Time-varying human mobility patterns with metapopulation epidemic dynamics

In this paper, explicitly considering the influences of an epidemic outbreak on human travel, a time-varying human mobility pattern is introduced to model the time variation of global human travel. The impacts of the pattern on epidemic dynamics in heterogeneous metapopulation networks, wherein each node represents a subpopulation with any number of individuals, are investigated by using a mean-field approach. The results show that the pattern does not alter the epidemic threshold, but can slightly lower the final average density of infected individuals as a whole. More importantly, we also find that the pattern produces different impacts on nodes with different degree, and that there exists a critical degree _kc$k_c$. For nodes with degree smaller than _kc$k_c$, the pattern produces a positive impact on epidemic mitigation; conversely, for nodes with degree larger than _kc$k_c$, the pattern produces a negative impact on epidemic mitigation.     

Influence of the surface morphology on the melting of polymer crystals. I. Loops of random length and adjacent reentry

A polymer crystal with a noncrystalline surface layer formed by chain loops of different lengths is considered. It is assumed that the length of each loop can be changed by longitudinal diffusion of the molecule through the crystal lattice. From the condition that the free energy of the system is minimum, the loop length distribution and the average loop length as function of temperature are calculated. In contrast to the results for loops of equal length, for the present model, a substantial thickness of the noncrystalline surface layer and a broad melting range is obtained also for the case of adjacent reentry. In order to get this result one has to take into account that even an “ideal fold” consists of at least four rigidly arranged CH2 groups in energetically unfavored conformation.     

DRDF analysis of wide-angle x-ray scattering of natural rubber

A differential radial distribution function (DRDF) of molten natural rubber (NR) was derived from its wide-angle x-ray scattering (WAXS) data. Three peaks with Bragg spacings 4.85, 2.31, and 1.23 Å corresponding, respectively, to interchain, C₁-C₃ and C₁ -C₂ distances are present in the corrected WAXS curve. The derived DRDF, which is shown to be greatly improved than the ones published so far, contains six peaks located at 1.51, 2.48, 3.98, 5.68, 10.65, and 15.25 Å. Maximum contributions of intramolecular atomic distances to the radial distribution peaks were estimated and compared with the experimental results. The comparison shows that the first three peaks are intramolecular in origin and the remaining peaks are predominantly due to intermolecular regularities. A periodicity of an approximately constant interval of 5.26 Å is found between the intermolecular peaks and is attributable to the organizations of more or less parallel chain segments in the material. This finding provided additional evidence for the presence of local lateral ordering to the extent of about 30 Å in molten-state natural rubber.     

Polycrystalline silicon films prepared by metal-induced crystallisation using pre- and post-deposited aluminium on amorphous silicon

We report on the successful fabrication of polycrystalline silicon films by aluminium-induced crystallisation (AIC) of Radio frequency (rf) plasma-enhanced chemical vapour deposited (PECVD) a-Si films. The effects of annealing at different temperatures (300 and 400°C), below the eutectic temperature of the Si–Al binary system, on the crystallisation process have been studied. This work emphasises the important role of the position of the Al layer with respect to the Si layer on the crystallisation process. The properties of the crystallised films were characterised using X-ray diffraction, Raman spectroscopy, ellipsometry, field-emission scanning electron microscopy (FESEM) and atomic force microscopy (AFM). With an increase in the annealing temperature, it was found that the degree of crystallisation of annealed a-Si/Al and Al/a-Si films increased. The results showed that the arrangement where the Al was on top of the a-Si had a more prominent effect on crystallisation enhancement than when Al was below the a-Si. The interfacial layer between the Al and a-Si film is crucial because it influences the layer-exchange process during annealing. The oxide layer formed between the Al and the a-Si layers greatly retards the crystallisation process in the case of the Al/Si arrangement. Our investigations suggest that polycrystalline Si films formed by AIC can be used as a seed layer in solar cell fabrication.     

Banana fiber/chemically functionalized polypropylene composites with in-situ fiber/matrix interfacial adhesion by Palsule process

Chemically functionalized maleic anhydride (MAH)-grafted polypropylene matrix has been used (in place of polypropylene as matrix with compatibilizer) to process banana fiber/chemically functionalized polypropylene (BF/CFPP) composites, without using any compatibilizer and without any fiber modification by Palsule process. Fiber/matrix interfacial adhesion generated, in-situ, due to interactions between BF and the MAH of the CFPP matrix has been established by Fourier transform infrared spectroscopy and scanning electron microscopy. Mechanical properties of the BF/CFPP composites developed by Palsule process with in-situ fiber/matrix interfacial adhesion in this study have been found to be higher than those of the matrix and it increases with increasing amounts of fibers in composites, and are better than properties of literature reported BF/polypropylene composites processed with compatibilizers. Measured modulus of BF/CFPP composites compares well with values predicted by rule of mixtures, Hrisch model, Halpin-Tsai equations and its modified Nielsen version, and with Palsule equation. The feasibility of developing natural fiber/MAH grafted polyolefin composites by Palsule process without using any compatibilizer and without any fiber treatment is demonstrated.     

Asymptotic distribution of maximal autoregressive process with weight tending to 1

The maximal operator plays the similar role as the summation operator in the sense of stability of operation. So, we could discussARMA processes in the maximal operation by the same way as in the summation operation. However, many papers already treated with moving order statistics. In this paper, we discuss asymptotic behaviors of maximal autoregressive (MAR) processes with the weight tending to 1.     

Joint availability of systems modelled by finite semi–markov processes

Consider a repairable system at the time instants t and t + x, where t, x ≥0. The joint availability of the system at these time instants is defined as the probability of the system being functional in both t and t + x. A set of integral equations is derived for the joint availability of a system modelled by a finite semi–Markov process. The result is applied to the semi–Markov model of a two–unit system with sequential preventive maintenance. The method used for the numerical solution of the resulting system of integral equations is a two–point trapezoidal rule. The system of implementation is the matrix computation package MATLAB on the Apple Macintosh SE/30. The numerical results obtained by this method are shown to be in good agreement with those from simulation.     

矩形域上散乱数据多元最优插值的误差估计及其超收敛性（Ⅰ）──带连续边界条件

本文我们讨论了矩形域上带连续边界条件的一类多元散乱数据最优插值。给出了某些情形插值的误差估计，误差估计表明在某些点上还具有超收敛性。     

The Cauchy Problem for a Class of Semilinear Wave Equations with Piecewise Constants Data

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