Mechanism for CuPt-type ordering in mixed III–V epitaxial layers

A model is proposed to rationalize the occurence of CuPt-type ordering in mixed III–V epitaxial layers grown on (001) substrates. It is invoked that 2× surface reconstruction occuring on group V terminated (001) surfaces produces dilated and compressed regions in sub-surface layers. The presence of these regions biases the occupation of certain sites during the growth of a layer consisting of atoms differing in their tetrahedral radii. By assuming that the reconstruction always occurs at the growing surface, it is possible to explain the evolution of CuPt-type ordering in epitaxial layers. Also, based on the model, experimental observations pertaining to the influence of growth conditions, surface misorientation and steps on ordering can be rationalized.     

Maximizing the descent statistic

For a subsetS, let the descent statistic (S) be the number of permutations that have descent setS. We study inequalities between the descent statistics of subsets. Each subset (and its complement) is encoded by a list containing the lengths of the runs. We define two preorders that compare different lists based on the descent statistic. Using these preorders, we obtain a complete order on lists of the form (k ⁱ ,P,k ^n–i , whereP is a palindrome, whose first entry is larger thank. We prove a conjecture due to Gessel, which determines the list that maximizes the descent statistic, among lists of a given size and given length. We also have a generalization of the boustrophedon transform of Millar, Sloane and Young.     

Poisson's effects in electrical field flow fractionation

Recent and earlier models of electrical field flow fractionation (ELFFF) have assumed that the electric field within the fluid domain is governed by Laplace's equation. This assumption results in a linear potential and a spatially constant field across the channel and is generally true for very dilute systems and relatively high effective potentials. Experimental studies show, however, that the effective potential within the channel may be less than 1% of the applied potential; this is apparently due to double layer formation and charge buildup at the poles. In such cases, local analyte concentrations can, nonetheless, be orders of magnitude higher than the bulk mean and the local potential small, both of which can lead to a nonlinear spatial distribution of the field strength. In such cases Poisson's equation must be used rather than Laplace's equation. Steady-state ELFFF simulations were performed using a Poisson's equation-based model. The domain in which Laplace's equation is valid was identified and the effects of concentration and effective field strength on device performance were explored.     

Visible Light Mediated Halogen Atom Transfer to Access Polyhalogenated and Deuterated Lactams from Alkyl Halides

A visible light mediated protocol for the synthesis of polyhalogenated and deuterated δ- and γ-lactams from readily available alkyl halides is reported. The reaction involves the generation of haloalkyl radicals through halogen atom transfer (XAT) and subsequent arylalkylation of olefins to afford dihydroisoquinolinones and oxindoles. This new XAT protocol exhibits wide scope under mild conditions and enables access to new halogenated chemical space.     

Gold(I)-Catalyzed and PTSA-Promoted Cycloisomerization of Ynamides to Access Pyrrole Substituted α,β-Unsaturated Ketones**

Substituted pyrroles are prevalent aromatic ring systems encountered in numerous natural products and bioactive molecules. Herein, a novel ynamide scaffold has been designed, synthesized and subsequently applied to an unprecedented gold-catalyzed and para-toluenesulfonic acid (PTSA)-assisted cascade cycloisomerization reaction for the synthesis of β-pyrrole substituted α,β-unsaturated ketones. Notably, the reaction is stereoselective, offering E-isomer as major product with low to moderate yield.     

The Neumann Problem for the Kohn-Laplacian on the Heisenberg Group ℍn$\mathbb H_{n}$

The existence and uniqueness of the solution of the Neumann problem for the Kohn-Laplacian relative to the Korányi ball on the Heisenberg group \(\mathbb {H}_{n}\) are discussed. Explicit representation for a Green’s type function (Neumann function) for the Korányi ball in \(\mathbb {H}_{n}\) for circular functions has been obtained. This function is then used on the above region in \(\mathbb {H}_{n}\) to solve the inhomogeneous Neumann boundary value problem for certain circular data.     

