Kinetics of n-Butoxy and 2-Pentoxy Isomerization and Detection of Primary Products by Infrared Cavity Ringdown Spectroscopy

The primary products of n-butoxy and 2-pentoxy isomerization in the presence and absence of O_2 have been detected using pulsed laser photolysis-cavity ringdown spectroscopy (PLP-CRDS). Alkoxy radicals n-butoxy and 2-pentoxy were generated by photolysis of alkyl nitrite precursors (n-butyl nitrite or 2-pentyl nitrite, respectively), and the isomerization products with and without O_2 were detected by infrared cavity ringdown spectroscopy 20 μs after the photolysis. We report the mid-IR OH stretch (ν_1) absorption spectra for δ-HO-1-C_4H_8•, δ-HO-1-C_4H_8OO•, δ-HO-1-C_5H_(10)•, and δ-HO-1-C_5H_(10)OO•. The observed ν_1 bands are similar in position and shape to the related alcohols (n-butanol and 2-pentanol), although the HOROO• absorption is slightly stronger than the HOR• absorption. We determined the rate of isomerization relative to reaction with O_2 for the n-butoxy and 2-pentoxy radicals by measuring the relative ν_1 absorbance of HOROO• as a function of [O_2]. At 295 K and 670 Torr of N_2 or N_2/O_2, we found rate constant ratios of k_(isom)/k_(O2) = 1.7 (±0.1) × 10^(19) cm^(–3) for n-butoxy and k_(isom)/k_(O2) = 3.4(±0.4) × 10^(19) cm^(–3) for 2-pentoxy (2σ uncertainty). Using currently known rate constants k_(O2), we estimate isomerization rates of k_(isom) = 2.4 (±1.2) × 10^5 s^(–1) and k_(isom) ≈ 3 × 10^5 s^(–1) for n-butoxy and 2-pentoxy radicals, respectively, where the uncertainties are primarily due to uncertainties in k_(O2). Because isomerization is predicted to be in the high pressure limit at 670 Torr, these relative rates are expected to be the same at atmospheric pressure. Our results include corrections for prompt isomerization of hot nascent alkoxy radicals as well as reaction with background NO and unimolecular alkoxy decomposition. We estimate prompt isomerization yields under our conditions of 4 ± 2% and 5 ± 2% for n-butoxy and 2-pentoxy formed from photolysis of the alkyl nitrites at 351 nm. Our measured relative rate values are in good agreement with and more precise than previous end-product analysis studies conducted on the n-butoxy and 2-pentoxy systems. We show that reactions typically neglected in the analysis of alkoxy relative kinetics (decomposition, recombination with NO, and prompt isomerization) may need to be included to obtain accurate values of k_(isom)/k_(O2)

Unsteady Subsonic and Transonic Potential Flow over Helicopter Rotor Blades

Differential equations and boundary conditions for a rotor blade in forward flight, with subsonic or transonic tip Mach number, are derived. A variety of limiting flow regimes determined by different limits involving blade thickness ratio, aspect ratio, advance ratio and maximum tip Mach number is discussed. The transonic problem is discussed in some detail, and in particular the conditions that make this problem quasi-steady or essentially unsteady are determined. Asymptotic forms of equations and boundary conditions that are valid in an appropriately scaled region of the tip and an azimuthal sector on the advancing side are derived. The equations are then put in a form that is valid from the blade tip inboard through the strip theory region

Comments on Closed Bianchi Models

We show several kinematical properties that are intrinsic to the Bianchi models with compact spatial sections. Especially, with spacelike hypersurfaces being closed, (A) no anisotropic expansion is allowed for Bianchi type V and VII(A\not=0), and (B) type IV and VI(A\not=0,1) does not exist. In order to show them, we put into geometric terms what is meant by spatial homogeneity and employ a mathematical result on 3-manifolds. We make clear the relation between the Bianchi type symmetry of space-time and spatial compactness, some part of which seem to be unnoticed in the literature. Especially, it is shown under what conditions class B Bianchi models do not possess compact spatial sections. Finally we briefly describe how this study is useful in investigating global dynamics in (3+1)-dimensional gravity.Comment: 14 pages with one table, KUCP-5

The Noether-Lefschetz Problem and Gauge-Group-Resolved Landscapes: F-Theory on K3 x K3 as a Test Case

Four-form flux in F-theory compactifications not only stabilizes moduli, but gives rise to ensembles of string vacua, providing a scientific basis for a stringy notion of naturalness. Of particular interest in this context is the ability to keep track of algebraic information (such as the gauge group) associated with individual vacua while dealing with statistics. In the present work, we aim to clarify conceptual issues and sharpen methods for this purpose, using compactification on ${\rm K3} \times {\rm K3}$ as a test case. Our first approach exploits the connection between the stabilization of complex structure moduli and the Noether-Lefschetz problem. Compactification data for F-theory, however, involve not only a four-fold (with a given complex structure) $Y_4$ and a flux on it, but also an elliptic fibration morphism $Y_4 \longrightarrow B_3$, which makes this problem complicated. The heterotic-F-theory duality indicates that elliptic fibration morphisms should be identified modulo isomorphism. Based on this principle, we explain how to count F-theory vacua on ${\rm K3} \times {\rm K3}$ while keeping the gauge group information. Mathematical results reviewed/developed in our companion paper are exploited heavily. With applications to more general four-folds in mind, we also clarify how to use Ashok-Denef-Douglas' theory of the distribution of flux vacua in order to deal with statistics of sub-ensembles tagged by a given set of algebraic/topological information. As a side remark, we extend the heterotic/F-theory duality dictionary on flux quanta and elaborate on its connection to the semistable degeneration of a K3 surface.Comment: 81 pages, 5 figure

Hyperbolic Structures on 3-manifolds, III: Deformations of 3-manifolds with incompressible boundary

This is the third in a series of papers constructing hyperbolic structures on all Haken three-manifolds. This portion deals with the mixed case of the deformation space for manifolds with incompressible boundary that are not acylindrical, but are more complicated than interval bundles over surfaces. This is a slight revision of a 1986 preprint, with a few figures added, and slight clarifications of some of the text, but with no attempt to connect this to later developments such as groups acting on R-trees, etc.Comment: 19 pages, 4 figure