Electricity continuous distribution

If we consider a molecule as having a static but continuous distribution of electronic charge around a rigid nuclear framework, then its electrical or electrostatic potential will have a term similar to Eq. (3.2), with Q. being the positive charges of the nuclei, ZA, and a... 

The density p(r) might also be described as the fractional probability of finding the (entire) electron at point r. However, chemical experiments generally do not probe the system in this manner, so it is preferable to picture p(r) as a continuous distribution of fractional electric charge. This change from a countable to a continuous picture of electron distribution is one of the most paradoxical (but necessary) conceptual steps to take in visualizing chemical phenomena in orbital terms. Bohr s orbits and the associated particulate picture of the electron can serve as a temporary conceptual crutch, but they are ultimately impediments to proper wave-mechanical visualization of chemical phenomena. 

Although the quantum problem seems to be solved by the hydrodynamics of a continuous distribution of electricity with charge density proportional to mass density, this approach has never been accepted as a serious alternative, largely because of doubts raised by Madelung himself. The most important of these, concerns the self-interaction between the charge elements of an extended electron. 

We can generalize the analogy by considering the viscoelastic materials as a continuum where the theory of transmission lines can be applied. In this way, a continuous distribution of passive elements such as springs and dash-pots can be used to model the viscoelastic behavior of materials. Thus the relevant equations for a mechanical transmission line can be written following the same patterns as those in electrical transmission lines. By representing the impedance and admittance per unit of length by g and j respectively, one has... 

In the model experiment under consideration, the field is represented by the outgoing and incoming spherical waves of photons, which are specified by a continuous distribution of k or of co = ck. Assume that the two identical atoms are the two-level atoms of the type of (34) with the electric dipole transition. Because of the simple geometry of the problem (Fig. 17), it can be considered as a quasiunidimensional integrable system [69]. The effective spatial dependence of the photon operators can be introduced with the aid of the Fourier transformation... 

The field application of electrical resistivity techniques can be affected by the presence of nearby power lines, fences, railroad tracks, and buried pipes and cables. These cultural features may create electrical interference or alter the subsurface pattern of current flow distribution. In addition, in order to complete electrical resistivity surveys you must be able to "seat" the electrodes in the ground to establish electrical continuity with the subsurface materials to be studied. 

From a quantum-mechanical point of view, it is said that electron wave functions are spread out over the entire solid atomic levels are transformed into an energy band, where differences between energy levels are so small that it can be thought of as a continuous distribution of states. Electrons in a band can no longer be assigned to a particular cation. They are delocalised and become free, in the sense that having energy states available, they can easily be excited by an external electrical field to transport current, for example. 

For example, the limit of a continuous distribution of an electrical charge /o(r) shrunken to a point charge q at ro can be represented by... 

The electric potential distribution is given by the equation (5.94), which is essentially a continuity equation for the electric current density. Indeed, taking into account the condition (5.91) of electric neutrality, one can rewrite (5.87) as... 

Equation 1 is the Poisson equation. This equation should be solved in order to obtain the electric potential distribution in the computational domain. On the right hand of this equation, the term F Z] iZ,c, shows the gradient influence of the co-ions and counterions on the electric potential inside the domain. The electric field is the gradient of the electric potential (Eq. 2). Equation 3 is the Nemst-Planck equation, where the definition of ionic flux is given by Eq. 4. On the right-hand side of this equation, (m c,), (D, Vc,), and (z,/t,c,V( ) represent flow field (the electroosmosis), diffusion, and electric field (the electrophoresis), respectively, which contribute to the ionic mass transfer. The ionic concentrations of each species can be found by solving these two equations. Equations 5 and 6 are the Navier-Stokes and the continuity equations, respectively, which describe the velocity field and the pressure gradient in the computational domain. 

The distribution of the reinforcement agent within the matrix can be very effectively impacted by the use of multiphase polymer blends. The microstructure morphology is determined by the polymer structure in the blend, the system composition and miscibility, which can lead to immiscible or co-continuous distribution of phases. (Utracki 1989). The incorporation of the filler into one of the polymer phases or into the phase interface has a strong influence on the electrical conductivity of composites, concomitantly reducing the percolation concentration. 

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