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Gibbs phenomenon - translation to russian
PECULIAR MANNER IN WHICH THE FOURIER SERIES OF A PIECEWISE CONTINUOUSLY DIFFERENTIABLE PERIODIC FUNCTION BEHAVES AT A JUMP DISCONTINUITY
Gibbs' phenomenon; Gibbs effect; Gibbs Constant; Gibbs constant; Gibbs phenomena; Gibb's phenomenon; Wilbraham–Gibbs constant; Wilbraham-Gibbs constant
![The [[sinc function]], the [[impulse response]] of an ideal [[low-pass filter]]. Scaling narrows the function, and correspondingly increases magnitude (which is not shown here), but does not reduce the magnitude of the undershoot, which is the integral of the tail.](https://commons.wikimedia.org/wiki/Special:FilePath/Sinc function (both).svg?width=200 "The [[sinc function]], the [[impulse response]] of an ideal [[low-pass filter]]. Scaling narrows the function, and correspondingly increases magnitude (which is not shown here), but does not reduce the magnitude of the undershoot, which is the integral of the tail.")
![The [[sine integral]], exhibiting the Gibbs phenomenon for a step function on the real line.](https://commons.wikimedia.org/wiki/Special:FilePath/Sine integral.svg?width=200 "The [[sine integral]], exhibiting the Gibbs phenomenon for a step function on the real line.")
Gibbs phenomenon
общая лексика
явление Гиббса
Gibbs energy
![The reaction C<sub>(s)</sub><sup>diamond</sup> → C<sub>(s)</sub><sup>graphite</sup> has a negative change in Gibbs free energy and is therefore thermodynamically favorable at 25 °C and 1 atm. However, the reaction is too slow to be observed, because of its very high [[activation energy]]. Whether a reaction is thermodynamically favorable does not determine its rate.](https://commons.wikimedia.org/wiki/Special:FilePath/Diamond.jpg?width=200 "The reaction C<sub>(s)</sub><sup>diamond</sup> → C<sub>(s)</sub><sup>graphite</sup> has a negative change in Gibbs free energy and is therefore thermodynamically favorable at 25 °C and 1 atm. However, the reaction is too slow to be observed, because of its very high [[activation energy]]. Whether a reaction is thermodynamically favorable does not determine its rate.")
![thermodynamic surface]]''' diagram for a fictitious water-like substance, transposed the two figures of Gibbs (above right) onto the volume-entropy coordinates (transposed to bottom of cube) and energy-entropy coordinates (flipped upside down and transposed to back of cube), respectively, of a three-dimensional [[Cartesian coordinates]]; the region AB being the first-ever three-dimensional representation of Gibbs free energy, or what Gibbs called "available energy"; the region AC being its capacity for [[entropy]], what Gibbs defined as "the amount by which the entropy of the body can be increased without changing the energy of the body or increasing its volume.](https://commons.wikimedia.org/wiki/Special:FilePath/Gibbs-Maxwell surfaces.png?width=200 "thermodynamic surface]]''' diagram for a fictitious water-like substance, transposed the two figures of Gibbs (above right) onto the volume-entropy coordinates (transposed to bottom of cube) and energy-entropy coordinates (flipped upside down and transposed to back of cube), respectively, of a three-dimensional [[Cartesian coordinates]]; the region AB being the first-ever three-dimensional representation of Gibbs free energy, or what Gibbs called \"available energy\"; the region AC being its capacity for [[entropy]], what Gibbs defined as \"the amount by which the entropy of the body can be increased without changing the energy of the body or increasing its volume.")
![volume]]) and passing through point A, which represents the initial state of the body. MN is the section of the surface of [[dissipated energy]]. Q''ε'' and Q''η'' are sections of the planes ''η'' = 0 and ''ε'' = 0, and therefore parallel to the axes of ''ε'' ([[internal energy]]) and ''η'' ([[entropy]]), respectively. AD and AE are the energy and entropy of the body in its initial state, AB and AC its ''available energy'' (Gibbs free energy) and its ''capacity for entropy'' (the amount by which the entropy of the body can be increased without changing the energy of the body or increasing its volume), respectively.](https://commons.wikimedia.org/wiki/Special:FilePath/Wykres Gibbsa.svg?width=200 "volume]]) and passing through point A, which represents the initial state of the body. MN is the section of the surface of [[dissipated energy]]. Q''ε'' and Q''η'' are sections of the planes ''η'' = 0 and ''ε'' = 0, and therefore parallel to the axes of ''ε'' ([[internal energy]]) and ''η'' ([[entropy]]), respectively. AD and AE are the energy and entropy of the body in its initial state, AB and AC its ''available energy'' (Gibbs free energy) and its ''capacity for entropy'' (the amount by which the entropy of the body can be increased without changing the energy of the body or increasing its volume), respectively.")
