second, the BVP component of pythODE is used to perform two research studies. In the first study, four known global-error estimation algorithms are compared in pythODE. These algorithms are based on the use of Richardson extrapolation, higher-order formulas, deferred corrections, and a conditioning constant. Through numerical experimentation, the algorithms based on higher-order formulas and deferred corrections are shown to be computationally faster than Richardson extrapolation while having similar accuracy. In the second study, pythODE is used to solve a newly developed one-dimensional model of the agglomerate in the catalyst layer of a proton exchange membrane fuel cell

Imparting work based skills on vocational courses, pedagogy of using industrial simulation in surveying education: a study of a model run at Sheffield Hallam University in 2011

The paper relates to delivering vocational higher education to prospective building surveyors. Preparing students for the workplace requires inclusion of academic knowledge, workplace skills and practical vocational experience. This is reinforced by feedback from the four stakeholders to surveying education, learner, employer, education provider and professional institution. Successful delivery of learning to distinct vocational groups requires specific pedagogy. The paper analyses a realistic industrial simulation delivered to teach knowledge and skills to undergraduate building surveying students. Initial pedagogy was proposed by CEEBL, Centre for Excellence in Enquiry Based Learning. Work based skills requirements were taken from published work including leading building surveying academics and practitioners like Professor Mike Hoxley and Professor Malcolm Hollis. Data analysis is used to evolve future simulations. These become better suited to delivering appropriate learning, valid assessment and usable vocational skills, against academic, student focused and industrial criteria. An action research approach is utilised by the author to develop specialist pedagogy through analysis of outcome data and stakeholder feedback. Action research is undertaken through an approach using trial, evaluation and development. The paper concludes, simulation can be a valid tool for delivering teaching, learning, assessment and vocational skills training to surveying students and justifies further research

Explicit Runge-Kutta algorithm to solve non-local equations with memory effects: case of the Maxey-Riley-Gatignol equation

A standard approach to solve ordinary differential equations, when they describe dynamical systems, is to adopt a Runge-Kutta or related scheme. Such schemes, however, are not applicable to the large class of equations which do not constitute dynamical systems. In several physical systems, we encounter integro-differential equations with memory terms where the time derivative of a state variable at a given time depends on all past states of the system. Secondly, there are equations whose solutions do not have well-defined Taylor series expansion. The Maxey-Riley-Gatignol equation, which describes the dynamics of an inertial particle in nonuniform and unsteady flow, displays both challenges. We use it as a test bed to address the questions we raise, but our method may be applied to all equations of this class. We show that the Maxey-Riley-Gatignol equation can be embedded into an extended Markovian system which is constructed by introducing a new dynamical co-evolving state variable that encodes memory of past states. We develop a Runge-Kutta algorithm for the resultant Markovian system. The form of the kernels involved in deriving the Runge-Kutta scheme necessitates the use of an expansion in powers of $t^{1/2}$. Our approach naturally inherits the benefits of standard time-integrators, namely a constant memory storage cost, a linear growth of operational effort with simulation time, and the ability to restart a simulation with the final state as the new initial condition.Comment: 26 pages, 5 figures, 1 table (v2) Typos correcte

Review of the Synergies Between Computational Modeling and Experimental Characterization of Materials Across Length Scales

With the increasing interplay between experimental and computational approaches at multiple length scales, new research directions are emerging in materials science and computational mechanics. Such cooperative interactions find many applications in the development, characterization and design of complex material systems. This manuscript provides a broad and comprehensive overview of recent trends where predictive modeling capabilities are developed in conjunction with experiments and advanced characterization to gain a greater insight into structure-properties relationships and study various physical phenomena and mechanisms. The focus of this review is on the intersections of multiscale materials experiments and modeling relevant to the materials mechanics community. After a general discussion on the perspective from various communities, the article focuses on the latest experimental and theoretical opportunities. Emphasis is given to the role of experiments in multiscale models, including insights into how computations can be used as discovery tools for materials engineering, rather than to "simply" support experimental work. This is illustrated by examples from several application areas on structural materials. This manuscript ends with a discussion on some problems and open scientific questions that are being explored in order to advance this relatively new field of research.Comment: 25 pages, 11 figures, review article accepted for publication in J. Mater. Sc

