A Hopf Bifurcation in a Generalized Mckean Type of Free Boundary Problem Satisfying the Dirichlet Boundary Condition

In this paper, we consider the free boundary problem satisfying the Dirichlet boundary condition. This problem is derived from the reaction diffusion equations with the generalized McKean reaction dynamics. We shall show a Hopf bifurcation occurs at some critical point τ when the stationary solution (v^⋅ (x), s^⋅) satisfies 1/3 < s^⋅ < 1.     

Realization of Tip Tilting By 8-Step Line Tilting

By direct calculation of rotation matrices of SO（3）, we show how certain specific sequence of eight consecutive rotations of digital angles can yield a tilting of a facet mirror. We also design a detailed program specifically to tilt an array of mirrors from planar orientation to the required focusing orientation. We describe how to use the 8-step to realize the focusing of the mirror array. We have found, in our designed program, an important feature of row-sharing during the rotations for the columns and similarly the column-sharing during the rotations for the row. This feature can save a lot of operating time during the actual realization of the mechanical movements.     

Digitalized Mirror Array and Its Application in Large Telescope： Principle and Case Studies

In this article, we report the principle and conceptual design of a fundamentally different technology in fabricating high precision aberration free optical devices. The tip-tilt of facet in a mirror array is produced by digitally controlled line-tilts of rows and columns. It has not only provided a cost-effective designing methodology in optical physics but also led to a much finer precision of 1 mili arc sec or less. As examples of the application of the proposed digitalised optics, two case studies have been given： a 10 m Schmidt telescope （off-axis） and an 8 m Cassegrain telescope （on-axis）.     

β‐Ionone reactions with the nitrate radical: Rate constant and gas‐phase products

The bimolecular rate constant of k (9.4 ± 2.4 × 10^?12 cm³ molecule^?1 s^?1 was measured using the relative rate technique for the reaction of the nitrate radical (NO₃?) with 4‐(2,6,6‐trimethyl‐1‐cyclohexen‐1‐yl)‐3‐buten‐2‐one (β‐ionone) at (297 ± 3) K and 1 atmosphere total pressure. In addition, the products of β‐ionone + NO₃? reaction were also investigated. The identified reaction products were glyoxal (HC(?O)C(?O)H), and methylglyoxal (CH₃C(?O)C(?O)H). Derivatizing agents O‐(2,3,4,5,6‐pentafluorobenzyl)hydroxylamine and N,O‐bis(trimethylsilyl)trifluoroacetamide were used to propose the other major reaction products: 3‐oxobutane‐1,2‐diyl nitrate, 2,6,6‐trimethylcyclohex‐1‐ene‐carbaldehyde, 2‐oxo‐1‐(2,6,6‐trimethylcyclohex‐1‐en‐1‐yl)ethyl nitrate, pentane‐2,4‐dione, 3‐oxo‐1‐(2,6,6‐trimethylcyclohex‐1‐en‐1‐yl)butane‐1,2‐diyl dinitrate, 3,3‐dimethylcyclohexane‐1,2‐dione, and 4‐oxopent‐2‐enal. The elucidation of these products was facilitated by mass spectrometry of the derivatized reaction products coupled with plausible β‐ionone + NO₃? reaction mechanisms based on previously published volatile organic compound + NO₃? gas‐phase mechanisms. The additional gas‐phase products 5‐acetyl‐2‐ethylidene‐3‐methylcyclopentyl nitrate, 1‐(1‐hydroxy‐7,7‐dimethyl‐2,3,4,5,6,7‐hexahydro‐1 H‐inden‐2‐yl)ethanone, 1‐(1‐hydroxy‐3a,7‐dimethyl‐2,3,3a,4,5,6,‐hexahydro‐1 H‐inden‐2‐yl)ethanone, and 5‐acetyl‐2‐ethylidene‐3‐methylcyclopentanone are proposed to be the result of cyclization through a reaction intermediate. © 2009 Wiley Periodicals, Inc. *

