exponential decay function
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2020 ◽  
Vol 492 (3) ◽  
pp. 4175-4188 ◽  
Author(s):  
Mieczyslaw Leszek Paradowski

ABSTRACT This paper presents a new method of determining the brightness and size of cometary nuclei that has been applied to the following 32 observed comets: 2P/Encke, 29P/Schwassmann-Wachmann 1, 102P/Shoemaker 1, 103P/Hartley 2, 168P/Hergenrother, 189P/NEAT, 260P/McNaught, 315P/LONEOS, P/2012 NJ (La Sagra), P/2013 J2 (McNaught), C/2006 S3 (LONEOS), C/2009 P1 (Garradd), C/2010 S1 (LINEAR), C/2010 X1 (Elenin), C/2011 J2 (LINEAR), C/2011 L4 (PANSTARRS), C/2011 W3 (Lovejoy), C/2012 F6 (Lemmon), C/2012 J1 (Catalina), C/2012 K1 (PANSTARRS), C/2012 S1 (ISON), C/2013 R1 (Lovejoy), C/2013 US10 (Catalina), C/2014 B1 (Schwartz), C/2014 E2 (Jacques), C/2014 Q2 (Lovejoy), C/2015 F4 (Jacques), C/2015 V2 (Johnson), C/2015 ER61 (PANSTARRS), C/2015 VL62 (Lemmon-Yeung-PANSTARRS), C/2016 A8 (LINEAR), and C/2017 O1 (ASASSN). The method consists in fitting the exponential decay function to the measured coma brightness in the aperture radius range from 0.5 to 2 pixels, and extrapolating this function to 0 pixels to obtain nuclear brightness. The R-band absolute nuclear magnitude RN(1, 1, 0), and the logarithm of the nucleus diameter DN expressed in kilometres, follow a linear dependence with the absolute total visual magnitude H. This dependence is of the form RN(1, 1, 0) = 12.5943 + 0.648H, and log DN[km] = 1.2415 − 0.13H. Comet 2P/Encke does not fit this dependence due to its high nuclear density of 800 kg m−3 (Sosa & Fernández 2009). The mean bulk density of the observed comets (except 2P/Encke) is 453 ± 29 kg m−3. The accuracy of the method in determining the brightness of comet nuclei at a level of 1σ is 8 per cent.


2018 ◽  
Vol 36 (7-8) ◽  
pp. 1512-1537 ◽  
Author(s):  
Dingyi Hao ◽  
Lei Zhang ◽  
Mingxue Li ◽  
Shihao Tu ◽  
Cun Zhang ◽  
...  

Moisture content in coal is an important factor affecting the coal seam gas extraction. It directly affects the storage and flow of gas in bituminous coal. In this paper, the cylindrical bituminous coal cores of Xutuan coal mine in Huaibei coal mine group were studied as experimental objects, using the laboratory self-designed experimental device Gas Adsorption and Strain Testing Apparatus system. The influence of the bituminous coal moisture content on gas adsorption characteristics was studied. Drying experiments of coal samples showed that they lose the original moisture content following the exponential decay function of time. At wetting, the saturated moisture content in coal samples increased following the Exponential Association function of time. The experimental results show that the average original moisture content and average saturated moisture content of raw coal samples are 1.3 and 2.4%, respectively. On this basis, the gas adsorption experiments on samples with different moisture contents under different gas pressures were carried out. With the moisture content increase, the gas adsorption capacity and saturation value decreased and the decrease rate gradually reduced. The single exponential decay function describes the gas adsorption capacity dependence on moisture content. Moisture content also affects the adsorption deformation of bituminous coal. At high moisture content, the adsorption deformation of bituminous coal is less.


Ophthalmology ◽  
2018 ◽  
Vol 125 (7) ◽  
pp. 1122-1124 ◽  
Author(s):  
James W. Aylward ◽  
Kanmin Xue ◽  
Maria I. Patrício ◽  
Jasleen K. Jolly ◽  
Jonathan C. Wood ◽  
...  

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