4 1. Building Your Basic ToolBox
molecular mechanics simulation to make sure the tires will not overheat before you
get there.” Instead, they will be useful simulations and models that fill a unique spot
because they operate on a simple set of rules that play themselves out in complicated
and sometimes extravagant detail. For example, Newton’s second law tells us how force,
mass and acceleration are related. We’re no strangers to that law—we’ve known it for
centuries now and discovered it intuitively when we were children. Most people also
know about gravity and how to solve gravity—driven problems on pencil and paper
where there’s weight and maybe air resistance. But now consider a model where we
have to determine if the surface roughness of a soccer ball affects its flight—this is a
very difficult problem with subtleties necessary to take into account to make it relevant
and useful, usually impossible to solve with just pencil and paper.
So how would I like this text to get you to model things? I would like it to encour-
age nonscientists to leverage their familiarity and proficiency with computers to help
understand everyday things better, equipping your toolbox for simulations from the
ground up and perhaps most importantly, enticing us all to “lift the hood” and try our
hand at constructing abstract models. Consider real scenarios where it would be very
useful to conduct a computer simulation. Some situations are personal, others may
occur in a professional setting, and all are precisely the kind discussed in this book,
where we build from the ground up.
Suppose that you invested in a house and you’ve been there for 20 years; you just
found out that its cinder block foundation is leaking. Repair costs are more than you
can afford in a lump sum but you also know that as time progresses the leak will con-
tinue to do more damage. e question is whether to take a loan out to fix the house, or
if you should save money and fix it in 5 years. How does the interest you pay on the loan
compare to increased repair costs if you wait until you can afford to fix the leak using
your own savings? e scientific issue is a diffusion through porous medium problem
and you could utilize a finite element computer simulation to estimate the water seep-
age and hence the extent of leakage and damage over the next 5 years to see whether or
not the cost to remediate is likely to exceed the interest of the loan. Sometimes, real life
processes are too slow to provide useful information but computer simulations can help
us understand how they might unfold.
Enter a mechanical engineer who had a family member badly hurt in a car accident.
In this particular case the fenders of the car crumpled as they should have. at is, they
did their job of taking energy away from the cars’ motion and dissipating it so the col-
lision was not so dangerous as it would have been otherwise. However, it was very cold
that day and the collision angle was such that the doors cracked in certain spots and
crumpled inwards, causing injury to the driver. As would be expected, the engineer is
now on a mission to make cars safer in cold weather collisions, where metal alloys are
more likely to crack and fail. eir first thought is to prevent the doors from fracturing
at low temperatures by either modifying the metal alloy composition or perhaps adding
an anti-fracture coating to the inner surface of the door, much like is already done for
glass in cars. In either case, the physical issue is an understanding of material fracture
and fracture propagation as a response to stress. A Material Point Method/Equation of
State simulation or possibly a large scale Molecular Mechanics method could be used
to understand how the material fractures and how the fracture propagates, ultimately
causing material failure. Sometimes, real life processes are too fast to provide useful
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