Canards and curvature: nonsmooth approximation by pinching

In multiple time-scale (singularly perturbed) dynamical systems, canards are counterintuitive solutions that evolve along both attracting and repelling invariant manifolds. In two dimensions, canards result in periodic oscillations whose amplitude and period grow in a highly nonlinear way: they are slowly varying with respect to a control parameter, except for an exponentially small range of values where they grow extremely rapidly. This sudden growth, called a canard explosion, has been encountered in many applications ranging from chemistry to neuronal dynamics, aerospace engineering and ecology. Canards were initially studied using nonstandard analysis, and later the same results were proved by standard techniques such as matched asymptotics, invariant manifold theory and parameter blow-up. More recently, canard-like behaviour has been linked to surfaces of discontinuity in piecewise-smooth dynamical systems. This paper provides a new perspective on the canard phenomenon by showing that the nonstandard analysis of canard explosions can be recast into the framework of piecewise-smooth dynamical systems. An exponential coordinate scaling is applied to a singularly perturbed system of ordinary differential equations. The scaling acts as a lens that resolves dynamics across all time-scales. The changes of local curvature that are responsible for canard explosions are then analyzed. Regions where different time-scales dominate are separated by hypersurfaces, and these are pinched together to obtain a piecewise-smooth system, in which curvature changes manifest as discontinuity-induced bifurcations. The method is used to classify canards in arbitrary dimensions, and to derive the parameter values over which canards form either small cycles (canards without head) or large cycles (canards with head)

Bifurcations of piecewise smooth flows:perspectives, methodologies and open problems

In this paper, the theory of bifurcations in piecewise smooth flows is critically surveyed. The focus is on results that hold in arbitrarily (but finitely) many dimensions, highlighting significant areas where a detailed understanding is presently lacking. The clearest results to date concern equilibria undergoing bifurcations at switching boundaries, and limit cycles undergoing grazing and sliding bifurcations. After discussing fundamental concepts, such as topological equivalence of two piecewise smooth systems, discontinuity-induced bifurcations are defined for equilibria and limit cycles. Conditions for equilibria to exist in n-dimensions are given, followed by the conditions under which they generically undergo codimension-one bifurcations. The extent of knowledge of their unfoldings is also summarized. Codimension-one bifurcations of limit cycles and boundary-intersection crossing are described together with techniques for their classification. Codimension-two bifurcations are discussed with suggestions for further study

Army Support of Military Cyberspace Operations: Joint Contexts and Global Escalation Implications

View the Executive SummaryMilitary cyberspace operations have evolved significantly over the past 2 decades and are now emerging into the realm of military operations in the traditional domains of land, sea, and air. The goal of this monograph is to provide senior policymakers, decisionmakers, military leaders, and their respective staffs with a better understanding of Army cyberspace operations within the context of overall U.S. military cyberspace operations. It examines the development of such operations in three major sections. First, it looks at the evolution of Department of Defense cyberspace operations over the past decade to include the founding of U.S. Cyber Command from its roots in various military units focused on defensive and offensive cyberspace operations. Second, it examines the evolution of the Army implementation of cyberspace operations toward the initial establishment of Army Cyber Command as well as recent efforts to establish Fort Gordon, Georgia as the center of gravity for Army cyberspace activities. Third, it explores the role of cyberspace operations in the escalation of international conflict, focusing on the sufficiency of the current cyberspace force structure to address an international environment of multiple actors interacting with varying degrees of tension.https://press.armywarcollege.edu/monographs/1470/thumbnail.jp

Evaluating the Influences of Domestic Violence Training on the Attitudes and Perceptions of Police Recruits at the East Tennessee Regional Law Enforcement Academy

A sample of recruits attending the East Tennessee Regional Law Enforcement Academy were surveyed about attitudes relating to a variety of topics, including their perceived role as police officers, domestic violence, its victims, perpetrators, and police interactions with domestic violence. The recruits completed the survey during their first week at the academy. The recruits completed the identical survey on the last week of academy training. No significant change in attitudes were found following the completion of the Regional Law Enforcement Academy training program. Conclusively, the results of this study show that the training provided at the East Tennessee Regional Law Enforcement Academy does not significantly change the attitudes and perceptions of the recruits toward domestic violence

Distinguishing Acts of War in Cyberspace: Assessment Criteria, Policy Considerations, and Response Implications

