scholarly journals Lagrangian controllability of inviscid incompressible fluids: a constructive approach

2017 ◽  
Vol 23 (3) ◽  
pp. 1179-1200
Author(s):  
Thierry Horsin ◽  
Otared Kavian

We present here a constructive method of Lagrangian approximate controllability for the Euler equation. We emphasize on different options that could be used for numerical recipes: either, in the case of a bi-dimensionnal fluid, the use of formal computations in the framework of explicit Runge approximations of holomorphic functions by rational functions, or an approach based on the study of the range of an operator by showing a density result. For this last insight in view of numerical simulations in progress, we analyze through a simplified problem the observed instabilities.

1996 ◽  
Vol 07 (04) ◽  
pp. 543-561 ◽  
Author(s):  
WOLFGANG KALTHOFF ◽  
STEFAN SCHWARZER ◽  
GERALD RISTOW ◽  
HANS J. HERRMANN

We present a numerical method to deal efficiently with large numbers of particles in incompressible fluids. The interactions between particles and fluid are taken into account by a physically motivated ansatz based on locally defined drag forces. We demonstrate the validity of our approach by performing numerical simulations of sedimenting non-Brownian spheres in two spatial dimensions and compare our results with experiments. Our method reproduces qualitatively important aspects of the experimental findings, in particular the strong anisotropy of the hydrodynamic bulk self-diffusivities.


Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2627-2633
Author(s):  
Kieu Chi

In this paper, we are interested in finding sufficient conditions on a Borel set X lying either inside a bounded domain D ? Cn or in the boundary ?D so that if {rm}m?1 is a sequence of rational functions and {fm}m?1 is a sequence of bounded holomorphic functions on D with {fm-rm}m?1 is convergent fast enough to 0 in some sense on X then the convergence occurs on the whole domain D. The main result is strongly inspired by Theorem 3.6 in [3] whether the f fmg is a constant sequence.


2021 ◽  
Vol 7 (2) ◽  
Author(s):  
Johann Franke

AbstractWith the help of so called pre-weak functions, we formulate a very general transformation law for some holomorphic functions on the upper half plane and motivate the term of a generalized Eisenstein series with real-exponent Fourier expansions. Using the transformation law in the case of negative integers k, we verify a close connection between finite cotangent sums of a specific type and generalized L-functions at integer arguments. Finally, we expand this idea to Eichler integrals and period polynomials for some types of modular forms.


2020 ◽  
Vol 640 ◽  
pp. A53
Author(s):  
L. Löhnert ◽  
S. Krätschmer ◽  
A. G. Peeters

Here, we address the turbulent dynamics of the gravitational instability in accretion disks, retaining both radiative cooling and irradiation. Due to radiative cooling, the disk is unstable for all values of the Toomre parameter, and an accurate estimate of the maximum growth rate is derived analytically. A detailed study of the turbulent spectra shows a rapid decay with an azimuthal wave number stronger than ky−3, whereas the spectrum is more broad in the radial direction and shows a scaling in the range kx−3 to kx−2. The radial component of the radial velocity profile consists of a superposition of shocks of different heights, and is similar to that found in Burgers’ turbulence. Assuming saturation occurs through nonlinear wave steepening leading to shock formation, we developed a mixing-length model in which the typical length scale is related to the average radial distance between shocks. Furthermore, since the numerical simulations show that linear drive is necessary in order to sustain turbulence, we used the growth rate of the most unstable mode to estimate the typical timescale. The mixing-length model that was obtained agrees well with numerical simulations. The model gives an analytic expression for the turbulent viscosity as a function of the Toomre parameter and cooling time. It predicts that relevant values of α = 10−3 can be obtained in disks that have a Toomre parameter as high as Q ≈ 10.


2019 ◽  
Author(s):  
V.B. Kalmanova

В статье представлены результаты исследования экологогеохимического состояния снежного покрова как индикатора качества атмосферного воздуха г. Биробиджана. Выявлены основные природные и антропогенные факторы, предопределяющие экологическое состояние городской территории в зимний период (климатические, планировочная структура, стационарные и мобильные источники загрязнения). Определено, что выбросы основных загрязнителей во время отопительного сезона превышает летний в 6,5 раз. Проведены геохимические исследования снежного покрова на 60 экспериментальных площадках, заложенных в различных функциональных зонах города. Выявлено значительное превышение тяжелых металлов над фоновым уровнем: железа до 60, марганца до 50, меди до 40, цинка до 20, никеля до 12, свинца до 10, кобальта до 6 раз. С 2003 по 2018 годы содержание химических элементов в снеге увеличилось в 2 раза за счет мобильных источников загрязнения, ТЭЦ, котельных. Проведена сравнительная характеристика накопления тяжелых металлов в снеге за 2003 и 2018 годы и установлен ранжированный ряд загрязняющих токсичных веществ. Разработана шкала оценки загрязнения депонирующих сред по суммарному показателю концентрации тяжелых металлов, согласно которой в Биробиджане выявлено 5 уровней загрязнения снежного покрова. В целом экологическое состояние урбанизированной территории признано неудовлетворительным (8 площади территории относится к очень высокому, 14 к высокому, 21 к выше среднему, 27 к среднему уровням загрязнения, 30 к относительно чистым районам города). По полученным результатам разработана карта в программе ArcView GIS Экологогеохимическое районирование территории г. Биробиджана по уровню загрязнения снежного покрова с выделением наиболее загрязненных участков (70 от общей площади города является загрязненной). По результатам проведенных исследований предложены конструктивные методы планирования урбанизированной территории с целью улучшения ее экологического состояния: проведение геомониторинга (контроль загрязнения снежного покрова и своевременный его вывоз на специально оборудованные полигоны). Snow cover is taken as an indicator of air quality using Birobidzhan, a middlesize city in the Russian Far East, as a case study. The main natural and manmade determinants influencing the ecological state of the urban area in winter are identified: climate, a planning structure, and the stationary and mobile sources of pollution. During the heating season the emission of major pollutants exceeds the summer level by 6.5 times. The geochemical study of snow cover was performed at 60 experimental sites in different functional urban areas. A significant excess of heavy metals over the regional background level was revealed: iron up to 60 times, manganese up to 50, copper up to 40, zinc up to 20 , nickel up to 12, lead up to 10, cobalt up to 6 times. From 2003 to 2018 the content of chemical elements in snow increased in 2 times due to the mobile sources of pollution, thermal power plants, and boilers. The comparative characteristic of accumulation of heavy metals in snow for 2003 and 2018 is carried out, and the ranked number of polluting toxic substances is established. The scale of pollution assessment in depositing environments was developed using the cumulative indicator of heavy metal concentration. Five levels of snow cover pollution are found in Birobidzhan: low, moderate, above moderate, high and very high. As a whole, the ecological state of the urban area is considered as unsatisfactory (8 of the area with a very high level of pollution, 14 with high, 21 above moderate, 27 a moderate level of pollution, 30 a relatively clean area). According to the results, a map was developed in the ArcView GIS program Ecological and geochemical zoning of Birobidzhan, using the level of the snow cover pollution with the allocation of the most polluted areas (70 of the total area of the city is polluted). According to the results, a constructive method of planning in an urban area is proposed in order to improve its environmental condition: geomonitoring as a control of pollution in snow cover and its prompt removal to specially equipped landfills.


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