Fluctuating phases

One also finds that fixing the director generates a new equilibrium ensemble where the Green-Kubo relations for the viscosities are considerably simpler compared to the conventional canonical ensemble. They become linear functions of time correlation function integrals instead of rational functions. The reason for this is that all the thermodynamic forces are constants of motion and all the thermodynamic fluxes are zero mean fluctuating phase functions in the constrained ensemble. 

X) and (1/2)V x u - The bulk viscosity is rjy. Note that the numerical values of these viscosities are different from those in Section 4. Therefore we have primed these viscosities. In order to find simple fluctuation relations for them we have to use an ensemble where the thermodynamic forces are constants of motion and the fluxes are zero mean fluctuating phase functions. This can be done if both the director angular velocity and the streaming angular... 

Ohmine and M. Sasai, Prog. Theor. Phys. Supplement, 103, 61 (1991). Relaxations, Fluctuations, Phase Transitions and Chemical Reactions in Liquid Water. 

NIE Nies, E., Ramzi, A., Berghmans, H., Li, T., Heenan, R.K., and King, S.M., Composition fluctuations, phase behavior, and complex formation in poly(vinyl methyl ether)/D20 investigated by small-angle neutron scattering. Macromolecules, 38, 915, 2005. 

For a laser with a fluctuating phase, the simulation procedure is similar to that of the collision. Several models may be assumed for the stochastic phase fluctuations. In this calculation we have assumed a random jump between 0 and 2ir with no memory of the previous phase. This is a model of Markovian "hard" phase jumps, which is different than the phase diffusion model assumed in our analytic work. This model may be applicable for actual lasers suffering from acoustic mirror jitter or other mundane laboratory noises. 

The phonon spectrum is one of the fundamental characteristics of crystals. The behavior of phonon dispersion branches reflects specific features of the crystal structure and the interatomic interactions, and therefore gives the most comprehensive and detailed information about the dynamical properties of crystals. Phonons are straightforward signatures of bond lengths and chemical species, and phonon parameters can be used to obtain information on strain, alloy composition, freedevice structures. Phonon mode parameters can be also used to study compositional fluctuations, phase mixing, interface morphologies, as well as defects and impurities. To use the phonons as a gauge and tool to extract information on material properties and characteristics, it is mandatory to establish first the phonon mode behavior. 

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