8-(3-methylphenoxy)-16H-dinaphtho[2,1-d;1',2'-g][1,3,2]dioxaphosphocine 8-oxide

In the title compound, C28H21O4P, the eight-membered heterocyclic dioxaphosphocine ring has a distorted boat conformation, with the phosphoryl O atom axial and the phenoxy group equatorial. The P=O distance is 1.451 (1) Angstrom and the average length of the three P-O bonds is 1.573 (1) Angstrom. The phenyl ring is nearly perpendicular to both naphthalene planes, making dihedral angles of 91.30 (3) and 97.65 (5)degrees with them. The angle between the two naphthalene planes is 67.73 (3)degrees. The crystal structure is stabilized by van der Waals interactions.

Local polynomial convexity of the union of two totally-real surfaces at their intersection

We consider the following question: Let S (1) and S (2) be two smooth, totally-real surfaces in C-2 that contain the origin. If the union of their tangent planes is locally polynomially convex at the origin, then is S-1 boolean OR S-2 locally polynomially convex at the origin? If T (0) S (1) a (c) T (0) S (2) = {0}, then it is a folk result that the answer is yes. We discuss an obstruction to the presumed proof, and provide a different approach. When dim(R)(T0S1 boolean AND T0S2) = 1, we present a geometric condition under which no consistent answer to the above question exists. We then discuss conditions under which we can expect local polynomial convexity.

Structure of 4,6-Diacetylresorcinol

C10H10O4, M(r) = 194.19, monoclinic, P2(1)/c, a = 7.089 (1), b = 11.361 (1), c = 11.656 (1) angstrom, beta = 100.45 (3)-degrees, V = 922.92 (1) angstrom 3, Z = 4, D(m) = 1.410 (5), D(x) = 1.397 Mg m-3, lambda(Cu K-alpha) = 1.5418 angstrom, mu(Cu K-alpha) = 0.89 mm-1, T = 300 K, F(000) = 408, final R = 0.057 for 1701 observed reflections. The molecule is almost planar, with O(9) and O(12) of the acetyl groups deviating by 0.074 (1) and 0.071 (2) angstrom from the mean plane of the benzene ring. The bond lengths and bond angles of the benzene ring are normal. There are intramolecular hydrogen bonds between O(9) and H(14) and between O(12) and H(13); there are no intermolecular hydrogen bonds. The molecules are packed in layers parallel to the ac plane and are held together essentially by van der Waals interactions.

Analysis of Parameter Values in the van der Waals and Platteeuw Theory for Methane Hydrates Using Monte Carlo Molecular Simulations

The van der Waals and Platteuw (vdVVP) theory has been successfully used to model the thermodynamics of gas hydrates. However, earlier studies have shown that this could be due to the presence of a large number of adjustable parameters whose values are obtained through regression with experimental data. To test this assertion, we carry out a systematic and rigorous study of the performance of various models of vdWP theory that have been proposed over the years. The hydrate phase equilibrium data used for this study is obtained from Monte Carlo molecular simulations of methane hydrates. The parameters of the vdWP theory are regressed from this equilibrium data and compared with their true values obtained directly from simulations. This comparison reveals that (i) methane-water interactions beyond the first cage and methane-methane interactions make a significant contribution to the partition function and thus cannot be neglected, (ii) the rigorous Monte Carlo integration should be used to evaluate the Langmuir constant instead of the spherical smoothed cell approximation, (iii) the parameter values describing the methane-water interactions cannot be correctly regressed from the equilibrium data using the vdVVP theory in its present form, (iv) the regressed empty hydrate property values closely match their true values irrespective of the level of rigor in the theory, and (v) the flexibility of the water lattice forming the hydrate phase needs to be incorporated in the vdWP theory. Since methane is among the simplest of hydrate forming molecules, the conclusions from this study should also hold true for more complicated hydrate guest molecules.

Computing Reeb Graphs as a Union of Contour Trees

The Reeb graph of a scalar function tracks the evolution of the topology of its level sets. This paper describes a fast algorithm to compute the Reeb graph of a piecewise-linear (PL) function defined over manifolds and non-manifolds. The key idea in the proposed approach is to maximally leverage the efficient contour tree algorithm to compute the Reeb graph. The algorithm proceeds by dividing the input into a set of subvolumes that have loop-free Reeb graphs using the join tree of the scalar function and computes the Reeb graph by combining the contour trees of all the subvolumes. Since the key ingredient of this method is a series of union-find operations, the algorithm is fast in practice. Experimental results demonstrate that it outperforms current generic algorithms by a factor of up to two orders of magnitude, and has a performance on par with algorithms that are catered to restricted classes of input. The algorithm also extends to handle large data that do not fit in memory.

Modified Adomian Decomposition Method for Van der Pol equations

In the paper, the well known Adomian Decomposition Method (ADM) is modified to solve the parabolic equations. The present method is quite different than the numerical method. The results are compared with the existing exact or analytical method. The already known existing Adomian Decomposition Method is modified to improve the accuracy and convergence. Thus, the modified method is named as Modified Adomian Decomposition Method (MADM). The Modified Adomian Decomposition Method results are found to converge very quickly and are more accurate compared to ADM and numerical methods. MADM is quite efficient and is practically well suited for use in these problems. Several examples are given to check the reliability of the present method. Modified Adomian Decomposition Method is a non-numerical method which can be adapted for solving parabolic equations. In the current paper, the principle of the decomposition method is described, and its advantages are shown in the form of parabolic equations. (C) 2014 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).

Emergent photophenomena in three dimensional van der Waals heterostructures

We report on the fabrication and observation of emergent opto-electronic phenomena in three dimensional, micron-sized van der Waals heterostructures self-assembled from atomic layers of graphene and hexagonal boron nitride in varying ratios.

Pull-in Instability Study of Carbon Nanotube Tweezers Under the Influence of Van der Waals Forces

The pull-in instability of two nanotubes under van der Waals force is studied. The cantilever beam with large deformation model is used. The influence of nanotube parameters such as the interior radius, the gap distance between the two nanotubes, etc, on the pull-in instability is studied. The critical nanotube length is determined for each specific set of nanotube parameters. The Galerkin method is applied to discretize the governing equations, and it shows good convergence.