297,070 research outputs found
Urban air pollution dispersion model
Three-dimensional integrated puff model simulates smoke plume dispersion processes and estimates pollutant concentration during periods of low wind speed. Applications for model are given
Conformal Transformation of the Schr\"{o}dinger Equation for Central Potential Problems in Three-Dimensions
In a recent paper, it has been shown the Schr\"{o}dinger equation for the
three-dimensional harmonic oscillator can be simplified through the use of an
isometric conformal transformation. Here, it is demonstrated that the same
transformation technique is also applicable to the Schr\"{o}dinger equation for
the hydrogen atom. This approach has two interesting features. Firstly, it
eliminates potential fields from the Schr\"{o}dinger equation. The Coulomb and
harmonic binding terms are instead represented as imaginary parts of complex
time. Secondly, the method leads to a general relationship between potential
energy and ground state energy that encompasses both the hydrogen atom and the
harmonic oscillator as special cases.Comment: 8 page
Local Warming
Using 55 years of daily average temperatures from a local weather station, I
made a least-absolute-deviations (LAD) regression model that accounts for three
effects: seasonal variations, the 11-year solar cycle, and a linear trend. The
model was formulated as a linear programming problem and solved using widely
available optimization software. The solution indicates that temperatures have
gone up by about 2 degrees Fahrenheit over the 55 years covered by the data. It
also correctly identifies the known phase of the solar cycle; i.e., the date of
the last solar minimum. It turns out that the maximum slope of the solar cycle
sinusoid in the regression model is about the same size as the slope produced
by the linear trend. The fact that the solar cycle was correctly extracted by
the model is a strong indicator that effects of this size, in particular the
slope of the linear trend, can be accurately determined from the 55 years of
data analyzed.
The main purpose for doing this analysis is to demonstrate that it is easy to
find and analyze archived temperature data for oneself. In particular, this
problem makes a good class project for upper-level undergraduate courses in
optimization or in statistics.
It is worth noting that a similar least-squares model failed to characterize
the solar cycle correctly and hence even though it too indicates that
temperatures have been rising locally, one can be less confident in this
result.
The paper ends with a section presenting similar results from a few thousand
sites distributed world-wide, some results from a modification of the model
that includes both temperature and humidity, as well as a number of suggestions
for future work and/or ideas for enhancements that could be used as classroom
projects.Comment: 12 pages, 5 figures, to appear in SIAM Revie
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