MNDO study of coupled strained hydrocarbons: Additivity of exocyclic C---C bond contraction induced by different ring systems

MNDO geometry optimizations were carried out on a series of symmetrically and unsymmetrically coupled strained ring hydrocarbons, R1-R1 and R1–R2 (R1=methyl, cyclopropyl, 1-bicyclo[1.1.0]butyl, 1-bicyclo[1.1.1]pentyl, prismyl, cubyl, 6-tricyclo [3.1.1.03,6]heptyl, and tetrahedryl groups; R2=methyl and cyclopropyl). The remarkable contraction of the C---C bond connecting the strained rings found experimentally in a few cases was reproduced correctly by the calculations. A linear correlation was found between the bond length shortening and the bond angle widening at the corresponding carbon atoms for all the structures considered. The reduction in C---C bond lengths due to various ring systems is additive. The additivity indicates that inter-ring interactions which effect the central bond length are absent and confirms the common electronic origin of bond contraction in these systems, viz. enhanced s-character in the exocyclic bonds of strained rings.

The reaction of lambda 3-cyclotriphosphazanes with tetrachloro-ortho-benzoquinone: An unusual ring contraction-rearrangement

Oxidative addition of tetrachloro-ortho-benzoquinone to lambda(3)-cyclotriphosphazanes, [EtNP(OR)](3) results in an unprecedented ring contraction-rearrangement to give diazadiphosphetidines (EtN)(2)[P(OR)(O2C6Cl4)] [P(O2C6Cl4)-[N(Et)P(OR)(2)}] (R = C6H4Br-4 or C(6)H(3)Me(2)-2,6), a process indicated to be thermodynamically favourable on the basis of PM3 calculations.

Oxidative addition of tetrachloro-1,2-benzoquinone to lambda(3)-cyclotriphosphazanes. An unusual ring contraction-rearrangement

The lambda(3)-cyclotriphosphazanes, [EtNP(OR)](3) [R = 2,6-Me2C6H3 (1), 4-BrC6H4 (2), or CH2CF3(3)], on treatment with tetrachloro-1,2-benzoquinone (TCB) give the lambda(5)-cyclodiphosphazanes, [EtNP(O2C6Cl4)(OR)][EtNP(O2C6Cl4){N(Et)P(OR)(2)}] (5-7) by an unusual ring contraction-rearrangement. The reaction of the mixed substituent lambda(3)-cyclotriphosphazane, [(EtN)(3)P-3(OR)(2)(OR')] [R = 2,6-Me2C6H3, R' = 4-BrC6H4] (4), with TCB gives the lambda(5)-cyclodiphosphazane, [EtNP(O2C6Cl4)(OR')][EtNP(O2C6Cl4){N(Et)P(OR)(2)}] (8), in which 4-bromophenoxide resides on one of the ring phosphorus atoms. The lambda(3)-bicyclic tetraphosphapentazane, (EtN)(5)P-4(OPh)(2), on treatment with TCB undergoes a double ring contraction-rearrangement to give the lambda(5)-cyclodiphosphazane, (EtN)[(EtN)(2)P-2(O2C6Cl4)(2)(OPh)](2) (9). Variable-temperature and high-field P-31 NMR studies indicate the presence of more than one isomer in solution for the rearranged products 5-9. The solid state structure of 8 reveals a trans arrangement of the substituents with respect to the P2N2 ring in contrast to the gauche arrangement observed for 5.

On the solution of bivariate population balance equations for aggregation: X-discretization of space for expansion and contraction of computational domain

A new structured discretization of 2D space, named X-discretization, is proposed to solve bivariate population balance equations using the framework of minimal internal consistency of discretization of Chakraborty and Kumar [2007, A new framework for solution of multidimensional population balance equations. Chem. Eng. Sci. 62, 4112-4125] for breakup and aggregation of particles. The 2D space of particle constituents (internal attributes) is discretized into bins by using arbitrarily spaced constant composition radial lines and constant mass lines of slope -1. The quadrilaterals are triangulated by using straight lines pointing towards the mean composition line. The monotonicity of the new discretization makes is quite easy to implement, like a rectangular grid but with significantly reduced numerical dispersion. We use the new discretization of space to automate the expansion and contraction of the computational domain for the aggregation process, corresponding to the formation of larger particles and the disappearance of smaller particles by adding and removing the constant mass lines at the boundaries. The results show that the predictions of particle size distribution on fixed X-grid are in better agreement with the analytical solution than those obtained with the earlier techniques. The simulations carried out with expansion and/or contraction of the computational domain as population evolves show that the proposed strategy of evolving the computational domain with the aggregation process brings down the computational effort quite substantially; larger the extent of evolution, greater is the reduction in computational effort. (C) 2011 Elsevier Ltd. All rights reserved.

