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Now let s use the string theory considerations to nd the entropy. This is done by applying the adiabatic procedure to the string coupling gs 0 and noting that the entropy remains unchanged during the process. We follow the procedure outlined in Susskind (please see References). What is found is that as gs 0 , the black hole turns into a single string which has the same entropy as the black hole. The black hole transitions into a single string when the radius of the horizon is the same as the fundamental string length s. The Planck length p can be related to the fundamental string length using:

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} mesh.vertexCount = vertexIndex; [BBSceneController sharedSceneController].totalVerts += vertexIndex; }

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please make your way to the exit. Shoppers begin to make their way to the doors, but some wander from store to store, window-shopping along the way, while others take a relatively straight route to the exit. The result is that some shoppers take longer than others to exit the mall because there are different modes. Now consider a mall that has a single, very narrow corridor that is only as wide as a person s shoulders. Now when the announcement comes, everyone heads for the exit, but they must form a single file line and head out in an orderly fashion. If you understand the difference between these two examples, you understand multimode vs. singlemode fiber. The first example represents multimode; the second represents single mode.

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You then set your vertexCount in the mesh object so that it knows how many vertexes to render. Finally, you are going to jam the particle count into a state variable in the scene controller. This is a bit of a hack, but I want to be able to display the number of particles on the screen, because I have another object that comes around later and uses this to render that number. It is important to note the order in which you are building these vertexes. Currently, I am using front-face culling to make the 3D models slightly smaller in terms of vertexes rendered. However, the 3D models I am using require front-face culling, which means that the 3D models have clockwise (CW) windings, so I need to build these triangles in CW order as well. Astute readers will notice that you are building what amounts to the same array of UV coordinates every time. In theory, you could just build that array once, since they are all the same. This is true, and if I didn t have a plan that involved multiple sets of UV coordinates in mind for later in the chapter, then it would be silly to build the same array over and over again.

The first of these examples was multimode fiber, which arrived in a variety of different forms. Multimode fiber bears this name because it allows more than a single mode or ray of light to be carried through the fiber simultaneously because of the relatively wide core diameter that characterizes the fiber. And while the dispersion that potentially results from this phenomenon can be a problem, there are advantages to the use of multimode fiber. For one thing, it is far easier to couple the relatively wide and forgiving end of a multimode fiber to a light source than that of the much narrower single-mode fiber. It is also significantly less expensive to manufacture (and purchase) and relies on LEDs and inexpensive receivers rather than the more expensive laser diodes and ultrasensitive receiver devices. However, advancements in technology have caused the use of multimode fiber to fall out of favor; single-mode fiber is far more commonly used today. Multimode fiber is manufactured in two forms: step-index fiber and graded-index fiber. We will examine each in turn.

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In step-index fiber, the index of refraction of the core is slightly higher than the index of refraction of the cladding. Remember that the higher the refractive index, the slower the signal travels through the medium. Thus, in step-index fiber, any light that escapes into the cladding because it enters the core at too oblique an angle will actually travel slightly faster in the cladding (assuming it does not escape altogether) than it

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-(void)addVertex:(CGFloat)x y:(CGFloat)y u:(CGFloat)u v:(CGFloat)v { NSInteger pos = vertexIndex * 2.0; vertexes[pos] = x; vertexes[pos + 1] = y; uvCoordinates[pos] = u; uvCoordinates[pos + 1] = v; vertexIndex++; }

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Here is the add vertex method. It just populates the vertex and UV arrays with data and increments the vertexIndex. Almost there! Now to emit new particles! But first, let s talk about random numbers.

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