Driving potential

Figure 12-12 illustrates water and air relationships and the driving potential which exist in a counterflow tower, where air flows parallel but opposite in direction to water flow. An understanding of this diagram is important in visualizing the cooling-tower process. 

However, a potential may give rise to more than one type of flux. There are cross-effects A temperature difference can also result in diffusion, called thermal diffusion, and a concentration difference can result in a heat current. The general relation between fluxes 7, and the driving potentials A) is of the form of linear relations... 

Zinc should give a potential of -1 - 05 V vs. CU/CUSO4 and should have a driving potential of about -0-25 V with respect to cathodically protected steel. Zinc is therefore sufficiently negative to act as a sacrificial anode, and its first use for such purposes was on the copper-sheathed hulls of warships more than a century ago. The first attempts to fit zinc anodes to steel hulls, however, were a complete failure, for the sole reason that it had not been realised that the purity of the zinc was of paramount importance. The presence of even small amounts of certain impurities leads to the formation of dense adherent films, which cause the anodes to become inactive. 

Where the use of zinc anodes is practicable, the low driving potential is a great advantage since the resistance of the steel to be cathodically protected is the controlling resistance, and the current output of the anode varies with the requirements of the cathode. Thus it can be said that zinc anodes are largely self-governing. 

The choice between Al-Zn-In and Al-Zn-Hg may well be influenced by their respective operating potentials and capacities. Where an additional driving voltage is required (such as in seabed mud), Al-Zn-In anodes may be preferred to ensure adequate structure polarisation. Alternatively, a lower driving potential may be acceptable where the additional capacity (and hence weight saving) is the predominant factor this favours Al-Zn-Hg anodes. 

The reaction occurring at the photoanode (CdS or CdSe) is the oxidation of sulfide or polysulfide, while at the cathode (Pt) some polysulfide species are reduced, so that the electrolyte undergoes no net chemical change. Here, the previous problem of poor stability in Fe(CN)g solutions could be minimized, at the expense of lowering the driving potential (and thus the conversion efficiency), by using fhe... 

One such reaction that uses ATP as the source of the driving potential is the synthesis of sucrose from glucose and fmctose ... 

The initial and the target state wave functions are To(r, 0) and T oCr, T) at times t = 0 and t = T, respectively. We aim to derive the driving potential Fpp(r, t) that generates the target state from the initial state in time Tp < T. The wave function of the intermediate state in the acceleration is assumed to be representable in the form... 

We now briefly review the derivation of the fast-forward driving potential that accelerates an adiabatic process [15]. Consider a system with the potential energy function Vq = o(r, a(O), in which R (t) = R, -I- et, is a parameter with infinitesimal rate of change, that is, e 1. We take the wave function of the system to be... 

Noting that dR/dt = ea t) the driving potential takes the form... 

The driving potential generally depends on the energy level n, and the auxiliary potential Epp - Vq must be calculated by solving Eq. (3.20) for each However, for some specific processes, transport and compression/expansion, the analytic form of the auxiliary potential derived has been shown to be the same for any n no matter the form of Eg [15,16]. The auxiliary potential for transport is [15]... 

We now assume that an external magnetic field is directed in the z-direction. Each eigenstate 0 (r,A) has a spin that is an eigenvalue of the operator 5. We seek the driving potential Vpp and the vector potential App that generates 0 (r,A )exp -i E m ))dt /n... 

We divide Eq. (3.23) by Tpp and substitute Eq. (3.17). Rearranging the equation by using Eq. (3.24) and decomposing the resultant equation into real and imaginary parts, we obtain two equations, one for the driving potential... 

We now consider control of the quantum dynamics of a one-component gas composed of N particles with mass m and charge q without spin. We derive the driving potential and the vector potential, which generate... 

The wave function of the intermediate state evolving under the driving potential Vpp and the vector potential App is assumed to be representable in the form... 

Following the same analysis as for the case of one-particle system the equation for the driving potential is found to be... 

Although Vj does not appear explicitly in Eqs. (3.32) and (3.34), the interaction influences the driving potential and the vector potential via in Eq. (3.29). In general, there is no one-body potential and vector potential that satisfies Eqs. (3.32) and (3.34), hence the driving potential in Eq. (3.32) is unrealistic. However, it turns out that the driving potential and the vector potential for rotation of the orientation and translation of the wave function distribution of one-component gas of charged particles without spin are the same as those for the one-particle system in Section 3.5.3. 

Equation (3.46) is used to obtain the additional phase/. Unfortunately, the driving potential is, in general, a many-body potential, that cannot be realized in the laboratory. 

Despite the many-body character of the exact fast-forward driving potential, it is worthwhile considering a simple limiting case for which the driving potential becomes a one-body potential. We assume that the ground state is well approximated by the mean field wave function... 

The harmonic potential in the second term in Eq. (3.88) is necessary to avoid unwanted compression or expansion of the wave function in the x-y plane. However, the driving potential in Eq. (3.88) does not satisfy the Laplace equation. The difficulty is overcome by combining this electromagnetic field and the field that compresses (expands) a wave function in a harmonic potential in the z-direction in a fashion that suppresses unwanted excitation. Below we examine the rotation... 

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