Anomalous diffusion temperature

Do we expect this model to be accurate for a dynamics dictated by Tsallis statistics A jump diffusion process that randomly samples the equilibrium canonical Tsallis distribution has been shown to lead to anomalous diffusion and Levy flights in the 5/3 < q < 3 regime. [3] Due to the delocalized nature of the equilibrium distributions, we might find that the microstates of our master equation are not well defined. Even at low temperatures, it may be difficult to identify distinct microstates of the system. The same delocalization can lead to large transition probabilities for states that are not adjacent ill configuration space. This would be a violation of the assumptions of the transition state theory - that once the system crosses the transition state from the reactant microstate it will be deactivated and equilibrated in the product state. Concerted transitions between spatially far-separated states may be common. This would lead to a highly connected master equation where each state is connected to a significant fraction of all other microstates of the system. [9, 10]... 

Criteria 1-3 are the cardinal characteristics of Fickian diffusion and disregard the functional form of D(ci). Violation of any of these is indicative of non-Fickian mechanisms. Criterion 4 can serve as a check if the D(ci) dependence is known. As mentioned, it is crucial that the sorption curve fully adhere to Fickian characteristics for a valid determination of D from the experimental data. At temperatures well above the glass transition temperature, 7 , Fickian behavior is normally observed. However, caution should be exercised when the experimental temperature is either below or slightly above 7 , where anomalous diffusion behavior often occurs. 

In this chapter, we have showed that a particle undergoing normal or anomalous diffusion constitutes a system conveniently allowing one to illustrate and to discuss the concepts of FDT violation and effective temperature. Our study was carried out using the Caldeira-Leggett dissipation model. Actually this model, which is sufficiently versatile to give rise to various normal or anomalous diffusion behaviors, constitutes an appropriate framework for such a study, in quantum as well as in classical situations. 

It is shown that the applicability of fractal model of anomalous diffusion for quantitative description of thermogravimetric analysis results in case of high density polyethylene modified by high disperse mixture Fe/FeO (Z). It is shown the influence of diffusion type on the value of sample 5%-th mass loss temperature and was offered structural analysis of this effect. The critical content Z it is determined, at which degradation will be elapse so, as in inert gas atmosphere. 

Since translational diffusion process is sensitive to the microscopic structure in the solution, understanding the diffusion provides an important insight into the structure as well as the intermolecular interaction. Therefore, dynamics of molecules in solution have been one of the main topics in physical chemistry for a long time. 1 Recently we have studied the diffusion process of transient radicals in solution by the TG method aiming to understand the microscopic structure around the chemically active molecules. This kind of study will be also important in a view of chemical reaction because movement of radicals plays an essential role in the reactions. Here we present anomalous diffusion of the radicals created by the photoinduced hydrogen abstraction reaction. The origin of the anomality is discussed based on the measurments of the solvent, solute size, and temperature dependences. 

Latora et al. [18] discussed a relation between the process of relaxation to equilibrium and anomalous diffusion in the HMF model by comparing the time series of the temperature and of the mean-squared displacement of the phases of the rotators. They showed that anomalous diffusion changes to a normal diffusion after a crossover time, and they also showed that the crossover time coincides with the time when the canonical temperature is reached. They also claim that anomalous diffusion occurs in the quasi-stationary states. 

There seems to be a general consensus [282—285] that this is a non-reactive interface, i.e. while Ag might be chemically bonded to Si, the interface is essentially planar with no dissociation of the semiconductor and no anomalous diffusion. However, no definitive results have been reported to support this belief and there is evidence which suggests the formation of a silicide phase at room temperature [283]. 

In the course of the past decade several explanations have been put forward to account for the anomalous diffusion in bcc metals. The different models based on the presence of extrinsic vacancies (Kidson, 1963), on the temperature dependence of elastic constants (Aaronson and Shewmon, 1967), on dislocation enhanced diffusion (Peart and Askill, 1967) or on vacancy anharmonicity (Gilder and Lazarus, 1975) have been thoroughly discussed in the original and in the various review papers. Two additional models, the activated interstitial and, more recently, the w-embryo model, have been proposed as alternative explanations for anomalous bcc diffusion. These two models and their possible common interpretation on the basis of the Engel-Brewer electron correlation theory will be discussed in the next sub-section. 

In a more recent study, Muller-Plathe, Rogers, and van Gunsteren have pointed out a case of anomalous diffusion in polyisobutylene near room temperature [48], in harmony with the findings by TSA for gas motion in dense polymers [56]. For He in PIB, anomalous behavior could be clearly shown, and the transition to normal diffusion at around 0.1 ns could be captured. The log-log plot that shows this crossover, is reproduced in Fig. 6. For the much slower diffusing O2, the mean-square displacement data were not accurate enough to determine unambiguously if the curve represented diffusive behavior... 

The diffusion of liquid crystals into polymers is particularly intriguing given that the liquid crystal may be in an organized state or an isotropic state depending on the temperature. The diffusion of a liquid crystal (5CB) into a PBMA matrix was studied by using the contact method to prepare a gradient [114]. Concentration profiles were obtained as a function of time and temperature. The presence of an anomalous diffusion process was detected. It was shown that fast FTIR was able to correctly identify the diffusion process as anomalous. As opposed to this, a bulk... 

In contrast, at temperatures below Tg, we have the so-called Case II and Super Case II transport, the other extreme, in which diffusion is very rapid compared with simultaneous relaxation processes. Sorption processes may be complicated by a strong dependence on swelling kinetics. Finally we have anomalous diffusion, which occurs when the diffusion and relaxation rates are comparable. 

If we consider a simple liquid (e.g., Lennard-Jones liquid) and trace the diffusion along an isotherm, we find that the diffusion decreases under densification. This observation is intuitively clear If density increases, the free volume decreases and the particles have less freedom to move. However, some substances have a region in density temperature plane where diffusion grows under densification. This is called anomalous diffusion region that reflects the contradiction of this behavior with the free volume picture already described. This means that diffusion anomaly involves more complex mechanisms, which will be discussed in the following. 

For both a = 2.1 and a = 3.3, in the reentrant-fluid region coexisting with the bcc solid, a density anomaly occurs, that is, the number density decreases upon cooling at constant pressure. This region is bounded from above by the temperature of the maximum density line (see Figs. 4 and 5). Similarly to water, the region of density anomaly is encompassed by the region of anomalous diffusion that in turn is enclosed by that of structural anomaly. A compendium of anomalous behaviors of the YK system with a = 3.3 is shown in Fig. 6. 

---