Chemical feedback

Diflfiisive processes nonnally operate in chemical systems so as to disperse concentration gradients. In a paper in 1952, the mathematician Alan Turing produced a remarkable prediction [37] that if selective diffiision were coupled with chemical feedback, the opposite situation may arise, with a spontaneous development of sustained spatial distributions of species concentrations from initially unifonn systems. Turmg s paper was set in the context of the development of fonn (morphogenesis) in embryos, and has been adopted in some studies of animal coat markings. With the subsequent theoretical work at Brussels [1], it became clear that oscillatory chemical systems should provide a fertile ground for the search for experimental examples of these Turing patterns. 

A mechanical system, typified by a pendulum, can oscillate around a position of final equilibrium. Chemical systems cannot do so, because of the fundamental law of thermodynamics that at all times AG > 0 when the system is not at equilibrium. There is nonetheless the occasional chemical system in which intermediates oscillate in concentration during the course of the reaction. Products, too, are formed at oscillating rates. This striking phenomenon of oscillatory behavior can be shown to occur when there are dual sets of solutions to the steady-state equations. The full mathematical treatment of this phenomenon and of instability will not be given, but a simplified version will be presented. With two sets of steady-state concentrations for the intermediates, no sooner is one set established than the consequent other changes cause the system to pass quickly to the other set, and vice versa. In effect, this establishes a chemical feedback loop. 

The dynamics of controlled systems is an open problem that has recently attracted the attention of scientific community [13]. In fact, oscillatory behavior in chemical systems is an interesting topic (which has been typically studied in autocatalytic reactions, e.g., the Lotka system see [44] and references therein). Dynamics of controlled systems can be explained in terms of interconnections. Indeed, by analogy with control systems, autocatalytic chemical systems can be described as examples of chemical feedback [44]. 

Chemical feedback may work, for example, by chain branching or autocatalysis . The mechanism by which hydrogen and oxygen react spontaneously involves a cycle of three elementary steps ... 

In the preceding chapters we investigated the basic patterns of behaviour which might be exhibited by a reaction scheme which involved a certain form of chemical feedback under isothermal conditions. Here we make a similar analysis for systems with purely first-order chemical reactions but under conditions in which the heat produced by the natural exothermicity can lead to departures from isothermal operation. Feedback is then provided from thermal coupling as the increase in temperature of the reacting mixture leads to an increase in the local value of the reaction rate constant. 

In chapters 2-5 two models of oscillatory reaction in closed vessels were considered one based on chemical feedback (autocatalysis), the other on thermal coupling under non-isothermal reaction conditions. To begin this chapter, we again return to non-isothermal systems, now in a well-stirred flow reactor (CSTR) such as that considered in chapter 6. 

However, the pathway of pain signals arising from tissue and then traveling to the spinal cord and brain is not a one-way street. It turns out that nerve endings in the skin or tissue can also release peptides such as substance P, which can alter the activity of immune cells or cause blood vessels to dilate. This causes swelling or further alters the pain response. Thus, not only does damaged tissue communicate with the central nervous system, but the central nervous system also sends chemical feedback to the site of injury or tissue damage. 

Fig. 5.1. Variation of reaction rate R with extent of reaction (a) linear relationship for first-order reaction (b) non-linear deceleratory reactions of overall order n (c) reactions showing chemical feedback in the form of autocatalysis (d) comparison of chemical and...

The higher order, with respect to the autocatalyst, skews the rate curve so that the maximum lies at higher extents of conversion and there is a longer induction phase during which the reaction rate is close to zero at low extents of conversion. Cubic autocatalysis is apparently less significant than quadratic which is relatively common as chemical feedback in combustion systems, although cubic-type curves have been reported and exploited in the oxidation of H2 for which a rate expression of the form d[H20]/dr = / [H2][H20] was observed [7] and also the oxidation of CS2 in heavily-diluted air mixtures [8]. 

An important example of chemical feedback in combustion reactions is provided by the so-called branching cycle in the H2 -I- O2 reaction [9] which... 

In many combustion systems there will be the possibility of both thermal and chemical feedback, with the two processes coupled together through the heat and mass balance equations just for added fun. A simple model... 

