Regenerative soot as a source of broad band VUV light

Certain important and pertinent questions have been raised by E. Träbert in his comment on the paper [Eur. Phys. J. D 22, 189 (2003)] by one of us. We provide explanations as well as new and recent data using a calibrated monochromator on the existence of the main intercombination multiplet 233 nm which is the bone of contention. It is shown that there is no conflict with the established atomic physics in the regenerative sooting discharges; only the interpretations are at variance with those of the comment.Received: 30 July 2003, Published online: 30 September 2003PACS: 32.70.Fw Absolute and relative intensities - 34.50.Dy Interactions of atoms and molecules with surfaces; photon and electron emission; neutralization of ions - 34.80.Dp Atomic excitation and ionization by electron impact     

Photografting of polymers onto nanosized silica surface initiated by eosin moieties immobilized onto the surface

The photograft polymerization of various vinyl monomers onto nanosized silica surfaces was investigated. It was initiated by eosin moieties introduced onto the silica surface. The preparation of the silica with eosin moieties was achieved by the reaction of eosin with benzyl chloride groups on the silica surface.These were introduced by the reaction of surface silanol groups with 4‐(chloromethyl)phenyltrimethoxysilane in the presence of t‐butyl ammonium bromide as a phase‐transfer catalyst. The photopolymerization of various vinyl monomers, such as styrene, acrylamide, acrylic acid, and acrylonitrile was successfully initiated by eosin moieties on the silica surface in the presence of ascorbic acid as a reducing agent and by oxygen. The corresponding polymers were grafted from the silica surface. The grafting efficiency (percentage of grafted polymer to total polymer formed) in the photoinitiation system was much larger than that in the radical polymerization initiated by surface radicals; these radicals were formed by the thermal decomposition of azo groups introduced onto the silica surface. It was found that the polymer‐grafted silica gave stable dispersions in good solvents of grafted polymer and the wettability of the surfaces can be easily controlled by grafting of polymers. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 600–606, 2005     

Computer-oriented, n-body modelling of minimal surfaces

In this paper a new approach to the modelling of minimal surfaces is described and applied. Rather than use a continuous model, we develop a discrete, _n-body model with basic tensile interactions derived from classical molecular force formulae. Computer results are described and discussed.     

On Decomposing N=2 Line Bundles as Tensor Products of N=1 Line Bundles

We obtain the existence of a cohomological obstruction to expressing N=2 line bundles as tensor products of N=1 bundles. The motivation behind this paper is an attempt at understanding the N=2 super KP equation via Baker functions, which are special sections of line bundles on supercurves.     

Huang diffuse scattering from interstitials in an hcp lattice

Using the continuum theory of linear elasticity, the Huang diffuse scattering from interstitials in an hcp lattice has been calculated to distinguish between the possible interstitial configurations. The symmetry of the lattice permits four such configurations. In each case, the Huang diffuse scattering is averaged over all possible equivalent orientations (assumed to be equally populated) of the defect configuration. The limitations of Huang diffuse scattering in discriminating between defect configurations having the same long-range symmetry are discussed, considering the specia I cases of Mg and Zn.     

Optimal immunization rules for an epidemic with recovery

The classical Kermack-McKendrick model for the spread of an epidemic through a closed population has recently been extended by Billard to allow for the recovery and possible reinfection of infective cases. In this paper, we study the optimal control of such an epidemic through immunization of susceptibles when costs are proportional to the area under the infectives trajectory plus the total number of immunizations. When the immunization rate is bounded, optimal controls are of bang-bang type and are characterized by switching curves in the epidemic state space. Explicit expressions for these curves are obtained in the case of deterministic dynamics. When the epidemic is described by a Markov chain, numerical solutions for the switching curve are easy to obtain by dynamic programming, and useful analytic approximations to them are described. The results include those for the so-called general epidemic in which no recovery is allowed.The author is grateful to the referees for their detailed and constructive criticism of an earlier version of this paper.     

Atom-surface scattering with velocity-selected H and D atomic beams from LiF and NaF (001)

Hydrogen and deuterium atoms with an energy between 20 and 140 meV have been scattered from LiF and NaF (001) cleavage planes in UHV. The atomic beam was nearly monoenergetic by use of a slotted disk type velocity selector with a velocity resolution of $\text{Δv}\text{v}\text{=12\%}$ (FWHM). The scattering showed diffraction with a pronounced specular beam. The energies of several bound surface states have been determined by analysis of selective adsorption minima. These energies together with relative intensities of diffracted beams and specular intensity versus incident energy measurements may be represented by an interaction potential of Morse-type with additional terms which are periodic parallel to the surface. The parameters of the Morse-potential have been found to be: depth D=17.8 meV and reciprocal range $\text{κ=1.04}\text{A}\text{?}{}^{\mathrm{?1}}$ for H₁/LiF (001) and D = 17.9 meV, k = 1.15 Å^?1 for H₁/NaF (001); the additional periodic terms have relative strength β₁₀=0.04 and $\text{β}{}_{11}\text{≈}\text{β}{}_{10}\text{2}$ in the case of H ₁/LiF, but β₁₁≈β₁₀=0.03 in the case of H₁/NaF. From the observed influence of surface temperature on the position of selective adsorption minima the coefficient of thermal expansion of the topmost surface layer turns out to be approximately twice the bulk value.     

Time-optimal control of multivariable systems near the origin

This article deals with bang-bang solutions of linear time-optimal control problems. Linear multivariable systems are considered which have one or more control components. It is shown in which way the control components act together to make the system achieve the ultimate aim (namely, the origin in the state space) as quickly as possible. The theory only applies to initial positions sufficiently near the origin. Criteria are given which give the number of switches per control component.Asymptotic dependences of the switching times and the final time on the distance of the initial position from the origin are established. The theory provides a numerical procedure to calculate the time-optimal control. These calculations are very simple. Basic to the proof of these results is a generalized implicit function theorem due to Artin (Ref. 1).     

Counting generic genus- curves on Hirzebruch surfaces

Hirzebruch surfaces provide an excellent example to underline the fact that in general symplectic manifolds, Gromov-Witten invariants might well count curves in the boundary components of the moduli spaces. We use this example to explain in detail that the counting argument given by Batyrev for toric manifolds does not work.

     

On finiteness of the number of boundary slopes of immersed surfaces in 3-manifolds

For any hyperbolic 3-manifold with totally geodesic boundary, there are finitely many boundary slopes for essential immersed surfaces of a given genus. There is a uniform bound for the number of such boundary slopes if the genus of is bounded from above.