β Scribed by G Kemeny
No coin nor oath required. For personal study only.
The Langevin equation is derived for a system of interacting molecules by a double Fourier transformation of the Hamiltonian. The transformations are with respect to the molecular equilibrium positions and the deviations, respectively. The potential energy term is then the generator of mode interactions to all orders. For the regime of large anharmonicities part of the "force" is shown to be proportional to the time derivative of the momentum. This leads to the Langevin equation.
π SIMILAR VOLUMES
A free-boundary problem of describing a joint motion of two compressible fluids with different viscosities is considered. The passage to the limit is studied as the shear viscosity of one of the fluids vanishes.
The use of simplified equations utilizing the Z- and F-values to calculate the level of sterilization achieved in isothermal processes is very common in industry. This method assumes that the Z-value is independent of temperature. This is a simplifying assumption that is not based on a physically re