30 resultados para Mathematical transformations


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The surface structures of the Si(113)-(1 X 1), Si(113)-(3 X 1) and Si(113)-(3 X 2) have been studied theoretically by means of an ab initio quantum chemical CNDO method. We address not only the importance of the surface energy but also the energy minimization and the barrier height in the different structural conversion. We found that (1) the relaxed Si(113)-(1 X 1) structure. (2) the Si(113)-(3 X 1) close to the Si(113) Ranke (3 X 1)-2 model; (3) the atomic positions of Si(113)-(3 X 2) corrugated arrangement. (C) 1997 Elsevier Science B.V.

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Thermally induced evolution of phase transformations is a basic physical-chemical process in the dissociation of gas hydrate in sediment (GHS). Heat transfer leads to the weakening of the bed soil and the simultaneous establishment of a time varying stress field accompanied by seepage of fluids and deformation of the soil. As a consequence, ground failure could occur causing engineering damage or/and environmental disaster. This paper presents a simplified analysis of the thermal process by assuming that thermal conduction can be decoupled from the flow and deformation process. It is further assumed that phase transformations take place instantaneously. Analytical and numerical results are given for several examples of simplified geometry. Experiments using Tetra-hydro-furan hydrate sediments were carried out in our laboratory to check the theory. By comparison, the theoretical, numerical and experimental results on the evolution of dissociation fronts and temperature in the sediment are found to be in good agreement.

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A predictive and self-consistent mathematical model incorporating the electrochemical, chemical and ionic migration processes characterizing the propagation stage of crevice and pitting corrosion in metals is described. The model predicts the steady-state solution chemistry and electrode kinetics (and hence metal penetration rates) within an active corrosion cavity as a function of the many parameters on which these depend, such as external electrode potential and crevice dimensions. The crevice is modelled as a parallel-sided slot filled with a dilute sodium chloride solution. The cavity propagation rates are found to be faster in the case of a crevice with passive walls than one with active walls. The distribution of current over the internal surface of a crevice with corroding walls can be assessed using this model, giving an indication of the future shape of the cavity. The model is extended to include a solid hydroxide precipitation reaction and considers the effect of consequent changes in the chemical and physical environment within the crevice on the predicted corrosion rates. In this paper, the model is applied to crevice and pitting corrosion in carbon steel.

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Land-cover changes in China are being powered by demand for food for its growing population and by the nation's transition from a largely rural society to one in which more than half of its people are expected to live in cities within two decades. Here we use an analysis of remotely sensed data gathered between 1990 and 2000, to map the magnitude and pattern of changes such as the conversion of grasslands and forests to croplands and the loss of croplands to urban expansion. With high-resolution ( 30 m) imagery from Landsat TM for the entire country, we show that between 1990 and 2000 the cropland area increased by 2.99 million hectares and urban areas increased by 0.82 million hectares. In northern China, large areas of woodlands, grasslands and wetlands were converted to croplands, while in southern China large areas of croplands were converted to urban areas. The land-cover products presented here give the Chinese government and international community, for the first time, an unambiguous understanding of the degree to which the nation's landscape is being altered. Documentation of these changes in a reliable and spatially explicit way forms the foundation for management of China's environment over the coming decades.

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A main-chain nonracemic chiral liquid crystalline polymer was synthesized from (R)-(-)4'-{w-[2-(p-hydroxy-o-nitrophenyloxy)-1-propyloxy]-1-decyloxyl-4-biphenylcarboxylic acid. This polymer contained 10 methylene units in each chemical repeating unit and was abbreviated PET(R*-10). On the basis of differential scanning calorimetry, wide-angle X-ray diffraction, and polarized light microscopy experiments, chiral smectic C (S-C*) and chiral smectic A (S-A*) phases were identified. Both flat-elongated and helical lamellar crystal morphologies were observed in transmission electron microscopy. Of particular interest was the flat-elongated lamellar crystals were constructed via microtwinning of an orthorhombic cell with dimensions of a = 1.42 nm, b = 1.28 nm, and c = 3.04 nm. On the other hand, the helical lamellar crystals were exclusively left-handed, which was opposite to the right-handed helical crystals grown in PET(R*-9) and PET(R*-11) (having 9 and 11 methylene units, respectively). Note that these three polymers had identical right-handed chiral centers (R*-). Therefore, a single methylene unit difference on the polymer backbones on an atomic length scale substantially changed the chirality of the crystals in the micrometer length scale. Furthermore, aggregates of these helical crystals in PET(R*-10) did not generate banded spherulites in polarized light microscopy. Possible reasons for this change and loss of helical senses (handedness) on different length scales in chirality transferring processes were discussed.

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This paper studies the radiation properties of the immiscible blend of nylon1010 and HIPS. The gel fraction increased with increasing radiation dose. The network was found mostly in nylon1010, the networks were also found in both nylon1010 and HIPS when the dose reaches 0.85 MGy or more. We used the Charleby-Pinner equation and the modified Zhang-Sun-Qian equation to simulate the relationship with the dose and the sol fraction. The latter equation fits well with these polymer blends and the relationship used by it showed better linearity than the one by the Charleby-Pinner equation. We also studied the conditions of formation of the network by the mathematical expectation theorem for the binary system. Thermal properties of polymer blend were observed by DSC curves. The crystallization temperature decreases with increasing dose because the cross-linking reaction inhibited the crystallization procession and destroyed the crystals. The melting temperature also reduced with increasing radiation dose. The dual melting peak gradually shifted to single peak and the high melting peak disappeared at high radiation dose. However, the radiation-induced crystallization was observed by the heat of fusion increasing at low radiation dose. On the other hand, the crystal will be damaged by radiation. A similar conclusion may be drawn by the DSC traces when the polymer blends were crystallized. When the radiation dose increases, the heat of fusion reduces dramatically and so does the heat of crystallization. (C) 1999 Elsevier Science Ltd. All rights reserved.

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Stretching a stacked sPP lamellar morphology at room temperature leads to a mechanical induced transformation from the (t(2)g(2))(2) (helical) into the (tttt) (zigzag) chain conformation of the polymer. The so prepared samples exhibit after annealing above 80 degreesC a thermal induced retransformation into the cell I and cell III crystal structure of the helical chain conformation. The mechanical induced chain conformational transformation as well as the thermal induced retransformation was studied by means of transmission electron microscopy and electron diffraction. (C) 2001 Kluwer Academic Publishers.

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A multi-plate (NIP) mathematical model was proposed by frontal analysis to evaluate nonlinear chromatographic performance. One of its advantages is that the parameters may be easily calculated from experimental data. Moreover, there is a good correlation between it and the equilibrium-dispersive (E-D) or Thomas models. This shows that it can well accommodate both types of band broadening that is comprised of either diffusion-dominated processes or kinetic sorption processes. The MP model can well describe experimental breakthrough curves that were obtained from membrane affinity chromatography and column reversed-phase liquid chromatography. Furthermore, the coefficients of mass transfer may be calculated according to the relationship between the MP model and the E-D or Thomas models. (C) 2004 Elsevier B.V. All rights reserved.