Analytical formulae for the enumeration of substitutional isomers of planar molecules

1991 ◽  
Vol 233 ◽  
pp. 13-20
Author(s):  
Yu.A. Kruglyak ◽  
M.E. Dochtmanov
Keyword(s):  
Planar Molecules ◽  
Analytical Formulae ◽  
Substitutional Isomers

Microscopic versus process parameters in heavy-oil upgrading

1992 ◽  
Vol 50 (1) ◽  
pp. 366-367
Author(s):  
V.A. Munoz ◽  
R.J. Mikula ◽  
C. Payette ◽  
W.W. Lam
Keyword(s):  
Molecular Weight ◽  
Liquid Fuels ◽  
Chemical Components ◽  
Heavy Oils ◽  
Synthetic Fuels ◽  
High Hydrogen ◽  
Optical Texture ◽  
Polar Groups ◽  
Anisotropic Character ◽  
Planar Molecules

The transformation of high molecular weight components present in heavy oils into useable liquid fuels requires their decomposition by means of a variety of processes. The low molecular weight species produced recombine under controlled conditions to generate synthetic fuels. However, an important fraction undergo further recombination into higher molecular weight components, leading to the formation of coke. The optical texture of the coke can be related to its originating components. Those with high sulfur and oxygen content tend to produce cokes with small optical texture or fine mosaic, whereas compounds with relatively high hydrogen content are likely to produce large optical texture or domains. In addition, the structure of the parent chemical components, planar or nonplanar, determines the isotropic or anisotropic character of the coke. Planar molecules have a tendency to align in an approximately parallel arrangement to initiate the formation of the nematic mesophase leading to the formation of anisotropic coke. Nonplanar highly alkylated compounds and/or those rich in polar groups form isotropic coke. The aliphatic branches produce steric hindrance to alignment, whereas the polar groups participate in cross-linking reactions.

Synthesis of isomeric 1,1'-phenylene-bis(6-azauracil-5-carbonitriles)

1990 ◽  
Vol 55 (12) ◽  
pp. 2967-2976 ◽  
Author(s):  
Jan Slouka
Keyword(s):  
General Formula ◽  
Mutual Distance ◽  
Planar Molecules ◽  
Amino Derivatives

The described synthesis of all three isomeric 1,1'-phenylene-bis(6-azauracil-5-carbonitriles) IVa-IVc starts from the respective 1-nitrophenyl-6-azauracil-5-carbonitriles Ia-Ic which were reduced to the corresponding amino derivatives IIa-IIc, diazotized, and coupled with ethyl cyanoacetylcarbamate to give the isomeric hydrazones IIIa-IIIc which were finally cyclized to the title compounds containing two 6-azauracil rings. A general formula is presented for calculation of mutual distance of arbitrary atoms in any planar molecules.

scholarly journals Two-component galaxy models with a central BH – II. The ellipsoidal case

2020 ◽  
Vol 500 (1) ◽  
pp. 1054-1070
Author(s):  
Luca Ciotti ◽  
Antonio Mancino ◽  
Silvia Pellegrini ◽  
Azadeh Ziaee Lorzad
Keyword(s):  
Dark Matter ◽  
Stellar Dynamics ◽  
Azimuthal Velocity ◽  
Dark Matter Halo ◽  
Gas Flows ◽  
Total Density ◽  
Density Distributions ◽  
Stellar Component ◽  
Two Component ◽  
Analytical Formulae

ABSTRACT Recently, two-component spherical galaxy models have been presented, where the stellar profile is described by a Jaffe law, and the total density by another Jaffe law, or by an r−3 law at large radii. We extend these two families to their ellipsoidal axisymmetric counterparts: the JJe and J3e models. The total and stellar density distributions can have different flattenings and scale lengths, and the dark matter halo is defined by difference. First, the analytical conditions required to have a nowhere negative dark matter halo density are derived. The Jeans equations for the stellar component are then solved analytically, in the limit of small flattenings, also in the presence of a central BH. The azimuthal velocity dispersion anisotropy is described by the Satoh k-decomposition. Finally, we present the analytical formulae for velocity fields near the centre and at large radii, together with the various terms entering the virial theorem. The JJe and J3e models can be useful in a number of theoretical applications, e.g. to explore the role of the various parameters (flattening, relative scale lengths, mass ratios, rotational support) in determining the behaviour of the stellar kinematical fields before performing more time-expensive integrations with specific galaxy models, to test codes of stellar dynamics and in numerical simulations of gas flows in galaxies.

