Recent Developments in the Chemistry of Cellulose which Pertain to the Cross-Linking of Cotton

1969 ◽  
Vol 39 (8) ◽  
pp. 749-759 ◽  
Author(s):  
S. P. Rowland ◽  
E. J. Roberts ◽  
A. L. Bullock ◽  
V. O. Cirino ◽  
C. P. Wade ◽  
...  

The distributions of sites of attachment of substituents or cross linkages (a) at the 2–0-, 3–0-, and 6–0-positions of the d-glucopyranosyl units, (b) along the molecular chains of cellulose, (c) on or in the microstructural units, and (d) within the fiber cross sections are reviewed in order to develop perspective for the factors that influence and control these distributions. Among the factors determining the site of attachment in the d-glucopyranosyl unit are: (1) the type of reaction (e.g., reversible or nonreversible), (2) the specific nature of the reagent (e.g., molecular size), and (3) the medium from which the reagent is introduced. Means of controlling this distribution are discussed. There is no available information on the distributions of linkages introduced along the molecular chains of cellulose from reactions that occur without disruption of the crystalline order. It is evident, however, that, even under these conditions, every molecule in the cellulose matrix has one or more accessible segments along its chain. Measurements that are specific to the distribution of substituents among the total d-glucopyranosyl units, but which are applicable, in first-order approximation, to the units along the molecular chain, are discussed in connection with reactions conducted in mercerizing media. Evidence indicative of reactions occurring on the surfaces of highly ordered micro-structural units (microfibrils or bundles of microfibrils) has been obtained from measurement of the distribution of substituents introduced into the d-glucopyranosyl units of cotton cellulose under nonmercerizing conditions. Penetration within these units is evident under mercerizing conditions of reaction. An interrelationship between the site of attachment in the d-glucopyranosyl unit and the site of reaction in the microstructural unit is discussed. At the fiber level of structure, the complex interplay between rate of chemical reaction and rate of diffusion into the fibers is considered. Gross variations of distribution of substituents or cross linkages in the fiber cross section (from peripheral to uniform) result from changes in the two rates noted. In a case examined in some detail, wrinkle-recovery angles benefit from the more uniform distribution of cross linkages.

AIAA Journal ◽  
1998 ◽  
Vol 36 ◽  
pp. 1721-1727
Author(s):  
Prasanth B. Nair ◽  
Andrew J. Keane ◽  
Robin S. Langley

2021 ◽  
Vol 76 (3) ◽  
pp. 265-283
Author(s):  
G. Nath

Abstract The approximate analytical solution for the propagation of gas ionizing cylindrical blast (shock) wave in a rotational axisymmetric non-ideal gas with azimuthal or axial magnetic field is investigated. The axial and azimuthal components of fluid velocity are taken into consideration and these flow variables, magnetic field in the ambient medium are assumed to be varying according to the power laws with distance from the axis of symmetry. The shock is supposed to be strong one for the ratio C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ to be a negligible small quantity, where C 0 is the sound velocity in undisturbed fluid and V S is the shock velocity. In the undisturbed medium the density is assumed to be constant to obtain the similarity solution. The flow variables in power series of C 0 V s 2 ${\left(\frac{{C}_{0}}{{V}_{s}}\right)}^{2}$ are expanded to obtain the approximate analytical solutions. The first order and second order approximations to the solutions are discussed with the help of power series expansion. For the first order approximation the analytical solutions are derived. In the flow-field region behind the blast wave the distribution of the flow variables in the case of first order approximation is shown in graphs. It is observed that in the flow field region the quantity J 0 increases with an increase in the value of gas non-idealness parameter or Alfven-Mach number or rotational parameter. Hence, the non-idealness of the gas and the presence of rotation or magnetic field have decaying effect on shock wave.


1999 ◽  
Vol 08 (05) ◽  
pp. 461-483
Author(s):  
SEIYA NISHIYAMA

First-order approximation of the number-projected (NP) SO(2N) Tamm-Dancoff (TD) equation is developed to describe ground and excited states of superconducting fermion systems. We start from an NP Hartree-Bogoliubov (HB) wave function. The NP SO(2N) TD expansion is generated by quasi-particle pair excitations from the degenerate geminals in the number-projected HB wave function. The Schrödinger equation is cast into the NP SO(2N) TD equation by the variation principle. We approximate it up to first order. This approximate equation is reduced to a simpler form by the Schur function of group characters which has a close connection with the soliton theory on the group manifold.


Author(s):  
Bappaditya Banerjee ◽  
Anil K. Bajaj

Abstract Dynamical systems with two degrees-of-freedom, with quadratic nonlinearities and parametric excitations are studied in this analysis. The 1:2 superharmonic internal resonance case is analyzed. The method of harmonic balance is used to obtain a set of four first-order amplitude equations that govern the dynamics of the first-order approximation of the response. An analytical technique, based on Melnikov’s method is used to predict the parameter range for which chaotic dynamics exist in the undamped averaged system. Numerical studies show that chaotic responses are quite common in these quadratic systems and chaotic responses occur even in presence of damping.


2014 ◽  
Vol 20 (1) ◽  
pp. 132-141 ◽  
Author(s):  
Jianfeng Guo

The iteratively reweighted least-squares (IRLS) technique has been widely employed in geodetic and geophysical literature. The reliability measures are important diagnostic tools for inferring the strength of the model validation. An exact analytical method is adopted to obtain insights on how much iterative reweighting can affect the quality indicators. Theoretical analyses and numerical results show that, when the downweighting procedure is performed, (1) the precision, all kinds of dilution of precision (DOP) metrics and the minimal detectable bias (MDB) will become larger; (2) the variations of the bias-to-noise ratio (BNR) are involved, and (3) all these results coincide with those obtained by the first-order approximation method.


1992 ◽  
Vol 47 (3) ◽  
pp. 683-694 ◽  
Author(s):  
H.S. Kheshgi ◽  
S.F. Kistler ◽  
L.E. Scriven

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