Field-induced

Tang S L, McGhie A J and Suna A 1993 Molecular-resolution imaging of insulating macromolecules with the scanning tunnelling microscope via a nontunnelling, electric-field-induced mechanism Phys. Rev. B 47 3850... 

If we compare with figure C2.2.I I, we can see that this defonnation involves bend and splay of the director field. This field-induced transition in director orientation is called a Freedericksz transition [9, 106, 1071. We can also define Freedericksz transitions when the director and field are both parallel to the surface, but mutually orthogonal or when the director is nonnal to the surface and the field is parallel to it. It turns out there is a threshold voltage for attaining orientation in the middle of the liquid crystal cell, i.e. a deviation of the angle of the director [9, 107]. For all tliree possible geometries, the threshold voltage takes the fonn [9, 107]... 

Now the Lagrangean associated with the nuclear motion is not invariant under a local gauge transformation. Eor this to be the case, the Lagrangean needs to include also an interaction field. This field can be represented either as a vector field (actually a four-vector, familiar from electromagnetism), or as a tensorial, YM type field. Whatever the form of the field, there are always two parts to it. First, the field induced by the nuclear motion itself and second, an externally induced field, actually produced by some other particles E, R, which are not part of the original formalism. (At our convenience, we could include these and then these would be part of the extended coordinates r, R. The procedure would then result in the appearance of a potential interaction, but not having the field. ) At a first glance, the field (whether induced internally... 

Ire boundary element method of Kashin is similar in spirit to the polarisable continuum model, lut the surface of the cavity is taken to be the molecular surface of the solute [Kashin and lamboodiri 1987 Kashin 1990]. This cavity surface is divided into small boimdary elements, he solute is modelled as a set of atoms with point polarisabilities. The electric field induces 1 dipole proportional to its polarisability. The electric field at an atom has contributions from lipoles on other atoms in the molecule, from polarisation charges on the boundary, and where appropriate) from the charges of electrolytes in the solution. The charge density is issumed to be constant within each boundary element but is not reduced to a single )oint as in the PCM model. A set of linear equations can be set up to describe the electrostatic nteractions within the system. The solutions to these equations give the boundary element harge distribution and the induced dipoles, from which thermodynamic quantities can be letermined. 

Nonlinear Optical Devices. A transparent, optically active, sol—gel-derived organic—inorganic glass has been synthesized (68). This hybrid consists of a 2,4-dinitroaminophenylpropyl-triethoxysilane covalently bound to a siUcon alkoxide-derived siUca network. This hybrid exhibits a strong electric field-induced second harmonic signal and showed no signs of crystallization. 

Assuming that the current in the gas is carried mostly by electrons, the induced electric field uB causes transverse electron motion (electron drift), which, being itself orthogonal to the magnetic field, induces an axial electric field, known as the Hall field, and an axial body force, F, given by... 

The lesponsivity becomes independent of the bias voltage, V when the electric field-induced sweep time of the holes equals the hole lifetime. 

Both C and C, are related to the system voltage, as can be inferred from Table 24,1(b). The field induced by them is termed an electric field (non-magnetic). This field, i.e. content of Qand Cj, rises with an increase in the system voltage. 

X (p in Q cm) as in Table 30.1 /= frequency of the system in Hz p = effective permeability of the medium in which the field exists (aluminium in the present case), and will depend upon the electric field induced in the enclosure... 

For many problems it is convenient to separate the piezoelectric (i.e., strain induced) polarization P from electric-field-induced polarizations by defining D = P + fi , where s is the permittivity tensor. For uniaxial strain and electric field along the 1 axis, when the material is described by Eq. (4.1) with the E term omitted. 

A brief review is given on electronic properties of carbon nanotubes, in particular those in magnetic fields, mainly from a theoretical point of view. The topics include a giant Aharonov-Bohm effect on the band gap and optical absorption spectra, a magnetic-field induced lattice distortion and a magnetisation and susceptibility of ensembles, calculated based on a k p scheme. 

The situation changes drastically in the presence of a high magnetic field perpendicular to the axis. As has been discussed in Sec. 2, Landau levels without dispersion appear at the Fermi level considerably, leading to a magnetic-field induced distortion [13,14]. 

Electronic properties of CNTs, in particular, electronic states, optical spectra, lattice instabilities, and magnetic properties, have been discussed theoretically based on a k p scheme. The motion of electrons in CNTs is described by Weyl s equation for a massless neutrino, which turns into the Dirac equation for a massive electron in the presence of lattice distortions. This leads to interesting properties of CNTs in the presence of a magnetic field including various kinds of Aharonov-Bohm effects and field-induced lattice distortions. 

Generally speaking, tbe flow field induced by a gas explosion is characterized by two different gas-dynamic discontinuities ... 

Deshaies, B., and J. D. Leyer. 1981. Flow field induced by unconfined spherical accelerating flames. Combust, and Flame. 40 141-153. 

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