{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

prjparticles2 - (7 in cartesian geometry while in spherical...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
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 effects 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 summationdisplay 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 )
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern