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We can reason that, if the diameter, 2ai, of the sphere is large compared with the skin depth at that frequency, there will be little amplitude remaining to reemerge back into the medium, so almost all of the power incident to the sphere will be absorbed by the copper But, if the diameter 2ai is comparable to the skin depth, we will expect some of the incident power to reemerge back into the external medium Unless the reemerging wave front interferes constructively with the incident wave, the total incoming power will be lost to the incident wave However, if the reemerging wave front interferes constructively, it will so with a time delay relative to the incident wave; that is, there will be a phase shift of the total wave that we would interpret as an inductive characteristic in a circuit model.

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Because we are modeling many snowballs of different sizes and the delay of the reemerging wave front is dependent on size, we would expect random interference with the incident wave from an assembly of spheres We would thus conclude that the sum of the incoming power and the outgoing (scattered) power is phase shifted relative to the power of the incident wave To nd the lost power to a linear propagating wave, we need to determine how much power is outgoing from a conducting sphere and add that to the power that is incoming toward a conducting sphere This can be accomplished by using the techniques of partial wave scattering analysis used by particle physicists and radar engineers.

Figure 5.4 Regions in the 0 C -plane (the Cp -plane in our notation) with an indication of the maximal number of ECM that may occur (roman numerals). The saddle-node bifurcation curves are dashed and the Hopf bifurcation curve is a solid curve. (The Hopf curve has two parts, which match up by identifying 0 with 2 ; the dotted line is the lower boundary for possible multiple solutions.) Source: Reproduced from G.H.M. Van Tartwijk and D. Lenstra, Quantum Semiclass. Opt., 7, 87 143 (1995) 1995 by Institute of Physics Publishing.

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However, as we will discuss in 7, the total scattered power from a large number of conducting spheres can add constructively to the incident wave to produce a total intensity that is attenuated and phase shifted (delayed) relative to the incident wave This will give us an electromagnetic wave foundation for resistance and inductance to compare with a circuit model interpretation..

Whenever a new version of a technology is in the market, older versions face the risk of becoming obsolete as everyone prefers the applications to cover the newer version. This is why all new versions have to consider the question of backward compatibility. This is less of a problem when the newer technology simply adds to the functionality of a previous one. Addition of functionality is related to the availability of more hardware resources. But when we are faced with a new technology such as J2ME, the situation is different. In this case, the hardware resources available are few, sometimes drastically so. For example, the resources on a pager and those on a PC are just not comparable. This means that, if we want to use existing Java applications intended for the PCs on a pager, we are faced with a much bigger problem than just the question of compatibility. Our task in this chapter is to find out whether converting applications is possible, and if it is, how existing Java applications can be used for devices that run J2ME. The differences between J2ME and J2SE can be really vast so much so that they may turn out to be unbridgeable. The real extent of these differences depends on what part of J2ME is being considered. There is a very wide gap between CLDC (and the profiles made for it) and J2SE. On the other hand, when it comes to CDC and the Foundation Profile, the differences are marginal. This situation will further change when more profiles become available and the devices with which we are concerned get equipped with better hardware. PersonalJava technology, which is going to be merged in J2ME in the form of Personal Profile, has more or less the functionality of JDK1.1.

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