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Maths & Physics fun: Animation of Laplacian Spherical Harmonics in Blender with morphing between l values for each m

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Maths & Physics illustrated using Blender (and with some help from Wolfram Mathematica).

This maths & physics education video by Dr Darren R C Kelly of Webel IT Australia presents animations of Laplacian Spherical Harmonics in Blender with morphing between l values for some m values.

Please note that this video is about the mathematics, not about how Blender was used; there may also be a video later about how Blender Geometry Nodes was used for the animations.

Physics fun: Animation of linear vs circular polarisation of electromagnetic waves in Blender 3D using a novel colour map (with supplementary Mathematica animations and analysis)

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Physics illustrated using Blender and Wolfram Mathematica. Dr Darren explains:
A mate of mine said he was having a bit of trouble wrapping his head around circular polarisation. I thought of a novel way of illustrating it that I hope helps others who are curious about physics but perhaps are not formally training physicists (and it served as a fun way for me to hone my Blender 3D skills).

Visuals: Amazing super long play Maths Art 3D video creating using scenes generated by Wolfram Mathematica and combined with FX!

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A breathtaking Maths Art presentation created by Dr Darren of Webel IT Australia using Wolfram Mathematica and FX tools, presented here under his digital artist name PLAYlogo. Be sure to set the video player to 4K quality and use full screen!

Mathematica 3D with Manipulate GUI: The ARCHITIME Design kinetic/dynamic wall reproduced in Wolfram Mathematica

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The parametric architecture company ARCHITIME Design has a wonderful kinetic/dynamic wall installation outside their office building. You can view their original videos of their installation at these links:

http://www.architime.ru/works/dynamic_wall_papushevo.htm

http://www.architime.ru/works/dynamic_wall/papushevo/animate.gif

SECTION: Miscellaneous examples of applications of Webel libraries for Mathematica to air conditioners and heat exchangers. With SysMLv1 models.

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

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The Shah 1982 CHART correlation for saturated boiling heat transfer as SysML Activity Diagrams (1)
The Shah 1982 CHART correlation for saturated boiling heat transfer as SysML Activity Diagrams (2): Detailed view of the hex$SI$Shah$twophase$htc$combined SI Real convention function variant
hex$E$Shah$twophase$htc$combined as a single expression using ‘sym$’ markup
Gungor-Winterton method for boiling heat transfer 1987 as SysML Activity Diagram ('$SI$' Real convention version)
hex$E$GungorWinterton$1987$twophase$htc$horizontal as a single expression using ‘sym$’ markup
SysMLv1 Parametric Diagram of the Effectiveness-NTU Method for a finned tube cross flow air conditioner heat exchanger

SECTION: CASE STUDY: Applications of the Webel MTools class extensions to Psychrometrics (humid air physics). With SysMLv1 models.

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

If you want to navigate the entire section including the additional explanatory text click on the title link of the first slide to view the full slide page, then use the next links to move through the slide pages. If you just want to view the slide images only in sequence, click on any slide to view it larger in a viewer, then click again to move through each slide in this tutorial trail section.
Overview of the Psy` package and the "one shot" MPsy humid air state class
The MPsy “one shot” humid air state class
MPsy object creation examples
Psychrometrics exercise references (and about some naming conventions)
Psy`Psychrometrics package variables registry
CONVENTION: ‘$EQ$’, ‘$E$’, ‘eq$’ and ‘sym$’: Examples from the Psy` Psychrometrics package
About the Psy` package Psychrometrics exercises slides (in this trail)
Psy` package equations/functions (some correspond to exercise cases)
Psy`humid air physics package: Example: Sensible Heating in SysMLv1
Psy` humid air physics package: Example: Sensible Heating results
‘$E$’, ‘$Q$’,‘$SI$’ and ‘$C$’ function variants: Simple demo using a trivial Psy` function

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[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

If you are interested in Mathematica, the Wolfram Language, or Systems Modeling Language v1 (SysML®) you may be interested in accessing the very comprehensive accompanying

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SECTION: Webel ADT case study: Extracting structured data from unstructured Open XML spreadsheet data

