prjparticles2 - (7) in cartesian geometry, while in...

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4 Pollution Tracking In order to track pollutants with a particle tracking code, it is useful to imagine that the particles are actually blobs with an umbrella representing the amount of pollution they carry. This umbrella is usually represented by a Gaussian dis- tribution: q decays exponentially fast with radial distance from the center of the sphere. To compute the combined eFects of multiple blobs on the pollution at a point, one must sum-up their individual contributions. This type of representation is sometimes referred to as a radial basis function; in mathematical form it is: q ( x j ) = P s i =1 ˆ q i e - r 2 2 i (6) where ˆ q i is the maximum strength carried by the i -th particle. σ i is the width of the i -th blob. x i is vector position of the i -th blob. x j is vector position of the point of interest r is the distance between the two points x j and x i . It is r 2 = | x j - x i | 2 = ( x j - x i ) 2 + ( y j - y i ) 2
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Unformatted text preview: (7) in cartesian geometry, while in spherical geometry it is: r = R E arccos [sin θ j sin θ i + cos θ j cos θ i cos( λ j-λ i )] (8) where R E is the Earth radius. ±or the present problem we assume that ˆ q i remains constant as the blobs are carried by the wind. The concentration of q should be computed every 12 hours over a grid that spans a domain that encompasses a wide swath around the particle trajectories. Choose σ i = 1 km and ˆ q i = 1 for all particles. The concentration q ( x j ) should be computed on a set of points laid out on 1 / 8 degree grid. Note that the particles should be tracked for a period of 7 days. It is probably best if the output of q be written in binary form using the ²leio module. The data can then be read in matlab with the help of fortread.m. 5...
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This note was uploaded on 01/08/2012 for the course MSC 321 taught by Professor Staff during the Fall '08 term at University of Miami.

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