Chemical wave systems, phenomena

The formation and evolution of multiple waves becomes more complicated when chemical reactions or phase transitions occur. Volume decreasing phase transformations cause the pressure at point B in Figure 2 and Figure 7 to decrease with time. This common phenomenon is known as elastic precursor decay in elastic-plastic wave system. [9] The timescale for this pressure decay depends primarily on the timescale for the chemical reaction or phase transition that gives rise to the 2" wave. 

The BZ reaction is carried out in two-dimensional, i.e., Petri dish filled with the reaction mixture followed by the monitoring of oscillatory phenomenon in the stirred system which can manifest itself formation of traveling chemical waves as could be seen in Fig. 1.6. In the oxidized state of the reaction, the autocatalyst... 

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. 

To confirm the above conjectures we have performed a numerical simulation of equation (29) on the Brusselator model chemical reaction.46 The results are shown in Fig. 7. We start with an initial condition corresponding to a clockwise wave. Under the effect of the counterclockwise field this wave is deformed and eventually its sense of rotation is reversed. In other words, the system shows a clear-cut preference for one chirality. As a matter of fact we are witnessing an entrainment phenomenon of a new kind, whereby not only the frequency but also the sense of rotation of the system are adjusted to those of the external field. More complex situations, including chaotic behavior, are likely to arise when the resonance condition w = fl, is not satisfied, but we do not address ourselves to this problem here. 

The concepts of hybridisation and resonance are the cornerstones of VB theory. Unfortunately, they are often misunderstood and have consequently suffered from much unjust criticism. Hybridisation is not a phenomenon, nor a physical process. It is essentially a mathematical manipulation of atomic wave functions which is often necessary if we are to describe electron-pair bonds in terms of orbital overlap. This manipulation is justified by a theorem of quantum mechanics which states that, given a set of n respectable wave functions for a chemical system which turn out to be inconvenient or unsuitable, it is permissible to transform these into a new set of n functions which are linear combinations of the old ones, subject to the constraint that the functions are all mutually orthogonal, i.e. the overlap integral J p/ip dT between any pair of functions ip, and op, (i = j) is always zero. This theorem is exploited in a great many theoretical arguments it forms the basis for the construction of molecular orbitals as linear combinations of atomic orbitals (see below and Section 7.1). 

Resonance, strictly speaking, is not a real physical phenomenon but only an interpretation, as a consequence of the way in which the wave function of the stationary state, for example of the benzene molecule, can be constructed approximately by linear combination of other wave functions. This construction is possible in a way which fits in well with the interpretation of these systems based on the theory of chemical structure. 

The theory of the chemical bond is one of the clearest and most informative examples of an explanatory phenomenon that probably occurs in some form or other in many sciences (psychology comes to mind) the semiautonomous, nonfundamental, fundamentally based, approximate theory (S ANFFBAT for short). Chemical bonding is fundamentally a quantum mechanical phenomenon, yet for all but the simplest chemical systems, a purely quantum mechanical treatment of the molecule is infeasible especially prior to recent computational developments, one could not write down the correct Hamiltonian and solve the Schrodinger equation, even with numerical methods. Immediately after the introduction of the quantum theory, systems of approximation began to appear. The Born Oppenheimer approximation assumed that nuclei are fixed in position the LCAO method assumed that the position wave functions for electrons in molecules are linear combinations of electronic wave functions for the component atoms in isolation. Molecular orbital theory assumed a characteristic set of position wave functions for the several electrons in a molecule, systematically related to corresponding atomic wave functions. 

We have already nad occasion to refer to the phenomenon of chemical sensitisation Reference must also be made to a phenomenon known as optical sensitisation This consists m making a system sensitive to a certain range of wave lengths by the addition of some foreign... 

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