Fluctuating Phenomena

In the last twenty-live years of his life, Piccardi focused his research on the study of time as an essential coordinate of the dynamics of natural processes. He investigated so-called phenomena, or, rather, non-inertial evolved processes as 

From Piccardi s observations, the realization emerged that sun spots and associated phenomena have an influence upon chemical reactions [16]. One of the most important factors is the annual cycle linked to variations in the position and velocity of Earth in its helicoidal movement with respect to the galaxy, due to the combination of the elliptical movement of Earth with the rectilinear one of translation of the sun toward the constellation Hercules. In March, when Earth is on the equatorial plane and its velocity is at a maximum, the coagulation of bismuth salt is (on average) low, while it is high in September when the movement of our planet is perpendicular to the equatorial plane and Earth s velocity is at a minimum [27]. 

---

When a system is not in equilibrium, the mathematical description of fluctuations about some time-dependent ensemble average can become much more complicated than in the equilibrium case. However, starting with the pioneering work of Einstein on Brownian motion in 1905, considerable progress has been made in understanding time-dependent fluctuation phenomena in fluids. Modem treatments of this topic may be found in the texts by Keizer [21] and by van Kampen [22]. Nevertheless, the non-equilibrium theory is not yet at the same level of rigour or development as the equilibrium theory. Here we will discuss the theory of Brownian motion since it illustrates a number of important issues that appear in more general theories. 

The current frontiers for the subject of non-equilibrium thennodynamics are rich and active. Two areas dommate interest non-linear effects and molecular bioenergetics. The linearization step used in the near equilibrium regime is inappropriate far from equilibrium. Progress with a microscopic kinetic theory [38] for non-linear fluctuation phenomena has been made. Carefiil experiments [39] confinn this theory. Non-equilibrium long range correlations play an important role in some of the light scattering effects in fluids in far from equilibrium states [38, 39]. 

Lanthanides with fractional valences have II, III and IV valences, as well as mixed II/III and III/IV valences. Depending on temperature and pressure, the degree of oxidation can change. This effect may result in a change in the different properties of nanoparticles, such as the stability, heat capacity, conductivity and magnetic susceptibility [218]. Valence fluctuation phenomena have been reported to occur... 

FLUCTUATION PHENOMENA IN AN EQUILIBRIUM MICROSTRUCTURE ON METAL SURFACES... 

A characteristic feature of nonlinear science generally, and of nonlinear optics in particular, is the common necessity of having to make simplifications, and then approximations in order to solve the equations of even the simplified models. These considerations apply a fortiori to the study of fluctuation phenomena in nonlinear systems, and thus account for the increasing role being played by analog and digital simulations, which enable the behaviour of the model systems to be investigated in considerable detail. 

E. W. Montroll and J. L. Lebowitz, Fluctuation Phenomena. North-Holland, Amsterdam, 1979. 

Because the properties of liquids are essentially different from those of gases, impinging streams with liquid and gas as the continuous phases exhibit totally different performances and it is therefore necessary to discuss them separately. Part II focuses on liquid-continuous impinging streams and related problems, including the features of LIS that efficiently promote micromixing, pressure fluctuation phenomena in LIS, promotion of kinetic processes by LIS, and the application of LIS in the preparation of ultrafine particles, etc. Finally, this we will introduce some important research and development on LIS devices and look forward to the future applications of LIS. 

Microscopic foam films are most successfully employed in the study of surface forces. Since such films are small it is possible to follow their formation at very low concentrations of the amphiphile molecules in the bulk solution. On the other hand, the small size permits studying the fluctuation phenomena in thin liquid films which play an important role in the binding energy of amphiphile molecules in the bilayer. In a bilayer film connected with the bulk phase, there appear fluctuation holes formed from vacancies (missing molecules) which depend on the difference in the chemical potential of the molecules in the film and the bulk phase. The bilayer black foam film subjected to different temperatures can be either in liquid-crystalline or gel state, each one being characterised by a respective binding energy. 

J. R. Henderson and F. van Swol, On the Approach to Complete Wetting by Gas at a Liquid-Wall Interface, Mol. Phys. 56 (1985) 1313-1356 Fluctuation Phenomena at a First-Order Phase Transition, J. Phys. Condens. Matter 2 (1990) 4537-4542. 

A. van der Ziel, Fluctuation Phenomena in Semiconductors (New York Academic Press, 1959). 

E. Montroll and B. J. West, An enriched collection of stochastic processes, in Fluctuation Phenomena, E. W. Montroll and J. L. Lebowitz, eds., North Holland Personal Library, Amsterdam, 1987 1st ed. 1979. 

The evaluation of Avogadro s number given above is of course rather rough. We get a more exact method by considering fluctuation phenomena. Thus, if we take 1 cm. of a gas, we shall find exactly as many molecules in it as in another cm. , viz., at room temperature, about 10 differences of a few hundred molecules in these huge numbers are of course of no moment. It is another matter if we pass to... 

Fluctuation phenomena in ionic solutions are a subject of growing interest (49-51). However, for several reasons (48), experimental approaches to studies of conductance fluctuations in liquid phase samples are not as well established as those in the solid state. Strong electric fields that are used to measure conductance fluctuations (to produce noise in excess of the Johnson noise) cause pronounced electroosmotic and electrophoretic complications. As a result, the measurements of conductance fluctuations are usually made with a significant uncertainty factor (cited as 0.4 in reference 52). 

---