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.     

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.     

Mechanisms of decomposition of mixtures of ethyl acetate and isopropyl bromide subjected to pulsed infrared laser irradiation

The infrared laser induced decomposition of mixtures of ethyl acetate and isopropyl bromide has been studied. The ratio of the yields of products ethylene and propylene, arising from the unimolecular decomposition reactions: ethyl acetate → ethylene + acetic acid, and isopropyl bromide → propylene + hydrogen bromide, were measured as a function of the ratio of ethyl acetate to isopropyl bromide and pressure of added helium. The results indicate clearly that in these systems non-equilibrium behavior is found up to the highest pressures used (about one atmosphere). A two level kinetic model is suggested which qualitatively explains the observations.     

Record-high near-band-edge optical nonlinearities and two-level model correction of poled polymers by spectroscopic electromodulation and ellipsometry

The determination of nonlinearities near the band edge of organic and polymeric electro-optic(EO)materials is important from the viewpoint of molecular nonlinear optics(NLO)and photonic device applications.Based on transmission-mode Stark effect electromodulation(EM)spectroscopy,we study the electric-field-induced changes in optical absorption and refraction of newly developed EO polymers from the visible to near-infrared(NIR)wavelengths and report record-high near-band-edge complex EO effects from poled thin films.Values ofΔn andΔk up to 10^-3 and 10^-2 are found at an applied electric field of 2.0×10⁵-3.0×10⁵V/cm.The study of linear optical properties of poled films by spectroscopic ellipsometry shows large polinginduced birefringence and a nearly two-fold increase in the extinction coefficients at the extraordinary polarization.Through the Kramers-Kronig analysis,we obtained the real and imaginary second-order nonlinear coefficients up to~3,500 and~5,600 pm/V,respectively,which are believed to be the highest NLO coefficients of poled polymers through the resonance enhancement.Our approach goes beyond the previous works,applicable only to several discrete wavelengths,to a full-spectral analysis with independent verification of slab waveguide measurements.By considering both the electroabsorption and electrorefraction effects,our study overcomes the limitation of the classic qualitative two-level model and provides a quantitative understanding of near-resonance optical nonlinearities of organic EO materials.It can inspire the exploration of high-speed,absorptive,or phase-shifting light-modulators using EO polymers for on-chip applications.     

Recent progress on the Dirichlet divisor problem and the mean square of the Riemann zeta-function

Let Δ(x) and E(t) denote respectively the remainder terms in the Dirichlet divisor problem and the mean square formula for the Riemann zeta-function on the critical line.This article is a survey of recent developments on the research of these famous error terms in number theory.These include upper bounds,Ω-results,sign changes,moments and distribution,etc.A few open problems are also discussed.     

Anomalous surface enhanced molecular Raman scattering from inelastic tunneling spectroscopy junctions

Anomalously strong Raman spectra have been obtained from molecular monolayers adsorbed on the insulator in metal-insulator-metal tunnel junctions. We show unambiguously that Raman spectroscopy can readily detect molecular monolayers and consider the effects of surface roughness, the molecule-metal interface and the metal on our results.     

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.     

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