The effect of rapid rotation on a vertical bridgman furnace at large Rayleigh number

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.     

Conversions between ordered and disordered cellulose. Effects of mechanical treatment followed by cyclic wetting and drying

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.     

Enumeration of Almost-Convex Polygons on the Square Lattice

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 S_m(x) for polygons of concavity m. We analyze the series S_m(x) for m = 0 to 3. If N_m,n denotes the number of polygons of perimeter 2n and concavity m, with m = o(n^1/2), we prove that N_m,n ? 2^2n?m?7n^m+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(n^1/2), a result confirmed for m = 0 and 1.     

Controlled hydrothermal growth of ZnO nanostructures by sequestering the Zn metal ions with the chelating agent EDTA

In the present work, a controlled growth of ZnO nanostructures by manipulating Zn metal ion concentration by the chelating action of ethylene diaminetetra acetic acid in hydrothermal method is studied. EDTA produces metal–chelate complex by the formation of bidentate ligand with Zn²⁺ in the solution and diminishes the reactivity of Zn metal cations. Concentration of EDTA in the mother solution was varied in different ranges like 3, 5 and 10 mM while retaining the zinc metal salt and the NaOH concentration the same. Three different morphologies of wurtzite structured ZnO nanostructures such as nanorods-bunch, separate/discrete uniformly sized hexagonal nanorods and tapered flower petals like shapes are achieved by 3, 5 and 10 mM strengths of EDTA, respectively. The medium concentration 5 mM of EDTA is found to have moderate control over producing ZnO nanostructures of uniform diameter and a high aspect (length to diameter) ratio. An array of vertically aligned free standing ZnO nanorods with uniform spacing is successfully achieved by the addition of 5 mM of EDTA in the mother solution and the same is studied for its fluorescence property at an excitation of 325 nm and it has exhibited a characteristic UV emission of ZnO around 383 nm.     

The threshold for combs in random graphs

For let denote the tree consisting of an ‐vertex path with disjoint ‐vertex paths beginning at each of its vertices. An old conjecture says that for any the threshold for the random graph to contain is at . Here we verify this for with any fixed . In a companion paper, using very different methods, we treat the complementary range, proving the conjecture for (with ). © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 794–802, 2016     

Disjoint Hamilton cycles in the random geometric graph

We consider the standard random geometric graph process in which n vertices are placed at random on the unit square and edges are sequentially added in increasing order of edge‐length. For fixed k?1, weprove that the first edge in the process that creates a k‐connected graph coincides a.a.s. with the first edge that causes the graph to contain k/2 pairwise edge‐disjoint Hamilton cycles (for even k), or (k?1)/2 Hamilton cycles plus one perfect matching, all of them pairwise edge‐disjoint (for odd k). This proves and extends a conjecture of Krivelevich and M ler. In the special case when k = 2, our result says that the first edge that makes the random geometric graph Hamiltonian is a.a.s. exactly the same one that gives 2‐connectivity, which answers a question of Penrose. (This result appeared in three independent preprints, one of which was a precursor to this article.) We prove our results with lengths measured using the ?_p norm for any p>1, and we also extend our result to higher dimensions. © 2011 Wiley Periodicals, Inc. J Graph Theory 68:299‐322, 2011     

Largest 4-connected components of 3-connected planar triangulations

Let T_n be a 3-connected n-vertex planar triangulation chosen uniformly at random. Then the number of vertices in the largest 4-connected component of T_n 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).     

Asymptotic enumeration of sparse 2‐connected graphs

We determine an asymptotic formula for the number of labelled 2‐connected (simple) graphs on n vertices and m edges, provided that m ‐ n →∞ and m = O(nlog n) as n →∞. This is the entire range of m not covered by previous results. The proof involves determining properties of the core and kernel of random graphs with minimum degree at least 2. The case of 2‐edge‐connectedness is treated similarly. We also obtain formulae for the number of 2‐connected graphs with given degree sequence for most (“typical”) sequences. Our main result solves a problem of Wright from 1983. © 2012 Wiley Periodicals, Inc. Random Struct. Alg., 2013     

Interaction of phospholipids with rhodamine 6G in toluene.

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.