Far infrared absorption in ultrafine metallic particles: Calculations based on classical and quantum mechanical theories

Detailed calculations of far infrared absorption in ultrafine metallic particles are reported. Effective medium treatments of the composite of particles and their surrounding are carried out within the Maxwell Garnett and Bruggeman theories. Generalizations of these to encompass dipole-dipole interaction and oxide pellicles are discussed. The dielectric permeability of the particles is specified either by the Drude (D) model with a size limited mean free path, or by the quantum mechanical derivation of Gor'kov and Éliashberg (GE). Excepting narrow diameter (x) and frequency ( ) intervals the absorption coefficients can be approximated by =fCx , wheref is the filling factor (taken to be small),C is a constant which depends on the free electron parameters, and and are integers. Results for largerfs are included also. The magnitudes ofC, and differ in general for the Drude and Gor'kov-Éliashberg theories; they are also different forxx ^C , wherex _D ^C 5 nm andx _GE ^C is typically 20 nm. The quantityx ^c signifies a transition from a range where is dominated by the dielectric polarisation to one where the magnetic polarisation is largest. An interesting multiple peak structure is found from detailed calculations of _GE vs. for sufficiently small identical particles. Effects of log-normal size distributions are derived explicitely; any fine structure in the _GE vs.x functions is found to be completely washed out for practically attainable distribution widths.Work at Cornell University was supported by the National Science Foundation through the Materials Science CenterWork at Chalmers University of Technology was supported by the Swedish Natural Science Research Council     

Toward the spectrum of free polyethylene: linear alkanes studied by carbon 1s photoelectron spectroscopy and theory

Trends in carbon 1s ionization energies for the linear alkanes have been investigated using third-generation synchrotron radiation. The study comprises CH(4), C(2)H(6), C(3)H(8), C(4)H(10), C(5)H(12), C(6)H(14), and C(8)H(18). Both inter- and intramolecular shifts in ionization energy have been determined from gas-phase spectra and ab initio calculations. The shifts are decomposed into initial-state and final-state contributions and are shown to relate to the fundamental chemical properties of group electronegativity and polarizability. By extrapolation, we predict C1s spectra of larger n-alkanes, converging toward isolated strands of polyethylene.     

Improving worst-case behavior of heaps

It is possible to improve the worst-case behavior of operations on heaps, when counting number of comparisons between elements in the heap, by modifying the traditional binary heap. The improvement suggested is the use of a heap with scattered leaves. This method can be combined with the use of a ternary heap for even greater improvement.Some other improvements of worst-case behavior compared to standard algorithms are discussed at the end of the paper, where the gain of at least (N-2) comparisons when sortingN elements with HEAPSORT is of great interest in implementations. An algorithm for inserting a new element in a heap inO(log logn) comparisons between elements is mentioned.     

Asymptotic normality of fringe subtrees and additive functionals in conditioned Galton–Watson trees

We consider conditioned Galton–Watson trees and show asymptotic normality of additive functionals that are defined by toll functions that are not too large. This includes, as a special case, asymptotic normality of the number of fringe subtrees isomorphic to any given tree, and joint asymptotic normality for several such subtree counts. Another example is the number of protected nodes. The offspring distribution defining the random tree is assumed to have expectation 1 and finite variance; no further moment condition is assumed. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 48, 57–101, 2016     

Solvent effect of alcohols at the L-edge of iron in solution: X-ray absorption and multiplet calculations

The local electronic structure of Fe(III) and Fe(II) ions in different alcohol solutions (methanol, ethanol, propan-1-ol) is investigated by means of soft X-ray absorption spectroscopy at the iron L 2,3-edge. The experimental spectra are compared with ligand field multiplet simulations. The solvated Fe(III) complex is found to exhibit octahedral symmetry, while a tetragonal symmetry is observed for Fe(II). A decrease in the solvent polarity increases the charge transfer from the oxygen of the alcohol to the iron ions. This conclusion is supported by Hartree-Fock calculations of the Mulliken charge distribution on the alcohols. A larger charge transfer is further observed from the solvent to Fe(III) compared to Fe(II), which is connected to the higher positive charge state of the former. Finally, iron ions in solution are found to prefer the high-spin configuration irrespective of their oxidation state.     

Complexes of Graphs with Bounded Matching Size

For positive integers k,n, we investigate the simplicial complex of all graphs G on vertex set [n] such that every matching in G has size less than k. This complex (along with other associated cell complexes) is found to be homotopy equivalent to a wedge of spheres. The number and dimension of the spheres in the wedge are determined, and (partially conjectural) links to other combinatorially defined complexes are described. In addition we study for positive integers r,s and k the simplicial complex of all bipartite graphs G on bipartition such that there is no matching of size k in G, and obtain results similar to those obtained for . S. Linusson and V. Welker supported by EC’s IHRP program through grant HPRN-CT-2001-00272. J. Shareshian partially supported by National Science Foundation grants DMS-0070757 and DMS-0030483.     

On Edge Exchangeable Random Graphs

We study a recent model for edge exchangeable random graphs introduced by Crane and Dempsey; in particular we study asymptotic properties of the random simple graph obtained by merging multiple edges. We study a number of examples, and show that the model can produce dense, sparse and extremely sparse random graphs. One example yields a power-law degree distribution. We give some examples where the random graph is dense and converges a.s. in the sense of graph limit theory, but also an example where a.s. every graph limit is the limit of some subsequence. Another example is sparse and yields convergence to a non-integrable generalized graphon defined on \((0,\infty )\).     

Molecular-field splitting in S2p photoelectron spectra of dimethyl sulfide and sulfur dichloride

High-resolution S2p photoelectron spectra have been measured for sulfur dichloride and dimethyl sulfide. By means of efficient fitting procedures and theoretical analyses, the vibrational fine structure has been disentangled from the molecular-field induced splitting of the S2p_3/2 core-ionized level. The resulting molecular-field splitting is determined to be 177 meV in the case of SCl₂ and 104 meV for (CH₃)₂S. Ab initio calculations that include core–valence electron correlation are able to reproduce these values to within 3 meV. Theoretical predictions of the molecular-field splitting are presented for a series of related sulfur compounds, SX₂, where X=H, NH₂, CN, and F.     

Orthogonal signal correction, wavelet analysis, and multivariate calibration of complicated process fluorescence data

In this paper, multivariate calibration of complicated process fluorescence data is presented. Two data sets related to the production of white sugar are investigated. The first data set comprises 106 observations and 571 spectral variables, and the second data set 268 observations and 3997 spectral variables. In both applications, a single response, ash content, is modelled and predicted as a function of the spectral variables. Both data sets contain certain features making multivariate calibration efforts non-trivial. The objective is to show how principal component analysis (PCA) and partial least squares (PLS) regression can be used to overview the data sets and to establish predictively sound regression models. It is shown how a recently developed technique for signal filtering, orthogonal signal correction (OSC), can be applied in multivariate calibration to enhance predictive power. In addition, signal compression is tested on the larger data set using wavelet analysis. It is demonstrated that a compression down to 4% of the original matrix size — in the variable direction — is possible without loss of predictive power. It is concluded that the combination of OSC for pre-processing and wavelet analysis for compression of spectral data is promising for future use.     

Reverse juggling processes

Knutson introduced two families of reverse juggling Markov chains (single and multispecies) motivated by the study of random semi‐infinite matrices over . We present natural generalizations of both chains by placing generic weights that still lead to simple combinatorial expressions for the stationary distribution. For permutations, this is a seemingly new multivariate generalization of the inversion polynomial.