Affiliation(s)
1. Golden Gate University, Ageno School of Business, San Francisco, California 94105, USA
2. Department of Physics, University Campus 2, University of Guilan, Rasht, Iran
3. Galaxy Advanced Engineering, Albuquerque, New Mexico 87111, USA
ABSTRACT
Nearly all scientists, at conjunction with simplifying a differential
equation, have probably used dimensional analysis. Dimensional analysis (also called
the Factor-Label Method or the Unit Factor Method) is an approach to the
problem that uses the fact that one can multiply any number or expression
without changing its value. This is a useful technique. However, the reader
should take care to understand that chemistry is not simply a mathematics
problem. In every physical problem, the result must match the real world. In
physics and science, dimensional analysis is a tool to find or check relations
among physical quantities by using their dimensions. The dimension of a
physical quantity is the combination of the fundamental physical dimensions
(usually mass, length, time, electric charge, and temperature) which describe
it; for example, speed has the dimension length/time, and may be measured in
meters per second, miles per hour, or other units. Dimensional analysis is
necessary because a physical law must be independent of the units used to
measure the physical variables in order to be general for all cases. One of the
most derivation elements from dimensional analysis is scaling
and consequently arriving at similarity methods that branch out to two
different groups namely self-similarity as the first one, and second kind that
through them one can solve the most complex none-linear ODEs (Ordinary
Differential Equations) and PDEs (Partial Differential Equations) as well.
These equations can be solved either in Eulearian or Lagrangian coordinate systems
with their associated BCs (Boundary Conditions) or ICs (Initial Conditions).
Exemplary ODEs and PDEs in the form of none-linear can be seen in strong
explosives or implosives scenario, where the results can easily be converted to
induction of energy in a control forms for a peaceful purpose (i.e., fission or
fusion reactions).
KEYWORDS
Renewable, nonrenewable source of energy, fusion and fission reactors,
small modular reactors and generation four system, nuclear micro reactor, space
reactor, dynamic site, return on investment, total cost of ownership.
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