Self-oscillation

Physicists are very familiar with forced and parametric resonance, but usually not with self-oscillation, a property of certain dynamical systems that gives rise to a great variety of vibrations, both useful and destructive. In a self-oscillator, the driving force is controlled by the oscillation itself so that it acts in phase with the velocity, causing a negative damping that feeds energy into the vibration: no external rate needs to be adjusted to the resonant frequency. The famous collapse of the Tacoma Narrows bridge in 1940, often attributed by introductory physics texts to forced resonance, was actually a self-oscillation, as was the swaying of the London Millennium Footbridge in 2000. Clocks are self-oscillators, as are bowed and wind musical instruments. The heart is a "relaxation oscillator," i.e., a non-sinusoidal self-oscillator whose period is determined by sudden, nonlinear switching at thresholds. We review the general criterion that determines whether a linear system can self-oscillate. We then describe the limiting cycles of the simplest nonlinear self-oscillators, as well as the ability of two or more coupled self-oscillators to become spontaneously synchronized ("entrained"). We characterize the operation of motors as self-oscillation and prove a theorem about their limit efficiency, of which Carnot's theorem for heat engines appears as a special case. We briefly discuss how self-oscillation applies to servomechanisms, Cepheid variable stars, lasers, and the macroeconomic business cycle, among other applications. Our emphasis throughout is on the energetics of self-oscillation, often neglected by the literature on nonlinear dynamical systems.Comment: 68 pages, 33 figures. v4: Typos fixed and other minor adjustments. To appear in Physics Report

Debunking the myth of shareholder ownership of companies: Some implications for corporate governance and financial reporting

The shareholder primacy model is dominant in Anglo-Saxon corporate governance and financial reporting even though it is considered to be dysfunctional and a source of crisis. The possibilities of reforms are routinely stymied with the claims that shareholders are the owners of large corporations and management should promote their interests. This paper seeks to debunk such claims. It shows that a corporation is a distinct legal person and cannot be owned by its shareholders. It argues that shareholders in contemporary corporations are owners of ?fictitious? capital which is very distinct from ?real? capital. The systemic pressures require the holders of fictitious capital to constantly buy/sell shares in pursuit of short-term gains. The paper further shows that in a globalised economy, the shareholding duration in major UK companies has shrunk and shareholders are more dispersed than ever before. They are not in any position to control or direct corporations for the benefit of other stakeholders and society generally. The paper calls for abandonment of the shareholder model of governance and calls for empowerment of stakeholders with a long-term interest in the wellbeing of corporations

Two Tudor subsidy assessments for the County of Somerset 1558 and 1581-82

Includes bibliographical references and indexSIGLEAvailable from British Library Document Supply Centre- DSC:8327. 8305(vol 88) / BLDSC - British Library Document Supply CentreGBUnited Kingdo

An architectural account of the churches of Shropshire /

Illustrations: 119 prints : reproduction of photographs ; full-page. -- 30 prints : plans ; full-page. -- 91 ill. in the text; ornamental initials.Paged continuously. Vol. 1: xl, 449, [1] p., lii, [16] leaves of plates; v. 2: [xli]-lii, [451]-1140 p., liii-cxix, [14] leaves of plates.Each part in the original quarter brown or black cloth and yellowish orange or pinkish orange illustrated paper covers, as issued. Each part except pts. 5 and 10 contains overall title page. Special t.p. (dated 1901) and other preliminaries to v. 1 in pt. 5; special t.p. and other preliminaries to v. 2 in pt. 10. Cancels for p. 165-172 in pt. 5.500 copies printed.pt. 1. The hundred of Brimstree -- pt. 2. The hundred of Munslow -- pt. 3. The franchise of Wenlock. The hundred of Overs -- pt. 4. The hundred of Stottesdon -- pt. 5. Preface. Glossary. The hundred of Purslow. The hundred of Clun -- pt. 6. The hundred of Condover. The hundred of Ford -- pt. 7. The hundred of Chirbury. The hundred of Bradford (South) -- pt. 8. The hundred of Bradford (North) -- pt. 9. The hundred of Pimhill. The hundred of Oswestry -- pt. 10. The liberties of Shrewsbury. Appendix. General survey. Retrospect. Index.Mode of access: Internet.Arents copy: Author's presentation copy to the Royal Institute of British architects, inscribed on t.p. of pts. 1-4, and on cover of pt. 1. With the Institute's bookplate in pts. 1, 4, 7, 8, 9, and 10 (cancelled in pt. 1).Copy in 3-MRBH bound in 4 vols

An architectural account of the churches of Shropshire,

Preface and glossary bound at front in v. 1.Five hundred copies printed.Paged continuously. Issued in 10 pts.; 1894-1912.[v.1] pt. 1. The hundred of Brimstree. pt. 2. The hundred of Munslow. pt. 3. The franchise of Wenlock. The hundred of Overs. pt. 4. The hundred of Stottesdon. pt. 5. Preface. Glossary. The hundred of Purslow. The hundred of Clun. -- [v.2.] pt. 6. The hundred of Condover. The hundred of Ford. pt. 7. The hundred of Chirbury. The hundred of Bradford (South) pt. 8. The hundred of Bradford (North) pt. 9. The hundred of Pimhill. The hundred of Oswestry. pt. 10. The liberties of Shrewsbury. Appendix. General survey. Retrospect. Index.Mode of access: Internet