May 27th, 2021

песец

Новости лебединого озера

- А в нашем лесу тоже есть звезда!
- Звезда?.. В вашем болоте!?
...
- Смотри!

м/ф "Большой Ух"


Вчера на лебедином озере не было видно ни лебедей, ни цапель. Зато уже несколько дней там наблюдались какие-то множественные штрихи на поверхности воды. Осмотр подтвердил возникшую гипотезу: чуть ли не на половине озера массово вылезли и расцвели белые кувшинки! На речке их еще и в помине нет, а тут озеро мелкое, вода прогрелась, и вот они! К тому же, там топко и нет дятлов, их тупо рвущих*

Вот нечто вроде общего плана (панораму снять не получилось, кусты мешают, но, поверьте, она впечатляет!):


DSC_7292_корр.jpg © qedqed.iMGSRC.RU


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лошадь, диаграмма, Фейнман

После бала

Не так давно я писал о выпускном у стрекоз. А вчера на глаза попались многочисленные "выползки", то есть упомянутые в том посте чехлы - оболочки личинок на водных растениях, из которых вылупились те самые стрекозы:


DSC_6550_выполз.jpg © qedqed.iMGSRC.RU


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лошадь, диаграмма, Фейнман

Что-то суровое

Interplay Between Approximation Theory and Renormalization Group: https://arxiv.org/abs/2105.12176
V.I. Yukalov
The review presents general methods for treating complicated problems that cannot be solved exactly and whose solution encounters two major difficulties. First, there are no small parameters allowing for the safe use of perturbation theory in powers of these parameters, and even when small parameters exist, the related perturbative series are strongly divergent. Second, such perturbative series in powers of these parameters are rather short, so that the standard resummation techniques either yield bad approximations or are not applicable at all. The emphasis in the review is on the methods advanced and developed by the author. One of the general methods is {\it Optimized Perturbation Theory} now widely employed in various branches of physics, chemistry, and applied mathematics. The other powerful method is {\it Self-Similar Approximation Theory} allowing for quite simple and accurate summation of divergent series. These theories share many common features with the method of renormalization group, which is briefly sketched in order to stress the similarities in their ideas and their mutual interconnection.
Comments: review, 138 pages
Journal reference: Phys. Part. Nucl. 50 (2019) 141-209
лошадь, диаграмма, Фейнман

Роль кварков в ядерной структуре

Role of Quarks in Nuclear Structure: https://arxiv.org/abs/2105.12327
Anthony W Thomas
The strong force that binds atomic nuclei is governed by the rules of Quantum Chromodynamics. Here we consider the suggestion the internal quark structure of a nucleon will adjust self-consistently to the local mean scalar field in a nuclear medium and that this may play a profound role in nuclear structure. We show that one can derive an energy density functional based on this idea, which successfully describes the properties of atomic nuclei across the periodic table in terms of a small number of physically motivated parameters. Because this approach amounts to a new paradigm for nuclear theory, it is vital to find ways to test it experimentally and we review a number of the most promising possibilities.
Subjects: Nuclear Theory (nucl-th)
Journal reference: Oxford Encyclopedia of Science July 2020
лошадь, диаграмма, Фейнман

Вычисление линейного интеграла Био-Савара

Computation of the Biot-Savart Line Integral: https://arxiv.org/abs/2105.12522
Nick McGreivy, Caoxiang Zhu, Lee Gunderson, Stuart R. Hudson
One common approach to computing the magnetic field produced by a filamentary current-carrying coil is to approximate the coil as a series of straight segments. The Biot-Savart field from each straight segment is known analytically. However, if the endpoints of the straight segments are chosen to lie on the coil, then the accuracy of the Biot-Savart computation is generally only second-order in the number of endpoints. We propose a simple modification: shift each endpoint off the coil in the outwards normal direction by an amount proportional to the local curvature. With this modification, the Biot-Savart accuracy is higher order and the numerical error is dramatically reduced for a given number of discretization points.