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Technique of the step-by-step integration of ordinary differential equations

In Part 1 step-by-step methods are examined critically and emphasis is placed on the dependence of the error on the number n of steps used for a given range of the independent variable. The index of a process is defined and it is shown that the errors can be assessed and partially corrected when the index is known and results obtained for two or more values of n. Attention is drawn to the advantages in certain cases of a part-analytical process. In Part 2 methods of numerical integration in general are classified and briefly reviewed. The chart, Table 2.2.1, summarises the classification

Demographic and psychological variables affecting test subject evaluations of ride quality

Ride-quality experiments similar in objectives, design, and procedure were conducted, one using the U.S. Air Force Total In-Flight Simulator and the other using the Langley Passenger Ride Quality Apparatus to provide the motion environments. Large samples (80 or more per experiment) of test subjects were recruited from the Tidewater Virginia area and asked to rate the comfort (on a 7-point scale) of random aircraft motion typical of that encountered during STOL flights. Test subject characteristics of age, sex, and previous flying history (number of previous airplane flights) were studied in a two by three by three factorial design. Correlations were computed between one dependent measure, the subject's mean comfort rating, and various demographic characteristics, attitudinal variables, and the scores on Spielberger's State-Trait Anxiety Inventory. An effect of sex was found in one of the studies. Males made higher (more uncomfortable) ratings of the ride than females. Age and number of previous flights were not significantly related to comfort ratings. No significant interactions between the variables of age, sex, or previous number of flights were observed

Shortcuts to Adiabaticity Assisted by Counterdiabatic Born-Oppenheimer Dynamics

Shortcuts to adiabaticity (STA) provide control protocols to guide the dynamics of a quantum system through an adiabatic reference trajectory in an arbitrary prescheduled time. Designing STA proves challenging in complex quantum systems when the dynamics of the degrees of freedom span different time scales. We introduce Counterdiabatic Born-Oppenheimer Dynamics (CBOD) as a framework to design STA in systems with a large separation of energy scales. CBOD exploits the Born-Oppenheimer approximation to separate the Hamiltonian into effective fast and slow degrees of freedom and calculate the corresponding counterdiabatic drivings for each subsystem. We show the validity of the CBOD technique via an example of coupled harmonic oscillators, which can be solved exactly for comparison, and further apply it to a system of two-charged particles.Comment: 14 pages, 3 figures, published New Journal of Physic

Unsteady flows in axial turbomachines

Of the various unsteady flows that occur in axial turbomachines certain asymmetric disturbances, of wave length large in comparison with blade spacing, have become understood to a certain extent. These disturbances divide themselves into two categories: self-induced oscillations and forced disturbances. A special type of propagating stall appears as a self-induced disturbance; an asymmetric velocity profile introduced at the compressor inlet constitutes a forced disturbance. Both phenomena have been treated from a unified theoretical point of view in which the asymmetric disturbances are linearized and the blade characteristics are assumed quasi-steady. Experimental results are in essential agreement with this theory wherever the limitations of the theory are satisfied. For the self-induced disturbances and the more interesting examples of the forced disturbances, the dominant blade characteristic is the dependence of total pressure loss, rather than the turning angle, upon the local blade inlet angle

1. Strengthening International Regulation Through Transnational New Governance: Overcoming the Orchestration Deficit. 2. International Regulation without International Government: Improving IO Performance through Orchestration

