Square well potential , capacity

Figure 6.2 Energies of single-particle orbitals in harmonic-oscillator and rounded square-well potentials, the latter with and without spin-orbit coupling. Numbers in parentheses indicate orbital capacities and those in square brackets give cumulative capacity up to the given point. [Reproduced by permission from Gordon and Coryell (1967).]...

We show in Section IV that the LJ(12,6), commonly employed in atomistic simulations, performs poorly when applied to inter-residue interactions. Therefore other continuous potentials of the type described in Eq. (5) were investigated. We propose a shifted LJ potential (SLJ) that has significantly higher capacity compared to LJ and is closer in performance to that of the square well potential. 

To test the above explanation and in a search for a better model, we also tried a shifted U function (SLJ) as well as an LJ-Uke potential with different powers (m = 6, = 2, LJ(6,2) see also Fig. 1). As can be seen from Table IV, the softer potentials are performing better than the steep LJ(12,6) potential. For example, a LJ(6,2) potential trained on the HL set with 110 parameters (only 10 types of amino acids were used) recognizes correctly 530 proteins of the TE set. Thus, LJ(6,2) has a similar capacity to a square well potential, trained on the same set with 210 parameters. 

In Fig. 2.20, we also show the molar heat capacity for a square-well (SW) potential with a = 1 and e = — 1. Here also, we have a maximum of molar heat capacity of about two. The additional heat capacity in this case is due to the structural changes induced by the change in temperature. These structural changes occur in any liquid, as was discussed in Sec. 2.4. 

Measurement Setup. The buffer capacity measuring setup is shown in Fig. 14. Since the current source is not floating, the grounded counter electrode works as a reference electrode as well. In this case, the current at low frequency will cause a certain polarization in spite of the very large area of the counter electrode. This polarization potential of the counter electrode will be superposed on the output of the ISFET amplifier and interfere with the measurement. Therefore an additional saturated calomel electrode (denoted S.C.E. in Fig. 14) is used to measure separately the polarization potential, and the signal is sent to the lock-in amplifier for subtraction. The measured current and voltage are presented in effective (root-mean-square or RMS) values. 

Finally, it should be noted that in many cases where < 0, is determined by the capacity method uncertainty arises, which is related to the frequency dependence of Mott-Schottky plots. (In particular, the frequency of the measuring current is increased in order to reduce the contribution of surface states to the capacity measured.) As the frequency varies, these plots, as well as the plots of the squared leakage resistance R vs. the potential (in the electrode equivalent circuit, R and C are connected in parallel), are deformed in either of two ways (see Figs. 6a and 6b). In most of the cases, only the slopes of these plots change but their intercepts on the potential axis remain unchanged and are the same for capacity and resistance plots (Fig. 6b). Sometimes, however, not only does the slope vary but the straight line shifts, as a whole, with respect to the potential axis, so that the intercept on this axis depends upon the frequency (Fig. 6a). 

Focusing of ions in curved FAIMS (4.3.1) means a pseudopotential bottoming near the gap median. Devices using such wells to guide or trap ions (e.g., quadrupole filters or traps and electrodynamic funnels) have finite charge capacity or saturation current (/sat) the Coulomb potential scales as the charge density squared and, above some density, exceeds the well depth and expels excess ions from the device. Simulations... 

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