A moving finite element method for the population balance equation

A moving finite element algorithm has been compared against the upwind-differencing and Smolarkiewicz methods for the population balance equation of multicomponent particle growth processes. Analytical solutions and an error function have been used to test the numerical methods. The moving finite elements technique is much more accurate than other methods for a wide range of parameters. Since this method uses moving grids, it is able to model very narrow particle size distributions. It is also shown that the method can be extended to solve condensational growth problems which include particle curvature and non-continuum mass transfer effects.     

The effect of Reynolds number on a turbulent far-wake

The turbulent far-waked generated by a circular cylinder is investigated for two values (1350 and 4600) of the Reynolds number Re _θ (based on the free stream velocity and the momentum thickness). Two arrays of sixteen X-wires, eight in the (x,?y)-plane and eight in the (x,?z)-plane, are used to capture the main features of the large-scale motion in two orthogonal planes. Both the magnitude of the measured Reynolds stresses and the size of the two-point velocity and vorticity correlation contours increase with Reynolds number. The probability density function and spectra of the velocity signals also exhibit differences with Re _θ. A comparison of centerline turbulence intensities with those in the literature suggests that the Reynolds number dependence may disappear for Re _θ?5000.     

Low-complexity compression of holograms based on delta modulation

Past research has demonstrated that hologram of a real world object can be acquired by scanning it with a single two-dimensional optical scan. The technology commonly referred to as optical scanning holography (OSH), have found important applications such as in microscopy, pattern recognition, 3D holographic display, and optical remote sensing. As holograms are often employed to capture three dimensional objects with high resolution, large amount of data is required to represent them. In this paper we propose a method for compressing holograms based on Delta modulation. Specifically, we apply our proposed method for holograms captured by OSH. Experimental evaluation reveals that our proposed approach is capable of attaining a compression ratio of 64 times, and still preserves favorable fidelity on the reconstructed images. In addition, both the encoding and decoding processes of the proposed method are very low in complexity, hence enabling real-time operation.     

Morphology study of Nafion membranes prepared by solutions casting

The structures of Nafion membranes prepared by solutions casting from low aliphatic alcohols/water mixture solvents and N,N′‐dimethyl formamide (DMF) solvent were investigated using differential scanning calorimeter and small angle X‐ray scattering. The aggregation behavior of Nafion molecules in the casting solutions was also investigated using dynamic light scattering. We show that the morphology of membranes was strongly influenced by the conformations of Nafion molecules in the solutions. In aliphatic alcohol/water mixture solvents, which have a worse compatibility with Nafion backbones, the Nafion molecules aggregate and form fringed rod‐like structures. These primary rod‐like structures then aggregate again through fringed side chains to form secondary ionic aggregations. In DMF solvent, owing to its better compatibility with Nafion backbones, less Nafion molecules aggregate. The high degree of Nafion molecular aggregations in aliphatic alcohol/water mixture solvents leads to a high degree of hydrophobic and hydrophilic phase separation for membranes prepared by casting from Nafion/aliphatic alcohol/water solutions. However, the lower degree of molecular aggregations in DMF solvent results in a lower degree of hydrophobic and hydrophilic phase separation for membranes prepared by casting from Nafion/DMF solution. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 3044–3057, 2005     

Solvent‐induced crystallization in poly(ethylene terephthalate) during mass transport

Solvent transport in poly(ethylene terephthalate) (PET) and related phase transformation were investigated. The data of mass sorption were analyzed according to Harmon's model for Case I (Fickian), Case II (swelling), and anomalous transport. This transport process in PET is accompanied by the induced crystallization of the original amorphous state. The transformation was examined by wide‐angle X‐ray scattering, small‐angle X‐ray scattering, differential scanning calorimetry, and Fourier transform infrared spectroscopy. During this process, the matrix is under a strain state that causes different kinetic paths of crystallization as compared with that by thermal annealing. This state of strain assists the development of the solvent‐induced crystallization. The model regarding crystallization was proposed in terms of the study of long period L, the crystal thickness l_c, and the thickness of amorphous layer l_a obtained from the one‐dimensional correlation function and interface distribution function. Different kinetic paths were discovered for different crystallization processes. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1444–1453, 2002     

Lamellar morphology and equilibrium melting temperature of syndiotactic polystyrene in β‐crystalline form

Lamellar morphology and thickness of syndiotactic polystyrene (sPS) samples melt‐crystallized at various temperatures were probed using transmission electron microscopy (TEM) and small‐angle X‐ray scattering (SAXS). In addition, the melting temperature and enthalpy of the crystallized samples were characterized with differential scanning calorimetry. Under appropriate thermal treatments, all the samples investigated in this study were crystallized into β′ crystal modification, as revealed by wide‐angle X‐ray diffraction. From the SAXS intensity profiles, a scattering peak (or shoulder) associated with lamellar features as well as the presence of anomalous scattering at the zero‐scattering vector were evidently observed. The peculiar zero‐angle scattering was successfully described by the Debye–Bueche model, and subtraction of its contribution from the raw intensity profiles was carried out to deduce the intensity profile merely associated with the lamellar feature. The lamellar thickness obtained from Lorentz‐corrected intensity profiles in this manner agrees with that measured from the TEM images, provided that the two‐phase model is applied. On the basis of the Gibbs–Thomson equation, the modest estimations of equilibrium melting temperature and the surface free energy of the fold lamellar surface are 292.7 ± 2.7 °C and 20.2 ± 2.6 erg/cm², respectively, when lamellar thicknesses measured by TEM are applied. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 1626–1636, 2002     

All-Optical Wavelength Conversion with Amplitude Equalization and Pulse Shaping

A dual-wavelength-injection-locked (DWIL) Fabry-Perot (FP) laser is used as an all-optical wavelength converter and regenerator.Regenerated pulses have narrower pulse-width of 37ps.Power penalty and extinction-ratio improvement of 1.5dB and 4dB respectively were achieved.     

Tidal effects and the proximity decay of nuclei

We examine the decay of the 3.03 MeV state of (8)Be evaporated from an excited projectilelike fragment following a peripheral heavy-ion collision. The relative energy of the daughter alpha particles exhibits a dependence on the decay angle of the (8)Be(*), indicative of a tidal effect. A comparison of the measured tidal effect with a model suggests a measurable nuclear proximity interaction.     

On some mean values for the divisor function and the Riemann zeta-function

Let Δ(x) and E(x) denote respectively the error terms in the summatory formula for the divisor function and in the mean square formula for ζ(s) on the critical line. We consider some general mean values for Δ(x) and E(x) and discover interesting differences between these two functions. In particular, this yields evidence that E(x) is more negative than Δ(x).