Jeans length

On small scales, these sources of pressure determine the evolution of perturbations. Consider once again Eq. 10.10. When the wavenumber k > kj, or conversely when the wavelength is smaller than the Jeans length, pressure dominates over gravity and the fluid oscillates with angular frequency u csk. The detailed solution actually involves Bessel functions when expansion is correctly taken into account, and there are additional complications due to gravitational interactions with any pressureless component such as CDM which can continue to collapse. 

Before recombination, the radiation pressure is so great that the Jeans length is greater than the horizon size, and so no perturbations within the horizon can grow they can only oscillate as sound waves. Conversely, after recombination, the pressure drops precipitously and all of a sudden, perturbations within the horizon can grow. 

Although we modern chemists go to some lengths to let the public know that we play tennis, like fast cars and stylish clothes, and are down-to-earth social-mixer types, we must admit that our passion for smelly, smoky mixtures will likely get us booted from most respectable country clubs. Henry Cavendish (1731-1810) was definitely an unworldly type. He lived with his father until the latter died in 1783, did not marry, communicated with his housekeeper using daily notes, and dressed in shabby, outdated clothing despite Inheriting a fortune when he was 40. The French physicist Jean-Baptiste Biot described him as the richest of all learned men, and very likely also the most learned of all the rich. ... 

We now have experimental values for both the constants a and b occurring in (6). It only remains to compare the limiting form of (6) for long wave lengths and high temperatures with the dassical Rayleigh-Jeans formula. From (6) we have... 

The dimensionless group ud/Dsx is called the axial Peclet number for mass Pem.ax (named after Jean Claude Peclet, see box), and d is a characteristic length. For empty tubes, d is the tube diameter dt, and for packed beds the particle diameter dp is mostly used. 

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