|
We know applied mathematics is a very rich field that is constantly evolving. The field has always been driven by applications
in science and industry and the mineral industry has been a significant source for creative ideas. Mining engineering is
responsible for the program design, operation, management, extraction and processing minerals from naturally occurring
environment and mathematical formulated solutions are critical for the successful completion of very complex tasks.
There is no need to go very far to find cases of successful applications with mathematical models of use in mining, which
produce enormous savings to the industry, not only applicable in planning mining, but in extraction and processing of minerals.
Generally, when we refer to the use of applied mathematics in industry, we imply the use of numerical analysis techniques to
implement proven mathematical theory.
The largest or smallest value of a numerical function depending on several parameters. Such a function is often called the
objective or goal function. Many kinds of problems can be expressed in optimization , i.e, finding the maximum or the
minimum of a goal function. In mining it is frequently used to determine allocation of laborers to work areas and also
to calculate optimum load extraction based on expected total output production volume and ore grade requirements.
Many other prototypical solutions involve theory based on non-linear analysis, numerical integration, function evaluation,
complex numbers, boundary value solutions, eigenvalue solutions, and differential equations. A few cases to mention:
Underground mining operations requiring construction of platforms to carry assorted equipment with specific dimensions;
Exploratory drilling tasks for obtaining sample core bits in a formation where several methods of combined drilling are
used in somewhat complex geological sections and finding stress concentrations around holes; Use of the Fourth-Order Runge-Kutta
integration methods to resolve polluted reservoirs exacerbated by large-scale earth disturbances and acid drainage and find
acceptable levels of concentration of the pollutants as fresh water would replenish the reservoir; Applications
in underground mining for tubing diameter variations due to diametric contractions regarding site temperatures;
Applications in Cut-and-Fill stoping mining methods problems using rock mechanics techniques including finite element,
finite difference and boundary integral methods.
Many mathematical functions used in numerical computation are defined by an integral, a recurrence formula, or
a series expansion. While such definitions can be useful to a mathematician, they are quite complicated to implement
in a computer. For one, mining engineers may know how to evaluate an integral numerically, but then there
is the problem of accuracy, and the evaluation of a function as defined mathematically involves complexity. Plus programming
expertise is paramount to produce application module solutions that are accurate, useful and timely.
This being the case, the mathematical representation via numerical modeling represents a major challenge. The importance
of applied mathematics in the mineral industry is so significant that future generations of mining engineers need to be
very knowledgeable in numerical analysis procedures, possess solid command of high level programming languages and feel
comfortable with mathematics reasoning in general.
Practical samples and further interesting discussions
on mineral engineering can be found at http://www.keystoneminingpost.com
|