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Brownian diffusion of particles with Knudsen number large compared to one is analyzed both in equilibrium and nonequilibrium environments. For air in equilibrium it is shown, using only Newton's laws and the central limit theorem that for specular reflection of the molecules, equipartition is a consequence of the motion. For diffuse reflections the diffusion coefficient is found to depend upon the temperature of the particle and on the number of molecules reflected diffusely. This illustrates a limitation of the fluctuation-dissipation theorem. The motion of Brownian particles in air that is in thermal and translational nonequilibrium, is influenced by heat flux and viscous stress. A new force is described which is similar to that used to explain the thermophoresis effect but which depends upon the viscous stress. The solution is found to the new Fokker-Planck equation. In the generalized convective-diffusion equation, the diffusion coefficient appears as a second order tensor and contains the influence of the viscous stress tensor on diffusion.
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The work in your hand contains three main chapters, covering the chemistry of the condensed phase in the atmosphere, first, the different forms of atmospheric waters (precipitation, fog and clouds, dew), and secondly dust, now mostly termed particulate matter and, more scientifically, atmospheric aerosol. A third section treats the gases in the atmosphere. An introductory chapter covers the roots of the term atmospheric chemistry in its relations to chemistry in general and biogeochemistry as the chemistry of the climate system. Furthermore, a brief overview of understanding chemical reactions in aqueous and gaseous phase is given. It is my aim to pay respect to all persons who studied the s...
Told in detail for the first time, the birth of Sheffield Wednesday FC
Proceedings of the NATO Advanced Study Institute, Durham, New Hampshire, U.S.A., July 19-30, 1982