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Spatiotemporal nonlocal diffusion in a bounded system is addressed by considering fractional diffusion in a linear, composite system. By considering limiting conditions, solutions for combinations of Neumann and Dirichlet boundary conditions (either zero or nonzero) at the ends of a finite system are derived in terms of Mittag–Leffler functions by the Laplace transformation. Computational viability is demonstrated by inverting the solutions numerically and comparing resulting calculations with asymptotic solutions. Time and space fractional derivatives, defined by variables \(\alpha \) and \(\beta \), respectively, are employed in the Caputo sense; a single-sided, asymmetric space derivative is used. Inspection of the asymptotic solutions leads to insights on the structure of the solutions that may not be available otherwise; the resulting deductions are verified through the numerical inversions. For pure superdiffusion, characteristics of some of the solutions presented here are very similar to those of classical diffusion but combined effects for the corresponding situation result in power-law behaviors. Incidentally, to our knowledge, the pressure distribution for space fractional diffusion at long enough times in a finite system is derived based on first principles for the first time. 相似文献
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An Efficient Labelling Approach to Harness Backbone and Side‐Chain Protons in 1H‐Detected Solid‐State NMR Spectroscopy 下载免费PDF全文
Deni Mance Dr. Tessa Sinnige Mohammed Kaplan Siddarth Narasimhan Mark Daniëls Dr. Klaartje Houben Prof. Marc Baldus Dr. Markus Weingarth 《Angewandte Chemie (International ed. in English)》2015,54(52):15799-15803
1H‐detection can greatly improve spectral sensitivity in biological solid‐state NMR (ssNMR), thus allowing the study of larger and more complex proteins. However, the general requirement to perdeuterate proteins critically curtails the potential of 1H‐detection by the loss of aliphatic side‐chain protons, which are important probes for protein structure and function. Introduced herein is a labelling scheme for 1H‐detected ssNMR, and it gives high quality spectra for both side‐chain and backbone protons, and allows quantitative assignments and aids in probing interresidual contacts. Excellent 1H resolution in membrane proteins is obtained, the topology and dynamics of an ion channel were studied. This labelling scheme will open new avenues for the study of challenging proteins by ssNMR. 相似文献
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Field measurements were made of soil density and moisture patterns under different vehicle tire paths with varying external pressures and number of passes. In addition, laboratory index tests were performed to determine the compaction behaviour of the same soil. Using these results, a prediction equation of dry density in terms of applied pressure and moisture content was obtained for the clay soil. A previously developed equation for sandy soil was modified for the complete range of moisture contents encountered. Estimation of shear strength for the clay soil was made using plastic and liquid limits. 相似文献
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G.S.V. Raghavan E. McKyes F. Taylor P. Richard A. Watson 《Journal of Terramechanics》1979,16(2):69-76
A 52 plot experiment was performed during the growing season of 1977 in a Ste. Rosalie clay soil, using a randomized complete-block design with 13 treatments of machinery traffic within each of four blocks. Three vehicle contact pressures, four numbers of tractor passes, and a control of zero traffic were used to relate the growth and yield variables to wheel traffic and the resulting soil compaction. The number of days required for (a) plant emergence, (b) tasselling, and (c) silking were minimum in moderately compacted plots. The plant growth rate monitored at 41, 54, 68, and 105 days from the seeding time was different from plot to plot. Growth models at different times of the season were derived in terms of the wheel traffic variables, and plant and ear moisture content variation with traffic treatment was investigated. Yield and ear yield increased with increases in machine contact pressure and passes reaching a peak around 500 kPa and dropped off for further increases. The reduction in yield was over 35% in some cases, suggesting that careful traffic planning is essential to obtain better production in agricultural fields. Prediction models were obtained for all the plant growth characteristics in terms of traffic variables. A relation for yield in terms of soil bulk density was established for a dry season. 相似文献
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Despite the wide use of 1,2,4,5- tetrazines in biomaterials and materials science, currently there does not exist synthetic method(s) that can yield significant amount of 1,2,4,5- tetrazines without the use of potentially toxic metal catalysts. Here, we report a less energy intensive and more efficient metal catalyst free approach for the synthesis of an asymmetric tetrazine. A range of operating parameters such as extraction pH and temperature were regulated to achieve a practical yield nearly 1.5 times greater than the yields reported in the literature for similar synthetic procedures. 相似文献
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K.N. Raghavan 《代数通讯》2013,41(10):2827-2831
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A simple, efficient, regioselective and environmentally safe method for oxybromination of activated aromatics catalyzed by HZSM-5 is reported. The electrophilic substitution of bromine generated from KBr using HZSM-5 as a catalyst and H2O2 as an oxidant. 相似文献
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The direct correlation function for water near its triple point is obtained from published X-ray data. The core part of the function can be approximated by a hard-sphere function. The part beyond the core is discussed rather tentatively in the light of the Percus-Yevick relation. 相似文献