In order to model the oscillatory waveform and to predict the p-T locus for the (Hopf) bifurcation from oscillatory ignition to steady flame accurately, it is in fact necessary to include more reaction steps. Johnson et al. [45] examined the 35 reaction Baldwin-Walker scheme and obtained a number of reduced mechanisms from this in order to identify a minimal model capable of semi-quantitative p-T limit prediction and also of producing the complex, mixed-mode waveforms observed experimentally. The minimal scheme depends on the rate coefficient data used, with an updated set beyond that used by Chinnick et al. allowing reduction to a 10-step scheme. It is of particular interest, however, that not even the 35 reaction mechanism can predict complex oscillations unless the non-isothermal character of the reaction is included explicitly. (In computer integrations it is easy to examine the isothermal system by setting the reaction enthalpies equal to zero this allows us, in effect, to examine the behaviour supported by the chemical feedback processes in this system in isolation... 

Basis of mechanistic interpretation A full mechanistic account follows in the next chapter. Here we simply indicate the important features of the currently-accepted interpretation of the above facts. The key feature in these thermokinetic phenomena is that there are both thermal and chemical feedback processes combining to produce the various exotic responses, including the ntc. At the heart of the clockwork is the equilibrium involving the methyl radical CH3 and molecular oxygen [78]... 

Could inorganic chemical feedbacks have succeeded, alone, in maintaining planetary temperature ... 

Thus, if s is proportional to ns, the integrated sink strength is also proportional to Gs. It may happen that the number densities nr depend, in part, on ns due to chemical feedback processes, and when this occurs kv will depend to some extent on Gs. We cannot pursue this problem here and... 

Species with chemical feedbacks that change the duration of the atmospheric response. The first number is the global mean atmospheric lifetime for example, the global mean atmospheric lifetime of CH4 against reaction with OH is 8.4 years. The second number is the perturbation lifetime, which is the time required for a perturbation to decay back to its initial state. For example, an increase in CH4 leads to a decrease in the OH level in the atmosphere and this reduced OH level, in turn, leads to a slower rate of removal of CH4 thus the perturbation lifetime of CH4 is 12 years. 

To illustrate the nonlinear chemical feedbacks in the atmospheric system, let us consider methane. One kilogram of CH4 released from the surface becomes well mixed in the troposphere. A portion of this CH4 is transported into the stratosphere. As we have just described, the added kilogram of CH4 is removed with an adjustment time of about 12 years (and not with its global lifetime of 8.4 years due to OH reaction and stratospheric loss). That amount of the CFLt perturbation that makes it into the stratosphere directly affects stratospheric chemistry that controls stratospheric 03 abundance. More CH4 will... 

A preindustrial level of 700 ppb would have required a source of 210 Tg(CH4> yr if the lifetime has remained constant, and 280 Tg (CH4) yr if current tropospheric chemical feedbacks can be extrapolated back. The total anthropogenic emissions of CH4 based on identified sources, 375 (300-450), is slightly higher than the inferred range from preindustrial levels, 270-340, but is well within the uncertainties. 

The chemoreflex model provides a satisfactory explanation for the chemical regulation of ventilation as well as respiratory instabihty. However, it fails to explain a fundamental aspect of ventilatory control experienced by everyone in everyday fife the increase in ventilation during muscular exercise. Typically, Vp increases in direct proportion to the metaboHc demand (17002, VO2) such that the outputs of the chemical plant. Equation 11.1 and Equation 11.2, are well regulated at constant levels from rest to exercise. As a result, homeostasis of arterial blood chemistry is closely maintained over a wide range of work rates. The dilemma is if increases in metaboHc rate are not accompanied by corresponding increases in chemical feedback, then what causes exercise hyperpnea ... 

Another possible explanation of exercise hyperpnea is that the proportional controller maybe driven by two sets of inputs a chemical feedback component via the chemoreflex loop and a feedforward component induced by some exercise stimulus [Grodins and Yamashiro, 1978]. The feedforward-feedback control hypothesis offers a simple remedy of the chemoreflex model, but its validity can be verified only if the... 

Among the variously proposed mechanisms of exercise hyperpnea, the PCO2 oscillation hypothesis of Yamamoto [1962] has received widespread attention. According to this hypothesis, the controller may be responsive not only to the mean value of chemical feedback but also to its oscillatory waveform which is induced by the tidal rhythm of respiration. This hypothesis is supported by the experimental finding that alterations of the temporal relationship of the PaC02 waveform could profoundly modulate the exercise hyperpnea response (Poon, 1992b]. 

Could we construct chemical feedback Why would we want to do that Those who have ever seen feedback working know the answer -this is the very basis of control. Such control of chemical concentrations is at the heart of how biological systems operate. 

In particular, they may create the autocatalytic cycle, which represents chemical feedback. 

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