The Leaves of a Tree
"How much do the leaves on a tree weigh?" How might one estimate the actual
weight of the leaves (or for that matter any other parts of the tree)? How might one
classify leaves? Build a mathematical model to describe and classify leaves. Consider
and answer the following:
• Why do leaves have the various shapes that they have?
• Do the shapes “minimize” overlapping individual shadows that are cast, so as to
maximize exposure? Does the distribution of leaves within the “volume” of the tree
and its branches effect the shape?
• Speaking of profiles, is leaf shape (general characteristics) related to tree
profile/branching structure?
• How would you estimate the leaf mass of a tree? Is there a correlation between the
leaf mass and the size characteristics of the tree (height, mass, volume defined by the
profile)?
In addition to your one page summary sheet prepare a one page letter to an editor of a
scientific journal outlining your key findings.
Nowadays the heavy metal pollution is so common that people pay more and
more attention to it. The aim of this paper is to calculate the maximum of
methylmercury in human body during their lifetime and the maximum number of fish
the average adult can safely eat per month. From City Officials research[1], we get
information thatthemeanvalue of methylmercury in bass samples of the Neversink
Reservoir is 1300 ug/kg and the average weight of bass people consume per month is
0.7 kg. According to the different consuming time in every month, we construct a
discrete dynamical system model for the amount of methylmercury that will be
bioaccumulated in the average adult body.In ideal conditions, we assume people
consume bass at fixed term per month. Based on it, we construct fixed-ingestion
model and wereach the conclusion that the maximum amount of methylmercury the
average adult human will bioaccumulate in their lifetime is 3505 ug. As
methylmercury ingestedis not only coming from bass but also from other food, hence,
we make further revise to our model so that the model is closer to the actual situation.
As a result, we figure out the maximum amount of methylmercury the average adult
human will bioaccumulate in their lifetime is 3679 ug. As a matter of fact, although
we assume people consume one fish per month, the consuming time has great
randomness. Taking the randomness into consideration, we construct a
random-ingestion model at the basis of the first model. Through computer simulations,
we obtain the maximum of methylmercury in human body is 4261 ug. We also
calculate the maximum amount is 4420 ug after random-ingestion model is revised.As it is known to us, different countries and districts have different criterions for mercury
toxicity. In our case, we adopt LD50 as the toxic criterions(LD50 is the dosage at
which 50% of the humans exposed to a particular chemical will die. The LD50 for
methylmercury is 50 mg/kg.). We speculate mercury toxicity has effect on the ability
of eliminating mercury, therefore, we set upvariable-elimination model at the basis of
the first model. According to the first model, the amount of methylmercury in human
body is 50 ug/kg, far less than 50 mg/kg, so we reach the conclusion that the fish
consumption restrictions put forward by the reservoir advisories can protect the
average adult. If the amount of methylmercury ingested increases, the amount of
bioaccumulation will go up correspondingly. If 50 mg/kg is the maximum amount of
methylmercury in human body, we can obtain the maximum number of fish that
people consume safely per month is 997.
Keywords: methylmercury discrete dynamical system model variable-elimination
model
discrete uniform random distributionmodelrandom-ingestion model
Introduction
With the development of industry, the degree of environmental pollution is also
increasing. Human activities are responsible for most of the mercury emitted into the
environment. Mercury, a byproduct of coal, comes from acid rain from the
smokestack emissions of old, coal-fired power plants in the Midwest and South. Its
particles rise on the smokestack plumes and hitch a ride on prevailing winds, which
often blow northeast. After colliding with the Catskill mountain range, the particles
drop to the earth. Once in the ecosystem, micro-organisms in the soil and reservoir
sediment break down the mercury and produce a very toxic chemical form known as
methylmercury. It has great effect on human health.
Public officials are worried about the elevated levels of toxic mercury pollution
in reservoirs providing drinking water to the New York City. They have asked for our
assistance in analyzing the severity of the problem. As a result of the bioaccumulation
