Z direction , and

In order to evaluate equation B1.2.6, we will consider the electric field to be in the z-direction, and express the interaction Hamiltonian as... 

Figure Bl.14.2. Gradient-recalled echo pulse sequence. The echo is generated by deliberately dephasing and refocusing transverse magnetization with the readout gradient. A slice is selected in the z-direction and v- and y-dimension are frequency and phase encoded, respectively.

The electronic contribution to the dipole moment is thus determined from the density matrix and a series of one-electron integrals J dr< (-r)0. The dipole moment operator, r, h.)-components in the x, y and z directions, and so these one-electron integrals are divided into their appropriate components for example, the x component of the electronic contribution to the dipole moment would be determined using ... 

Again, ion tunnels have no electric-field component in the z-direction, and ions must be injected with some initial kinetic energy if they are to pass through the device. 

Fick s second law of diffusion can be derived from Fick s first law by using a mass balance approach. Consider the differential fluid element shown in Figure 4. This differential fluid element is simply a small cube of liquid or gas, with volume Ax Ay Az, and will be defined as the system for the mass balance. Assume now that component A enters the cube at position x by diffusion and exits the cube at x + Ax by the same mechanism. For the moment, assume that no diffusion occurs in the y or z directions and that the faces of the cube that are perpendicular to the y and z axes thus are impermeable to the diffusion of A. Under these conditions, the component mass balance for A in this system is... 

Together with Eq. (93), this equation forms a set of equations from which explicit expressions for the derivatives of the velocities can readily be obtained. Expressions for the y- and z-direction and for the other elements of the Jacobi matrix are obtained in a similar manner. 

Solution If the two Cp rings are labeled a and b, the disposition of radical (X) and dative (I, and I.") coordination sites may be assigned to the oriented sd3 cube (4.124a) as shown in the diagram below, with Cpa as the upper face (+z direction) and Cpb the lower face (-z direction) ... 

A linear quadrupole mass analyzer consists of four hyperbolically or cyclindrically shaped rod electrodes extending in the z-direction and mounted in a square configuration (xy-plane, Figs. 4.31, 4.32). The pairs of opposite rods are each held at the same potential which is composed of a DC and an AC component. 

Fig. 4.40. Schematic of a quadmpole ion trap, (a) QIT with external ion source (illustration stretched in z-direction) and (b) section in the rz-plane (in scale), (a) Reproduced from Ref. [144] by permission. lohn Whey Sons, 2000.

Consider a one-dimensional optical structure that consists of nonlinear layers. The structure is illustrated in Fig. 1. Assuming no field variation in the X and z directions and the convention exp(icot) for the time dependence of the fields, Maxwell s equations take the form... 

The FDTD approach is based on direct numerical solution of the time dependent Maxwell s curl equations. In the 2D TM case the nonzero field components are E Hy and E, the propagation is along the z direction and the transverse field variations are along x. In lossless media. Maxwell s equations... 

Two driving forces for flow exist in the metering section of the screw. The first flow is due just to the rotation of the screw and is referred to as the rotational flow component. The second component of flow is due to the pressure gradient that exist in the z direction, and it is referred to as pressure flow. The sum of the two flows must be equal to the overall flow rate. The overall flow rate, Q, the rotational flow, 0 and the pressure flow, Qp, for a constant depth metering channel are related as shown in Eq. 1.12. The subscript d is maintained in the nomenclature for historical consistency even though the term is for screw rotational flow rather than the historical drag flow concept. 

Figure 7.2 Transforming the Cartesian reference frame a) cylindrical cross section of the screw and barrel with flow out of the surface of the page, and b) the unwound rectangular channel with a stationary barrel and the Cartesian coordinate frame positioned on the screw, is the velocity of the screw core in the z direction and it is negative...

The viscous dissipation that occurs due to pressure-induced flow is caicuiated in the same manner and it has two components due to the motion at the core and at the flights. For pressure-induced flow in the z direction and the motion of the screw... 

For pressure-induced flow in the z direction and the motion of the screw core ... 

For a molecule with N atoms, its 3iV degrees of freedom would be split into three translational degrees of freedom (corresponding to x-, y-, and z-directions), and three rotational degrees of freedom for nonlinear molecules and two for linear ones. Therefore, 3N—6 and 3N— 5 vibrational degrees of freedom exist for nonlinear and linear molecules, respectively. Vibrational frequencies can be obtained from convenient tabulations (see, for example, Shimanouchi, 1972 Chase et al., 1985). 

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