Equipotential plot

Figure Al.6.27. Equipotential contour plots of (a) the excited- and (b), (c) ground-state potential energy surfaces. (Here a hamionic excited state is used because that is the way the first calculations were perfomied.) (a) The classical trajectory that originates from rest on the ground-state surface makes a vertical transition to the excited state, and subsequently undergoes Lissajous motion, which is shown superimposed, (b) Assuming a vertical transition down at time (position and momentum conserved) the trajectory continues to evolve on the ground-state surface and exits from chaimel 1. (c) If the transition down is at time 2 the classical trajectory exits from chaimel 2 (reprinted from [52]).

Fig. 5. The left hand side figure shows a contour plot of the potential energy landscape due to V4 with equipotential lines of the energies E = 1.5, 2, 3 (solid lines) and E = 7,8,12 (dashed lines). There are minima at the four points ( 1, 1) (named A to D), a local maximum at (0, 0), and saddle-points in between the minima. The right hand figure illustrates a solution of the corresponding Hamiltonian system with total energy E = 4.5 (positions qi and qs versus time t).

Figures 8(a) and 8(b) show potential energy diagrams for such a system [70], The potential energy is plotted as equipotential lines in a coordinate system...

Once the electric potential is impressed on the paper, an ordinary voltmeter may be used to plot lines of constant electric potential. With these constant-potential lines available, the flux lines may be easily constructed since they are orthogonal to the potential lines. These equipotential and flux lines have precisely the same arrangement as the isotherms and heat-flux lines in the corresponding heat-conduction problem. The shape factor is calculated immediately using the method which was applied to the curvilinear squares. 

Figure 1.11 gives the scaled potential distribution y(r) around a positively charged spherical particle of radius a with yo = 2 in a symmetrical electrolyte solution of valence z for several values of xa. Solid lines are the exact solutions to Eq. (1.110) and dashed lines are the Debye-Hiickel linearized results (Eq. (1.72)). Note that Eq. (1.122) is in excellent agreement with the exact results. Figure 1.12 shows the plot of the equipotential lines around a sphere with jo = 2 at ka = 1 calculated from Eq. (1.121). Figures 1.13 and 1.14, respectively, are the density plots of counterions (anions) (n (r) = exp(+y(r))) and coions (cations) ( (r) = MCxp(—y(r))) around the sphere calculated from Eq. (1.121). 

Fig. 3 Electrostatic field simulation for a sharp-edged collector. Equipotential lines of the electric potential and electrostatic field lines are plotted [81]...

As equipotential eoatonr plot of the potential surface is given... 

Consider then an adiabatic well in the hyperspherical coordinate system. Classically, the motion of the periodic orbit at the well would be an oscillation from a point on the inner equipotential curve in the reactant channel to a point on the same equipotential curve in the product channel. This is qualitatively the motion of what are termed "resonant periodic orbits" (RPO s). For example the RPO s of the IHI system are given in Fig. 5. Thus, finding adiabatic wells in the radial coordinate system corresponds to finding RPO s and quantizing their action. Note that in Fig. 5 we have also plotted all the periodic orbit dividing surfaces (PODS) of the system, except for the symmetric stretch. By definition, a PODS is a periodic orbit that starts and ends on different equi-potentials. Thus the symmetric stretch PODS would be an adiabatic well for an adiabatic surface in reaction path coordinates. However, the PODS in the entrance and exit channels shown in Fig. 5 may be considered as adiabatic barrieres in either the radial or reaction path coordinate systems. Here, the barrier in radial coordinates, has quantally a tunneling path between the entrance and exit channels. 

It is evident that the equipotential in the electrolyte is cylindrical but not coaxial with the conductors. It is clear that the electric potential varies from Vapp from a distance r in the electrolyte and specifically depends on the geometric parameters, d and r0, but also with 0. For example, for Vapp = 1 V, d = 10 pm and r() 1 pm. The variation of with r is plotted in Figure 13.2. 

Figure Al.6.27. Equipotential contour plots of (a) the excited- and (b), (c) ground-state potential energy surfaces. (Here a harmonic excited state is used because that is the way the first calculations were performed.)...

Figure 9 Configuration-space plots of 12 low-order periodic orbits (POs) obtained from the Henon-Heiles Hamiltonian at = 0.1, surrounded by the equipotential curve y q, qz) Note that certain POs touch the equipotential curve (e.g., 1,...

In addition, if we make a plot of the equipotentials of Y in a system of coordinates OXiYiZi defined by... 

Potential as a function of position (X) along the bar is shown in Fig, lb. The zero of the potential scale is chosen as the low resistivity plate which is an equipotential surface. The left hand side of the high resistivity electrode is held at V +Vq while the right hand side is held at Vq, One particular voltage is of special interest for all LCD s the threshold voltage Vc Figure 2 shows that the optical properties of an LCD exhibit a threshold behavior at The threshold voltage is plotted on... 

Figure 9 An equipotential contour plot for the potential energy (in kJ/mol) specified by Eqs. (1-3) and the LEPS potential [11] for a rectangular configuration of atoms in the four-center N2 + N2 - 2NN reaction. The axes are the old and new bond distances (in A) which specify a rectangular configuration.

Figure 16.3 Equipotential curves representing reactant and product in an electron exchange reaction as a function of a solvent reorganisation coordinate and an internal coordinate, both treated as harmonic. The heavy line represents the classical reaction path (path of steepest descent from the top of the barrier). The dotted line represents the Evans-Polanyi diabatic path , whose energy dependence is determined by the generalised internal coordinate q. In this plot, = 5 and the energy change from to is very close to the energy change from [ (R),...

Using the calcirlated energies, we plot every equipotential cirrve in the axis system chosen (see Figttre 11.5). Starting fiom the initial state of the gas molecirle... 

The voltage profile of Fig. 2.6a exhibits a reasonably smooth slope on both the charge and discharge cycles. The differential capacity, d x /d , where x is the lithium concentration and E is the cell potential, is used to accentuate changes in the slope of the potential curve (Fig. 2.6b]. Peaks in the differential capacity indicate regions of the potential where lithium ions are entering nearly equipotential sites. This plot suggests that the lithium insertion in nanocrystalline silicon occurs at 100 and 250 mV and lithium... 

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