Positive solutions and dynamics of a finite difference reaction–diffusion system

We investigate the dynamics and methods of computation for some nonlinear finite difference systems that are the discretized equations of a time-dependent and a steady-state reaction–diffusion problem. The formulation of the discrete equations for the time-dependent problem is based on the implicit method for parabolic equations, and the computational algorithm is based on the method of monotone iterations using upper and lower solutions as the initial iterations. The monotone iterative method yields improved upper and lower bounds of the solution in each iteration, and the sequence of iterations converges monotonically to a solution for both the time-dependent and the steady-state problems. An important consequence of this method is that it leads to a bifurcation point that determines the dynamic behavior of the time-dependent problem in relation to the corresponding steady-state problem. This bifurcation point also determines whether the steady-state problem has one or two non-negative solutions, and is explicitly given in terms of the physical parameters of the system and the type of boundary conditions. Numerical results are presented for both the time-dependent and the steady-state problems under various boundary conditions, including a test problem with known analytical solution. These numerical results exhibit the predicted dynamic behavior of the time-dependent solution given by the theoretical analysis. Also discussed are the numerical stability of the computational algorithm and the convergence of the finite difference solution to the corresponding continuous solution of the reaction–diffusion problem. © 1993 John Wiley & Sons, Inc.     

Synthesis and Mesogenic Properties of Liquid Crystals Containing Terminal Cyclohexylmethanol,Cyclopentylmethanol, Cyclobutylmethanol and Cyclopropylmethanol Moiety

Four series of compounds 11?50 containing terminal alicyclic rings such as cyclohexylmethyl, cyclopentylmethyl, cyclobutylmethyl, and cyclopropylmethyl rings were synthesized and their liquid crystal behavior studied. The ring size and the length of flexible alkoxy chain influence the phase formation in different ways. While the smaller ring and the shorter alkoxy chain tend to favor the formation of the N phase, the larger ring and the longer alkoxy chain tend to favor the formation of the SmC phase. All the compounds except 11 and 21 exhibit SmA phases. The widest temperature range of the N, SmA, and SmC phases are found in the compounds 41 , 46 , and 20 , respectively, which are 75 °C for 41 , 115 °C for 46 , and 100 °C for 20 .     

Synthesis and Second‐Order Nonlinearities of Chiral Prolinol‐Substituted Chromophores

A new series of thiophene‐ and furan‐containing chromophores with a chiral prolinol donor and a sulfone acceptor has been synthesized. The UV‐vis absorptions, second‐order nonlinear optical properties, and X‐ray crystal structures are described.     

Radiation patterns of electric dipole antenna in the presence of a biisotropic sphere

Analytic expressions of the dyadic Green's function of an arbitrary electric current source embedded in a general biisotropic sphere are presented at first, and the radiation characteristics of an electric dipole antenna placed on the surface of a biisotropic sphere lens are examined. The effects of the electric-and the magnetic-coefficients ( _e and _m ) of biisotropic medium on the radiation patterns of electric dipole antenna are investigated in detail.     

Discoloration Investigations of Yellow Lantern Pepper Sauce (Capsicum chinense Jacq.) Fermented by Lactobacillus plantarum: Effect of Carotenoids and Physiochemical Indices

Color is one of the important indicators affecting the quality of fermented pepper sauces, and it is closely related to carotenoid composition. This study systematically analyzed the changes in carotenoids and related physiochemical indices during the fermentation of yellow lantern pepper sauce. The CIELab color values indicated that L* and C* displayed a significant decreasing trend during fermentation. After 35 days of fermentation, the total carotenoid content significantly reduced from 3446.36 to 1556.50 μg/g DW (p < 0.05), and the degradation rate was 54.84%. Among them, the total content of carotene decreased by 56.03% during fermentation, whereas the degradation rate of xanthophylls and their esters was 44.47%. According to correlation analysis, violaxanthin myristate and lutein played a pivotal role in L*, a *, b *, chroma (C*), and yellowness index (YI). Moreover, PCA analysis indicated that lactic acid and acetic acid were the important qualities affecting the stability of pigment in fermented yellow lantern pepper sauce, which might also be the inducement of the color change. This work gives additional information concerning the discoloration of yellow lantern pepper sauce during fermentation and provides theory evidence regulating and improving the sensory qualities of yellow lantern pepper sauce.     

Rapid analysis of phthalic acid esters in environmental water using fast elution gas chromatography with mass spectrometry and adaptive library spectra

A method for the fast determination of the components in a complex sample by using gas chromatography with mass spectrometry was developed and used for the quantitative analysis of phthalic acid esters in environmental water. In the method, the adaptively corrected mass spectra were used to compensate for the differences between the library spectra and the measured ones in the experiment. The correction was obtained by the iterative transformation of the library spectra using iterative target transformation factor analysis, and the resolution was performed by non‐negative immune algorithm using the corrected spectra. Rapid analysis of 16 phthalic acid esters in water samples was achieved using fast elution gas chromatography with mass spectrometry measurements. The results show that the mass spectra and chromatographic profiles of the phthalic acid esters can be obtained from the overlapping signal of 13 min elution, and accurate quantitative analysis can be obtained. The recoveries of the phthalic acid esters obtained by standard addition are between 90.3 and 107.4%, and the relative standard deviations obtained in repeated measurements are less than 9%.     

Dislocation injection, reconstruction, and atomic transport on {001} Au terraces

High-resolution electron microscopy investigations of Au films show that adatoms on (100) surfaces insert into the underlying terrace to form surface dislocations. This injection readily occurs when the number of adatoms on a terrace is approximately 20 atoms or less. The surface dislocation glides along the terrace, but is repelled from the edges. The dislocation escapes by squeezing out in the dislocation line direction (not gliding out the terrace edge). Atomistic simulations confirm the dislocation stability, easy glide along the terrace and trapping at the terrace edge. These results have profound implications for film growth.