Thermal C2-C6 cyclization of enyne-allenes. Experimental evidence for a stepwise mechanism and for an unusual thermal silyl shift

Enyne-allenes 4a-c bearing various cyclopropyl systems as radical clock reporter groups at the allene terminus have been synthesized and subjected to thermal C2-C6 cyclization. The ratio of ene versus formal Diels-Alder products could be rationalized on the basis of steric effects. Only the thermolysis of 4c, equipped with the fast diphenylcyclopropylcarbinyl radical clock, afforded a 1,3-butadienyl benzofulvene clearly formed via cyclopropyl ring opening. This finding provides unambiguous evidence for a stepwise mechanism of the C2-C6 cyclization making it possible to suggest a lifetime for the intermediate diradical of >1x10(-10) s (at 170 degrees C). An interesting corollary was the isolation of an unexpected silyl shift product in the thermolysis of all three enyne-allenes that allows explanation of the loss of the TIPS group in some of the Diels-Alder products. For a full understanding of the mechanism, silyl and hydrogen shift processes were interrogated using DFT.     

Adaptive finite element analysis of structures under transient dynamic loading using modal superposition

In this paper, the error estimation and adaptive strategy developed for the linear elastodynamic problem under transient dynamic loading based on the Z–Z criterion is utilized for 2D and plate bending problems. An automatic mesh generator based on “growth meshing” is utilized effectively for adaptive mesh refinement. Optimal meshes are obtained iteratively corresponding to the prescribed domain discretization error limit and for a chosen number of basis modes satisfying modal truncation errors. Numerous examples show the effectiveness of the integrated approach in achieving the target accuracy in finite element transient dynamic analysis.     

Indirect enantioresolution of (R,S)‐mexiletine by reversed‐phase high‐performance liquid chromatography via diastereomerization with [(S,S)‐O,O'‐di‐p‐toluoyl tartaric acid anhydride], (S)‐naproxen and nine chiral reagents synthesized as variants of Marfey's reagent

Eleven chiral derivatizing reagents (CDRs) were used for preparation of diastereomers of (R,S)‐mexiletine containing a primary amino group in close proximity to the stereogenic center. One anhydride, namely [(S,S)‐O,O'‐di‐p‐toluoyl tartaric acid anhydride] was synthesized and (S)‐naproxen was used as such as the chiral derivatizing reagent. The other nine CDRs were synthesized by substituting one of the fluorine atoms in 1,5‐difluoro‐2,4‐dinitrobenzene with six amino acid amides and three amino acids. The diastereomers were separated by reversed‐phase high‐performance liquid chromatography. The method was validated for linearity, accuracy, limit of detection and limit of quantification. The limit of detection was found in the range of 10–30 pmol. Copyright © 2010 John Wiley & Sons, Ltd.     

A nonlinear stability analysis for rotating magnetized ferrofluid heated from below saturating a porous medium

A nonlinear (energy) stability analysis is performed for a rotating magnetized ferrofluid layer heated from below saturating a porous medium, in the stress-free boundary case. By introducing a generalized energy functional, a rigorous nonlinear stability result for a thermoconvective rotating magnetized ferrofluid is derived. The mathematical emphasis is on how to control the nonlinear terms caused by magnetic body force. It is found that the nonlinear critical stability magnetic thermal Rayleigh number does not coincide with that of linear instability analysis, and thus indicates that the subcritical instabilities are possible. However, it is noted that, in case of non-ferrofluid, global nonlinear stability Rayleigh number is exactly the same as that for linear instability. For lower values of magnetic parameters, this coincidence is immediately lost. The effect of magnetic parameter, M ₃, medium permeability, D _a , and rotation, , on subcritical instability region has also been analyzed. It is shown that with the increase of magnetic parameter, M ₃, and Darcy number, D _a , the subcritical instability region between the two theories decreases quickly while with the increase of Taylor number, , the subcritical region expands. We also demonstrate coupling between the buoyancy and magnetic forces in the presence of rotation in nonlinear energy stability analysis as well as in linear instability analysis.