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Delta Functions
Published in Kenneth B. Howell, Ordinary Differential Equations, 2019
Suppose we have some material spread out along the X–axis. Recall that the linear density of the material at position x, ρ(x), is the “mass per unit length” of the material at point x. More precisely, it is the function such that, if x0< x1, then ∫x0x1ρ(x)dx
Nanotubes, Nanowires, and Nanofibers
Published in Klaus D. Sattler, st Century Nanoscience – A Handbook, 2020
The International System of Units (SI unit) for linear density is gram per kilometer (g/km). However, it is tedious to obtain a lab measurement of the mass of 1 km-long yarn. An adequate method is to weigh a few meters, then multiply and normalize the values up to the unit weight.
Effects of chemical treatments and degumming methods on physical and mechanical properties of okra bast and corn husk fibers
Published in The Journal of The Textile Institute, 2020
G. M. Arifuzzaman Khan, Nazire Deniz Yilmaz, Kenan Yilmaz
Physical, mechanical, chemical and morphological characterization of the okra bast and corn husk fiber samples was carried out. The samples were subjected to conditioning at 21 °C and 65% relative humidity for at least 24 h before characterization processes. Linear density was evaluated as per the test method ASTM D 1577-07 with measuring 13 replicates (ASTM D 1577 07 standard test methods for linear density of textile fibers, 2007). The linear density in (tex) corresponds to mass (g) of fiber per unit length (km). It is commonly used to define the coarseness/fineness of textile fibers as it is very difficult to determine the diameter of the plant fibers due to their irregular cross-sections. The tensile properties were characterized according to ASTM D 3822 (ASTM D 3822 07 standard test method for tensile properties of single textile fibers, 2007) by using Tinius Olsen H10KT(R) Tester (Tinius Olsen, Horsham, PA) equipped with QMat for Textiles(R) software, and the testing conditions were 10 N load cell, 1 mm/min crosshead, 2.54 cm gauge length. Twenty-five specimens of each fiber batch were measured. The moisture content of the fibers was evaluated according to ASTM D2495–07 (ASTM D 2495 07 Standard Test Method for Moisture in Cotton by Oven-Drying, 2007). As specified by the standard, fiber bundles were subjected to conditioning for at least 24 h and weighed to the 0.1 mg digit, then oven dried at 105 °C for 16 h, cooled in a desiccator and weighed again. The moisture content was calculated using the following formula: where MC stands for the moisture content, OS represents the mass of original (moist) sample, and OD corresponds to the mass of oven dry sample. Three specimens of each sample batch were measured. The findings were statistically interpreted by applying analysis of variance with α at 0.05 significance level.