Electromagnetic field singularities

An integral transform based method is given for determining information about the locating and properties of singularities of electromagnetic fields associated with axially symmetric radiating sources.     

Approximations of relations by continuous functions

Let X be a Tychonoff space, C(X) be the space of all continuous real-valued functions defined on X and CL(X×R) be the hyperspace of all nonempty closed subsets of X×R. We prove the following result. Let X be a countably paracompact normal space. The following are equivalent: (a) dimX=0; (b) the closure of C(X) in CL(X×R) with the Vietoris topology consists of all F∈CL(X×R) such that F(x)≠∅ for every x∈X and F maps isolated points into singletons; (c) each usco map which maps isolated points into singletons can be approximated by continuous functions in CL(X×R) with the locally finite topology. From the mentioned result we can also obtain the answer to Problem 5.5 in [L'. Holá, R.A. McCoy, Relations approximated by continuous functions, Proc. Amer. Math. Soc. 133 (2005) 2173-2182] and to Question 5.5 in [R.A. McCoy, Comparison of hyperspace and function space topologies, Quad. Mat. 3 (1998) 243-258] in the realm of normal, countably paracompact, strongly zero-dimensional spaces. Generalizations of some results from [L'. Holá, R.A. McCoy, Relations approximated by continuous functions, Proc. Amer. Math. Soc. 133 (2005) 2173-2182] are also given.     

Analytic Calculation of B 4 for Hard Spheres in Even Dimensions

We exactly calculate the fourth virial coefficient for hard spheres in even dimensions for D = 4, 6, 8, 10, and 12.     

New results for virial coefficients of hard spheres inD dimensions

We present new results for the virial coefficientsB _k for κ<- 10 for hard spheres in dimensionsD = 2,..., 8.     

Femtosecond study of Cu(H(2)O) dynamics

The short-time nuclear dynamics of Cu(H(2)O) is investigated using femtosecond photodetachment-photoionization spectroscopy and time-dependent quantum wave packet calculations. The Cu(H(2)O) dynamics is initiated in the electronic ground state of the complex by electron photodetachment from the Cu(-)(H(2)O) complex, where hydrogen atoms are oriented toward Cu. Several time-resolved resonant multiphoton ionization schemes are used to probe the ensuing reorientation and dissociation. Immediately following photodetachment, the neutral complex is far from its minimum energy geometry and possesses an internal energy comparable to the Cu-H(2)O dissociation energy and undergoes both large-amplitude H(2)O motion and dissociation. Dissociation is observed to occur on three distinct time scales: 0.6, 8, and 100 ps. These results are compared to the results of time-dependent J=0 wave packet calculations, propagating the initial anion vibrational wave functions on the ground-state potential of the neutral complex. An excellent agreement is obtained between the experimental results and the ionization signals derived from the calculated probability amplitudes. Related experiments and calculations are carried out on the Cu(D(2)O) complex, with results very similar to those of Cu(H(2)O).     

Role of OH-stretch/torsion coupling and quantum yield effects in the first OH overtone spectrum of cis-cis HOONO

A joint theoretical and experimental investigation is undertaken to study the effects of OH-stretch/HOON torsion coupling and of quantum yield on the previously reported first overtone action spectrum of cis-cis HOONO (peroxynitrous acid). The minimum energy path along the HOON dihedral angle is computed at the coupled cluster singles and doubles with perturbative triples level with correlation consistent polarized quadruple zeta basis set, at the structure optimized using the triple zeta basis set (CCSD(T)/cc-pVQZ//CCSD(T)/cc-pVTZ). The two-dimensional ab initio potential energy and dipole moment surfaces for cis-cis HOONO are calculated as functions of the HOON torsion and OH bond length about the minimum energy path at the CCSD(T)/cc-pVTZ and QCISD/AUG-cc-pVTZ (QCISD-quadratic configuration interaction with single and double excitation and AUG-augmented with diffuse functions) level of theory/basis, respectively. The OH-stretch vibration depends strongly on the torsional angle, and the torsional potential possesses a broad shelf at approximately 90 degrees , the cis-perp conformation. The calculated electronic energies and dipoles are fit to simple functional forms and absorption spectra in the region of the OH fundamental and first overtone are calculated from these surfaces. While the experimental and calculated spectra of the OH fundamental band are in good agreement, significant differences in the intensity patterns are observed between the calculated absorption spectrum and the measured action spectrum in the 2nu(OH) region. These differences are attributed to the fact that several of the experimentally accessible states do not have sufficient energy to dissociate to OH+NO(2) and therefore are not detectable in an action spectrum. Scaling of the intensities of transitions to these states, assuming D(0)=82.0 kJ/mol, is shown to produce a spectrum that is in good agreement with the measured action spectrum. Based on this agreement, we assign two of the features in the spectrum to Deltan=0 transitions (where n is the HOON torsion quantum number) that are blue shifted relative to the origin band, while the large peak near 7000 cm(-1) is assigned to a series of Deltan=+1 transitions, with predominant contributions from torsionally excited states with substantial cis-perp character. The direct absorption spectrum of cis-cis HOONO (6300-6850 cm(-1)) is recorded by cavity ringdown spectroscopy in a discharge flow cell. A single band of HOONO is observed at 6370 cm(-1) and is assigned as the origin of the first OH overtone of cis-cis HOONO. These results imply that the origin band is suppressed by over an order of magnitude in the action spectrum, due to a reduced quantum yield. The striking differences between absorption and action spectra are correctly predicted by the calculations.