Locator vector

Figure 1.4. Two dipoles at distance R = IR2 - R l, where R,- is the locational vector of the center of the dipole i. The orientation of the dipoles is defined by the two angles 6j and < )j. Only the relative dihedral angle < >,2 =

Where D. is the Euclidean distance between an input vector and the location vector for... 

A simpler version of (3.5) may be obtained for spherical particles, for which each configuration X consists only of the locational vector R. This is the most frequently used case in the theory of simple fluids. The corresponding expression for the average quantity in this case is... 

Enter the basic sto-3g) parameters, the location vectors, R, and the Slater exponents for hydrogen in cells C 6 to H 7, including the various labels as appropriate. 

Generate the cylindrical integration array as in the previous spreadsheet from A 41 to GT 143, based on the formula for the primitive Gaussian formed with the dummy product sum and location vector of cells I 4 and J 4, for... 

Since this is an atomic problem, remove the redundant location vector entries and the cylindrical integration mesh. 

According to the geometrical model presented in Figure 12.2, the instantaneous global location vector for the center of the workpiece is given by... 

The location vectors of the point A with respect to both global origin and carrier center, ta/o a./o are, respectively, described by the relations ... 

Fig. 6.19. Coordinate system for a pair of particles / and j. ifc and j ( = 1, 2, 3) are unit vectors along which a bond may be formed. The vectors Rj and are the locational vectors for the centers of particles i and y, respectively, is the angle between the vector and the positive direction of the x axis.

The difference in fhe moment of inertia vectors is equal to the difference in the absolute location vectors of the subchains 4 - Sy = 4. The second average is then equal to the scattering fxmction for a single molecule, S i(ij) (Equation 3.7). The total scattering fxmction is then expressed as the product of the center-of-mass structure factor and the intramolecular structure factor ... 

Now, the macroscopic behavior of all systems, whether in equilibrium or nonequilibrium states, is classically described in terms of the thermodynamic variables pressure P, temperature T, specific volume V (volume per mole), specific internal energy U (energy per mole), specific entropy S (entropy per mole), concentration or chemical potential /r, and velocity v. In nonequilibrium states, these variables change with respect to space and/or time, and the subject matter is called nonequilibrium thermodynamics. When these variables do not change with respect to space or time, their prediction falls vmder the subject matter of equilibrium thermodynamics. As a matter of notation, we would indicate a nonequilibrium variable such as entropy hy (r,t), where r is a vector that locates a particular region in space (locator vector) and t is the time, whereas the equilibrium notation would simply be . 

Thus, a represents a sum of the kinetic, external potential ((pent), and intermolecular potential ((/>int) energies at the locator vector r and at a time t. Substituting Eq. (5.60) into Eq. (5.1), and following the same type of manipulations given in Secs. 5.3 and 5.4 leads to (Prob. 5.2)... 

We note that for systems at equilibrium, is independent of the locator vector r and Eq. (5.80) reduces to Gibbs entropy for equilibrium systems, Eq. (4.39).l Also, note that the introduction of Planck s constant in the logarithm term of Boltzmann s entropy, Eq. (5.79), is necessary on account of dimensional arguments, albeit it is often incorrectly left out. 

Figure 3. An external electric field is applied parallel to the location vector of the molecule.

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