Scattering theory relevant to the linear transport of particle swarms

The long-time behavior of the velocity distribution of a spatially uniform diluted guest population of charged particles moving within a host medium under the influence of a D.C. electric field is studied within the framework of scattering theory. We prove the existence of wave and scattering operators for a simplified one-dimensional model of the linearized Boltzmann equation. The theory is applied to the study of the long-term behavior of electrons and the occurrence of traveling waves in runaway processes.     

A neutral gas model for electron swarms

A BGK-type Boltzmann equation for a neutral gas is considered as a model for electron swarms, because the gas and the electron Boltzmann equation have a common diffusion approximation. Both full- and half-range theory are developed using orthogonality methods of solution. Preliminary comparisons with diffusion theory are presented.     

Facile generation of platinum(IV) compounds with mixed labile moieties. Hydrogen peroxide oxidation of platinum(II) to platinum(IV) compounds

Hydrogen peroxide oxidation of platinum(II) compounds containing labile groups such as Cl, OH, and alkene moieties has been carried out and the products characterized. The reactions of [Pt^II (X)₂ (N–N)] (X = Cl, OH, X₂ = isopropylidenemalorate (ipm); N–N 2,2-dimethyl-1,3-propanediamine [(dmpda), N-isopropyl-1,3-propanediamine (ippda)] with hydrogen peroxide in an appropriate solvent at room temperature affords [Pt^IV (OH)(Y)(X)₂(N–N)] (Y = OH, OCH₃). The crystal structures of [Pt^IV(OH)(OCH₃)(Cl)₂(dmpda)]·2H₂O (P-1 bar, a = 6.339(2) Å , b = 9.861(1) Å, c = 11.561(1) Å, a = 92.078(9)°, β = 104.78(1)°, γ=100.54(1)°, V = 684.3(2) ų, Z = 2R = 0.0503) and [Pt^IV(OH)₂(ipm)(ippda)]·3H₂O (C 2/c, a = 27.275(6) Å, b=6.954(2) Å, c = 22.331(4) Å, β = 118.30(2)°, V = 3729(2) ų, Z = 8, R = 0.0345) have been solved and refined. The local geometry around the platinum(IV) atom approximates to a typical octahedral arrangement with two added groups (OH and OCH₃; OH and OH) in a transposition. The platinum(IV) compounds with potential labile moieties may be important intermediate species for further reactions.     

H-NMR studies of duplex DNA decamer containing a uracil cyclobutane dimer: implications regarding the high UV mutagenecity of CC photolesions

To determine the origin of the UV-specific CC to TT tandem mutation at the CC site, we made a duplex DNA decamer containing a uracil cis-syn cyclobutane dimer (CBD) as the deaminated model of a cytosine dimer. Two-dimensional 1H-NMR spectroscopy studies were performed on this sequence where two adenines (Ade) were opposite to the uracil dimer. Two imino protons of the uracil dimer were found to retain Watson-Crick hydrogen bonding with the opposite Ade, although the 5'-U(NH) of the dimer site showed unusual upfield shift like that of the 5'-T(NH) of the TT dimer, which seemed to be associated with deshielding by the flanking base rather than with reduced hydrogen bonding. (McAteer et al. 1998, J. Mol. Biol. 282:1013-1032). Hydrogen bondings at the dimer site were also supported by detecting typical strong nuclear Overhauser effects (NOE) between two imino protons and the opposite Ade H2 or NH2. But sequential NOE interactions of base protons with sugar protons were absent at the two flanking nucleotides of the 5' side of the uracil dimer and at the intradimer site, contrasting with its thymine analog where sequential NOE was absent only at the A4-T5 step. In addition, NOE cross peak for U5(NH) <--> A4(H2) was detected, although the NOE interactions of U6(NH) with A7(H2) and A17(H2) were not observed in contrast to the thymine dimer duplex. This different local structural alteration may be affected by the induced right-hand twisted puckering mode of cis-syn cyclobutane ring of the uracil dimer in the B-DNA duplex, even though the isolated uracil dimer had left-hand twisted puckering rigidly. In parallel, these observations may be correlated with observed differences in mutagenic properties between cis-syn UU dimer and cis-syn TT dimer.     

Generalized kinetic equations

We study the abstract differential equation on a Hilbert space H, which represents a variety of different kinetic equations. T is assumed bounded and self-adjoint on H, and A (unbounded) positive self-adjoint and Fredholm. For partial range boundary conditions and 0x<, we prove existence and (non-) uniqueness theorems and give representations of the solution. Various examples from neutron transport, radiative transfer of polarized and unpolarized light, and electron transport are given.This paper is dedicated to K.M. Case on the occasion of his sixtieth birthday     

Excitation-energy migration in self-assembled cyclic zinc(II)-porphyrin arrays: a close mimicry of a natural light-harvesting system

The excitation-energy-hopping (EEH) times within two-dimensional cyclic zinc(II)-porphyrin arrays 5 and 6, which were prepared by intermolecular coordination and ring-closing metathesis reaction of olefins, were deduced by modeling the EEH process based on the anisotropy depolarization as well as the exciton-exciton annihilation dynamics. Assuming the number of energy-hopping sites N = 5 and 6, the two different experimental observables, that is, anisotropy depolarization and exciton-excition annihilation times, consistently give the EEH times of 8.0 +/- 0.5 and 5.3 +/- 0.6 ps through the 1,3-phenylene linkages of 5 and 6, respectively. Accordingly, the self-assembled cyclic porphyrin arrays have proven to be well-defined two-dimensional models for natural light-harvesting complexes.     

Porphyrin boxes constructed by homochiral self-sorting assembly: optical separation, exciton coupling, and efficient excitation energy migration

meso-Pyridine-appended zinc(II) porphyrins Mn and their meso-meso-linked dimers Dn assemble spontaneously, in noncoordinating solvents such as CHCl3, into tetrameric porphyrin squares Sn and porphyrin boxes Bn, respectively. Interestingly, formation of Bn from Dn proceeds via homochiral self-sorting assembly, which has been verified by optical separations of B1 and B2. Optically pure enantiomers of B1 and B2 display strong Cotton effects in the CD spectra, which reflect the length of the pyridyl arm, thus providing evidence for the exciton coupling between the noncovalent neighboring porphyrin rings. Excitation energy migration processes within Bn have been investigated by steady-state and time-resolved spectroscopic methods in conjunction with polarization anisotropy measurements. Both the pump-power dependence on the femtosecond transient absorption and the transient absorption anisotropy decay profiles are directly associated with the excitation energy migration process within the Bn boxes, where the exciton-exciton annihilation time and the polarization anisotropy rise time are well described in terms of the F?rster-type incoherent energy hopping model by assuming a number of hopping sites of N = 4 and an exciton coherence length of L = 2. Consequently, the excitation energy hopping rates between the zinc(II) diporphyrin units have been estimated for B1 (48 ps)(-1), B2 (98 +/- 3 ps)(-1), and B3 (361 +/- 6 ps)(-1). Overall, the self-assembled porphyrin boxes Bn serve as a well-defined three-dimensional model for the light-harvesting complex.     

Time-evolution-proof Scattering Data for the Focusing and Defocusing Zakharov-Shabat Systems

In this article we give sufficient conditions on the scattering data of a defocusing or focusing Zakharov-Shabat system in order that its potential is square integrable. For a dense subset of integrable as well as square integrable potentials, we show that the scattering data actually satisfy these sufficient conditions.