Quasistatic field

The initial explanation of how the ionization occurred and why it had an X l/3 scaling was based on a quasistatic field picture [6-8], which is easily understood by starting with the Stark effect in a static field. In an electric field the Stark shifts of hydrogenic m = 0 states are given by [3,4]... 

Special attention will be paid to the set of equations which describes the quasistation-ary or quasistatic fields and provides an accurate model for induction logging, with the exception of dielectric logging where very high frequencies are used. 

At this point we will consider a very important case, that of a quasistationary field, which is often also called a quasistatic field. 

Fig. 12. Production rate of seven triplet states of N2 as a fiaiction of time after initiation of the quasistatic field. Results are shown at altitudes of (a) 65 km and (b) 75 km (Morrill et al, 1998). The notation refers to the states A, B Ilg, W B C D, and E. ...

The magnitude of the spontaneous magnetization M in ordered magnets is temperature dependent due to spin wave excitations. Spin wave frequencies are so fast (THz) that they are fully motional-narrowed in jxSR. All one will observe is the expectation value of the internal field which is coupled (but not necessarily directly proportional) to the expectation value of M T). For this reason one calls the of an ordered magnet a quasistatic field. The spontaneous precession vanishes at a second-order magnetic transition point and reaches a saturation value for T —> 0. An example is shown in fig. 27. 

Combination with Static Fieids. A common technique, useful for optoelectronic devices, is to combine a monochromatic optical field with a DC or quasistatic field. This combination can lead to refractive index and absorption changes (linear or quadratic electrooptic effects and electroabsorption), or to electric-field induced second-harmonic generation (EFISH or DC-SHG, 2 > = > - - third-order process. In EFISH, the DC field orients the molecular dipole moments to enable or enhance the second-harmonic response of the material to the applied laser frequency. The combination of a DC field component with a single optical field is referred to as the linear electrooptic (Pockels) effect co = co + 0), or the quadratic electrooptic (Kerr) effect ( > = > - - 0 -I- 0). These electrooptic effects are discussed extensively in the article Electrooptical Applications (qv). EFISH is... 

It is well known that the orientation of a nematic layer can be influenced by external magnetic or quasistatic fields too. Thus it can be expected that the orientational deformation caused by a light field can be controlled by external fields. The aim of the present letter is to report experimental results on such an effect. 

As in previous chapters we work in the continuum limit employing quantities averaged over macroscopically infinitesimal volume elements and disregarding microscopic local variations associated with the molecular structure (see Brown 1956). These considerations will be limited to processes sufficiently slow to restrict the treatment to time independent or quasistatic fields. The validity of Maxwell s equations of electrostatics is presupposed. The basic electric state variables are the electric field strength vector E, the electric flux density (or electric displacement) vector D, and the electric polarization vector P, related by... 

Fig. 14.124. (a) The magnetization curve of DyCoNi obtained with fast and slow quasistatic field increases. The measurements shown by open circles were taken with a speed of 1 kOe s" , those shown by filled circles were obtained with a 60 s stay at each point, (b) The hysteresis loop and minor loops foi DyCoNi in quasistatic fields (Taylor et al., 1972). 

Levenston, M.E., Frank, E.H., and Grodzinsky, A.J. (1998) Variationally derived 3-field finite element formulations for quasistatic poroelastic analysis of hydrated biological tissues. Comput. Methods Appl. Mech. Eng. 156, 231-246... 

When all relevant Reynolds numbers are sufficiently small to permit neglect of inertial effects, the interstitial fluid velocity and pressure fields v and p, respectively, satisfy the quasistatic Stokes and continuity equations,... 

In Eq. (3), is the relevant molecular transition frequency, y is a dam >ing rate, is a polarizability, and (/) is the z-component of the total electric field in the vicinity of the molecule. If (t) were simply of the form i)Cos(fijr), then Eq. (3) is the well-known phenomenological Lorentzian oscillator model of absorption which leads to an approximate Lorentzian form for the absorption cross section [1]. Similar remarks hold for the SP dipole, fi/f), if E t) = ocos(mr), where E t) is the z-component of the total electric field near the SP dipole. The parameters 04,74 and a, in this case are chosen such that the resulting Lorentzian cross section proximates the known exact sur ce plasmon absorption cross section or its appropriate form in the quasistatic (a A=2 tic/cs) limit. Note that I am using a simplified notation compared to the various notations of Refs. [13-15]. (Relative to Ref. [13], for example, my definitions of surface plasmon dipole... 