View the Executive SummaryDetermining an act of war in the traditional domains of land, sea, and air often involves sophisticated interactions of many factors that may be outside the control of the parties involved. This monograph seeks to provide senior policymakers, decisionmakers, military leaders, and their respective staffs with essential background on this topic as well as introduce an analytical framework for them to utilize according to their needs. It develops this theme in four major sections. First, it presents the characterization of cyberspace to establish terms for broader dialogue as well as to identify unique technical challenges that the cyberspace domain may introduce into the process of distinguishing acts of war. Second, it explores assessment criteria involved with assaying cyber incidents to determine if they represent aggression and possible use of force; and if so, to what degree? Third, it looks at the policy considerations associated with applying such criteria by examining relevant U.S. strategies as well as the strategies of other key countries and international organizations, and considers how nonstate actors may affect U.S. deliberations. Fourth, it examines the influences that course of action development and implementation may have on the assessment of cyberspace incidents, such as reliable situational awareness, global and domestic environment considerations, and options and their related risks and potential consequences. It argues that the United States must also expect and accept that other nations may reasonably apply the criteria we develop to our own actions in cyberspace.https://press.armywarcollege.edu/monographs/1481/thumbnail.jp

Ebola Response: A Summary of Field Work Project

While epidemics and disease outbreaks are not uncommon world wide, the most recent outbreak of Ebola Virus Disease (EVD) has been the largest outbreak of the disease and the most wide spread in history. The outbreak has caused international concern and was declared a public health emergency of international concern by the World Health Organization (WHO) in August of 2014. Since the outbreak started there have been a total of 15,351 confirmed, probable and suspected cases of EVD reported in six affected countries including Guinea, Liberia, Mali, Sierra Leone, Spain and the United States. There have been 5459 reported deaths associated with EVD worldwide. In this paper, Ebola Response: A Summary of Field Work Project, Jeffrey Schmidt’s fieldwork with San Francisco General Hospital and Trauma Center and the San Francisco Department of Public Health is summarized. The main objective of the fieldwork project was to assist with developing an Ebola response plan and then test the response plan through simulations

Space-Based Solar Power: A Technical, Economic, and Operational Assessment

View the Executive SummaryWith growing international awareness of energy security challenges, the promise of space-based solar power for clean and unlimited energy for all humankind is certainly appealing. While significant progress continues in the enabling technologies of such systems, is there compelling evidence that space-based solar power systems will provide the best energy solution? How does the Army’s current approach to incorporating a diverse portfolio of renewable energy sources in distributed locations compare to the potential of enterprise ventures that beam energy from solar collectors in space? For over 4 decades, many credible organizations in government and industry have explored the concept of space-based solar power, but their serious studies often conclude that such systems remain on the future horizon, usually at least 10 years away from practical application. While space-based solar power systems may be technically feasible, the author believes there is no compelling evidence that such systems will be economically or operationally competitive with terrestrial power generation systems in use or in development. However, he does find that there may be some utility in the limited application of space-based solar power to enable operations in remote and forward operating locations.https://press.armywarcollege.edu/monographs/1456/thumbnail.jp

Visualizing Success: Investigating the Relationship between Ability and Self-Efficacy in the Domain of Visual Processing

The purpose of this study is to investigate the spatial reasoning capacities and related self-efficacy beliefs of student teachers. In recent years self-efficacy has been a focal point for those investigating various modes of determinism. The relationship between an individual’s perceptions of their ability to succeed within spatial reasoning tasks is examined in conjunction with their spatial reasoning ability. In this study three tests of spatial ability were administered to align with three unique spatial factors associated with mental rotation. These include Spatial Relations, Speeded Rotation and Spatial Orientation. Self-efficacy within the spatial domain is measured using an adapted Academic Self-Efficacy scale

Framing Spatial Cognition: Establishing a Research Agenda

A significant aim of research concerning human intelligence is to develop a comprehensive cognitive map of the human intelligence structure. The evolution of this knowledge base is mirrored through the chronological development of models which frame cognitive domains. The domain of Visual Processing (Gv), commonly known as spatial ability, is a domain which has seen significant advances in the pertinent knowledge base. Models framing this cognitive structure are arguably under-evolved through a lack of representation of factors identified in contemporary research. This paper presents the initial conception of a more comprehensive theoretical framework which builds upon existing theory. It is envisioned that such a framework could support further research exploring the nature of thinking in graphics and other related disciplines. A research agenda is discussed concerning the validation of this framework and its utilization in the holistic assessment of spatial ability