Mathcad

Science zone

Dr Darren of Webel originally trained as a computational physicist and applied mathematician, performed research from 1988 to 1993 in radio astronomy and astrophysics, and worked as a scientific computing expert and particle accelerator physicist from 1993 to 1999, as well as working on numerous science and education projects after establishing the Webel IT Australia Scientific IT Consultancy in 2000. You can find out more about his science career at: Dr Darren Kelly's full-career Curriculum Vitae.

From Wikipedia: Computational Physics (Aug 2016):

Computational physics is the study and implementation of numerical analysis to solve problems in physics for which a quantitative theory already exists. Historically, computational physics was the first application of modern computers in science, and is now a subset of computational science.

It is sometimes regarded as a subdiscipline (or offshoot) of theoretical physics, but others consider it an intermediate branch between theoretical and experimental physics, a third way that supplements theory and experiment.


This zone features various (mostly archival and historical) science projects, many of which demonstrate applications of the model-based software engineering and systems engineering technologies promoted on this site and offered as Webel services.


HERA particle accelerator: electron Beam Loss Monitor lifetime disruption plots
Example of numerical integation and visualisation of a differential equation in the Maple symbolic algebra system
Maple 3d plot animation example
Maple example: symbolic algebra equation and numerical solution
HERA particle accelerator: custom data analysis application
CT scan slice: visualisation example: 1
CT scan slice: visualisation example: 2
MOST radiotelescope: Java3D animation: steering (9.8M)
Figure 2: A diagram of MOST with the numbering system used in this  thesis report (1988)
Figure 3: MOST radiotelescope: A diagram of the coordinate system used in the report (1988)
Figure 10: the MOST radiotelescope synthesised beam
Figure 1: MOST radiotelescope "skymap" from observation of a strong point source at field centre
Figure 11: Model: UML2 composite structure diagram of the monochromator assembly
Figure 09: Model: bunker shield assembly for the Platypus reflectometer as "wrapped block" class diagram.
Figure 10: Model: UML2 composite structure diagram for the monochromation beam stage of the neutron diffractometers of the OPAL NBIs.
Figure 12: Model: UML2 composite structure diagram of the monochromator stage assembly with motorised goniometer rotation, tilt, and translation stages, which are driven by encoded devices.
Figure 13: Model: wrapped block class diagram (software engineering view) for the entire monochromation beam ("logical") stage.


Contents of: Science zone

Symbolic Algebra zone

Maple symbolic animation example: the Webel logo
Maple example: symbolic algebra equation and numerical solution
Example of numerical integation and visualisation of a differential equation in the Maple symbolic algebra system
Maple 3d plot animation example

Dr Darren says:

"I consider symbolic algebra languages and applications to be amongst the greatest technological achievements of humanity."

My interest in symbolic algebra started during my PhD research from 1989-1993 when I became interested in automating the tedious task of calculating Jacobians of numerical difference schemes for implicit gas/hydro dynamics solvers. I successfully used the REDUCE symbolic algebra system to generate FORTRAN code representing implicit integration methods, and I used it to model supernova shock waves.

Since then symbolic algebra has played a role in nearly all of my scientific activities, whether using the Maple, Mathematica, Mathcad, or MATLAB/Simulink symbolic application (thankfully the REDUCE command-line days are long gone).

I'm a symbolic algebra evangelist: I like to introduce others to the incredible possiblities of symbolic algebra at every opportunity.

My applications of symbolic algebra have included:

  • Development of a symbolic algebra system for generating compilable code for implementing implicit 3D time-dependent PDE equation solvers. The system has been tested on an advanced gasdynamics solvers using adaptive gridding.
  • Symbolic worksheets for modelling dust disruptions in electron particle accelerators (example: MapleV.3: HERA particle collider beam dynamics: Maple symbolic worksheet example.)
  • Symbolic data analysis and visualisation of multi-dimensional datasets.

For more examples of some of my applications of symbolic algebra please visit the Maple zone.

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