Fluctuations disordered system

In summary, following a fluctuation the system is initially dynamically disordered, and the flux is zero. If the flux were constrained to be zero for an intermediate time, the second entropy would be less than the first entropy of the fluctuation, and it would have decreased at a constant rate,... 

While many researchers believe that the above mentioned three ingredients for rl behavior to appear are more or less independent, we have argued since long [6] that the primary cause of RL behavior is the lattice disorder, which is at the origin of the occurrence of polar nanodomains and their fluctuations within the highly polarizable lattice. In order to describe disordered systems and to explore their basic thermodynamic behavior simple spin models are frequently used. The model Hamiltonian... 

Faivre, A., David, L., VassoUle, R., Vigier, G., Etienne, S., and Geissler, E., Electronic density fluctuations in disordered systems 1. Effect of thermal treatments bon the dynamics and local microstructure of poly(methyl methacrylate). Macromolecules, 29, 8387-8390 (1996). 

Some progress has been made in the direction of applying the thermodynamic and stochastic theory of rate processes presented here to disordered systems. In some cases [35] it is possible to construct a stochastic potential with the properties the same as that for ordered systems discussed in Chaps. 2-11. A general set of fluctuation-dissipation relations has been derived that establishes a connection between the expression of the average kinetic curve,... 

Part III explains stochastic theory and fluctuations in systems far from equilibrium, fluctuation-dissipation relations, including disordered systems. 

The Coherent Potential Approximation (CPA) of the electronic structure of a disordered system is based on the idea that the disordered system should be replaced by an effective medium. This medium has the property that the statistical average of the fluctuation from its potential (the so-called coherent potential) should be equal to zero. In other words, each site but one is replaced by an unknown coherent potential. One then puts at the reference site (see Figure 4.13) an A or a B component (in the simplest case of a binary disordered system) with respective probabilities 1 — /and /. After that one solves the problem of this single impurity imbedded in the effective medium characterized by the coherent potential, which is determined by the requirement that the average scattering (fluctuation) from the reference site is also zero. 

It is not clear what the equivalent of this pseudo-momentum would be in a disordered system like a liquid. Presumably, if the potential changes associated with the disorder are small, as it appears to be in the case of liquids similar to the rare gases heavier than Ne, the concepts developed in the case of the crystals are a good approximation. In the case of molecules that are neither spherical nor have a shape represented by one of the cubic groups, the fluctuations of the potential resulting from changes of molecular orientation can be large. 

In both cases the late stages of kinetics show power law domain growth, the nature of which does not depend on the mitial state it depends on the nature of the fluctuating variable(s) which is (are) driving the phase separation process. Such a fluctuating variable is called the order parameter for a binary mixture, tlie order parameter o(r,0 is tlie relative concentration of one of the two species and its fluctuation around the mean value is 5e(/,t) = c(r,t) - c. In the disordered phase, the system s concentration is homogeneous and the order... 

Equation (A3.3.57) must be supplied with appropriate initial conditions describing the system prior to the onset of phase separation. The initial post-quench state is characterized by the order parameter fluctuations characteristic of the pre-quench initial temperature T.. The role of these fluctuations has been described in detail m [23]. Flowever, again using the renomialization group arguments, any initial short-range correlations should be irrelevant, and one can take the initial conditions to represent a completely disordered state at J = xj. For example, one can choose the white noise fomi (i /(,t,0)v (,t, 0)) = q8(.t -. ), where ( ) represents an... 

It is, however, important to note tliat individual columns are one-dimensional stacks of molecules and long-range positional order is not possible in a one-dimensional system, due to tlieniial fluctuations and, therefore, a sliarji distinction between colj. and colj. g is not possible [20]. Phases where tlie columns have a rectangular (col. ) or oblique packing (col j of columns witli a disordered stacking of mesogens have also been observed [9, 20, 25,... 

To overcome such situations within acceptable parameters during normal operation, it has been found that an ideal series compensation is achieved at around 40-70% of X, preferably in the range of 45-60% only. The level of compensation will depend upon the expected load fluctuations and the presence of harmonic disorders in the system. 

To define the correlation functions of partly quenched systems requires one to consider fluctuations. There are two types of fluctuations thermal fluctuations for a given configuration of matrix species, and fluctuations induced by disorder. We characterize the average over disorder of thermal fluctuations by the variance... 

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