Dipole array model

Vibration Diagram Method. In actuality the last cases above are not described accurately by this dipole array model because actual phases of the electric fields are significantly altered from those of linear waves. (A more realistic, but complex model is to consider amplitude and phase characteristics of the oscillating vertically polarized component of electric field resulting from rotation of a line of transverse dipoles of equal magnitude but rotated relative to each other along the line such that their vertical components at some reference time are depicted by Figure 2.) For this reason and to handle details of focused laser beams one must resort to a more mathematically based description. Fortunately, numerical... 

Molecules do not consist of rigid arrays of point charges, and on application of an external electrostatic field the electrons and protons will rearrange themselves until the interaction energy is a minimum. In classical electrostatics, where we deal with macroscopic samples, the phenomenon is referred to as the induced polarization. I dealt with this in Chapter 15, when we discussed the Onsager model of solvation. The nuclei and the electrons will tend to move in opposite directions when a field is applied, and so the electric dipole moment will change. Again, in classical electrostatics we study the induced dipole moment per unit volume. 

Phthalocyanines and porphyrins are often used as model compounds for the manipulation (guest molecule) of surface-supported supramolecular two-dimensional arrays both in UHV and in solution. Spillmann et al. reported that zinc(II) 5,15-bis(3-cyanophcnyl)-10,20-bis 3,5-di(/c/7-bu(yl )phcnylj porphyrin, 2, molecules predominantly formed a hexagonal pattern by trimer formation, when 0.5-0.7 MLs of 2 was deposited on Ag(l 11) especially, 2 forms a characteristic nanostructure on Ag(l 11) at low coverage [163], As reported by Yokoyama et al., it is suggested that the molecular assembly is driven by both van der Waals and dipole-dipole interactions involving the polar 3-cyanophenyl residues [79], After further deposition of C60... 

Using a capacitor as a model for a two-dimensional array of effective dipoles considered perpendicular to the air/ water interface in a monolayer, the dipole-dipole interaction free energy can be approximated by 22]... 

The most common boundary representation is periodic boundary conditions which assumes that the system consists of a periodic array (or a crystal ) of identical systems [1], Another common method, developed for the simulation of biomacromolecules, is the stochastic boundary approach, in which the influences of the atoms outside the boundary are replaced by a simple boundary force [78, 79, 80], Warshel uses a Langevin dipoles model in which the solvent is explicitly replaced by a grid of polarizable dipoles. The energy is calculated in a similar way to the polarization energy in a molecular mechanics force field (see above) [15]. 

Robinson and Dalton use Monte Carlo statistical mechanics to explore concentration and shape dependencies of the chromophores. Monte Carlo methods provide valuable information about the distribution of a collection of chromophores but are not able to provide atomistic information about the systems. The Monte Carlo simulations performed by Robinson and Dalton employ an array of point dipoles on a periodic lattice with the given parameters for the shape of the chromophores and the chromophore spacing adjustable to achieve the desired chromophore concentration. The model system consisted of 1000 chromophores on a body-centered cubic... 

Figure 10. (a) The orientation distribution function (TV f -N i )/TVr for an oriented two-state array of dipoles in the Mott and Watts-Tobin/BDM model (Refs. 59 and 60) for various values of the interaction parameter Vc/ kT in Reference 60 [see Eq. 28]. (b) The configurational entropy and the librational entropy 5 for the two-state model of solvent orientation of electrodes as a function of (corresponding to data in Fig. 10a). (From B. E. Conway and L. G. M. Gordon, J. Phys. Chem. 73 (1969) 3609.)...

A key issue in nanostructured materials is the dipole coupling between nanocrystals which will cause the optical properties of a nanocrystal ensemble to become like those of the bulk material. There has been extensive investigation of the interactions between particles embedded within media for a range of boundary conditions. We have found that the effective dielectric function given by Eq. (10), based on the Maxwell-Garnett model [1] is very accurate for quite dense nanocrystal arrays. In practice, one measures the transmittance of a thin film of the dense nanoparticle based film. Conventional solutions are simply... 

Osdipy monolayer deposited onto a R(111) substrate is shown in Fig. 4(B). The image clearly shows molecular-scale features in a rectangular close packed array with unit cell dimensions of 9.3A by 12.4A. These dimensions were found to be in excellent agreement with model calculations which assmne that the head groups preferentially line up along their dipole [16]. 

The groundplane serves essentially two purposes. First of all it ensures that we have only a single mainbeam, not two. Second, as discussed in Chapter 2, the groundplane can lead to a significant reduction of the RCS of an active array. However, as discussed in Section 2.9, the area of the groundplane relative to the area of the active dipoles is crucial from an RCS point of view. Thus, the exact modeling of the finite groundplane becomes important. We shall discuss this issue in the next section. 

Thus, when calculating the scattering patter, we shall model the antenna as a circular array of dipoles loaded with the same load resistances. 

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