Pol Der Mark (8 results)

Hardcover. Condition: Good. No Jacket. Ex-library, Volume I of Lectures in Applied Mathematics, Proceedings of the Summer Seminar, Boulder, CO., 1957, 266pp, G/--. Ex-Library.

Condition: Very good.

(26,5 x 19 cm). SS. 353-392. Mit Abbildungen. Original-Broschur. Erste Ausgabe der ersten Veröffentlichung über den Van-der-Pol-Oszillator, ein schwingungsfähiges System mit nichtlinearer Dämpfung und Selbsterregung. Der niederländischen Physiker Balthasar van der Pol entdeckte es bei seinen Forschungen an Oszillatoren mit Vakuumröhren. - Einband mit handschriftlichem Namenszug und leicht fleckig, sonst gut erhalten.

Condition: Good. *Price HAS BEEN REDUCED by 10% until Tuesday, May 26 (SALE item)* First edition, first printing, (1959); 266 pp., hardcover, some scuffs to spine and covers, minor internal library markings else text clean & binding tight (lacks dust jacket). - If you are reading this, this item is actually (physically) in our stock and ready for shipment once ordered. We are not bookjackers. Buyer is responsible for any additional duties, taxes, or fees required by recipient's country.

VAN DER POL, Balthasar (1889-1959) & VAN DER MARK, Jan. The Heartbeat considered as a Relaxation Oscillation, and an Electrical Model of the Heart. Tiré à part (Offprint) du Philosophical Magazine, vol. 6, n° 38. LIEU & DATE : Londres, Taylor & Francis, Novembre 1928. In-8° (env. 14 x 22 cm), broché, sous sa couverture d'origine . Pages 763 à 775. Condition exceptionnelle. Couverture dans un état de fraîcheur rare, proche du neuf.

Condition: Hervorragend. Zustand: Hervorragend | Seiten: 126 | Sprache: Niederländisch | Produktart: Bücher | Keine Beschreibung verfügbar.

Soft cover. Condition: Very Good. ++ Perhaps one of the earliest experimental observations of deterministic chaos.++ Pol, B. van der. and Mark, J. van der. Frequency demultiplication in Nature, volume 120, number 3019, 10 September 1927, pp. 363-364 in the full weekly issue of pp 353-392, with 6pp of ads. VG copy. Parallel to the mathematical work of Birkhoff and others in the U.S. and Europe, interest in nonlinear oscillations was growing, driven largely by developments in electronics (indeed, Lefschetz, mentioned above, edited a series of books on the topic). B. van der Pol, a radio engineer at the Phillips labs in Eindhoven, published a remarkable short paper (van der Pol and van der Mark 1927 the paper offered here) which may contain the first experimental observation of deterministic chaos (they describe an "irregular noise" in a diode subject to periodic forcing). This paper also noted the coexistence of periodic orbits of different period (subharmonics of two distinct orders), which implied the existence of a complicated unstable invariant set, following (Birkhoff, 1932). Wikipedia, History of Dynamical Systems. See: Writing the History of Dynamical Systems and Chaos , Aubin and Dalmedico, Historia Mathematica 29 (2002), 273 339.

1st Edition. FIRST EDITION IN ORIGINAL WRAPPERS OF "ONE OF THE FIRST EXPERIMENTAL REPORTS OF CHAOS" (Tsatsos, Theoretical and Numerical Study of the Van der Pol Equation, 9). Van der Pol and van der Mark note the appearance "of â??irregular noise' before transition from one sub-harmonical regime to another. [this being] one of the first observations of chaotic oscillations" (ibid). Other scientific historians have gone further, citing this as "the experimental discovery of chaotic dynamics" (Rosser, Chaos Theory Before Lorenz, 9). The Dutch electrical engineer Balthasar van der Pol began with a vacuum tube. "A modern physics student would explore the behavior of such an oscillator by looking at the line traced on the screen of an oscilloscope. Van der Pol did not have an oscilloscope, so he had to monitor his circuit by listening to changing tones in a telephone handset. He was pleased to discover regularities in the behavior as he changed the current that fed it. The tone would leap from frequency to frequency as if climbing a staircase, leaving one frequency and then locking solidly onto the next. Yet once in a while van der Pol noted something strange. The behavior sounded irregular, in a way that he could not explain. Under the circumstances he was not worried. â??Often an irregular noise is heard in the telephone receivers before the frequency jumps to the next lower value,' he wrote in a letter to Nature. "However, this is a subsidiary phenomenon." He was one of many scientists who got a glimpse of chaos but had no language to understand it. For people trying to build vacuum tubes, the frequency-locking was important. But for people trying to understand the nature of complexity, the truly interesting behavior would turn out to be the â??irregular noise' created by the conflicting pulls of a higher and lower frequency" (Gleik, Chaos, 49). CONDITION & DETAILS: Lancaster: American Physical Society. 4to. (10.5 x 8 inches; 263 x 200mm). Ex-libris with a handsome pictorial bookplate on the pastedown, blacked out spine label, fewer than usual markings. llustration: In-text illustrations throughout. Binding: Bound in green cloth with gilt-lettered spines. Minor rubbing and scuffing to the edge and spine tips. Solidly and very tightly bound. Interior: Bright and very clean throughout.