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

If you want to navigate the entire section including the additional explanatory text click on the title link of the first slide to view the full slide page, then use the next links to move through the slide pages. If you just want to view the slide images only in sequence, click on any slide to view it larger in a viewer, then click again to move through each slide in this tutorial trail section.
Overview of the Webel OpenXML libraries ADT Case Study
ADT hierarchy for the XL` package for reading unstructured data from OpenXML XLSM bundles
ADT hierarchy for the US` package with intermediate unstructured data and identification of data groups
ADT hierarchy for the EX`package for extracted structured data
ADT hierarchy for a typical Client Data (CD) layer for identifying structured data groups
Typical unstructured spreadsheet data imported into the XL layer
XL$Row and XL$Cell under the hood
XL$Cell value resolution for “text” requires an XL$ResourcesMap (Real, Integer, and Boolean value resolution does not)
UUID-driven Once-caching. Example: XL$Cell value resolution with an XL$ResourcesMap
XL$Cell with a VBA formula and XL$F
XL$RowList vs XL$Row vs XL$Cell
Spreadsheet “units indicator” HACKS do NOT use a units-aware Quantity algebra!
Units and Quantity extraction with US$Row
US$RowList spanned rows filling
US$RowList sub-list extraction
US$RowList & EX$RowMap column extraction and custom styled tables
US$RowList “section” extraction
UD` demo package for US$Section
UD` demo: Basic US$ValuesSection
US$ValuesSection to EX$RowMap
US$SectionMap auto-detection
Specific Component-aware sub-ADTs
Demo Component values extraction (but not yet as EX Component ADTs)
The demo UD$EX$Component for extracted structured EX Layer data
The US$SheetManager as a bridge between the US Layer and EX Layer
Extracted demo UD$EX$Component:Demo UD$EX$Components: Creative views in the UD$SheetManager
Demo UD$EX$Components analyser
UD$EX$Components as (quick) XML
UD$EX$Component “database” demo (using a Wolfram Language EntityStore)

SECTION: The Webel Abstract Data Type (ADT) stateless pseudo-classes with inheritance (with SysMLv1 models)

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

If you want to navigate the entire section including the additional explanatory text click on the title link of the first slide to view the full slide page, then use the next links to move through the slide pages. If you just want to view the slide images only in sequence, click on any slide to view it larger in a viewer, then click again to move through each slide in this tutorial trail section.
Introduction to Webel Abstract Data Types (ADTs) with SysMLv1 models
Webel Abstract Data Types (ADTs) vs the user-contributed MTools for OO
Webel ADTs include inheritance (and aren’t actually formal ADTs)
Webel ADT hierarchy views as tree, graph, and SysML
Mini SysMLv1 BDD view of the Webel ADT Block
SysMLv1 Internal Block Diagram (IBD) of the Webel ADT base class
Webel ADT`package: Some ADT pseudo class utility functions in a ::usage help viewer. Diagnostic, help, and development functions.
Simple Webel ADT in the development view dV[adt] and class/methods help hC[adt]
Classes in the ADT` package: Extendable ADT pseudo classes have corresponding "definer functions"
Creating new ADTs that extend other classes using a definer function (and adt$addSuper)
Extending ADT sub-classes represented as SysML Blocks with redefined wrapped ‘$$’
Webel «adt:pseudo» elements in the SysMLv1 ADT model (1)
Webel «adt:pseudo» elements in the SysMLv1 ADT model (2)
Chained wrapped ADT pseudo Lists: Example: EX` package structured data ADTs
Chained wrapped ADT pseudos as a SysMLv1 Internal Block Diagram (IBD)
Clients of List ADTs don’t usually directly access the wrapped Lists (but can for testing with ADT⊙get which BREAKS ENCAPSULATION)
Webel ADT SysMLv1 Stereotypes
adt$graphHierarchy example: The EX` package for structured data
ADT finder functions and “methods” adt$findUp, adt$findUpArg, ADT⊙fM
ADT help functions and methods: adt$treeHierarchy (adt$tH), adt$hC, ADT⊙hC: Example: XL$Cell
ADT`: helpADT[class]: help on methods registered with HelpO`: Example: XL$Cell
adt$store, adt$fetch, and «adt:ref»: Example: Reference XL$ResourcesMap by ID in US$ResourcesHolder.

