The impact parameter dependence of the Pb + Pb K − MO spectrum

Molecular orbital X-rays are emitted during ion-atom collisions. The theoretical treatment, numerical results for the Pb + Pb system and a comparison with background radiation like NNB, SEB and γ-decay of Coulomb excited nuclei are presented.     

Calculation of wavefunctions and frequencies for noninfinitesimal vibrations: Comparison of various methods using ab initio CI potential curves

Three computational methods employing different means of representing molecular potentials are used to obtain wavefunctions and energy levels for noninfinitesimal vibrations. An interpolation scheme based on a cubic spline fitting procedure is introduced to supplement the CI energy results obtained explicitly in actual calculations. As long as a representative set of potential points is available it is found that the results of all three methods (two of variational and one of numerical integration type) are quite consistent, for both bending and stretching vibrations of ground and electronically excited states (examples for HCN and O₂ are considered). In addition a comparison of one- and two-dimensional bending vibrational treatments is made.     

Phase transitions in experimental systems

Scaling functions of the support and of the measure have been used to characterize the scaling behavior of a dynamical system. While scaling functions for the scaling of the measure, ƒ(), have been calculated for a number of experimental systems, examples of scaling functions φ(λ) for the scaling of the support are difficult to obtain. In this contribution, we report on a phase-transition-like effect of an experimental p-doped germanium semiconductor sample. It is found that the results obtained from the dynamical scaling function agree with those obtained by Horita et al. from model maps, indicating that scaling functions for the scaling of the support are a powerful method of characterizing experimental dynamical systems.     

A note to the paper “An efficient algorithm for linear programming” of V Ch Venkaiah

In Venkaiah [1] an algorithm for solving linear optimization problems based on the idea of the projective algorithm of Karmarkar, is proposed. The essential simplification in the new algorithm is the use of a fixed projection operator. In this way the algorithm requires onlyO(n ² ) operations to obtain a sufficient exact solution. In this note it is shown that in some special cases the algorithm of Venkaiah yields a feasible solution that is far from the optimal one.     

Compactly Supported Tight Affine Frames with Integer Dilations and Maximum Vanishing Moments

When a cardinal B-spline of order greater than 1 is used as the scaling function to generate a multiresolution approximation of L ²=L ²(R) with dilation integer factor M2, the standard matrix extension approach for constructing compactly supported tight frames has the limitation that at least one of the tight frame generators does not annihilate any polynomial except the constant. The notion of vanishing moment recovery (VMR) was introduced in our earlier work (and independently by Daubechies et al.) for dilation M=2 to increase the order of vanishing moments. This present paper extends the tight frame results in the above mentioned papers from dilation M=2 to arbitrary integer M2 for any compactly supported M-dilation scaling functions. It is shown, in particular, that M compactly supported tight frame generators suffice, but not M–1 in general. A complete characterization of the M-dilation polynomial symbol is derived for the existence of M–1 such frame generators. Linear spline examples are given for M=3,4 to demonstrate our constructive approach.     

Analysis of damping-induced phase flips of plasmonic nanowire modes

We launch surface plasmons from one end of a silver nanowire by asymmetric illumination with white light and use plasmon-to-light scattering at the nanowire ends to probe spectroscopically the plasmonic Fabry-Perot wire modes. The spectral positions of the maxima and minima in the scattered intensity from both nanowire ends are found to be either in-phase or out-of-phase, depending on the nanowire length and the spectral range. This behavior can be explained by a generalized Fabry-Perot model. The turnover point between the two regimes is sensitive to the surface plasmon round trip losses and thus opens a new possibility for detecting changes of the optical absorption in the nanowire environment.     

A stable high-order Spectral Difference method for hyperbolic conservation laws on triangular elements

Numerical schemes using piecewise polynomial approximation are very popular for high order discretization of conservation laws. While the most widely used numerical scheme under this paradigm appears to be the Discontinuous Galerkin method, the Spectral Difference scheme has often been found attractive as well, because of its simplicity of formulation and implementation. However, recently it has been shown that the scheme is not linearly stable on triangles. In this paper we present an alternate formulation of the scheme, featuring a new flux interpolation technique using Raviart–Thomas spaces, which proves stable under a similar linear analysis in which the standard scheme failed. We demonstrate viability of the concept by showing linear stability both in the semi-discrete sense and for time stepping schemes of the SSP Runge–Kutta type. Furthermore, we present convergence studies, as well as case studies in compressible flow simulation using the Euler equations.     

Nucleation of atmospheric aerosol particles

A significant fraction of the total number of particles present in the atmosphere is formed originally by nucleation from the gas phase. Binary nucleation of sulphuric acid and water, ternary nucleation of sulphuric acid, water and ammonia and ion-induced nucleation are thought to be the most important aerosol nucleation processes in the atmosphere. Within the last two decades, instrumentation to observe and characterize nucleation has improved greatly and numerous observations of nucleation have been made including quantification of the nucleation rate, characterization of the growth process and first chemical characterizations of the freshly formed particles. Nucleation has been observed at many different places in the atmosphere: in the boundary layer, in the free troposphere, in remote locations, in coastal areas, in boreal forests as well as urban areas and pollution plumes. In most cases gaseous sulphuric acid is assumed to be the key precursor gas. After nucleation, other supersaturated substances, especially low vapour pressure organics often take part in the subsequent aerosol growth. Iodine oxides seem to be responsible for nucleation observed in some coastal areas.Recent advances in modelling allow for a kinetic treatment of the nucleation process based on measured thermochemical data for the cluster formation. Considerable improvement over the classical nucleation treatment is expected from this approach.A detailed understanding of atmospheric aerosol nucleation processes is needed as the freshly formed particles directly influence the number concentration and size distribution of the atmospheric aerosol. The formation of clouds and precipitation is affected and influences on climate are anticipated. Anthropogenic emissions influence atmospheric aerosol nucleation processes considerably.Despite the comprehensive research efforts, substantial inconsistencies remain and conflicting results of laboratory studies, model studies as well as atmospheric observations persist. Several key questions about the predictability of atmospheric nucleation in general, about the substances, that take part in nucleation and subsequent growth and about the size and composition of the critical cluster, have not been resolved so far. To cite this article: J. Curtius, C. R. Physique 7 (2006).