Photoelectron spectroscopic study of the oxyallyl diradical

The photoelectron spectrum of the oxyallyl (OXA) radical anion has been measured. The radical anion has been generated in the reaction of the atomic oxygen radical anion (O center dot-) with acetone. Three low-lying electronic states of OXA have been observed in the spectrum. Electronic structure calculations have been performed for the triplet states (B-3(2) and B-3(1)) of OXA and the ground doublet state ((2)A(2)) of the radical anion using density, functional theory (DFT). Spectral simulations have been carried out for the triplet statics based on the results of the DFT calculations. The simulation identifies a vibrational progression of the CCC bending mode of the B-3(2) state of OXA in the lower electron binding energy (eBE) portion of the spectrum. On top of the B-3(2) feature, however, the experimental spectrum exhibits additional photoelectron peaks whose angular distribution is distinct from that for the vibronic peaks of the B-3(2) state. Complete active space self-consistent field (CASSCF) method and second-order perturbation theory based on the CASSCF wave function (CASPT2) have been employed to study the lowest singlet state ((1)A(1)) of OXA. The simulation based on the results of these electronic structure calculations establishes that the overlapping peaks represent the vibrational ground level of the (1)A(1) state and its vibrational progression of the CO stretching mode. The A, state is the lowest electronic state of,OXA, and the electron affinity (EA) of OXA is 1.940 +/- 0.010 eV. The B-3(2) state is the first excited state with an electronic term energy of 55 +/- 2 meV. The widths of the vibronic peaks of the (X) over tilde (1)A(1) state are much broader than those of the (a) over tilde B-3(2) state, implying that the (1)A(1) state is indeed a transition state. The CASSCF and CASPT2 calculations suggest that the (1)A(1) state is at a potential maximum along the nuclear coordinate representing disrotatory motion of the two methylene groups, which leads to three-membered-ring formation, i.e., cydopropanone. The simulation of (b) over tilde B-3(1) OXA reproduces the higher eBE portion of the spectrum very well. The term energy of the B-3(1) state is 0.883 +/- 0.012 eV. Photoelectron spectroscopic measurements have also been conducted for the other ion products of the O center dot- reaction with acetone. The photoelectron imaging spectrum of the acetylcarbene (AC) radical anion exhibits a broad, structureless feature, which is assigned to the (X) over tilde (3)A '' state of AC. The ground ((2)A '') and first excited ((2)A') states of the 1-methylvinoxy (1-MVO) radical have been observed in the photoelectron spectrum of the 1-MVO ion, and their vibronic structure has been analyzed.

Minimising wave drag for free surface flow past a two-dimensional stern

Free surface flow past a two-dimensional semi-infinite curved plate is considered, with emphasis given to solving for the shape of the resulting wave train that appears downstream on the surface of the fluid. This flow configuration can be interpreted as applying near the stern of a wide blunt ship. For steady flow in a fluid of finite depth, we apply the Wiener-Hopf technique to solve a linearised problem, valid for small perturbations of the uniform stream. Weakly nonlinear results found using a forced KdV equation are also presented, as are numerical solutions to the fully nonlinear problem, computed using a conformal mapping and a boundary integral technique. By considering different families of shapes for the semi-infinite plate, it is shown how the amplitude of the waves can be minimised. For plates that increase in height as a function of the direction of flow, reach a local maximum, and then point slightly downwards at the point at which the free surface detaches, it appears the downstream wavetrain can be eliminated entirely.

Analytical solutions for the multi-term time-fractional diffusion-wave/diffusion equations in a finite domain

Multi-term time-fractional differential equations have been used for describing important physical phenomena. However, studies of the multi-term time-fractional partial differential equations with three kinds of nonhomogeneous boundary conditions are still limited. In this paper, a method of separating variables is used to solve the multi-term time-fractional diffusion-wave equation and the multi-term time-fractional diffusion equation in a finite domain. In the two equations, the time-fractional derivative is defined in the Caputo sense. We discuss and derive the analytical solutions of the two equations with three kinds of nonhomogeneous boundary conditions, namely, Dirichlet, Neumann and Robin conditions, respectively.

Memory of past random wave conditions in submarine groundwater discharge

Submarine groundwater discharge (SGD) is an integral part of the hydrological cycle and represents an important aspect of land-ocean interactions. We used a numerical model to simulate flow and salt transport in a nearshore groundwater aquifer under varying wave conditions based on yearlong random wave data sets, including storm surge events. The results showed significant flow asymmetry with rapid response of influxes and retarded response of effluxes across the seabed to the irregular wave conditions. While a storm surge immediately intensified seawater influx to the aquifer, the subsequent return of intruded seawater to the sea, as part of an increased SGD, was gradual. Using functional data analysis, we revealed and quantified retarded, cumulative effects of past wave conditions on SGD including the fresh groundwater and recirculating seawater discharge components. The retardation was characterized well by a gamma distribution function regardless of wave conditions. The relationships between discharge rates and wave parameters were quantifiable by a regression model in a functional form independent of the actual irregular wave conditions. This statistical model provides a useful method for analyzing and predicting SGD from nearshore unconfined aquifers affected by random waves

An approximate method for the solution of an influence function foil rolling model

Fleck and Johnson (Int. J. Mech. Sci. 29 (1987) 507) and Fleck et al. (Proc. Inst. Mech. Eng. 206 (1992) 119) have developed foil rolling models which allow for large deformations in the roll profile, including the possibility that the rolls flatten completely. However, these models require computationally expensive iterative solution techniques. A new approach to the approximate solution of the Fleck et al. (1992) Influence Function Model has been developed using both analytic and approximation techniques. The numerical difficulties arising from solving an integral equation in the flattened region have been reduced by applying an Inverse Hilbert Transform to get an analytic expression for the pressure. The method described in this paper is applicable to cases where there is or there is not a flat region.

Smoothing a Discrete Hazard Function for the Number of Patients Colonized with Methicillin-Resistance Staphylococcus Aureus in an Intensive Care Unit

A new method for estimating the time to colonization of Methicillin-resistant Staphylococcus Aureus (MRSA) patients is developed in this paper. The time to colonization of MRSA is modelled using a Bayesian smoothing approach for the hazard function. There are two prior models discussed in this paper: the first difference prior and the second difference prior. The second difference prior model gives smoother estimates of the hazard functions and, when applied to data from an intensive care unit (ICU), clearly shows increasing hazard up to day 13, then a decreasing hazard. The results clearly demonstrate that the hazard is not constant and provide a useful quantification of the effect of length of stay on the risk of MRSA colonization which provides useful insight.