Nonlocal continuum mechanics formulation for axial, flexural, shear and contraction coupled wave propagation in single walled carbon nanotubes

This paper presents the effect of nonlocal scaling parameter on the coupled i.e., axial, flexural, shear and contraction, wave propagation in single-walled carbon nanotubes (SWCNTs). The axial and transverse motion of SWCNT is modeled based on first order shear deformation theory (FSDT) and thickness contraction. The governing equations are derived based on nonlocal constitutive relations and the wave dispersion analysis is also carried out. The studies shows that the nonlocal scale parameter introduces certain band gap region in all wave modes where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite or wave speed tends to zero. The frequency at which this phenomenon occurs is called the escape frequency. Explicit expressions are derived for cut-off and escape frequencies of all waves in SWCNT. It is also shown that the cut-off frequencies of shear and contraction mode are independent of the nonlocal scale parameter. The results provided in this article are new and are useful guidance for the study and design of the next generation of nanodevices that make use of the coupled wave propagation properties of single-walled carbon nanotubes.

A Contraction Mapping Approach for Robust Estimation of Lagged Autocorrelation

We consider the zero-crossing rate (ZCR) of a Gaussian process and establish a property relating the lagged ZCR (LZCR) to the corresponding normalized autocorrelation function. This is a generalization of Kedem's result for the lag-one case. For the specific case of a sinusoid in white Gaussian noise, we use the higher-order property between lagged ZCR and higher-lag autocorrelation to develop an iterative higher-order autoregressive filtering scheme, which stabilizes the ZCR and consequently provide robust estimates of the lagged autocorrelation. Simulation results show that the autocorrelation estimates converge in about 20 to 40 iterations even for low signal-to-noise ratio.

Mono- and Dialkyne Insertion Reactions of Cyclopalladated N,N `,N `'-Triarylguanidines kappa(2)(C,N)Pd(mu-Br)](2) and cis-/trans-kappa(2)(C,N)Pd(Lewis Base)Br]. Scaffolds for Enlarged, Rearranged, and Zwitterionic Palladacycles through Ring Contraction cum Amine-Imine Tautomerization

Insertion reactions of six-membered cyclopalladated N,N',N''-triarylguanidines, kappa(2)(C,N)Pd(mu-Br)](2) with various alkynes in CH2Cl2 under ambient conditions afforded diinserted eight-membered palladacycles, (kappa(2)(C,N):eta(2)(C=C)-PdBr] (1-11), in high yield (76-96%), while insertion reactions of six-membered cyclopalladated N,N',N''-triarylguanidines, kappa(2)(C,N)Pd(Lewis base)Br] (VI-XI), with various alkynes under the aforementioned conditions afforded monoinserted six-membered palladacycles, kappa(2)(C,N)-Pd(Lewis base)Br] (12-21), in high yield (81-91%) except for 14 (23%). The insertion reaction of VI with 2 equiv of dimethyl acetylenedicarboxylate (DMAD) and the insertion reaction of 12 with 1 equiv of DMAD in CH2Cl2 under ambient conditions resulted in the formation of a diinserted zwitterionic five-membered palladacycle, kappa(2)(C,C)Pd(2,6-lutidine)Br] (22), in 76% and 70% yields, respectively. Palladacycle 22 upon reaction with AgOTf in wet MeCN afforded the ionic palladacycle kappa(2)(C,C)Pd(2,6-lutidine)(H2O)]OTf] (23) in 78% yield. The ring size of the ``kappa(2)(C,N)Pd]'' unit in the structurally characterized diinserted palladacycles (1 center dot 2CH(2)Cl(2)center dot H2O, 2, 5, and 7), and monoinserted palladacycles (17, 18, and 20 center dot C7H8 H2O) is smaller than that anticipated for mono- and diinserted palladacycles, and this feature is mainly ascribed to the proclivity of III-XI to undergo ring contraction cum amine-imine tautomerization upon alkyne insertion. Palladacycle 22 represents the first diinserted product obtained in alkyne insertion reactions of kappa(2)(C,N)Pd(Lewis base)X] type palladarycles. The molecular structure of 22 center dot H2O determined by X-ray diffraction indicates that the positive charge on the guanidinium moiety is balanced by the negative charge on the palladium atom and thus represents the first structurally characterized zwitterionic palladacycle to be reported in alkyne insertion chemistry. Plausible mechanisms of formation of 12-21 and 22 have been outlined. The presence of more than one species in solution for some of the palladacycles in the series 1-7 and 12-21 was explained by invoking the C-N single-bond rotation of the CN3 unit of the guanidine moiety, while this process in conjunction with Pd-N(lutidine) bond rotation was invoked to explain the presence of four isomers of 15, as studied with the aid of variable-concentration H-1 NMR experiments carried out for 14 and 15.

