167 research outputs found
An elliptic property of parabolic trajectories
The curve joining the points of maximum height in the parabolas of ideal
projectile motion is shown to be an ellipse. Some features of the motion are
illustrated with the help of such ellipse.Comment: 4 pages, 1 figure. A shorter version of this typescript is scheduled
to be published in the Am. J. Phys. probably in May 200
Bioindicators as a tool for monitoring and control biofilm reactors : a simplified approach
The control of wastewater treatment plants requires an extensive monitoring programme based
on physicochemical costly routine analysis. Microbial populations are well known indicators of
operational conditions in biological reactors. This research was carried out by the CENTA and the
University of Minho in the scope of the Erasmus programme. The aim of the work was the
development of a simplified approach, based on biological indicators, for monitoring small biofilm
wastewater treatment processes. In that regard, protozoa and metazoan were monitored at
CENTA experimental plants - namely a trickling filter and a rotating biological contactor -, and
correlated with influent wastewater and effluent composition. The relationship between
wastewater performance and the microbiological composition of the biofilm was identified and
assessed. Results indicate that a methodology based on the bioindicators provides useful data
for process monitoring and control of small wastewater treatment plants, thus diminishing the
associated costs of routine analysis and providing information when such analysis arenât easily
available
Limitations on the superposition principle: superselection rules in non-relativistic quantum mechanics
The superposition principle is a very basic ingredient of quantum theory.
What may come as a surprise to many students, and even to many practitioners of
the quantum craft, is tha superposition has limitations imposed by certain
requirements of the theory. The discussion of such limitations arising from the
so-called superselection rules is the main purpose of this paper. Some of their
principal consequences are also discussed. The univalence, mass and particle
number superselection rules of non-relativistic quantum mechanics are also
derived using rather simple methods.Comment: 22 pages, no figure
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