Experimental and modeling study on the pyrolysis and oxidation of n-decane and n-dodecane

High pressure n-decane and n-dodecane shock tube experiments were conducted to assist in the development of a Jet A surrogate kinetic model. Jet A is a kerosene based jet fuel composed of hundreds of hydrocarbons consisting of paraffins, olefins, aromatics and naphthenes. In the formulation of the surrogate mixture, n-decane or n-dodecane represent the normal paraffin class of hydrocarbons present in aviation fuels like Jet A. The experimental work on both n-alkanes was performed in a heated high pressure single pulse shock tube. The mole fractions of the stable species were determined using gas chromatography and mass spectroscopy. Experimental data on both n-decane and n-dodecane oxidation and pyrolysis were obtained for temperatures from 867 to 1739 K, pressures from 19 to 74 atm, reaction times from 1.15 to 3.47 ms, and equivalence ratios from 0.46 to 2.05, and ∞. Both n-decane and n-dodecane oxidation showed that the fuel decays through thermally driven oxygen free decomposition at the conditions studied. This observation prompted an experimental and modeling study of n-decane and n-dodecane pyrolysis using a recently submitted revised n-decane/iso-octane/toluene surrogate model. The surrogate model was extended to n-dodecane in order to facilitate the study of the species and the 1-olefin species quantified during the pyrolysis of n-dodecane and n-decane were revised with additional reactions and reaction rate constants modified with rate constants taken from literature. When compared against a recently published generalized n-alkane model and the original and revised surrogate models, the revised (based on our experimental work) and extended surrogate model showed improvements in predicting 1-olefin species profiles from pyrolytic and oxidative n-decane and n-dodecane experiments. The revised and extended model when compared to the published generalized n-alkane and surrogate models also showed improvements in predicting species profiles from flow reactor n-decane oxidation experiments, but similarly predicted n-decane and n-dodecane ignition delay times.     

On integrable rational potentials of the Dirac equation

The one-dimensional Dirac equation with a rational potential is reducible to an ordinary differential equation with a Riccati-like coefficient. Its integrability can be studied with the help of differential Galois theory, although the results have to be stated with recursive relations, because in general the equation is of Heun type. The inverse problem of finding integrable rational potentials based on the properties of the singular points is also presented; in particular, a general class of integrable potentials leading to the Whittaker equation is found.     

Boundary Behavior of α-Harmonic Functions on the Complement of the Sphere and Hyperplane

We study α-harmonic functions on the complement of the sphere and on the complement of the hyperplane in Euclidean spaces of dimension bigger than one, for α?∈?(1,2). We describe the corresponding Hardy spaces and prove the Fatou theorem for α-harmonic functions. We also give explicit formulas for the Martin kernel of the complement of the sphere and for the harmonic measure, Green function and Martin kernel of the complement of the hyperplane for the symmetric α-stable Lévy processes. Some extensions for the relativistic α-stable processes are discussed.     

Synchronous states of slowly rotating pendula

Coupled systems that contain rotating elements are typical in physical, biological and engineering applications and for years have been the subject of intensive studies. One problem of scientific interest, which among others occurs in such systems is the phenomenon of synchronization of different rotating parts. Despite different initial conditions, after a sufficiently long transient, the rotating parts move in the same way — complete synchronization, or a permanent constant shift is established between their displacements, i.e., the angles of rotation — phase synchronization. Synchronization occurs due to dependence of the periods of rotating elements motion and the displacement of the base on which these elements are mounted.     

Principal eigenvalue of the fractional Laplacian with a large incompressible drift

We study the principal Dirichlet eigenvalue of the operator \({L_A=\Delta^{\alpha/2}+Ab(x)\cdot\nabla}\) , on a bounded C ^1,1 regular domain D. Here \({\alpha\in(1,2)}\) , \({\Delta^{\alpha/2}}\) is the fractional Laplacian, \({A\in\mathbb{R}}\) , and b is a bounded d-dimensional divergence-free vector field in the Sobolev space W ^1,2d/(d+α)(D). We prove that the eigenvalue remains bounded, as A→ + ∞, if and only if b has non-trivial first integrals in the domain of the quadratic form of \({\Delta^{\alpha/2}}\) for the Dirichlet condition.     

Magnetostructural transformations in Ni<Subscript>51</Subscript>Mn<Subscript>36</Subscript>Sn<Subscript>13</Subscript> Heusler alloy thin films

In this paper we report structural, magnetic and transport properties of strongly textured Ni₅₁Mn₃₆Sn₁₃ thin films. The off-stoichiometric Heusler alloy films with 200 nm thickness were sputter-deposited on a MgO(100) substrate at 500 K and after annealed at 1000 K in UHV conditions. The textured growth was confirmed by x-ray diffraction in Bragg-Brentano geometry. The temperature dependence of the magnetic properties was measured by VSM and FMR methods. The electron transport measurements were carried out in function of temperature in 0 Oe and 50 kOe fields. All measurements corroborate the existence of the martensitic transformation in the film. Furthermore, transport measurements reveal an influence of the magnetic field on the transition temperature.     

On a new class of functional equations satisfied by polynomial functions

Aequationes mathematicae - The classical result of L. Székelyhidi states that (under some assumptions) every solution of a general linear equation must be a polynomial function. It is known...     

Revealing the Bonding Pattern from the Molecular Electron Density Using Single Exponential Decay Detector: An Orbital‐Free Alternative to the Electron Localization Function

We introduce a new tool (single exponential decay detector: SEDD) to extract information about bonding and localization in atoms, molecules, or molecular assemblies. The practical evaluation of SEDD does not require any explicit information about the orbitals. The only quantity needed is the electron density (calculated or experimental) and its derivatives up to the second order.     

Stability of some aryllithiums in the presence of cyano group: synthesis of biaromatic cyanoarylboronic acids and silanes

Lithium diisopropylamine (LDA)‐mediated deprotonation reactions of halogenated cyanobenzyloxy‐benzenes and cyanobiphenyls were investigated. The resultant organolithium derivatives were converted into the corresponding arylboronic acids or silanes. It was found that the stability of the obtained aryllithiums towards isomerization to the respective benzyllithiums depends strongly on the number of fluorine atoms in the phenyl ring and on the position of the cyano group. Halogenated cyanobiaryls were selectively deprotonated in the position flanked by two halogen atoms; however, the yield depended strongly on the reaction conditions. Addition of LDA to the cyano group was observed on the lithiation of 4‐cyano‐3′,5′‐dichlorobiphenyl rather than deprotonation. Copyright © 2012 John Wiley & Sons, Ltd.