The flux

Diffusivity measures the tendency for a concentration gradient to dissipate to form a molar flux. The proportionality constant between the flux and the potential is called the diffusivity and is expressed in m /s. If a binary mixture of components A and B is considered, the molar flux of component A with respect to a reference plane through which the exchange is equimolar, is expressed as a function of the diffusivity and of the concentration gradient with respect to aji axis Ox perpendicular to the reference plane by the fpllqvving relatipn 6 /... 

Lew frequency Eddy current probing For frequencies below some 100 Hz the SQUID is coupled with a completely superconducting flux antenna. This antenna has to be within the cryogenic vessel. The Eddy current excitation is done in a conventional way. But care must be taken, that interference between the excitation field and the flux anteima and SQUID is... 

For the field calculation it more convenient to use a tx(B) curve than the normal ix(H) curve because the calculated vector potential A is derived from the flux density B. This ii(B) curve however can be calculated easily from the measured values. 

These formulas are completely general and may be applied to any material, any form of piece and any coil. in the formula, the conductance is proportional to the amplitude of the part of the flux crossing the coil in phase with the current in the solenoid. 

The variation of the Z of the solenoid mark a transfer of energy at distance between the solenoid and the conducting piece. The variation of the impedance is due to the modification of the magnetic flux d) crossing the solenoid. In fact, the flux differs in amplitude and in phase when the conducting piece is near the solenoid. Similarly, the flux will be influenced by the presence of defect. 

The total flux O in the coil is the sum of flux rta in section between coil and the tube and the flux Ok in the section of the tube and the flux inside the tube. 

If it is true, the flux in the tube is proportional to the surface area where the induction is not equal to zero, we may then write ... 

The final equation obtained by Becker and Doting may be written down immediately by means of the following qualitative argument. Since the flux I is taken to be the same for any size nucleus, it follows that it is related to the rate of formation of a cluster of two molecules, that is, to Z, the gas kinetic collision frequency (collisions per cubic centimeter-second). 

Assuming a thennal one-dimensional velocity (Maxwell-Boltzmaim) distribution with average velocity /2k iT/rr/tthe reaction rate is given by the equilibrium flux if (1) the flux from the product side is neglected and (2) the thennal equilibrium is retamed tliroughout the reaction ... 

Here, the symbol denotes an averaging over the flux-weighted distribution [7, 8] for positive or negative initial velocities of the reaction coordmate. In figure A3.8.2 is shown the correlation fimction K(t) for the particular case of the reaction of methyl vinyl ketone with cyclopentadiene in water. The leveling-off of this... 

A second recent development has been the application 46 of the initial value representation 47 to semiclassically calculate A3.8.13 (and/or the equivalent time integral of the flux-flux correlation fiinction). While this approach has to date only been applied to problems with simplified hannonic baths, it shows considerable promise for applications to realistic systems, particularly those in which the real solvent bath may be adequately treated by a fiirther classical or quasiclassical approximation. 

Day P N and Truhlar D G 1991 Benchmark calculations of thermal reaction rates. II. Direct calculation of the flux autocorrelation function for a canonical ensemble J. Chem. Phys. 94 2045-56... 

Figure Bl.23.2. (a) Shadow cone of a stationary Pt atom in a 4 keV Ne ion beam, appearing with the overlapping of ion trajectories as a fiinction of the impact parameter. The initial position of the target atom that recoils in the collision is indicated by a solid circle, (b) Plot of the nonnalized ion flux distribution density across the shadow cone in (a). The flux density changes from 0 inside the shadow cone, to much greater than l in the focusing region, converging to 1 away from the shadow cone edge, (c) Blocking cones...

Diffusion may be defined as the movement of a species due to a concentration gradient, which seeks to maximize entropy by overcoming inhomogeneities within a system. The rate of diffusion of a species, the flux, at a given point in solution is dependent upon the concentration gradient at that particular point and was first described by Pick in 1855, who considered the simple case of linear difflision to a planar surface ... 

However, the equation can be simplified, since the system is synmietrical and the radius of the disc is nomrally small compared to the insulating sheath. The access of the solution to the electrode surface may be regarded as imifomi and the flux may be described as a one-dimensional system, where the movement of species to the electrode surface occurs in one direction only, namely that perpendicular to the electrode surface ... 

If the molecules could be detected with 100% efficiency, the fluxes quoted above would lead to impressive detected signal levels. The first generation of reactive scattering experiments concentrated on reactions of alkali atoms, since surface ionization on a hot-wire detector is extremely efficient. Such detectors have been superseded by the universal mass spectrometer detector. For electron-bombardment ionization, the rate of fonnation of the molecular ions can be written as... 

The flux-flux expression and its extensions have been used to calculate reaction probabilities for several important reactions, including H2+02 H + H2O, by explicit calculation of the action of G in a grid representation with absorbmg potentials. The main power of the flux-flux fomuila over the long mn will be the natural way in which approximations and semi-classical expressions can be inserted into it to treat larger systems. 

The diffusion of small molecules in polymers can be described using Pick s first and second laws. In a onedimensional situation, the flux J(c, x) as a function of the concentration c and the position x is given by... 

The flux of F radicals to tire wafer is nearly isotropic. Anisotropic etching is due to ions tliat are incident on tire wafer essentially perjDendicular to tire surface (see above). 

If there are no reactions, the conservation of the total quantity of each species dictates that the time dependence of is given by minus the divergence of the flux ps vs), where (vs) is the drift velocity of the species s. The latter is proportional to the average force acting locally on species s, which is the thermodynamic force, equal to minus the gradient of the thermodynamic potential. In the local coupling approximation the mobility appears as a proportionality constant M. For spontaneous processes near equilibrium it is important that a noise term T] t) is retained [146]. Thus dynamic equations of the form... 

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