Mathematical modeling light scattering

MIE Theory a complex mathematical model that allows the computation of the amount of energy (light) scattered by spherical particles. 

They calculated the value of k by using mathematical models and found a value of 5/s for hard spheric particles. This value was obtained in an equivalent manner many years ago for a gas composed of hard spheric molecules (31). They derived this equation from osmotic pressure measurements and showed the parallelism between these virial coefficients and those obtained from light scattering. Stockmayer et al. (32) made an... 

Figure 30 shows a simple model of a typical laser diffraction instrument where the diffraction pattern of light scattered at various angles from the sample particles that pass through the He-Ne laser beam is measured by different detectors and recorded as numerical values relating to the scattering pattern. These numerical values are then converted to the particle size distribution in terms of the equivalent volume diameter using a mathematical model from the instrument s software. 

Though these chapters refer to each other they can be read independently. For the sake of convenience the references are listed at the end of each chapter, sorted by topic. Due to its broad scope, the book can only discuss the general ideas and procedures of physical theories, mathematical models or numerical tools, while details have to be elicited from the cited literature. Only a few topics with major relevance (e.g. the models on light scattering) are described more comprehensively in the appendices. 

A continuum theory implicitly assumes a model for the absorption by and scatter from a particle of infinitesimal size. This model is only a reasonable approximation for samples in which the fraction of light absorbed by an individual particle is a very small fraction of the light incident upon it. The advantage of this model is that it is simple, though the mathematics that describe it are not. The discontinuum method we will describe uses mathematics no more complex than the continuum theories. However, the description of the sample is more complex. This is both the power and limitation of the discontinuum theories they can describe more complex situations, but doing so requires a more detailed description. 

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