scholarly journals Extended analytical formulae for the perturbed Keplerian motion under low-thrust acceleration and orbital perturbations

2021 ◽  
Vol 133 (3) ◽  
Author(s):  
Marilena Di Carlo ◽  
Simão da Graça Marto ◽  
Massimiliano Vasile
Keyword(s):  
Gravitational Perturbation ◽  
Low Thrust ◽  
Orbital Elements ◽  
Third Body ◽  
The Third ◽  
Orbital Perturbations ◽  
Analytical Formulae ◽  
Numerical Orbit ◽  
Body Potential

AbstractThis paper presents a collection of analytical formulae that can be used in the long-term propagation of the motion of a spacecraft subject to low-thrust acceleration and orbital perturbations. The paper considers accelerations due to: a low-thrust profile following an inverse square law, gravity perturbations due to the central body gravity field and the third-body gravitational perturbation. The analytical formulae are expressed in terms of non-singular equinoctial elements. The formulae for the third-body gravitational perturbation have been obtained starting from equations for the third-body potential already available in the literature. However, the final analytical formulae for the variation of the equinoctial orbital elements are a novel derivation. The results are validated, for different orbital regimes, using high-precision numerical orbit propagators.

scholarly journals Fluctuation of magnitude of wave loads for a long array of bottom-mounted cylinders

2019 ◽  
Vol 868 ◽  
pp. 244-285 ◽  
Author(s):  
Xiaohui Zeng ◽  
Fajun Yu ◽  
Min Shi ◽  
Qi Wang
Keyword(s):  
Incidence Angle ◽  
Local Maximum ◽  
Destructive Interference ◽  
Horizontal Distance ◽  
Wave Loads ◽  
Wave Load ◽  
Intrinsic Mechanism ◽  
Fluctuation Phenomenon ◽  
Analytical Formulae ◽  
Incident Waves

For wave loads on cylinders constituting a long but finite array in the presence of incident waves, variations in the magnitude of the load with the non-dimensional wavenumber exhibit interesting features. Towering spikes and nearby secondary peaks (troughs) associated with trapped modes have been studied extensively. Larger non-trapped regions other than these two are termed Region III in this study. Studies of Region III are rare. We find that fluctuations in Region III are regular; the horizontal distance between two adjacent local maximum/minimum points, termed fluctuation spacing, is constant and does not change with non-dimensional wavenumbers. Fluctuation spacing is related only to the total number of cylinders in the array, identification serial number of the cylinder concerned and wave incidence angle. Based on the interaction theory and constructive/destructive interference, we demonstrate that the fluctuation characteristics can be predicted using simple analytical formulae. The formulae for predicting fluctuation spacing and the abscissae of every peak and trough in Region III are proposed. We reveal the intrinsic mechanism of the fluctuation phenomenon. When the diffraction waves emitted from the cylinders at the ends of the array and the cylinder concerned interfere constructively/destructively, peaks/troughs are formed. The fluctuation phenomenon in Region III is related to solutions of inhomogeneous equations. By contrast, spikes and secondary peaks are associated with solutions of the eigenvalue problem. This study of Region III complements existing understanding of the characteristics of the magnitude of wave load. The engineering significances of the results are discussed as well.

scholarly journals Accumulation of mutations in sexual and asexual populations

1987 ◽  
Vol 49 (2) ◽  
pp. 135-146 ◽  
Author(s):  
Pekka Pamilo ◽  
Masatoshi Nei ◽  
Wen-Hsiung Li
Keyword(s):  
Weak Selection ◽  
Population Variance ◽  
Asexual Population ◽  
Term Evolution ◽  
A Genome ◽  
Analytical Formulae ◽  
The Mean ◽  
Asexual Populations ◽  
Mutant Genes

