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1.
2.
In quasi-steady operation, convection currents in a Bridgmandevice, used for producing a semi-conductor crystal, createinhomogeneities that may make the crystal unusable. It has oftenbeen suggested that additional forces due to rotation or magnetismmight be efficacious in reducing the segregation of the elementsof the alloy. It has been found that, over a wide range of rotationrates, there is no improvement in performance due to rotationabout the vertical axis. However, numerical results that havebeen obtained previously (Lee & Pearlstein, J. Crys. Growth240, 2002) indicate that, when effects of centrifugal buoyancyare introduced, a substantial reduction in segregation is achieved.In the work reported here, by contrast, in which we extend previouslarge-Rayleigh-number asymptotic analysis to include centrifugalbuoyancy, we find no improvement in radial segregation, butrather increasing segregation with increasing rotation rate. 相似文献
3.
Philip Wormald Kristina Wickholm Per Tomas Larsson Tommy Iversen 《Cellulose (London, England)》1996,3(1):141-152
An investigation into the effects of mechanical treatment and hydration on the order of cellulose substrates (microcrystalline cellulose and Cladophora cellulose) was performed by the use of ball milling followed by cyclic wetting and drying. The results, monitored by13C-CP/MAS NMR-spectroscopy, were evaluated by calculation of the crystallinity indices and principal component analysis of the NMR data acquired. The results showed that a large part of the disorder induced by the mechanical treatment of cellulose by ball milling is reversible and reordering upon hydration leads to the cellulose I form initially present. The C4 signals corresponding to the reversibly disordered cellulose chains are observed in the amorphous region between 79 and 86 ppm in the13C-CP/MAS NMR-spectra together with signals from cellulose chains on the surface of ordered regions. The peak cluster which contains the C2, C3 and C5 ring carbons can be divided into two specific spectral regions; one between 74 and 77 ppm largely originates from ring carbons within disordered cellulose structures, and one between 70 and 74 ppm contains larger contributions from ordered cellulose. The behaviour of the celluloses upon milling is in accordance with a concept of ordered cellulose fibrils containing amorphous cellulose mainly as surface layers and induced reversible lattice distortions. 相似文献
4.
I. G. Enting A. J. Guttmann L. B. Richmond N. C. Wormald 《Random Structures and Algorithms》1992,3(4):445-461
We classify self-avoiding polygons on the square lattice according to a concavity measure, m, where 2m is the difference between the number of steps in the polygon and the perimeter of the minimal rectangle bounding the polygon. We generate series expansions for the perimeter generating functions Sm(x) for polygons of concavity m. We analyze the series Sm(x) for m = 0 to 3. If Nm,n denotes the number of polygons of perimeter 2n and concavity m, with m = o(n1/2), we prove that Nm,n ? 22n?m?7nm+1/m!, and that the radius of convergence of the series counting all polygons with m = o(n) is equal to 1/4. Our numerical data leads us to conjecture that in fact for m = o(n1/2), a result confirmed for m = 0 and 1. 相似文献
5.
Ahmed Waqar Chowdhury Z. Z. Kazi S. N. Johan MR. Akram Naveed Oon C. S. Abdelrazek Ali H. 《Journal of Thermal Analysis and Calorimetry》2021,144(4):1517-1534
Journal of Thermal Analysis and Calorimetry - In recent decades, the growth of heat transfer using nanomaterials in the conventional base fluid has caught the attention of researchers... 相似文献
6.
P Wormald B Lundgren K Andersson J W DePierre 《Acta chemica Scandinavica (Copenhagen, Denmark : 1989)》1992,46(1):100-102
Upon interaction of various glycerophospholipids with Rhodamine 6G in toluene, a typical difference spectrum with an absorption maximum at approximately 515 nm is obtained . This spectrum is obtained with phosphatidylcholine only after treatment with NaCl, which presumably weakens intra- and/or inter-molecular electrostatic binding between the negatively charged phosphate moiety and the protonated nitrogen in this molecule. Absorption at 515 nm was linear for all of the phospholipids investigated from a concentration of approximately 1.2 microM up to at least 50 microM. The highest extinction coefficient was obtained for diphosphatidylglycerol (251 mM-1 cm-1) and all of the compounds tested, with the exception of phosphatidylethanolamine, demonstrated extinction coefficients higher than that of palmitic acid. Thus, the absorption spectrum which results from the interaction of purified glycerophospholipids with Rhodamine 6G in organic solvent is a sensitive measure of the amount of phospholipid present. 相似文献
7.
Edward A. Bender L. Bruce Richmond Nicholas C. Wormald 《Random Structures and Algorithms》1995,7(4):273-285
Let Tn be a 3-connected n-vertex planar triangulation chosen uniformly at random. Then the number of vertices in the largest 4-connected component of Tn is asymptotic to n/2 with probability tending to 1 as n → ∞. It follows that almost all 3-connected triangulations with n vertices have a cycle of length at least n/2 + o(n). 相似文献
8.
Nicholas C. Wormald 《Discrete Mathematics》1981,36(2):205-225
Two planar maps are identified if one can be transformed to the other by any homeomorphism of the sphere. The number of such maps is found by determining the numbers of maps which have been rooted in various ways. 相似文献
9.
Zhicheng?GaoEmail author Nicholas C.?Wormald 《Probability Theory and Related Fields》2004,130(3):368-376
We give a general result showing that the asymptotic behaviour of high moments determines the shape of distributions which are asymptotically normal. Both the factorial and non-factorial (non-central) moments are treated. This differs from the usual moment method in combinatorics, as the expected value may tend to infinity quite rapidly. Applications are given to submap counts in random planar triangulations, where we use a simple argument to asymptotically determine high moments for the number of copies of a given subtriangulation in a random 3-connected planar triangulation. Similar results are also obtained for 2-connected triangulations and quadrangulations with no multiple edges.Revised version: 6 February 2004Research supported by NSERCC and University of Macau.Research supported by the Australian Research Council and the Canada Research Chairs program. Research carried mainly while the author was at the Department of Mathematics and Statistics, University of Melbourne. 相似文献
10.
In previous papers the authors showed that almost all d‐regular graphs for d≤3 are hamiltonian. In the present paper this result is generalized so that a set of j oriented root edges have been randomly specified for the cycle to contain. The Hamilton cycle must be orientable to agree with all of the orientations on the j root edges. It is shown that the requisite Hamilton cycle almost surely exists if and the limiting probability distribution at the threshold is determined when d=3. It is a corollary (in view of results elsewhere) that almost all claw‐free cubic graphs are hamiltonian. There is a variation in which an additional cyclic ordering on the root edges is imposed which must also agree with their ordering on the Hamilton cycle. In this case, the required Hamilton cycle almost surely exists if j=o(n2/5). The method of analysis is small subgraph conditioning. This gives results on contiguity and the distribution of the number of Hamilton cycles which imply the facts above. © 2001 John Wiley & Sons, Inc. Random Struct. Alg., 19: 128–147, 2001 相似文献