An Unusual Ring-Contraction/Rearrangement Sequence for Making Functionalized Di- and Triquinanes

A novel ring contraction/rearrangement sequence leading to functionalized 2,8-oxymethano-bridged di- and triquinane compounds is observed in the reaction of various substituted 1-methyl-4-isopropenyl-6-oxabicylo3.2.1]octan-8-ones with Lewis acids. The reaction is novel and is unprecedented for the synthesis of di- and triquinane frameworks.

An Unusual Ring-Contraction/Rearrangement Sequence for Making Functionalized Di- and Triquinanes

A novel ring contraction/rearrangement sequence leading to functionalized 2,8-oxymethano-bridged di- and triquinane compounds is observed in the reaction of various substituted 1-methyl-4-isopropenyl-6-oxabicylo3.2.1]octan-8-ones with Lewis acids. The reaction is novel and is unprecedented for the synthesis of di- and triquinane frameworks.

An Unusual Ring-Contraction/Rearrangement Sequence for Making Functionalized Di- and Triquinanes

A novel ring contraction/rearrangement sequence leading to functionalized 2,8-oxymethano-bridged di- and triquinane compounds is observed in the reaction of various substituted 1-methyl-4-isopropenyl-6-oxabicylo3.2.1]octan-8-ones with Lewis acids. The reaction is novel and is unprecedented for the synthesis of di- and triquinane frameworks.

Magneto-structural study of a Cr-doped CaRuO3

Temperature-dependent neutron powder diffraction, magnetization and XPS studies were carried out on an optimally Cr-doped CaRuO3, i.e. CaRu0.85Cr0.15O3 (CRC-15). XPS data revealed that Cr exist in 3+ and 6+ oxidation states. The charge dissociation preserves the overall 4+ nominal charge of the Ru site. Although ferromagnetic correlations develop around 100 K, the system exhibits a large coercive field below 50 K. The unit cell volume exhibits negative thermal expansion below 50 K since the lattice expansion due to the magnetostrictive effect outweighs the thermal contraction due to the phonon-driven mechanism.

On the unsteady flow of a fairly concentrated suspension due to contracting or expanding walls of a tube

Consummating our earlier work [1], the unsteady flow of a fairly concentrated suspension due to a single contraction or expansion of the walls of a tube is studied. A comparison of the results obtained by using two different formulae for the additional drag terms in the governing equations has been made. A region of circulation in the flow field is observed when the volume fraction Z greater-or-equal, slanted 0.3, the Schmidt number Sc < 1 and the density ratio (density of the particulate phase/density of the fluid phase) > 1.

Pressure and alloying effects on the metal to insulator transition in NiS2-xSex studied by infrared spectroscopy

The metal to insulator transition in the charge-transfer NiS2-xSex compound has been investigated through infrared reflectivity. Measurements performed by applying pressure to pure NiS2 (lattice contraction) and by Se alloying (lattice expansion) reveal that in both cases an anomalous metallic state is obtained. We find that optical results are not compatible with the linear Se-alloying vs pressure-scaling relation previously established through transport, thus pointing out the substantially different microscopic origin of the two transitions.

Studies on Unsteady Shock Interactions Near a Generic Scramjet Inlet

An experimental and numerical study is presented to show the effect of cowl length and angle on the ramp/cowl shock interaction phenomena fora two-dimensional planar scramjet inlet model. Experiments areconducted in a hypersonic shock tunnel, at Mach 8, at four lengths of owl and three cowl angles. Investigations include schlieren flow Visualization near the cowl region and static pressure and heat transfer rate measurement inside the inlet chamber. Various ramp/cowl shock interaction processes resulted for different cowl configurations have been visualized using a high-speed camera. Edney type-II interference pattern is observed for 131 and 141-mm cowl lengths,whereas it is an Edney type-I interference pattern in case of a 151 mm cowl with all their typical features resulting because of the ramp/cowl shock interaction. Experiments with a cowl configuration other than 0deg show the flow to he established through the inlet because or the reduced contraction ratio. Heat transfer peaks can be observed for the10 and 20-deg cowl cases where flow through the inlet is found to be established. These may serve as the possible locations of fuel injection.

On the Structure of Contractible Edges in k-connected Partial k-trees

Contraction of an edge e merges its end points into a new single vertex, and each neighbor of one of the end points of e is a neighbor of the new vertex. An edge in a k-connected graph is contractible if its contraction does not result in a graph with lesser connectivity; otherwise the edge is called non-contractible. In this paper, we present results on the structure of contractible edges in k-trees and k-connected partial k-trees. Firstly, we show that an edge e in a k-tree is contractible if and only if e belongs to exactly one (k + 1) clique. We use this characterization to show that the graph formed by contractible edges is a 2-connected graph. We also show that there are at least |V(G)| + k - 2 contractible edges in a k-tree. Secondly, we show that if an edge e in a partial k-tree is contractible then e is contractible in any k-tree which contains the partial k-tree as an edge subgraph. We also construct a class of contraction critical 2k-connected partial 2k-trees.