SummaryThe accumulation of beneficial and harmful mutations in a genome is studied by using analytical methods as well as computer simulation for different modes of reproduction. The modes of reproduction examined are biparental (bisexual, hermaphroditic), uniparental (selfing, automictic, asexual) and mixed (partial selfing, mixture of hermaphroditism and parthenogenesis). It is shown that the rates of accumulation of both beneficial and harmful mutations with weak selection depend on the within-population variance of the number of mutant genes per genome. Analytical formulae for this variance are derived for neutral mutant genes for hermaphroditic, selfing and asexual populations; the neutral variance is largest in a selfing population and smallest in an asexual population. Directional selection reduces the population variance in most cases, whereas recombination partially restores the reduced variance. Therefore, biparental organisms accumulate beneficial mutations at the highest rate and harmful mutations at the lowest rate. Selfing organisms are intermediate between biparental and asexual organisms. Even a limited amount of outcrossing in largely selfing and parthenogenetic organisms markedly affects the accumulation rates. The accumulation of mutations is likely to affect the mean population fitness only in long-term evolution.

Complexes of hybrid ligands. The synthesis of a thioanisole-substituted fluoro-alcohol and its complexes with Pd2+ and Pt2+; the structure of a palladium(II) complex containing alkoxide, phosphine, thioether, and chloride donors

1987 ◽  
Vol 65 (4) ◽  
pp. 798-803 ◽  
Author(s):  
René T. Boeré ◽  
David E. Esser ◽  
Christopher J. Willis ◽  
Douglas W. Stephan ◽  
Taras W. Obal
Keyword(s):  
Least Squares ◽  
Dihedral Angle ◽  
Chelate Ring ◽  
Monoclinic Space Group ◽  
Structural Determination ◽  
Bond Lengths ◽  
Square Planar ◽  
Planar Molecules ◽  
Hybrid Ligands ◽  
Cis And Trans

The compound 2-thioanisole-1,1,1,3,3,3-hexafluoro-2-propanol, CH3S—C6H4—C(CF3)2OH, HL2, has been prepared, and shown to act (in the ionized form) as a hybrid, chelating, ligand. Neutral bis-complexes M(L2)2 are formed with Pd2+ and Pt2+; the former reacts with PdCl42− to give the Cl-bridged dinuclear complex (L2)Pd(μ-Cl)2Pd(L2), which may in turn be cleaved by PPh3 or PPh2Me to give PdCl(L2)(PR3).A complete structural determination has been made for PdCl(L2)(PPh2Me); C23H20ClF6OPPdS. Crystals are monoclinic, space group P21/n, a = 15.526(5), b = 12.966(9), c = 12.900(8) Å, β = 101.84°, V = 2542(2) Å3, Z = 4. Least-squares refinement on F of 198 variables using 2801 observations converged at R1 = 0.0434, R2 = 0.0559. The complex consists of discrete square-planar molecules with phosphine and alkoxide trans-disposed. Bond lengths are Pd—O, 2.053(3); Pd—P, 2.242(1); Pd—Cl, 2.323(2); Pd—S, 2.252(2) Å. In the six-membered chelate ring, all atoms with the exception of Pd are close to coplanarity; there is a dihedral angle of 127.9° between the O—Pd—S plane and that of the aromatic ring.Multinuclear nmr measurements are used to show that both cis- and trans-forms of complexes PdCl(L2)(PR3) are present in solution, with inversion at coordinated sulfur occurring much more rapidly in the latter.

scholarly journals Performance and optimization of X-ray grating interferometry

2014 ◽  
Vol 372 (2010) ◽  
pp. 20130027 ◽  
Author(s):  
T. Thuering ◽  
M. Stampanoni
Keyword(s):  
Interference Fringe ◽  
Refraction Angle ◽  
Fringe Visibility ◽  
X Ray ◽  
Analytical Formulae ◽  
Grating Interferometer ◽  
Differential Phase Contrast ◽  
Energy Dependent ◽  
Application Specific ◽  
Contrast Image

The monochromatic and polychromatic performance of a grating interferometer is theoretically analysed. The smallest detectable refraction angle is used as a metric for the efficiency in acquiring a differential phase-contrast image. Analytical formulae for the visibility and the smallest detectable refraction angle are derived for Talbot-type and Talbot–Lau-type interferometers, respectively, providing a framework for the optimization of the geometry. The polychromatic performance of a grating interferometer is investigated analytically by calculating the energy-dependent interference fringe visibility, the spectral acceptance and the polychromatic interference fringe visibility. The optimization of grating interferometry is a crucial step for the design of application-specific systems with maximum performance.

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