69.17 Cross-Sections and Minimal Surface Area

1985 ◽  
Vol 69 (448) ◽  
pp. 122
Author(s):  
Gordon Haigh
Keyword(s):  
Minimal Surface ◽  
Surface Area ◽  
Cross Sections ◽  
Minimal Surface Area

Application of Raman Spectroscopy to the Study of Adsorption Effects at Liquid-Solid Interfaces

1982 ◽  
Vol 36 (4) ◽  
pp. 471-473 ◽  
Author(s):  
Klaus Witke
Keyword(s):  
Raman Spectroscopy ◽  
Carbon Tetrachloride ◽  
Adsorption Isotherm ◽  
Minimal Surface ◽  
Linear Relationship ◽  
Surface Area ◽  
Long Range ◽  
Raman Spectra ◽  
Sample Cell ◽  
Minimal Surface Area

A sample cell for investigating suspensions or emulsions by Raman spectroscopy in the optically favorable 90° scattering arrangement is described. The Raman spectra of pyridine in a suspension of Aerosil 200 in carbon tetrachloride are recorded. The adsorption isotherm of pyridine is determined from the intensities of the Raman lines at 1008 and 990 cm−1. Over a long range of coverage a linear relationship exists between reciprocal concentrations of chemisorbed and dissolved molecules. The minimal surface area that is occupied by a chemisorbed molecule is determined to be approximately 0.75 nm2.

scholarly journals Origin and structure of Ubisch bodies in Pinus sylvestris

2014 ◽  
Vol 56 (2) ◽  
pp. 215-227 ◽  
Author(s):  
John R. Rowley ◽  
Björn Walles
Keyword(s):  
Plasma Membrane ◽  
Pinus Sylvestris ◽  
Minimal Surface ◽  
Surface Area ◽  
Body Wall ◽  
Current State ◽  
Ubisch Bodies ◽  
Ubisch Body ◽  
Tapetal Cells ◽  
Minimal Surface Area

In <em>Pinus sylvestris</em> Ubisch bodies are produced repeatedly, and each crop is formed at a distinct phase in the secretory cycles of tapetal cells. While each production has a Ubisch body wall similar to the then current state of the exine with regard to thickening and ornamentation, the survivers of previous productions do not change. Examples of all the structurally different Ubisch body wall forms can be seen when terminally, at the time of pollen shedding, the relict Ubisch bodies become spatially concentrated on the minimal surface area of the senescent cells of the tapetum. In angiosperms after one or a few periods of initiation Ubisch bodies may remain in association with the surface of tapetal cells where the Ubisch body wall undergoes changes like those of the maturing pollen exine. We conclude that as a consequence of Ubisch body detachment from the plasma membrane of tapetal cells there is in <em>Pinus sylvestris</em> no updated information for modification of the wall and the Ubisch body wall remains static.

Comparing the M-position with some classical positions of convex bodies

2011 ◽  
Vol 152 (1) ◽  
pp. 131-152 ◽  
Author(s):  
E. MARKESSINIS ◽  
G. PAOURIS ◽  
CH. SAROGLOU
Keyword(s):  
Minimal Surface ◽  
Surface Area ◽  
Convex Bodies ◽  
Mean Width ◽  
Quantitative Results ◽  
Minimal Surface Area

AbstractThe purpose of this paper is to compare some classical positions of convex bodies. We provide exact quantitative results which show that the minimal surface area position and the minimal mean width position are not necessarily M-positions. We also construct examples of unconditional convex bodies of minimal surface area that exhibit the worst possible behavior with respect to their mean width or their minimal hyperplane projection.

scholarly journals Sections of Convex Bodies in John’s and Minimal Surface Area Position

2021 ◽  
Author(s):  
David Alonso-Gutiérrez ◽  
Silouanos Brazitikos
Keyword(s):  
Minimal Surface ◽  
Surface Area ◽  
Convex Bodies ◽  
Regular Simplex ◽  
Symmetric Convex ◽  
Polar Bodies ◽  
Mean Width ◽  
Centrally Symmetric ◽  
The Mean ◽  
Minimal Surface Area

Abstract We prove several estimates for the volume, the mean width, and the value of the Wills functional of sections of convex bodies in John’s position, as well as for their polar bodies. These estimates extend some well-known results for convex bodies in John’s position to the case of lower-dimensional sections, which had mainly been studied for the cube and the regular simplex. Some estimates for centrally symmetric convex bodies in minimal surface area position are also obtained.

scholarly journals Using snowflake surface-area-to-volume ratio to model and interpret snowfall triple-frequency radar signatures

2017 ◽  
Vol 17 (19) ◽  
pp. 12011-12030 ◽  
Author(s):  
Mathias Gergely ◽  
Steven J. Cooper ◽  
Timothy J. Garrett
Keyword(s):  
Surface Area ◽  
Cross Sections ◽  
Volume Ratio ◽  
High Sensitivity ◽  
Maximum Size ◽  
Strong Impact ◽  
Triple Frequency ◽  
Bounding Volume ◽  
Wide Range ◽  
Radar Signatures

Abstract. The snowflake microstructure determines the microwave scattering properties of individual snowflakes and has a strong impact on snowfall radar signatures. In this study, individual snowflakes are represented by collections of randomly distributed ice spheres where the size and number of the constituent ice spheres are specified by the snowflake mass and surface-area-to-volume ratio (SAV) and the bounding volume of each ice sphere collection is given by the snowflake maximum dimension. Radar backscatter cross sections for the ice sphere collections are calculated at X-, Ku-, Ka-, and W-band frequencies and then used to model triple-frequency radar signatures for exponential snowflake size distributions (SSDs). Additionally, snowflake complexity values obtained from high-resolution multi-view snowflake images are used as an indicator of snowflake SAV to derive snowfall triple-frequency radar signatures. The modeled snowfall triple-frequency radar signatures cover a wide range of triple-frequency signatures that were previously determined from radar reflectivity measurements and illustrate characteristic differences related to snow type, quantified through snowflake SAV, and snowflake size. The results show high sensitivity to snowflake SAV and SSD maximum size but are generally less affected by uncertainties in the parameterization of snowflake mass, indicating the importance of snowflake SAV for the interpretation of snowfall triple-frequency radar signatures.

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