Theory of fluctuation

As a result of long-range fluctuations, the local density will vary with position in the classical Landan-Ginzburg theory of fluctuations this introdnces a gradient tenn. A Ginzburg number N is defined (for a... 

According to the thermodynamic theory of fluctuations, the mean-square concentration fluctuation is given - by... 

Andersen, H. C. Diagrammatic Formulation of the Kinetic Theory of Fluctuations in Equilibrium Classical Fluids. III. Cluster Analysis of the Renormalized Interactions and a Second Diagrammatic Representation of the Correlation Functions. J. Phys. Chem. B 2003, 107, 10234-10242. 

However, even a less radical theory of discounting than the hyperbolic theory can solve the difficulties of Becker and Murphy s addiction theory. It is sufficient to assume that people s rate of discounting typically fluctuate unsystematically over time and that people are therefore not always equally farsighted. The theory of fluctuating discount functions postulate that people discount the future recursively and that they base their judgments on realistic expectations about their own future mental states. Hence, this theory can be seen as a straightforward extension of classical rational choice theory. Still, these consu-... 

In the Lyapunov classification they are called stable but not asymptotically stable . In the theory of fluctuations it is more natural to classify this case as unstable, pursuant to the footnote in X.3. 

A powerful tool for analyzing fluctuations in a nonequilibrium systems is based on the Hamiltonian [57] theory of fluctuations or alternatively on a path-integral approach to the problem [44,58-62]. The analysis requires the solution of two closely interrelated problems. The first is the evaluation of the probability density for a system to occupy a state far from the stable state in the phase space. In the stationary regime, the tails of this probability are determined by the probabilities of large fluctuations. 

We emphasize that the question of stability of a CA under small random perturbations is in itself an important unsolved problem in the theory of fluctuations [92-94] and the difficulties in solving it are similar to those mentioned above. Thus it is unclear at first glance how an analogy between these two unsolved problems could be of any help. However, as already noted above, the new method for statistical analysis of fluctuational trajectories [60,62,95,112] based on the prehistory probability distribution allows direct experimental insight into the almost deterministic dynamics of fluctuations in the limit of small noise intensity. Using this techique, it turns out to be possible to verify experimentally the existence of a unique solution, to identify the boundary condition on a CA, and to find an accurate approximation of the optimal control function. 

V. Kinetic Theory of Fluctuations in Partially Ionized Plasmas References... 

V. KINETIC THEORY OF FLUCTUATIONS IN PARTIALLY IONIZED PLASMAS... 

In this section we want to deal with the kinetic theory of fluctuations in partially ionized plasmas. 

The theory of fluctuations in partially ionized plasmas may be developed in full analogy to the fluctuation theory of gases or fully ionized plasmas. The latter is developed in detail in Refs, 5, 12, and 28. 

Yu. L. Klimontovich, Kinetic theory of fluctuations in gases and plasmas, in Fundamental Problems in Statistical Mechanics IV, E. G. D. Cohen and W. Fizdon, (eds). Warsaw, 1978. 

Ericson, T. (1963). A theory of fluctuations in nuclear cross sections, Ann. Phys. 23, 390 14. 

Bratkovsky AM, Marais SC, Heine V, Salje EKH (1994c) The theory of fluctuations and texture embryos in stractural phase transitions mediated by strain. J Phys Condens Matter 6 3679-3696... 

Investigation of the Brownian motion of dispersed particles made it possible to experimentally verify the theory of fluctuations, also formulated by Einstein and Smoluchowski. Svedberg s observations of Brownian motion indicated that the number of particles confined within a small... 

The necessary condition for spontaneous formation of disperse system and condition of its equilibrium with a macroscopic phase can be also obtained by utilizing the concepts of theory of fluctuations. This may be conveniently illustrated by the example of a highly mobile interface, such as liquid - liquid or liquid-vapor. The surface of liquid is not completely flat thermal fluctuations result in the appearance of capillary waves. It was shown by L. Mandelshtam (1914) that in the vicinity of critical point, e.g. around the temperature corresponding to a complete mixing of two liquids, the interface acquires substantial... 

In agreement with the general theory of fluctuations (see Chapter V), the average value for the squared radius of such fluctuations, r2, is determined by the second derivative of the work of fluctuation with respect to the fluctuating parameter, i.e., with respect to radius in the present case ... 

Besides active research he very much enjoys teaching. In the Physical-Technical Institute of Moscow he taught (1966-1992) general courses on Molecular Dynamics and Chemical Kinetics. In the Technion (since 1992) he has taught and still teaches graduate courses on different subjects Advanced Quantum Chemistry, Theory of Molecular Collisions, Kinetic Processes in Gases and Plasma, Theory of Fluctuations, Density Matrix Formalisms in Chemical Physics etc. 

Now, we consider the important limit of weak laser intensity. In this limit, the Wiener-Khintchine theorem relating the line shape to the one-time correlation function holds. As we shall show now, a three-time correlation function is the central ingredient of the theory of fluctuations of SMS in this limit. In Appendix B, we perform a straightforward perturbation expansion with respect to the Rabi frequency Q in the Bloch equation, Eq. (4.6), to find... 

The theory of fluctuation deals with the problem that a system far from equilibrium could move away from the direction of equilibrium for a short time, which is in contrast to the second law [12, 13]. The fluctuation theorem is also connected to the phenomenological formalism of reaction kinetics, in particular, to unimolecular reactions [14]. The fluctuation theorem predicts appreciable and measurable violations of the second law of thermodynamics for small systems over short time scales. 

Chapter 5. Projection Operator Techniques in the Theory of Fluctuations... 

O Connell, J. P. 1981. Thermodynamic properties of solutions and the theory of fluctuations. Fluid Phase Equilibria. 6, 21. 

The molecular theory of fluctuations and Brownian motion offers a generalization of the Langevin equations. These equations provide a set of equations of motion that are stochastic in nature and that can be modeled on the basis of phenomenology. For example the velocity of the yth Brownian particle in solution is described by the equation of motion... 

As a result of the long-range critical fluctuations, the local density will actually be a function of the position r. In the classical theory of fluctuations such a spatial dependence is accounted for by the presence of a gradient term (Vp) in the local Helmholtz-energy density which has an expansion of the form [11]... 

Nicolis, G., Allen, P. Van Nypelseer, A. (1974). Some remarks on the theory of fluctuations around nonequilibrium states. Prog. Theor. Phys., 52, 1481-97. 

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