A study of radiative properties of fractal soot aggregates using the superposition T-matrix method

We employ the numerically exact superposition T-matrix method to perform extensive computations of scattering and absorption properties of soot aggregates with varying state of compactness and size. The fractal dimension, D_f, is used to quantify the geometrical mass dispersion of the clusters. The optical properties of soot aggregates for a given fractal dimension are complex functions of the refractive index of the material m, the number of monomers N_S, and the monomer radius a. It is shown that for smaller values of a, the absorption cross section tends to be relatively constant when D_f<2 but increases rapidly when D_f>2. However, a systematic reduction in light absorption with D_f is observed for clusters with sufficiently large N_S, m, and a. The scattering cross section and single-scattering albedo increase monotonically as fractals evolve from chain-like to more densely packed morphologies, which is a strong manifestation of the increasing importance of scattering interaction among spherules. Overall, the results for soot fractals differ profoundly from those calculated for the respective volume-equivalent soot spheres as well as for the respective external mixtures of soot monomers under the assumption that there are no electromagnetic interactions between the monomers. The climate-research implications of our results are discussed.     

Magnetic rotation observation of the C2b3Σg− ← a3Πu transition using a color center laser

The magnetic rotation observation of the C₂b³Σ_g^? ← a³Π_u Ballik-Ramsay system using a color center laser is reported. This is the first detection of this system in absorption. Three bands, 0 ← 1, 1 ← 2, and 2 ← 3, were identified in the spectral range 3650–4030 cm^?1. The last two bands were observed for the first time. In magnetic rotation many satellite lines (ΔN ≠ ΔJ) which would be very weak in normal absorption have been observed with intensity comparable to the main branch lines. This permits a slight improvement in the accuracy of some of the fine structure constants. A variety of lineshapes are observed for the various branches by magnetic rotation. Because the b³Σ_g^? fine structure is small, giving a partial overlap, the peak frequency of a magnetic rotation signal usually does not correspond to the center frequency of the normal absorption signal of that transition. A computer program has been written to predict magnetic rotation lineshapes and obtain the peak frequency displacements. Various observed and calculated lineshapes are displayed and compared.     

Polyèdre de Newton et distributionf + s . II

Sans résumé

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The evolution of invariant manifolds in Hamiltonian-Hopf bifurcations

We consider the evolution of the stable and unstable manifolds of an equilibrium point of a Hamiltonian system of two degrees of freedom which depends on a parameter, ν. The eigenvalues of the linearized system are complex for ν<0 and pure imaginary for ν>0. Thus, for ν<0 the equilibrium has a two-dimensional stable manifold and a two-dimensional unstable manifold, but for ν>0 these stable and unstable manifolds are gone. If the sign of a certain term in the normal form is positive then for small negative ν the stable and unstable manifolds of the system are either identical or must have transverse intersection. Thus, either the system is totally degenerate or the system admits a suspended Smale horseshoe as an invariant set.     

Differential equations over polynomially bounded o-minimal structures

We investigate the asymptotic behavior at of non-oscillatory solutions to differential equations a$">, where is definable in a polynomially bounded o-minimal structure. In particular, we show that the Pfaffian closure of a polynomially bounded o-minimal structure on the real field is levelled.

     

Construction of best Bregman approximations in reflexive Banach spaces

An iterative method is proposed to construct the Bregman projection of a point onto a countable intersection of closed convex sets in a reflexive Banach space.

     

New amicable pairs of type

A UBASIC computer program was developed to implement a method of te Riele for finding amicable pairs of type . Hundreds of new pairs were found, including a new largest pair and several ``daughter', ``granddaughter', and ``great granddaughter' pairs.

     

A nonsmooth Newton method for variational inequalities,I: Theory

This paper presents a modified damped Newton algorithm for solving variational inequality problems based on formulating this problem as a system of equations using the Minty map. The proposed modified damped-Newton method insures convergence and locally quadratic convergence under the assumption of regularity. Under the assumption ofweak regularity and some mild conditions, the modified algorithm is shown to always create a descent direction and converge to the solution. Hence, this new algorithm is often suitable for many applications where regularity does not hold. Part II of this paper presents the results of extensive computational testing of this new method.Corresponding author.     

Characterization of polycrystalline (Na,K)β/β′- alumina ceramics

K β′-alumina is unstable at >1300°C. Mixed alkali β′-alumina has a variable stability depending on the alkali ratio, [K⁺]/([Na⁺]+[K⁺]). For f(β)<[K⁺]/([Na⁺]+[K⁺]), the β′-Al₂O₃ phase decomposes to Kβ-Al₂O₃ 0997 0815 V 3 and a solid solution of Na β′-Al₂O₃ and K β′-Al₂O₃. For f(β)=[K⁺]/([Na⁺]+[K⁺], the ceramic consists of K β-Al₂O₃ and Naβ′-Al₂O₃ and for f(β)>[K⁺]/([Na⁺]+[K⁺]), the excess Na⁺ after Na β′-Al₂O₃ dissolves in the β phase, giving Na β-Al₂O₃/K β-Al₂O₃ solid solution and Na β′-Al₂O₃. These sequences were confirmed by measuring the dependence of the c-axis lattice parameters of β- and β′-Al₂O₃ phases on the f(β), and the change of these parameters during the ion-exchange of Na⁺ and K⁺ ions.     

K-line X-ray fluorescence from highly charged iron ions under dense astrophysical plasma conditions

In the present work, we report an investigation of plasma environment effects on the atomic parameters associated with the K-vacancy states in highly charged iron ions within the astrophysical context of accretion disks around black holes. More particularly, the sensitivity of K-line X-ray fluorescence parameters (wavelengths, radiative transition probabilities, and Auger rates) in Fe XVII–Fe XXV ions has been estimated for plasma conditions characterized by an electron temperature ranging from 10⁵ to 10⁷ K and an electron density ranging from 10¹⁸ to 10²² cm⁻³. In order to do this, relativistic multiconfiguration Dirac-Fock atomic structure calculations have been carried out by considering a time averaged Debye-Hückel potential for both the electron–nucleus and electron–electron interactions.