# symbolic algebra

## Maple example: symbolic algebra equation and numerical solution

Brehmsstrahlung in the field of the nuclei of a macroparticle (for beam modelling of electron beam lifetime in the HERA (electron-proton synchrotron particle collider)).

## HERA particle collider beam dynamics: Maple symbolic worksheet example.

The attached worksheet was exported to PDF via LaTeX from a Maple V worksheet. It shows detailed symbolic calculations and numerical simulations for the electron beam of the HERA (electron-proton synchrotron particle collider)

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## Maple zone

While very familiar with many other symbolic algebra systems, I have most experience with the MapleTM. This Webel zone introduces MapleTM through some fun examples, and some detailed examples from real-world physics and engineering projects.

Webel Scientific IT Consultancy offers professional MapleTM symbolic algebra services: symbolic analysis, data analysis, symbolic-driven numerics, animation, scientific modelling, education and training.

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## Science zone

- symbolic algebra
- synthesis
- applied mathematics
- applied physics
- astronomy
- astrophysics
- computational physics
- data visualisation
- Maple
- Mathcad
- Mathematica
- mathematics
- mathematics
- MATLAB
- model-based engineering
- model-driven architecture
- model-driven development
- neutron beam instrument
- neutron scattering
- neutron science
- patch programming
- physics
- radioastronomy
- radiophysics
- radiotelescope
- real-time synthesis
- science
- space (mathematics)
- supernova
- tomography

**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.

### Contents of: Science zone

- Galleries index: Science
- Gallery: Science: examples
- Scientific instruments
- Radiotelescopes
- The Molonglo Observatory Synthesis radioTelescope (MOST) in UML & Java (and FORTRAN)
- Gallery: a UML Parsing Analysis of an analysis of image formation in the MOST radiotelescope (from 2005)
- MOST: UML: synthesis
- MOST: UML: top-level
- MOST: UML: Reflector
- MOST: UML: Circularly polarised ring Antenna
- MOST: UML: Feed
- MOST: UML: Waveguide
- MOST: UML: Module
- MOST: UML: Bay
- MOST: UML: Arm
- Gallery: the MOST radiotelescope in Java and UML
- Reverse-engineering into UML of the TJDO database table structure for the MOST radiotelescope information system application (2004)
- Snapshot from a JSP web application for the MOST radiotelescope
- Honours thesis (1988): "An analysis of image formation by MOST (Molonglo Observatory Synthesis radioTelescope)": figures, scans, and UML models
- Gallery: MOST rotational aperture radiosynthesis figures (1988)
- Figure 1: MOST radiotelescope "skymap" from observation of a strong point source at field centre
- 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 5: The MOST radiotelescope centre fan-beam with field centre at meridian (from 1988)
- Figure 10: the MOST radiotelescope synthesised beam
- Gallery: scans of (some of) the MOST thesis report from 1988
- On Dr Darren's involvement with the MOST radiotelescope
- MOST: Java3D animations
- Neutron Beam Instruments (NBIs)
- Gallery: Port-based systems engineering of block models for control and simulation of Neutron Beam Instruments of the OPAL research reactor using UML/SysML (from 2007, online extracts)
- Figure 01: Convention and notation for Class/Interface pairs and associated wrapper Component.
- Figure 02: Flowport notation for mapping UML2 to Java
- Figure 03: Example: neutron beam instrument flowports and blocks for UML2
- Figure 04: ExampleBlock convention for block wrapper components and organisation of engineering elements
- Figure 05: Example: UML2 composite structure diagram (systems engineering view) of a fictitious neutron beam conditioning bunker.
- Figure 06: Example: wrapped class diagram (software engineering view) of a fictitious neutron beam conditioning bunker
- Figure 07: Model: Top-level UML2 composite structure diagram (systems engineering view) for the Platypus Reflectometer
- Figure 08: Model: Bunker shield assembly for the the Platypus reflectometer as UML2 composite structure diagram with flowport notation.
- 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 11: Model: UML2 composite structure diagram of the monochromator assembly
- 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.
- Figure 14: SWT TableTree ModelClient showing an instance of the Platypus reflectometer model.
- Figure 15: Simplified SysML version of the Platypus neutron reflectometer model.
- Meeting of the NeXus International Advisory Committee (NIAC), 2006
- Meeting of the NeXus International Advisory Committee (NIAC), 2008
- Particle colliders
- HERA (electron-proton synchrotron particle collider)
- HERA particle collider beam dynamics: Maple symbolic worksheet example.
- On 30 Jun 2007 HERA shut down and DESY celebrated 15 years of groundbreaking science
- Particle Accelerator Conference PAC97
- European Particle Accelerator Conference EPAC96
- Particle Accelerator Conference PAC95
- Data analysis and visualisation
- CT scan slice: visualisation example: 1
- CT scan slice: visualisation example: 2
- HERA particle accelerator: custom data analysis application
- HERA particle accelerator: electron Beam Loss Monitor lifetime disruption plots
- Symbolic Algebra zone
- Gallery: symbolic algebra examples
- Maple zone
- 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
- Maple symbolic animation example: the Webel logo
- Mathematica zone
- Cognitive Science zone
- Biology zone
- Astrophysics & Astronomy zone
- 25th Annual General Meeting of the Astronomical Society of Australia
- Astronomy and Astrophysics
- Gallery: Astronomy & Astrophysics, Space Science
- Mechanisms of Chromospheric and Coronal Heating
- Proc. Astron, Soc. Australia.
- Publ. Astron. Soc. Aust.
- Supernova zone
- Synthesis zone
- Mathematics zone

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## REDUCE

Used in the early 1990s to generate massive Jacobians in FORTRAN for finite-difference schema for computational gas dynamics:

Radiation hydrodynamics of early stages of type II supernovae (PhD thesis)

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