Electrical Analogue Method

The problem of temperature determination within fuel elements of unusual geometries during exponential-type power surges is a difficult one to solve. This is easily appreciated by reference to the solution for some problems of this sort with very simple geometries. Therefore, an analogue which readily solves such problems is of great value. 

A modified electrical, geometrical analogue for time-dependent heat generation problems that utilizes a mechanical device for creating a simulated exponential power use has been previously described. This mechanism is limited, however, to problems involving rather long periods due to inherent mechanical difficulties. Therefore, to eliminate this difficulty, an electronic device has been developed. This device consists of a d-c amplifier, a resistance-capacitance feed-back circuit, and a shorting switch as illustrated. 

Temperatures Distribution with Exponential Rise, The Reactor Handbook, Vol. II, pp. 157-164. 

Since the over-all resistance, R, of the analogue is constant with time, is a pure exponential, thereby simulating an exponential power rise in the analpgue. 

This device may be used to generate other waveforms. If the gain of the amplifier is exactly one, then Eq. (l) degenerates to a straight line. For an amplifier gain of less than one, Eq. (l) takes the general form 

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In general, however, mechanical models are unwieldy in comparison with electrical models which form the main topic of this section. Two quite distinct types of electrical analogues have been employed for the solution of secular determinants. The first type to be described here Solves the sim iltaneous equations from which the secular determinant arises by a method closely related to the relaxation procedure described in Sec. 9-6. The essential function of the circuit consists merely in carrying out potentiometrically the two fundamental arithmetic operations of multiplication and addition which appear in the simultaneous equations... 

The solution of the secular equation by several of the methods to be described below, Secs. 9-5 to 9-7, is appreciably simplified if H is symmetric. Moreover, in the case of one of the electric analogue devices. Sec. 9-10, which can be used to eliminate the numerical work, it is necessary that H be symmetric. Therefore a method which transforms H = GF into a symmetrical matrix with the same characteristic values as H will now be described. 

Early models used a value for that remained constant throughout the day. However, measurements show that the deposition velocity increases during the day as surface heating increases atmospheric turbulence and hence diffusion, and plant stomatal activity increases (50—52). More recent models take this variation of into account. In one approach, the first step is to estimate the upper limit for in terms of the transport processes alone. This value is then modified to account for surface interaction, because the earth s surface is not a perfect sink for all pollutants. This method has led to what is referred to as the resistance model (52,53) that represents as the analogue of an electrical conductance... 

The previous chapters dealt with ISE systems at zero current, i.e. at equilibrium or steady-state. The properties of the interface between two immiscible electrolyte solutions (ITIES), described in sections 2.4 and 2.5, will now be used to describe a dynamic method based on the passage of electrical current across ITIES. Voltammetry at ITIES (for a survey see [3, 8, 9, 10, 11, 12,18]) is an inverse analogue of potentiometry with liquid-membrane ISEs and thus forms a suitable conclusion to this book. 

Both theoretical analysis and dipole moment measurements indicated that sulfonyl-substituted compounds may have ft coefficients similar in magnitude to their nitro analogues. Therefore, we have measured p for several sulfonyl- and nitro-substituted compounds using electric-field-induced second-harmonic generation method (EFISH) (11,25). In this experiment, one measures an effective third-order nonlinearity rEFISH for a solution containing the compound of interest, given by... 

Numerical solutions have been presented for the impedance response of semiconducting systems that accoimt for the coupled influence of transport and kinetic phenomena, see, e.g., Bonham and Orazem. Simplified electrical-circuit analogues have been developed to account for deep-level electronic states, and a graphical method has been used to facilitate interpretation of high-frequency measurements of capacitance. The simplified approaches are described in the following sections. 

Another essential component in the functioning of automated processes and servomechanisms is the feedback control systems that provide self-regulation and auto-adjustment of the overall system. Feedback control systems may be pneumatic, hydraulic, mechanical, or electrical in nature. Electrical feedback may be analogue in form, although digital electronic feedback methods provide the most versatile method of output sensing for input feedback to digital electronic control systems. 

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