Infinite source model

The data analysis procedure for the case of constant heat flux is based on the theory describing the response of an infinite line source model (Ingersoll and Plass, 1948 Mogeson, 1983). Although this model is a simplification of the actual experiment, it can successfully be used to derive the geothermal properties (e.g. Kavenaugh, 1984 Austin,. 1998 Gehlin, 1998). 

Samples of polycrystalline material were studied at 750 to 1050C by using a groove and stain technique. It was shown that the Fisher model for grain boundary diffusion accurately described the data when an infinite source was assumed. It was found that the grain boundary diffusivity was described by ... 

If the receptor is within an area source, or if emission rates do not vary markedly from one area source to another over most of the simulation area, the narrow-plume hypothesis can be used to consider only the variation in emission rates from each area source in the alongwind direction. Calculations are made as if from a series of infinite crosswind line sources whose emission rate is assigned from the area source emission rate directly upwind of the receptor at the distance of the line source. The ATDL model (22) accomplishes this for ground-level area sources. The RAM model (8) does this for ground-level or elevated area sources. 

For all reactions, the mass transport regime is controlled by the diffusion of the reacting ligand only, as the mercury electrode serves as an inexhaustible source for mercury ions. Hence, with respect to the mathematical modeling, reactions (2.205) and (2.206) are identical. This also holds true for reactions (2.210) and (2.211). Furthermore, it is assumed that the electrode surface is covered by a sub-monomolecular film without interactions between the deposited particles. For reactions (2.207) and (2.209) the ligand adsorption obeys a linear adsorption isotherm. Assuming semi-infinite diffusion at a planar electrode, the general mathematical model is defined as follows ... 

Another factor that is of great importance for the observed sulfur isotope variations of natural sulfides is whether sulfate reduction takes place in an open or closed system. An open system has an infinite reservoir of sulfate in which continuous removal from the source produces no detectable loss of material. Typical examples are the Black Sea and local oceanic deeps. In such cases, H2S is extremely depleted in " S while consumption and change in " S remain negligible for the sulfate. In a closed system, the preferential loss of the lighter isotope from the reservoir has a feedback on the isotopic composition of the unreacted source material. The changes in the " S-content of residual sulfate and of the H2S are modeled in Fig. 2.21, which shows that 5 S-values of the residual sulfate steadily increase with sulfate consumption (a linear relationship on the log-normal plot). The curve for the derivative H2S is parallel to the sulfate curve at a distance which depends on the magnitude of... 

Section IV reviews our more recently developed 4D ether model [102-104], which is based on the premise of the existence of E. Rest mass is associated to a flow of primordial fluid (preons). This novel dynamic concept of mass solves at once several longstanding difficulties two of them are (1) the infinities associated with electric and gravitational fields and (2) the stability of orbits under Coulomb attraction. Indeed, there is a permanent flow of momentum across a particle (source) the momentum flux is occasionally tapped by interaction with a (test) particle. Such process does not change the total momentum flux available at the source hence, there is no loss of potential energy as in the conventional interpretation. The total momentum that crosses a source is, of course, infinite in an infinite time, but the source is always finite. 

The theoretical model assumes a line heat source dissipating heat radially into an infinite solid, initially at uniform temperature. The fundamental heat conduction equation in cylindrical coordinates, assuming uniform radial heat transfer, is [3] ... 

In Section II, motivated by the fact that in typical experiments an aging system is not isolated, but coupled to an environment which acts as a source of dissipation, we recall the general features of the widely used Caldeira-Leggett model of dissipative classical or quantum systems. In this description, the system of interest is coupled linearly to an environment constituted by an infinite ensemble of harmonic oscillators in thermal equilibrium. The resulting equation of motion of the system can be derived exactly. It can be given, under suitable conditions, the form of a generalized classical or quantal Langevin equation. 

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