TYPE OF THERMODYNAMIC POTENTIAL; USEFUL FOR CALCULATING REVERSIBLE WORK IN CERTAIN SYSTEMS
Gibbs function; Gibbs energy; Gibbs free energy change of formation; Gibb's free energy; ΔG°; Standard Gibbs free energy change of formation; Gibbs Free Energy; Free enthalpy; Gibbs free energy change; Gibbs Energy; Gibbs' free energy; Free energy equation; Energetically favourable; Gibbs free energy of formation; DGdeg; Gibb's Free Energy; Gibbs Function; ΔG; Free energy calculation; Free energy relationship; Gibbs energy minimization; Energy of formation; Energetically favorable
общая лексика
(свободная) энергия Гиббса
синоним
Gibbs function
TYPE OF THERMODYNAMIC POTENTIAL; USEFUL FOR CALCULATING REVERSIBLE WORK IN CERTAIN SYSTEMS
Gibbs function; Gibbs energy; Gibbs free energy change of formation; Gibb's free energy; ΔG°; Standard Gibbs free energy change of formation; Gibbs Free Energy; Free enthalpy; Gibbs free energy change; Gibbs Energy; Gibbs' free energy; Free energy equation; Energetically favourable; Gibbs free energy of formation; DGdeg; Gibb's Free Energy; Gibbs Function; ΔG; Free energy calculation; Free energy relationship; Gibbs energy minimization; Energy of formation; Energetically favorable
общая лексика
функция энергии Гиббса
Definition
Гиббс
I
(Gibbs)
Джеймс (23.12.1682, Футдисмир, близ Абердина, - 5.8.1754, Лондон), английский архитектор. Учился в Голландии и Италии (в 1700-09 у К. Фонтаны (См. Фонтана)), сотрудничал с К. Реном. Представитель классицизма. Постройки Г. отличаются внушительной простотой и цельностью композиции, изяществом деталей (церкви Сент-Мэри-ле-Стрэнд, 1714-1717, и Сент-Мартин-ин-зе-Филдс, 1722-1726, в Лондоне; библиотека Рэдклиффа в Оксфорде, 1737-49).
Лит.: Summerson J., Architecture in Britain. 1530-1830, Harmondsworth, 1958.
Дж. Гиббс. Библиотека Рэдклиффа в Оксфорде. 1737-49.
II
(Gibbs)
Джозайя Уиллард (11.2.1839, Нью-Хейвен, - 28.4.1903, там же), американский физик-теоретик, один из основоположников термодинамики и статистической механики. Окончил Йельский университет (1858). В 1863 получил степень доктора философии в Йельском университете, с 1871 профессор там же. Г. систематизировал термодинамику и статистическую механику, завершив их теоретическое построение. Уже в первых своих статьях Г. развивает графические методы исследования термодинамических систем, вводит трёхмерные диаграммы и получает соотношения между объёмом, энергией и энтропией вещества. В 1874-78 в трактате "О равновесии гетерогенных веществ" разработал теорию потенциалов термодинамических (См. Потенциалы термодинамические), доказал правило фаз (общее условие равновесия гетерогенных систем), создал термодинамику поверхностных явлений и электрохимических процессов; Г. обобщил принцип энтропии, применяя второе начало термодинамики к широкому кругу процессов, и вывел фундаментальные уравнения, позволяющие определять направление реакций и условия равновесия для смесей любой сложности. Теория гетерогенного равновесия - один из наиболее абстрактных теоретических вкладов Г. в науку - нашла широкое практическое применение.
В 1902 были опубликованы "Основные принципы статистической механики, излагаемые со специальным применением к рациональному обоснованию термодинамики", явившиеся завершением классической статистической физики, первоосновы которой были заложены в работах Дж. К. Максвелла и Л. Больцмана. Статистический метод исследования, разработанный Г., позволяет получить термодинамические функции, характеризующие состояние вещества. Г. дал общую теорию флуктуаций величин этих функций от равновесных значений, определяемых формальной термодинамикой, и адэкватное описание необратимости физических явлений. Г. является также одним из создателей векторного исчисления в его современной форме ("Элементы векторного анализа", 1881- 1884).
В трудах Г. проявились замечательно точная логика, тщательность в отделке результатов. В работах Г. до сих пор не обнаружено ни одной ошибки, все его идеи сохранились в современной науке.
Соч.: The collected works, v. 1-2, N. Y. - L., 1928; The scientific papers, v. 1-2, N. Y., 1906; в рус. пер. - Основные принципы статистической механики, М. - Л., 1946; Термодинамические работы, М., 1950.
Лит.: Семенченко В. К., Д. В. Гиббс и его основные работы по термодинамике и статистической механике (К 50-летию со дня смерти), "Успехи химии", 1953, т. 22, в. 10; Франкфурт У. И., Френк А. М., Джозайя Виллард Гиббс, М., 1964.
О. В. Кузнецова.
Дж. У. Гиббс.
Wikipedia
Gibbs phenomenon
In mathematics, the Gibbs phenomenon is the oscillatory behavior of the Fourier series of a piecewise continuously differentiable periodic function around a jump discontinuity. The function's th partial Fourier series (formed by summing its lowest constituent sinusoids) produces large peaks around the jump which overshoot and undershoot the function's actual values. This approximation error approaches a limit of about 9% of the jump as more sinusoids are used, though the infinite Fourier series sum does eventually converge almost everywhere except the point of discontinuity.
The Gibbs phenomenon was observed by experimental physicists, but was believed to be due to imperfections in the measuring apparatus, and it is one cause of ringing artifacts in signal processing.