The SPR can be simply formalized, in a first approach, by solving Laplace s equation in tlie case of a single conducting sphere surrounded by a homogeneous transparent medium, with tlie appropriate continuity relations at the metal-dielectric interface and assuming tliat the sphere radius is much lower than the wavelength (quasistatic approximation). The homogeneous local electric field inside the particle, E, then writes... 

Having solved the elastic boundary value problem and from it obtained the relevant interfacial concentrations, we are then prepared to obtain the concentration fields throughout the solid from which we compute the flux to or away from the various particles. Since we are assuming the situation to be quasistatic, the instantaneous concentration fields must satisfy an equilibrium condition, namely,... 

The mechanisms of formation of discrete segments of fluids in microfiuidic flow-focusing and T-junction devices, that we outlined above point to (i) strong effects of confinement by the walls of the microchannels, (ii) importance of the evolution of the pressure field during the process of formation of a droplet (bubble), (iii) quasistatic character of the collapse of the streams of the fluid-to-be-dispersed, and (iv) separation of time scales between the slow evolution of the interface during break-up and last equilibration of the shape of the interface via capillary waves and of the pressure field in the fluids via acoustic waves. These features form the basis of the observed - almost perfect -monodispersity of the droplets and bubbles formed in microfiuidic systems at low values of the capillary number. 

Thus the electrons "see" the quasistatic instantaneous field of phonons. As a result, the phonons shorten the localization length but produce hardly any real transitions between the localized states. At high temperatures (T oj) where the phonons may be described classically, the effective localization length Leff i-s determined by... 

Fig. 8. Schematic of various phenomena (top) and mechanisms (bottom) of lightning-ionospheric interactions as a function of altitude. Phenomena can give rise to alterations (A) in optical emissions (ASco), atmospheric temperature (AT), and electron density (AAf, ) detected as scattering of VLF signals. Other abbreviations are cloud-to-ground discharges (CG), quasistatic electric (QSE) fields and heating, electromagnetic pulse (BMP), and spacecraft (s/c) (Pasko et at., 1997).

Effects of the earth s magnetic field, and the weaker magnetic field associated with the slow variation of the quasistatic electric field, are usually neglected. The atmosphere is collision-dominated, so that an electron experiences many disruptive collisions in a pitch length. 

A detailed study of the N2 emission rates has been carried out by Morrill et al (1998). In this study, the quasistatic electric field model (Pasko et al, 1997) was used to calculate the electric fields, and the solution to Boltzmann s equation was used to calculate the electron energy distribution function as a fimction of altitude. Results for excitation of seven triplet states of N2 are shown in Fig. 12 at A = 65 and 75 km. The temporal diuation of the excitations may be understood in terms of the faster relaxation (higher conductivity see Fig. 9) of the E field at the higher altitude. 

In addition, the strong fields at the surface and interface at elevated temperatures may lead to field-assisted diffusion of mobile ion species such as protons and alkali ions, and strong illumination will require a new quasistatic equilibration, accompanied possibly by photodesorption (or adsorption), which might require long-time relaxation back to the dark equilibrium. 

Consider a semiconductor film placed in the fringe field that exists above a piezoelectric crystal such as LiNbOj, which carries a surface acoustic Rayleigh wave. The geometry is shown in Fig. 16. One can use the quasistatic approximation for the traveling wave because the wave travels with the sound velocity which is nearly static when compared with the light veloc-... 

The Fitch method [50] and its various modifications [31] are the most common quasistatic techniques used to measure the thermal conductivity. The main advantage of this method is that the test is simple and can be carried out in 10 min. For absolute measurements, however, the accuracy is rather low. Figure 27.4 shows a modified Fitch apparatus [51]. The sliced sample is placed between two copper plates. One plate acts as a heat source and the other plate as a heat sink. The thermal conductivity is calculated by Equation 27.12, which is the solution of the governing differential equation for the temperature field within the sample [51]. 

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