Oscillatory dynamic operations

Finally, Section 2.4 analyses a simplified model of a bursting pancreatic /3-cell [12]. The purpose of this section is to underline the importance of complex nonlinear dynamic phenomena in biomedical systems. Living systems operate under far-from-equilibrium conditions. This implies that, contrary to the conventional assumption of homeostasis, many regulatory mechanisms are actually unstable and produce self-sustained oscillatory dynamics. The electrophysiological processes of the pancreatic /3-cell display (at least) two interacting oscillatory processes A fast process associated with the K+ dynamics and a much slower process associated with the Ca2+ dynamics. Together these two processes can explain the characteristic bursting dynamics in the membrane potential. 

In dynamic oscillatory measurements, however, higher order relaxation times (i.e. shorter times), which do not noticeably contribute to the zero shear viscosity, can become of importance when the frequency is increased. For this purpose, Ferry and co-operators 123, 14) proposed the following, rather crude approximation of the relaxation times [cf. eq. (3.50)] ... 

It is suggested that a CCN displays the following attributes Development-ally it is self-organized and self-adapting and, in the sense that it is epigenet-ically regulated, it is untrained. Operationally it is a stable, dynamic system, whose oscillatory behavior permits feedback in this regard, it is noted that a CCN operates in a noisy, non-stationary environment, and that it also employs useful and necessary inhibitory inputs. 

One further note, the University of Delaware gasifier model used in the pseudo steady state approximation assumes that the gas and solids temperatures are the same within the reactor. That assumption removes an important dynamic feedback effect between the countercurrent flowing gas and solids streams. This is particularly important when the burning zone moves up and down within the reactor in an oscillatory manner in response to a step change in operating conditions. 

Although these oscillations can he avoided by operating at sufficiently high emulsifier concentrations, the concentrations needed are often high for most commercial processes. Even if. under the conditions used, a non-oscillatory steady-state exists it is not unusual that during start-up or other disturbance transients an oscillation is induced which damps out only very slowly (20 or more residence times). Furthermore one is never certain whether steady-state models actually apply in any given situation unless one either has experimental confirmation or verifies it by first solving a dynamic model. 

Let us return to the problem of solving the response of the quantum mechanical system to an external electric field. The zeroth-order wave function of the quantum mechanical system is obtained by use of any of the standard approximate methods in quantum chemistry and the coupling to the field is described by the electtic dipole operator. There exist a number of ways to determine the response functions, some of which differ in formulation only, whereas others will be inherently different. We will give a short review of the characteristics of tire most common formulations used for the calculation of molecular polarizabilities and hyperpolarizabilities. The survey begins with the assumption that the external perturbing fields arc non-oscillatory, in which case we may determine molecular properties at zero frequencies, and then continues with the general situation of time-dependent fields and dynamic properties. 

In general, the interaction of two feedback loops constitutes the basis for complex dynamics. Hence also in HNDR oscillators, slow transport should be taken into account as a possible source of complex oscillatory phenomena. However, this mechanism should operate only in parameter regimes in which, or close to which, both suboscillators possess oscillatory solutions. 

A commercial instrument for extensional viscosity measurements is currently offered by the Thermo Electron Corporation [40], The device uses capillary breakup techniques and is called the Haake CaBER . Vilastic Scientific, Inc. also offers an orifice attachment to their oscillatory rheometer for extensional viscosity determinations [41,42], The principle of operation of the rheometer is oscillatory tube flow [43,44], Dynamic mechanical properties can be determined... 

If a semiconductor element with negative differential conductance is operated in a reactive circuit, oscillatory instabilities may be induced by these reactive components, even if the relaxation time of the semiconductor is much smaller than that of the external circuit so that the semiconductor can be described by its stationary I U) characteristic and simply acts as a nonlinear resistor. Self-sustained semiconductor oscillations, where the semiconductor itself introduces an internal unstable temporal degree of freedom, must be distinguished from those circuit-induced oscillations. The self-sustained oscillations under time-independent external bias will be discussed in the following. Examples for internal degrees of freedom are the charge carrier density, or the electron temperature, or a junction capacitance within the device. Eq.(5.3) is then supplemented by a dynamic equation for this internal variable. It should be noted that the same class of models is also applicable to describe neural dynamics in the framework of the Hodgkin-Huxley equations [16]. 

Biochemical oscillation. The availability or dynamic flux of substrates/cofactors may also cause fluctuation in the operational enzyme activities. For example, the coordinated regulation by the coupled effect of metabolites acting as activators and inhibitors gives rise to the periodic response (cyclic fluctuation) of the product or measurable intermediates known as oscillatory effect (Chance et al, 1973). Biochemical oscillation or biorhythmicity is also observed in the signal transduction systems (Myer and Stryer, 1988 Berridge, 1990). The necessary conditions for oscillations can be stated as ... 

Interest in flowing systems focuses on (i) the existence of multiple steady-state solutions of the reactor equations and (ii) the stability of such solutions. These are not independent the existence of parametrically sensitive regions of dynamic behaviour can give rise to oscillations in both temperature and concentration, constant in period and amplitude. The anticipation and control of such oscillatory modes of reaction is clearly of no less importance to the successful operation of the reactor than is the prediction of its stability. 

L. Glass and S. A. Kauffman, Co-operative components, spatial localization and oscillatory cellular dynamics, J. Theor. Biol. 34, 219-237 (1972). 

As mentioned previously the studied fermentation process to produce ethanol presents challenges in its process dynamics that exhibit oscillatory behavior, which affect process productivity and sustainabhity. To address these challenges, this section introduces a new sustainable process control framework that combines the biomimetic control strategy detailed earlier and the GREENSCOPE sustainabihty assessment tool. In this case study, the controlled variable is the concentration of product, Cp (see objective function defined earlier), and the dilution rate, Djn, is chosen as the manipulated variable. GREENSCOPE is employed to evaluate the sustainability performance of the system in open-loop and closed-loop operations. The obtained GITEENSCOPE indicator scores provide information on whether the implementation of the biomimetic controller for the fermentation process enables a more efficient and sustainable process operation. 

Mathematical model of three-way catalytic converter (TWC) has been developed. It includes mass balances in the bulk gas, mass transfer to the porous catalyst, diffusion in the porous structure and simultaneous reactions described by a complex microkinetic scheme of 31 reaction steps for 8 gas components (CO, O2, C2H4, C2H2, NO, NO2, N2O and CO2) and a number of surface reaction intermediates. Enthalpy balances for the gas and solid phase are also included. The method of lines has been used for the transformation of a set of partial differential equations (PDEs) to a large and stiff system of ordinary differential equations (ODEs . Multiple steady and oscillatory states (simple and doubly-periodic) and complex spatiotemporal patterns have been found for a certain range of operation parameters. The methodology of studies of such systems with complex dynamic patterns is briefly introduced and the undesired behaviour of the used integrator is discussed. 

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