On the Fourier Transform of Causal Distributions

We extend the distributional Bochner formula [1, p. 72, Theorem 26] to certain kinds of distributions. Theorem I.1 gives a formula [Eq. (I.1.14)] which makes it possible to obtain easily the Fourier transform of distributions of the form As applications of the formula (I.1.14) we evaluate the Fourier transforms of the distributions G_α(P±i0, m, n) [Eq. (I.4.1)] and H_α(P±i0,n) [Eq. (II.1.1)]. It follows from Theorem II.3 that H_zk(P±i0,n) is, for 2K≠n+2r, r=0,1..., an elementary solution of the n-dimensional ultrahyperbolic operator iterated k times.     

Activation energies for nucleation and growth and critical cluster size dependence in JMAK analyses of kinetic Monte-Carlo simulations of precipitation

Kinetic Monte-Carlo (KMC) methods are used as an approach to simulate precipitation in Cu-alloyed bcc Fe. In order to characterize the process, transformed fractions, that is, the precipitated atoms, are related to Johnson-Mehl-Avrami-Kolmogorov theory. However, simulated data often deviate from corresponding fit curves and so does the resulting growth exponent when compared to theoretical expectations. Furthermore, some data may suggest the development of a metastable phase. In our study, we show that the characteristics of the transformed fraction and, as a consequence, the derived growth exponents sensitively depend on the number of atoms that are considered to form a particle and hence contribute to the transformed fraction. With a temperature dependence of the critical cluster size and additionally accounting for severe impingement of the particles, we obtain growth exponents which lie close to the expected range between n = 1.5 and n = 2.5 for pre-existing nuclei or continuous nucleation, respectively. From these, we obtain activation energies for nucleation and growth of precipitates. In this way, atomistic KMC simulations yield thermodynamical quantities, which can be valuable input parameters for larger length scale simulation methods, for example, for Phase Field Method simulations.     

Interactions between cellulose nanofibers and retention systems in flocculation of recycled fibers

Although the positive effect that cellulose nanofibers (CNF) can have on paper strength is known, their effect on flocculation during papermaking is not well understood, and most relevant studies have been carried out in presence of only cationic starch. Flocculation is the key to ensuring retention of fibers, fines, and fillers, and furthermore floc properties have a great influence on paper quality. The aim of this research is to study the interactions between CNF and flocculants by assessing the effect of two types of CNF, from eucalyptus and corn, on the flocculation process induced by three different retention systems [a dual system, polyvinylamine (PVA), and cationic starch as reference]. The results showed that CNF interacted with the flocculants in different ways, affecting flocculation efficiency and floc properties. In general, addition of CNF increased floc stability and minimized overdosing effects. Moreover, presence of CNF increased floc size for given PVA dose; therefore, CNF addition could contribute to improve the wet end in the paper machine if combined with the optimal flocculant and dose.     

The Chromatographic Analysis of Reduced Sulfur Gases in Antarctic Waters Following Pre-Concentration onto Tenax

Abstract

A technique was developed using sparging and pre-concentration onto a Tenax trap at ambient temperature allowing field measurements to be made of reduced sulfur gases in Antarctic marine and glacial melt waters. Following thermal desorption, gases were determined by gas chromatography using a flame photometric detector. Detection limits in ng 1^?1 were: H₂S 50, OCS 8, SO₂ 160, CH₃SH 6, CH₃SCH₃ 20 and CS₂ 2. Storage of melt water samples for more than 24 hours resulted in concentration changes of the reduced sulfur gases present. While the Antarctic environment imposed limitations on the analytical method, an investigation of various pond and marine waters was undertaken.