1 This article is a U.S. Government work and, as such, is in the public domain of the United States of America.

Int J Chem Kinet 41: 629–641, 2009     

Gas‐phase chemistry of dihydromyrcenol with ozone and OH radical: Rate constants and products

A bimolecular rate constant, k_{OH + dihydromyrcenol}, of (38 ± 9) × 10^?12 cm³ molecule^?1 s^?1 was measured using the relative rate technique for the reaction of the hydroxyl radical (OH) with 2,6‐dimethyl‐7‐octen‐2‐ol (dihydromyrcenol,) at 297 ± 3 K and 1 atm total pressure. Additionally, an upper limit of the bimolecular rate constant, k, of approximately 2 × 10^?18 cm³ molecule^?1 s^?1 was determined by monitoring the decrease in ozone (O₃) concentration in an excess of dihydromyrcenol. To more clearly define part of dihydromyrcenol's indoor environment degradation mechanism, the products of the dihydromyrcenol + OH and dihydromyrcenol + O₃ reactions were also investigated. The positively identified dihydromyrcenol/OH and dihydromyrcenol/O₃ reaction products were acetone, 2‐methylpropanal (O?CHCH(CH₃)₂), 2‐methylbutanal (O?CHCH(CH₃)CH₂CH₃), ethanedial (glyoxal, HC(?O)C(?O)H), 2‐oxopropanal (methylglyoxal, CH₃C(?O)C(?O)H). The use of derivatizing agents O‐(2,3,4,5,6‐pentafluorobenzyl)hydroxylamine (PFBHA) and N,O‐bis(trimethylsilyl)trifluoroacetamide (BSTFA) clearly indicated that several other reaction products were formed. The elucidation of these other reaction products was facilitated by mass spectrometry of the derivatized reaction products coupled with plausible dihydromyrcenol/OH and dihydromyrcenol/O₃ reaction mechanisms based on previously published volatile organic compound/OH and volatile organic compound/O₃ gas‐phase reaction mechanisms. © 2006 Wiley Periodicals, Inc. *

1 This article is a US Government work and, as such, is in the public domain of the United States of America

Int J Chem Kinet 38: 451–463, 2006     

Static secondary ion mass spectrometry (S-SIMS) for the characterization of surface components in mineral particulates

The feasibility of static secondary ion mass spectrometry (S-SIMS) for the detection of molecule specific information from complex materials, such as natural clay and soil samples, has been investigated. Ion trap (IT), as well as triple quadrupole (TQ) instruments, have been used for mass analysis. Secondary ion images have been acquired using time-of-flight (TOF) S-SIMS. The generation of molecular adduct ions from thin and thick layers on the mineral substrates has been investigated using KBr as a simple model system. Results show that molecular adducts of KBr can be indeed detected from the spiked materials. However, the concentrations of the spiking solutions have to be significantly larger than expected from the surface area measured by gas adsorption techniques. In addition imaging analysis has evidenced that the detection of adduct ions in the mass spectra directly relates to the presence of local micro-crystallites.     

Atomic-level investigations on the amyloid-β dimerization process and its driving forces in water

We report the spontaneous dimerization process of the full-length Aβ42 proteins in water by using unguided, fully atomistic, explicit-water molecular dynamics simulations. Based on the thermodynamic analysis, we demonstrate that Aβ42 dimerization in water occurs via a two-step nucleation-accommodation mechanism driven by water-induced force and by protein internal force, respectively.     

Symmetric quadrature rules for tetrahedra based on a cubic close-packed lattice arrangement

A family of quadrature rules for integration over tetrahedral volumes is developed. The underlying structure of the rules is based on the cubic close-packed (CCP) lattice arrangement using 1, 4, 10, 20, 35, and 56 quadrature points. The rules are characterized by rapid convergence, positive weights, and symmetry. Each rule is an optimal approximation in the sense that lower-order terms have zero contribution to the truncation error and the leading-order error term is minimized. Quadrature formulas up to order 9 are presented with relevant numerical examples.