A human-centric approach for adopting bug inducing commit detection using machine learning models

When developing new software, testing can take up half of the resources. Although a considerable amount of work has been done to automate software testing, fixing bugs after adding them to the source repository is still a costly task from both management and financial perspectives. In recent times, the research community has proposed various methodologies to detect bugs just-in-time at the commit level. Unfortunately, this work, including state-of-the-art techniques, do not provide real-time solutions for the problem. Such a limitation restricts developers from utilizing them in their day-to-day programming tasks. Our study focuses on providing solutions that deliver real-time support to the developers by warning them about potential bug-inducing commits. Such support can help developers by preventing them from adding a bug-inducing commit to the source repository. Keeping this goal in mind, we conducted a developer survey to understand the expectations of developers for bug-inducing commit detection tools. Motivated by their responses, we built a GUI-based plug-in that warns the developers when they attempt to perform a potential buggy commit. We accomplished this by training machine learning models on relevant features. We also built a command-line tool for the developers who prefer to use a command-line interface. Our proposed solution has been designed to work with various machine learning models (e.g. random forest, decision tree, and logistic regression) and IDEs (e.g. Visual Studio, PyCharm, and WebStorm). It enables developers to work with a familiar interface without leaving the IDE. As a proof of concept, we implemented a VSCode plug-in and an accompanying command-line tool. Developers can customize these tools by choosing among various machine learning models and features. Such customizability empowers the developers to understand the toolchain better and lets them fit it into their specific use cases. Our user study shows that the toolchain offers satisfactory performance in detecting bug-inducing commits and provides a sound user experience. The decision tree model achieved the best performance with a 79% accuracy and an f1-score of 0.70 among the tested models. In addition, we performed a user study with developers working in the software industries to validate the usability of our toolchain. We found that the users can detect whether a commit is bug-inducing or not within a short period of time. Furthermore, they prefer our tool over the state-of-the-art to detect potential bugs before the commit operation. Alongside contributing a new multi-UI toolchain, our work enriches the research community’s knowledge regarding developer usability of real-time bug detection tools

SUPPLY CHAIN STRUCTURE, PRODUCT RECALLS AND FIRM PERFORMANCE: INVESTIGATING RECALL DRIVERS AND RECALL FINANCIAL PERFORMANCE RELATIONSHIPS

This dissertation is a two-essay study on globalization, sourcing structure and product quality and firm performance in global supply chain management. In the first essay, using a unique archival dataset on firms and their suppliers, the role of supply chain strategies in contributing to product safety and quality, as assessed through product recalls are investigated. The second essay investigates the relationship between product recalls and firm performance. Moreover, the moderating effects on the recall-profitability relationship of supply chain as well as recall management strategies are investigated . Essay 1 investigates how a number of supply chain strategies contribute to product recalls. In particular, I examine how the make or buy decision (i.e., outsourcing), the decision to concentrate the supply base (i.e., use few vs. several suppliers), the use of foreign suppliers (i.e., offshoring), and the extent of global operations, contribute to product recalls. The subject area of product quality and safety failures leading to product recalls is important because product recalls can have a major, negative impact on firm performance. For example, in the event of a product recall, replacement orders may need to be shipped, new suppliers may need to be found and vetted, and marketing expenditures may need to be made to counter negative publicity from the recall. Applying key theories in operations and supply chain management, I find that firms vary greatly in recall propensity and that these variations are related to heterogeneity in outsourcing, offshoring, and supply base concentration. In the second essay, I revisit the recall-performance relationship. First, I investigate the relationship between product recalls and profitability. Firms may choose to try to avoid product recalls by increasing their expenditures on product quality and inspection services. Or, on the other hand, they may emphasize short term profitability by reducing production and inspection costs, thereby increasing the risk of incurring a product recall. Since firms are expected to balance production and quality inspection costs against the costs associated with product recalls in order to maximize profit performance, the recall-profitability relationship is not clear, a priori. I further investigate the moderating effect of global operations, supply base structure and recall strategies on the relationship between product recalls and profit margins. My theory-based research suggests a curvilinear recall-profit relationship and that this relationship depends on key global supply chain practices and recall management strategies