External ordered field

The reversible path, which relates the disordered phase to the lamellar one, is comprised of two branches. First, as illustrated in Figure 5.5, we structure the homogeneous, disordered melt at low incompatibility, Ximthf, by applying an external ordering field, h(r), that is conjugated to the composition, (f) = c()b. The... 

Assuming that the system has no pennanent dipole moment, tire existence ofP(t) depends on a non-stationary j induced by an external electric field. For weak fields, we may expand the polarization in orders of the perturbation. 

Figure A2.5.19. Isothemis showing the reduced external magnetic field B. = P Bq/ZcTj versus the order parameter s = for various reduced temperatures J = TIT. ...

Here we shall consider two simple cases one in which the order parameter is a non-conserved scalar variable and another in which it is a conserved scalar variable. The latter is exemplified by the binary mixture phase separation, and is treated here at much greater length. The fonner occurs in a variety of examples, including some order-disorder transitions and antrferromagnets. The example of the para-ferro transition is one in which the magnetization is a conserved quantity in the absence of an external magnetic field, but becomes non-conserved in its presence. 

While all contributions to the spin Hamiltonian so far involve the electron spin and cause first-order energy shifts or splittings in the FPR spectmm, there are also tenns that involve only nuclear spms. Aside from their importance for the calculation of FNDOR spectra, these tenns may influence the FPR spectnim significantly in situations where the high-field approximation breaks down and second-order effects become important. The first of these interactions is the coupling of the nuclear spin to the external magnetic field, called the... 

Various external electric fields are now switched on, in order to calculate the second derivatives (Figure 17.3). 

In contrast, for flexible-chain polymers, the transition into the ordered state is possible only if the flexibility can be decreased to values below fcr (in the absence of external deformational fields, the crystallization of flexible-chain polymers occurs by the mechanism of chain folding). 

In other words, due to its interaction with the radiation field, a negaton interacts with a slowly varying external electromagnetic field magnetic moment were (approximately to order a) equal to... 

The linear polarizability, a, describes the first-order response of the dipole moment with respect to external electric fields. The polarizability of a solute can be related to the dielectric constant of the solution through Debye s equation and molar refractivity through the Clausius-Mosotti equation [1], Together with the dipole moment, a dominates the intermolecular forces such as the van der Waals interactions, while its variations upon vibration determine the Raman activities. Although a corresponds to the linear response of the dipole moment, it is the first quantity of interest in nonlinear optics (NLO) and particularly for the deduction of stracture-property relationships and for the design of new... 

As a consequence, field methods, which consist of computing the energy or dipole moment of the system for external electric field of different amplitudes and then evaluating their first, second derivatives with respect to the field amplitude numerically, cannot be applied. Similarly, procedures such as the coupled-perturbed Hartree-Fock (CPHF) or time-dependent Hartree-Fock (TDHF) approaches which determine the first-order response of the density matrix with respect to the perturbation cannot be applied due to the breakdown of periodicity. 

Since our objective is to evaluate the dynamic properties corresponding to a certain process of particular order with respect to an externally applied field... 

An external magnetic field has also been used to confine the plasma [143]. An arrangement where electromagnets are located under the cathode is known as the controlled plasma magnetron method [144]. The diffusion of electrons to the walls is prevented by the magnetic field between cathode and anode. This results in an increase in electron density, and consequently in a faster decomposition of silane and a higher deposition rate. At a deposition rate of 1 nm/s, device quality material is obtained [144]. In addition, a mesh is located near the anode, and the anode can by biased externally, both in order to confine the plasma and in order to control ion bombardment. 

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