Spectroscopic investigations and luminescence spectra of Nd and Dy doped different phosphate glasses

Spectral properties of Nd³⁺ and Dy³⁺ ions in different phosphate glasses were studied and several spectroscopic parameters were reported. Covalency of rare-earth-oxygen bond was studied in these phosphate glass matrices with the variation of modifier in host glass matrix. Using Judd-Ofelt intensity parameters (Ω₂, Ω₄ and Ω₆), radiative transition probabilities (A) and radiative lifetimes (τ_R) of certain excited states of Nd³⁺ and Dy³⁺ ions are estimated in these glass matrices. From the magnitudes of branching ratios (β_R) and integrated absorption cross-sections (Σ), certain transitions of both the ions are identified for laser excitation. From the emission spectra, peak stimulated emission cross-sections (σ_P) are evaluated for the emission transitions observed in all these phosphate glass matrices for both Nd³⁺ and Dy³⁺ ions.     

Effect of aggregation on the absorption cross-section of fractal soot aggregates and its impact on LII modelling

This study concerns the effect of particle aggregation on laser heating rate of soot aggregates in laser-induced incandescence. Three aggregate absorption models were investigated: the Rayleigh-Debye-Gans approximation, the electrostatics approximation, and the numerically exact generalized multi-sphere Mie-solution method. Fractal aggregates containing 5-893 primary particles of 30 nm in diameter were generated numerically using a combined particle-cluster and cluster-cluster aggregation algorithm with specific fractal parameters typical of soot. The primary particle size parameters considered are 0.089, 0.177, and 0.354. The Rayleigh-Debye-Gans approximation neglects the effect of particle aggregation on absorption; so it underestimates the aggregate absorption cross-section area by approximately 10%, depending on the aggregate size and primary particle size parameter. The electrostatics approximation is somewhat better than the Rayleigh-Debye-Gans approximation, but cannot account for the effect of primary particle size parameter. The aggregate absorption submodel affects the calculated soot temperature in laser-induced incandescence mainly in the low laser fluence regime. At high laser fluences, the effect diminishes due to the enhanced importance of soot sublimation cooling and neglect of aggregation effect in the sublimation in the present numerical model of laser-induced incandescence.     

Multiscaling analysis of a slowly varying anaerobic digestion model

We construct the slowly varying limiting state solutions to a nonlinear dynamical system for anaerobic digestion with Monod-based kinetics involving slowly varying model parameters arising from slow environmental variation. The advantage of these approximate solutions over numerical solutions is their applicability to a wide range of parameter values. We use these limiting state solutions to develop analytic approximations to the full nonlinear system by applying a multiscaling technique. The approximate solutions are shown to compare favorably with numerical solutions.     

Wavelet expansions and asymptotic behavior of distributions

We develop a distribution wavelet expansion theory for the space of highly time-frequency localized test functions over the real line S₀(R)⊂S(R) and its dual space , namely, the quotient of the space of tempered distributions modulo polynomials. We prove that the wavelet expansions of tempered distributions converge in . A characterization of boundedness and convergence in is obtained in terms of wavelet coefficients. Our results are then applied to study local and non-local asymptotic properties of Schwartz distributions via wavelet expansions. We provide Abelian and Tauberian type results relating the asymptotic behavior of tempered distributions with the asymptotics of wavelet coefficients.     

On the exponential exponents of discrete linear systems

In this paper we introduce the concepts of exponential exponents of discrete linear time varying systems. It is shown that these exponents describe the possible changes in the Lyapunov exponents under perturbation decreasing at infinity at exponential rate. Finally we present formulas for the exponential exponents in terms of the transition matrix of the system.     

ND阵列加权乘积和的完全收敛性

设（Xni：1≤i≤n,n≥1）为行间ND阵列,g（x）是R^＋上指数为α的正则变化函数,{αni：1≤i≤n,n≥1}为满足条件max1≤i≤n｜ani｜=0（（g（n））^-1）的实数阵列．本文采用截尾的方法,得到了使ND随机变量阵列加权乘积和完全收敛的条件,并推广了以前学者的结论．     

温度对β胡萝卜素结构有序的影响

本文测量了全反式β胡萝卜素在二甲基亚砜中81–25 ℃ 范围的紫外–可见吸收和拉曼光谱. 结果表明, 随温度降低, 紫外–可见吸收光谱、拉曼光谱都发生红移, 拉曼光谱线型变窄, 散射截面增加这些现象的发生是由于随温度降低, β胡萝卜素分子的热无序降低、分子结构有序性增加、π电子离域扩展, 有效共轭长度增加, 分子的电子能隙变窄. 另外, 随着温度的降低, 溶剂密度增加, 由Lorentz-Lorenz 关系得知相伴的折射率增加, 从而引起吸收光谱的红移. CC键键长增加, 使CC 键拉曼光谱红移; 振动弛豫时间变长, 各CC 键之间的键长差减小, 线宽变窄; 但由于声子, π电子耦合加强使CC键拉曼线型不对称程度增加, 低频端"肩"扩展, CC键的弱阻尼相干振动增加, 使拉曼散射截面增加. 关键词： β胡萝卜素 分子结构有序 红移 拉曼散射截面     

A comparative study of ion-induced damages in C60 and C70 fullerenes

The stability of fullerenes (C₆₀ and C₇₀) under swift heavy ion irradiation is investigated. C₆₀ and C₇₀ thin films were irradiated with 120 MeV Ag ions at fluences from 1×10¹² to 3×10¹³ ions/cm². The damage cross-section and radius of damaged cylindrical zone were found to be higher for C₆₀ than C₇₀ as evaluated by Raman spectroscopy, which shows that the C₇₀ molecule is more stable under energetic ion impact. The higher damage cross-section of the C₆₀ molecule compared with that of the C₇₀ molecule is explained on the basis of thermal conductivity in the framework of the thermal spike model. The surface morphology of pristine C₆₀ and C₇₀ films is studied by atomic force microscopy. UV-visible absorption studies revealed that band gap for C₆₀ and C₇₀ fullerenes thin films decreases with increasing ion fluence. Resistivity of C₆₀ and C₇₀ thin films decreases with increasing ion fluence but the decrease is faster for C₆₀ than C₇₀, indicating higher damage in C₆₀. Irradiation at a fluence of 3×10¹³ ions/cm² results in complete damage of fullerenes (C₆₀ and C₇₀) into amorphous carbon.