Case of a Boltzmann gas leading to the Smoluchowski coagulation equation

A special model of a rarefied hard-sphere gas is considered. The hard-sphere particles undergo absolutely elastic collisions. It is assumed that particles can collide only if their nonzero velocities are orthogonal to each other. The model makes it possible to proceed from the Boltzmann equation to the Smoluchowski coagulation equation, where coagulation means that the kinetic energies of the colliding particles are added. A Monte Carlo scheme for simulation of the phenomenon is described, and the convergence of the simulation algorithm is proved. The convergence of numerical results to exact solutions of the Smoluchowski equation and to finite-difference solutions is tested.     

X-ray metrology for advanced silicon processes

X-ray reflectivity (XRR), X-ray fluorescence (XRF) and small angle X-ray scattering (SAXS) techniques are used to the monitoring of Cu/porous low κ processes, which are developed for the next generation (≤65 nm) integrated circuits. Sensitivity of XRR and XRF is sufficient to detect drifts of the copper barrier layer, copper seed layer and Cu CMP (chemical-mechanical polishing) processes. Their metrology key parameters comply with production requirements. SAXS allows determining the pore structure of low κ films: average pore size and pore size distribution.     

Density functional theory study on antiferromagnetic interactions in a silver (I) complex of nitronyl nitroxide

A one-dimensional (1D) silver (I) complex of nitronyl nitroxide with fairly strong antiferromagnetic interaction, in which the metal ions are diamagnetic, is investigated by means of the ab initio crystal orbital method based on the density functional theory. The calculated values of the magnetic coupling constant (J) are close to the experimental measured J value in the periodic system. The magneto-structural correlation reveals that the existence of an antiferromagnetic coupling pathway along nitronyl nitroxide units via silver (I) ion in this system. The spin population distribution also shows the existence of spin delocalization along the ONCNO–Ag–ONCNO, which affords a rational interpretation for the antiferromagnetic interaction mechanism.     

Ba(Zr0.3Ti0.7)O3 铁电薄膜的制备

介绍了用溶胶-凝胶法(sol-gel)在Pt/Ti/SiO2/Si衬底和石英衬底上制备Ba(Zr0.3Ti0.7)O3铁电薄膜的基本原理、工艺过程及工艺特点;Sol-gel制备的Ba(Zr0.3Ti0.7)O3铁电薄膜表面平整、厚度均匀.     

An approximate solution to the integral radiative transfer equation in an optically thick slab

We consider the problem of solving the integral form of the radiative transfer equation in an atmosphere with optical thickness τ₀?1. We propose two methods transforming this problem to a finite set of the independent problems of the same type set in an atmosphere with optical thickness much less then τ₀. The error estimates are derived. Copyright © 2007 John Wiley & Sons, Ltd.     

A Fubini theorem

Let I₀ be the σ-ideal of subsets of a Polish group generated by Borel sets which have perfectly many pairwise disjoint translates. We prove that a Fubini-type theorem holds between I₀ and the σ-ideals of Haar measure zero sets and of meager sets. We use this result to give a simple proof of a generalization of a theorem of Balcerzak-Ros?anowski-Shelah stating that I₀ on N² strongly violates the countable chain condition.     

带干扰的Erlang(2)风险模型的不破产概率

本文讨论了带干扰的Erlang(2)风险模型,通过构造一个延迟更新过程,我们得到了不破产概率满足的积分-微分方程,进而得到了不破产概率的明确表达式．     

Nonlinear Cauchy problems with small analytic data

We study the lifespan of solutions to fully nonlinear Cauchy problems with small real- or complex-analytic data. Our proofs are based on the method of majorants and the fixed point theorem for a contraction mapping.

     

Pressure-Induced Shifts of R1 and R2 Lines of YAG:Cr3+

By means of improved ligand-field theory, the "pure electronic" pressure-induced shifts (PS's) and the PS's due to electron-phonon interaction (EPI) of R1 line and R2 line of YAG:Cr3 have been calculated, respectively.The calculated results are in very good agreement with the experimental data. It is demonstrated that the admixture of |t22(3T1)e4T2> and |t322E> bases in the wavefunction of R1 level of YAG:Cr3 and its change with pressure play a key role for the PS of R1 line. The behaviors of the "pure electronic" PS of R1 line and the PS of R1 line due to EPI are different. It is the combined effect of them that gives rise to the total PS of R1 line, which has satisfactorily explained the experimental results. The systematic analyses and comparisons between the feature of R1-line PS of YAG:Cr3 and the ones of three laser crystals (GSGG:Cr3 , GGG:Cr3 and ruby) have been made, and the origin of the difference between them has been revealed.