Continuous-field

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Scalar Fields Consider a continuous field theory in Euclidean space with action... 

Spin-locking If a continuous field is applied along the y -axis immediately... 

If no immediate hazards are identified during the approach to the site, the incident commander will likely approve the team to enter the site and perform the site characterization. During this stage, the team will continue field safety screening at the site and conduct a detailed site investigation. 

Note the similarity of Eqs. 2.43 and 2.44 with Eqs. 2.80 and 2.81 because both the vectors in the former equations and the functions of the latter are all elements of linear vector spaces. The main difference arises in the way in which the inner products are evaluated. Also, as was the case for vectors, if the field functions are non-negative functions, SCar(F, F pj will be non-negative. When this is not the case, however, Sr.ir(F (,F g) may become negative, a situation that also obtains for the other similarity indices discussed in the remainder of this section. Maggiora et al. (43) have treated this case in great detail for continuous field functions, but the arguments can be carried through for finite vectors as well (vide supra). 

The surface of a crystal is thus chemically unsaturated and the existence of a definite surface energy is due to the fact that the surface is unsaturated. Since the surface of a crystal consists of a regular lattice of orderly distributed atoms or ions the surface adhesional forces may be regarded as being distributed over the centres of these atoms (Haber, J.G.S.I. xxxiii. 50 Z it.f. Elektro-chem. XX. 521, 1914) although in all probability these points represent maxima in a continuous field. 

Given that the velocity vector is a continuous field variable, a differential increment in velocity can be represented generally through the following expansion as... 

Experimental and theoretical evidence indicates that pulsed fields cannot have greater effects than continuous fields of the same average power (51). Hence, modulation is not expected to have special effects. 

Only a few behavioral studies have so far been reported with these modulated RF fields. Chicks exposed to 450 MHz, 1 or 5 mW/cm2 fields sinusoidally modulated at 3 or 16 Hz during performance of a fixed-time 30 sec schedule of water reinforcement showed trends towards longer latency of response (44). In Soviet studies, rabbits and rats chronically exposed for 120 days to extremely low levels of 50 or 2500 MHz continuous fields or 10 GHz fields pulsed at 1000 or 20 Hz showed statistically significant alterations in conditioned reflexes with field intensities between 1.9 and 2.0 yW/cm2. A 2450 MHz, 1 mW/cm2 microwave field pulsed at 1000/sec had a synergic effect on the action of Valium (chlordiazepoxide) on fixed-interval behavior in rats (46). 

Let ub take a cylinder filled with gas and a piston holding the gas in the cylinder, and let us consider the action of some continuous field of force on this Bystem. As long ob the piston is not moved and the external field of force is unchanged, the above condition is fulfilled. However, if we move the piston, for example (considering the action of the piston as a field of elastic forces), the condition is violated in this case we act on the gas, inasmuch as we change in time the existing external field of force. Cf. Section 23b. 

P. Fevrier, O. Simonin, and K. Squires. Partitioning of particle velocities in gas-solid turbulent flows into a continuous field and a spatially uncorrelated random distribution Theoretical formalism and numerical study. J. Fluid Mech., 533 1-46, 2005. 

Broholm M. M., Riigge K., Tuxen N., Hpjbjerg A. L., Mosbaek H., and Bjerg P. L. (2001) Fate of herbicides in a shallow aerobic aquifer a continuous field injection experiment (Vejen, Denmark). Water Resour. Res. 37, 3163-3176. 

Another phenomenon of recent interest and debate which may benefit from a habit routine interpretation is filling in. In its simplest aspect, it has long been known that due to the particular structure of the eye, there is a small blind spot on each retina at the position of its attachment to the optic nerve. The portion of the visual scene projected here is therefore not represented in the visual cortex of the brain, yet we have no awareness that there are two blank spots in our field of view. (A simple experiment that all children are taught shows the reality of the blind spot.) The process whereby the brain nevertheless produces an apparent continuous field of view is called filling-in, and some examples of recent research and controversy are by Francis Crick. (14) Although the blind spot may be a quite simple process (the retina itself may play some... 

Fig. 9.50. Schematic representation of the use of continuous fields to represent grain boundaries. In particular, the interfacial region is characterized by gradients in the order parameter r).

The basic ideas in this section reflect an extension of the kinematic ideas of continuum mechanics in the sense that rather than enumerating the properties of a system on a discrete atom-by-atom basis, the state of the system is subsumed into either a set of continuous fields or a collection of coordinates which identify the positions of the defects that populate the system. We have seen that the class... 

In J. J. Thomson (Ed.), James Clerk Maxwell A Commemorative Volume 1831-1931, Cambridge Univ., 1931, Einstein said I incline to the belief that the physicists will. .. be brought back to the programme which may suitably be called Maxwell s the description of Physical Reality by fields which satisfy without singularity a set of Partial differential equations. In a letter that Einstein wrote to David Bohm in 1953, he said If it is not correct that reality is described as a continuous field, then all my efforts are futile, Einstein Archives, Jewish National and University Library, The Hebrew University of Jerusalem, Call No. 1576 8-053. 

Sakurai et al. [218] have used the atom probe field ion microscope [219] to make a direct study of hydride phases on silicon. Continuous field evaporation from 111 and 110 Si planes in the presence of hydrogen produced Si+, SiH+ and SiHj. Some Si atoms evaporate without forming hydrides to give Si+ SiH+ derives simply from the monohydride phase and SiHj from the dihydride. However, this latter comes from the 111 surface, whereas UPS data consistent with the presence of a dihydride came from 100 lxl. This apparent difference can be reconciled by the fact that some kink site atoms on 111 planes have two dangling orbitals per Si atom (as on 100 surfaces) and field evaporation occurs primarily at kink sites. 

In the same frame of the time-dependent two-term approximation, kinetic problems in quite different time-dependent fields have been dealt with (Wilhelm and Winkler, 1979 Winkler, 1993). So, for example, the temporal evolution of the kinetic properties initiated by jumplike and continuous field transitions between steady states, by pulselike field alterations, or by decaying electric fields and the periodic evolution (Winkler, 1993) caused by the action of high-frequency electric fields in a wide range of field frequencies should be mentioned in this context. 

Figure. —Continued. Field-electron emission microscopy of small, organic adsorbates. (C) With increased copper-phthalocyanine. (D) With flaventhrene adsorption. (Courtesy of Dr. A. J. Melmed, The National Bureau of Standards, Gaithersburg, MD.)...

How to balance chemical equations was always a continuing field because of its importance [2-6]. A critical review has been given by Herndon [7]. A general procedure to obtain the stoichiometric coefficient is to solve the system of the homogeneous linear equations that are obtained from the principles of conservation of matter and charge. The earliest chemical paper by J. Bottonily in 1878 used this method [8]. 

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