System, description state/patterns

Under non-equilibrium conditions, some nonlinear phenomena such as oscillation, chaos and stationary pattern occur are a result of the loss of stability by the steady states, caused by the feedback loops in the processes determining the dynamics of such systems. Such self-organization can be obvious itself as a function of either only time coordinate including simultaneous oscillations of the entire system s state or only spatial coordinate including Turing stmctures or both coordinates including both traveling and chemical waves. The universal fact discovered of such phenomenon in different systems is remarkable in the context of mathematical description. 

Ray Kapral came to Toronto from the United States in 1969. His research interests center on theories of rate processes both in systems close to equilibrium, where the goal is the development of a microscopic theory of condensed phase reaction rates,89 and in systems far from chemical equilibrium, where descriptions of the complex spatial and temporal reactive dynamics that these systems exhibit have been developed.90 He and his collaborators have carried out research on the dynamics of phase transitions and critical phenomena, the dynamics of colloidal suspensions, the kinetic theory of chemical reactions in liquids, nonequilibrium statistical mechanics of liquids and mode coupling theory, mechanisms for the onset of chaos in nonlinear dynamical systems, the stochastic theory of chemical rate processes, studies of pattern formation in chemically reacting systems, and the development of molecular dynamics simulation methods for activated chemical rate processes. His recent research activities center on the theory of quantum and classical rate processes in the condensed phase91 and in clusters, and studies of chemical waves and patterns in reacting systems at both the macroscopic and mesoscopic levels. 

During the Diels-Alder reaction [1] and in the electrocyclization of cis-1,3,5-hexatriene [2], bonds break and form in a homolytic fashion, with orbitals remaining associated with the same centres throughout the reaction. For such systems, there is a major recoupling of the electron spins. This last takes place most rapidly at or near the transition state. The resonance pattern, taken together with other characteristics, is reminiscent of the spin-coupled description... 

The first part eoncerns the generation of the residuals (waved pattern in the Figure 1). In order to obtain an observer of the physical system, a real-time simulation is done in parallel. So, a eomplete state of the system will be available at any time. Thus, it is based on the eomparison between the predicted behavior obtained thanks to the simulation of the reference model (values of state variables) and the real observed behavior (measurements from the process correlated thanks to the Extended Kalman Filter). The main idea is to reconstruct the outputs of the system from the measurement and to use the residuals for fault detection (Mehra and Peschon, 1971, Welch and Bishop, 1995, Simani and Fantuzzi, 2006). A description of the extended Kalman filter ean be found in (Olivier-Maget et al., 2007). Besides the residual is defined aeeording to the following equation ... 

The microscope spectrophotometer system in routine use at the TRL is described in reference (7), so no details of the apparatus and its use are given here. Instead a brief description of the reason for developing and continually refining the microscope spectrophotometer facility will be presented. Historically the way to characterize a solid-state sample of a transplutonium element has been by standard X-ray powder diffraction analysis. When a systematic study of element 99, einsteinium, was undertaken, it was found that obtaining useful diffraction data from Es-containing materials was a very difficult, if not an impossible, task (22). The intensely radioactive Es-253 not only caused rapid blackening of the film used to record the diffraction pattern, but more importantly, it degraded the crystallinity of the sample. 

In many cases, the performance of a combustion system can be quantified in terms of a few parameters, such as oxygen concentration and temperature of flue gases, pollutant emissions, steam production, and so on. However, these data may not be enough to describe the actual state of the combustion process. A clear example is the case of multiburner chambers, where global values do not represent necessarily the conditions at individual flames. Even for a single burner, bulk parameters (e.g., flue gas composition) can only afford a limited characterization of the flame. As it was pointed out in the introduction, a detailed description would require a vast amount of information in terms of the distributions in space (and maybe time) of many physicochemical variables. Imaging techniques are most valuable tools in this respect, since information on spatial patterns can be very helpful to describe, or even understand, important characteristics of a flame. 

Reliable characterization and description of sleeping and waking states of infants offer the potential for assessment of the functional integrity of the central nervous system (CNS) (1). As a basis for our work, the premise has been that because the phospholipids of the nervous system are characterized by high concentrations of docosahexaenoic acid (DHA), assessment of the sleep-wake states offers an instrument for defining infant functional outcome at birth as it relates to DHA status (2). We further propose that immediate postnatal sleep-wake patterns are arehable measure of CNS maturity. 

All these well-established concepts obviously are useful for the discussion of the planar cumuienes, such as ketenes, diazocompounds, thioketenes, and butatrienes. For nonplanar cumuienes (allenes, ketene imines, carbodiimides, pentatetraenes) the situation is not so simple, as the proper classification of electronic states depends essentially on the substitution patterns of the molecules (lc,24,25,73). The usual concepts based on VB arguments have led toclassiH-cations and analytical descriptions of allenic electronic systems (or orbitals) in terms of two perpendicular, isolated tt systems, especially in terms of two-center ethylenic tt systems (24). Sometimes, hyperconjugation of the eth-ylenic C=C tt system with the CH2 group orbitals of corresponding symmetry has been taken into consideration (24). 

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