Structure–property relationships of poly(vinyl alcohol). II. The influence of molecular regularity on the crystallization–dissolution temperature relationships of poly(vinyl alcohol)

Dissolution temperatures T_s have been determined for poly(vinyl alcohol) (PVA) samples of varying tacticity as a function of crystallization temperatures T_c. From the values of T_s and T_c, one can obtain values of (T_m)_∞, the dissolution temperature of crystals of infinite stepheight. (T_m)_∞ is a characteristic property of a given sample. This method of characterization is very sensitive and reliable for detecting differences in molecular regularity among PVA samples. The variation of (T_m)_∞ with stereoregularity is attributed in part to differences in hydrogen-bonding characteristics. Determinations of the crystallinities of solution-crystallized PVA have shown that stereoregularity in PVA does not result in higher crystallizability.     

The self-preserving size distribution theory. I. Effects of the Knudsen number on aerosol agglomerate growth

Gas-phase synthesis of fine solid particles leads to fractal-like structures whose transport and light scattering properties differ from those of their spherical counterparts. Self-preserving size distribution theory provides a useful methodology for analyzing the asymptotic behavior of such systems. Apparent inconsistencies in previous treatments of the self-preserving size distributions in the free molecule regime are resolved. Integro-differential equations for fractal-like particles in the continuum and near continuum regimes are derived and used to calculate the self-preserving and quasi-self-preserving size distributions for agglomerates formed by Brownian coagulation. The results for the limiting case (the continuum regime) were compared with the results of other authors. For these cases the finite difference method was in good in agreement with previous calculations in the continuum regime. A new analysis of aerosol agglomeration for the entire Knudsen number range was developed and compared with a monodisperse model; Higher agglomeration rates were found for lower fractal dimensions, as expected from previous studies. Effects of fractal dimension, pressure, volume loading and temperature on agglomerate growth were investigated. The agglomeration rate can be reduced by decreasing volumetric loading or by increasing the pressure. In laminar flow, an increase in pressure can be used to control particle growth and polydispersity. For D(f)=2, an increase in pressure from 1 to 4 bar reduces the collision radius by about 30%. Varying the temperature has a much smaller effect on agglomerate coagulation.     

Structure–property relationships of poly(vinyl alcohol). I. Influence of polymerization solvents and temperature on the structure and properties of poly(vinyl alcohol) derived from poly(vinyl acetate)

The solubility properties of poly(vinyl alcohol) (PVA) vary with the method of preparation of the poly(vinyl acetate) (PVAc) from which it is derived. PVAc was prepared with free-radical catalysts over a range of temperatures from ?78 to 90°C. with solvents of varying chain-transfer ability. The corresponding PVA samples varied in their resistance to dissolution in water. Their high-resolution proton nuclear magnetic resonance spectra showed on differences in tacticity. Data on 1,2-diol content showed only minor differences. Hence, the increase in resistance of PVA to dissolution in water arising from changes in chain-transfer activity of the solvent used in vinyl acetate polymerization is largely attributable to a decrease in molecular weight, and the increase in resistance of PVA to dissolution in water arising from a decrease in the temperature of the vinyl acetate polymerization is largely attributable to a decrease in both long and short branches. Evidently, with polar polymers having small side groups, tacticity is not the only factor influencing property variation; that is, variations in stereoregularity influence more the crystallinity of the sample as measured by density or x-ray methods than the ultimate crystallizability under conditions of mechanical and thermal treatment. In this regard polar polymers having small side groups differ from nonpolar polymers.     

Character sums over shifted primes

We obtain a new bound for sums of a multiplicative character modulo an integer q at shifted primes p + a over primes p ≤ N. Our bound is nontrivial starting with N ≥ q ^8/9+? for any ? > 0. This extends the range of the bound of Z. Kh. Rakhmonov that is nontrivial for N ≥ q ^1+? .     

Close encounters among the primes

This paper was written, apart from one technical correction, in July and August of 2013. The, then very recent, breakthrough of Y. Zhang [18] had revived in us an intention to produce a second edition of our book “Opera de Cribro”, one which would include an account of Zhang’s result, stressing the sieve aspects of the method. A complete and connected version of the proof, in our style but not intended for journal publication, seemed a natural first step in this project. Following the further spectacular advance given by J. Maynard (arXiv:1311. 4600, Nov 20, 2013), we have had to re-think our position. Maynard’s method, at least in its current form, proceeds from GPY in quite a different direction than does Zhang’s, and achieves numerically superior results. Consequently, although Zhang’s contribution to the distribution of primes in arithmetic progressions certainly retains its importance, the fact remains that much of the material in this paper would no longer appear in a new edition of our book. Because this paper contains some innovations that we do not wish to become lost, we have decided to make the work publicly available in its original format. We are extremely pleased to be able to include it in the current volume, commemorating the one hundred and twenty-fifth anninversary of the birth of Srinivasa Ramanujan.     

Robust inversion, dimensionality reduction, and randomized sampling

We consider a class of inverse problems in which the forward model is the solution operator to linear ODEs or PDEs. This class admits several dimensionality-reduction techniques based on data averaging or sampling, which are especially useful for large-scale problems. We survey these approaches and their connection to stochastic optimization. The data-averaging approach is only viable, however, for a least-squares misfit, which is sensitive to outliers in the data and artifacts unexplained by the forward model. This motivates us to propose a robust formulation based on the Student’s t-distribution of the error. We demonstrate how the corresponding penalty function, together with the sampling approach, can obtain good results for a large-scale seismic inverse problem with 50 % corrupted data.     

Working group report: Heavy-ion physics and quark-gluon plasma

This is the report of Heavy Ion Physics and Quark-Gluon Plasma at WHEPP-09 which was part of Working Group-4. Discussion and work on some aspects of quark-gluon plasma believed to have created in heavy-ion collisions and in early Universe are reported.     

Instability in Parallel Flows Revisited

An example of an unstable inviscid plane parallel shear flow with classical boundary conditions is presented. The complete unstable spectrum is exhibited using techniques of continued fractions for the shear flow with profile U ( y )=cos  m y . For such flows spectral instability implies nonlinear instability. A three-dimensional generalization is discussed.