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Famous examples of mathematical modelling include the Chancellor's economic model, F1 refuelling strategy, and even logistical optimisation for the D-day landing. Modern mathematical modelling offers some important advantages, such as getting a full understanding of a system without building it, optimising design parameters and comparing different design strategies.
In simple cases this can be accomplished with mechanical CAD, but for some applications dedicated software is required. Diverse are regularly called on to develop complex mathematical models and algorithms to either optimise a design or to embed complex models in the product software.
For those who are not mathematically minded a good example is a global positioning system (GPS) which uses a complex optimisation strategy to determine the position on the earths surface from the signals received by the GPS satellites.
DIVERSE has embedded similar mathematics into products used for car chassis straightening, optical filter design and TV camera control.
Modelling can be static or dynamic.
Dynamic Modelling
Dynamic models involve arrangements that vary in time - such as the dynamics of a car suspension, chemical reactions or a queuing system for internet data.
In the automotive industry we recently employed mathematical modelling to control the instrumentation needed for accurate measurement for repairs of twisted car chassis.
The industries and applications are very different, but the mathematics for the modelling is essentially the same.
Static Modelling
Static modelling involves taking inputs at an instant in time rather than over a period of time. An example of a static model would be a GPS which optimises the geometry of a complex physical arrangement.
One example of static modelling, recently undertaken by DIVERSE, involves automated camera control for real time tracking of objects. Using a mathematical model of the physical system the position of the object can be determined. This information, once processed can then be used to automatically direct a camera at the object. These mathematical models involve matrix analysis and three dimensional transformations to map coordinates between local and global systems.
For the above modelling it is important to 'know' positional information
about the detector and camera and this is then built into the model.
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