1. A new kind of international regulatory system is spontaneously arising out of the failure of international 'Old Governance' (i.e., treaties and intergovernmental organizations) to adequately regulate international business. Nongovernmental organizations, business firms, and other actors, singly and in novel combinations, are creating innovative institutions to apply transnational norms to business. These institutions are predominantly private and operate through voluntary standards. The Authors depict the diversity of these new regulatory institutions on the 'Governance Triangle,' according to the roles of different actors in their operations. To analyze this complex system, we adapt the domestic 'New Governance' model of regulation to the international setting. 'Transnational New Governance' potentially provides many benefits of New Governance and is particularly suitable for international regulation because it demands less of states and intergovernmental organizations (IGOs). However, Transnational New Governance does require states and IGOs to act as orchestrators of the international regulatory system, and that system currently suffers from a significant orchestration deficit. If states and IGOs expanded 'directive' and especially 'facilitative' orchestration of the Transnational New Governance system, they could strengthen high-quality private regulatory standards, improve the international regulatory system, and better achieve their own regulatory goals. 2. International organizations (IOs) have been widely criticized as ineffective. Yet scholars and practitioners assessing IO performance frequently focus on traditional modes of governance such as treaties and inter-state dispute-resolution mechanisms. When they observe poor performance, moreover, they often prescribe a strengthening of those same activities. We call this reliance on traditional state-based mechanisms 'International Old Governance' (IOG). A better way to understand and improve IO performance is to consider the full range of ways in which IOs can and do operate - including, increasingly, by reaching out to private actors and institutions, collaborating with them, and supporting and shaping their activities. Such actions are helping to develop an intricate global network of public, private and mixed institutions and norms, partially orchestrated by IOs, that we call 'Transnational New Governance' (TNG). With proper orchestration by IOs, TNG can ameliorate both 'state failure' - the inadequacies of IOG - and 'market failure' - the problems that result when the creation and evolution of norm-setting institutions is highly decentralized. Orchestration thus provides a significant way for IOs to improve their regulatory performance. Some IOs already engage actively with private actors and institutions - we provide a range of illustrations, highlighting the activities of the UN Environment Programme (UNEP). Yet there remains a significant 'orchestration deficit' that provides real opportunities for IOs. We draw on the lessons of existing IO activities to suggest additional possibilities for improving IO performance. -- 1. Ein internationales regulatorisches System neuer Art entsteht derzeit spontan aus dem Versagen der internationalen 'Old Governance' - also der bestehenden internationalen Verträge und Organisationen - dabei, den internationalen Handel angemessen zu regulieren. Nichtregierungsorganisationen, Unternehmen und andere Akteure - allein und in ganz neuen Kombinationen - schaffen sich neue internationale Einrichtungen, um transnationale Normen auf internationale Geschäftstätigkeit anzuwenden. Es geht dabei vornehmlich um private Einrichtungen, die vor allem über freiwillige Standardbefolgung wirken. In diesem Beitrag werden die unterschiedlichen Regulierungseinrichtungen als Teil eines 'Governance Dreiecks' beschreiben und das geschieht vor allem in Blick darauf, welche Rollen die unterschiedlichen Akteure in ihrer Tätigkeit spielen. Um dieses komplexe System zu untersuchen passen wir das innenpolitische Regulierungsmodell der 'New Governance' an den internationalen Rahmen an. Die 'Transnational New Governance' enthält viele Vorteile der 'New Governance' und sie ist für die internationale Regulierung besonders angemessen, weil sie geringere Anforderungen an die Staatenwelt und an die intergouvernementalen Organisationen, die IGOs, stellen. Allerdings ist es für eine wirksame 'Transnational New Governance' weiterhin erforderlich, dass die Staaten und die IGOs das internationale regulatorische System 'orchestrieren'. Das heutige internationale regulatorische System leidet allerdings unter einem Orchestrierungsdefizit. Würden die Staaten und die IGOs die 'anweisende' und 'ermöglichende' Orchestrierungsfunktion des 'Transnational New Governance System' ausbauen, dann stärkten sie die privaten regulatorischen Standards von hoher Qualität, verbesserten das internationale regulatorische System und könnten ihre eigenen regulatorischen Ziele besser verwirklichen. 2. Internationale Organisationen (IOs) werden vielfach ob Ihrer Ineffizienz kritisiert. Allerdings konzentrieren sich Wissenschaftler und Praktiker bei dieser Bewertung der Leistungsfähigkeit von IOs häufig auf Maßstäbe, die den herkömmlichen Formen von Governance - wie internationalen Verträgen und den Mechanismen für die Schlichtung zwischenstaatlicher Konflikte - entlehnt sind. Soweit eine ungenügende Leistung festgestellt wird, empfehlen sie zudem meist, Tätigkeiten der traditionellen Art zu verstärken. Wir bezeichnen dies als ein Sich-Verlassen auf die herkömmlichen staats-basierten Mechanismen, als 'International Old Governance' (IOG). Man versteht die IOs besser und verbessert ihre Leistungsfähigkeit aber der Situation weitaus angemessener, wenn man die gesamte Vielfalt wirklicher und möglicher IO-Tätigkeiten in den Blick nimmt: Das umfasst vor allem, dass die IOs private Akteure und Organisationen einbeziehen, mit ihnen zusammenarbeiten, ihre Aktivitäten stützen, sie formen und ihnen Richtung geben. Diese Tätigkeiten schaffen ein fein gesponnenes globales Netzwerk von öffentlichen, privaten und gemischten Organisationen und Normen, das seinerseits teilweise durch die IOs orchestriert wird. Dieses Netzwerk bezeichnen wir als 'Transnational New Governance' (TNG). Wenn die Orchestrierung durch IOs gut funktioniert kann sie auch Staatsversagen (state failure) abmildern - also hier die Inadäquanzen von 'International Organization Governance' - und ebenso kann sie Marktversagen ausgleichen, also die Probleme, die sich ergeben wenn Herausbildung und Schaffung normgebender Einrichtungen höchst dezentralisiert verläuft. Über die Orchestrierung können die IOs auch die Leistungsfähigkeit ihrer Regulierungen erhöhen. Einige IOs sind schon jetzt stark zusammen mit privaten Akteuren und Einrichtungen unterwegs; in diesem Beitrag mustern wir das Spektrum solcher Aktivitäten. Wir betonen dabei die Unternehmungen des UN Environment Programme (UNEP), des Umweltprogramms der VN. Allerdings verbleibt ein erhebliches 'Orchestrierungsdefizit', das für die IOs zugleich Herausforderung und Chance ist. Wir stützten uns auf den Erfahrungsschatz der vorgefundenen IO-Aktivitäten, um den Möglichkeitsraum der IOs für die Zukunft auszumessen und Maßnahmen zur Verbesserung der Leistungsfähigkeit von IOs anzuregen.

Driven Topological Systems in the Classical Limit

Periodically-driven quantum systems can exhibit topologically non-trivial behaviour, even when their quasi-energy bands have zero Chern numbers. Much work has been conducted on non-interacting quantum-mechanical models where this kind of behaviour is present. However, the inclusion of interactions in out-of-equilibrium quantum systems can prove to be quite challenging. On the other hand, the classical counterpart of hard-core interactions can be simulated efficiently via constrained random walks. The non-interacting model proposed by Rudner et al. [Phys. Rev. X 3, 031005 (2013)], has a special point for which the system is equivalent to a classical random walk. We consider the classical counterpart of this model, which is exact at a special point even when hard-core interactions are present, and show how these quantitatively affect the edge currents in a strip geometry. We find that the interacting classical system is well described by a mean-field theory. Using this we simulate the dynamics of the classical system, which show that the interactions play the role of Markovian, or time dependent disorder. By comparing the evolution of classical and quantum edge currents in small lattices, we find regimes where the classical limit considered gives good insight into the quantum problem.Comment: 15 pages, 15 figures, new content on the quantum mode