SECTION: The Webel MAll & MOptsSet classes MTools extensions (with SysMLv1 models)

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

If you want to navigate the entire section including the additional explanatory text click on the title link of the first slide to view the full slide page, then use the next links to move through the slide pages. If you just want to view the slide images only in sequence, click on any slide to view it larger in a viewer, then click again to move through each slide in this tutorial trail section.
Introduction to the Webel All` package and the MAll universal class extending MTools
The Webel W`MOO` packages: MOO = MTools OO support utilities
The Webel MAll universal (intermediate) base class
MDemo`: Overview of demo classes for MAll & MOptsSet
MAll: All public Methods with signatures
MAll: methodHelp and methodFind: Short aliases mH and mF
MAll: Methods related to classes and contracts: Example: MDemoAll: From the MAll self-test GUI
MAll: isContractOf for PatternTest (easier contract checks for MTools)
The Webel MAll universal class for MTools integrates with the HelpO` method registry
HelpO`: Options management for MTools methods (lookup replaces OptionValue[])
The MAllDemo class with MOptsSetDemo
Registering method options using a Webel AOR (Argument, Options, Rules) Map
Use a method with an option via a Webel opts Association
MOptSet options groups: Example: MOptSetDemo
Use an MOptsSet options group: Example: MAllDemo.methodWithOptsSet uses MOptsSetDemo
An MOptSet can also be used in function Options[]
The MNestAllDemo class with optional MAll ‘obj’ child
The MNestAllDemo class with MAll or MAllDemo as child
Every MAll has a default gui[] for methods that don’t need arguments
Command GUI configuration and nesting: Example: MNestAllDemo
The MAll class has a self-tester GUI (for DEVELOPMENT use only)
Convention-based MDemoConfig with fields for ‘$opt$’ options (works with any MTools class but prefer MOptsSet or MOpt)

SECTION: The Webel Var` package Entity-based variable registry

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

If you want to navigate the entire section including the additional explanatory text click on the title link of the first slide to view the full slide page, then use the next links to move through the slide pages. If you just want to view the slide images only in sequence, click on any slide to view it larger in a viewer, then click again to move through each slide in this tutorial trail section.
About the Webel Var` package variables registry
Var` package variables registry example: Heat exchanger calculations (just p1 of 227 variables!)
Var` package variables registry example: Heat exchanger calculations (just p2 of 227 variables!)
Var` package: Special '$e$' field convention
Var` package: Package function ::usage overview
Var` package: “qualified name” String as key
Var` package: Register variables with e$var$add
Var` package: ‘sym$’ markup reused in ‘$E$’ functions
Var` package: Extracted Associations
Var` package: Demo variables in e$var$table[] view
Var` package: e$var$table[] filtering by package

SECTION: The Webel Doc` package and the HelpF, HelpO`& HelpM` help registry packages

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

If you want to navigate the entire section including the additional explanatory text click on the title link of the first slide to view the full slide page, then use the next links to move through the slide pages. If you just want to view the slide images only in sequence, click on any slide to view it larger in a viewer, then click again to move through each slide in this tutorial trail section.
Doc` package ::usage help generation using the docV and docF functions (1)
Doc` package ::usage help generation using the docV and docF functions (2)
Why the Webel HelpF` & HelpO` registries?
The Webel HelpF` function registry
HelpF`example: helpFunction[$pac$HelpF, addFunction]
HelpF`example: helpPackage[$pac$HelpF]
HelpF`example: addFunction (1)
HelpF`example: addFunction (2)
Generate shared option groups using ‘$opt$’ helpers: wl$optsFromOpts, docsFromOpts, rulesFromOpts, and odrMap triplet
HelpF`: OptionsPattern groups as SysML shared between functions
Webel ODR (Options, Docs, Rules) as SysML
HelpF`: Pull Mathematica Options[] from a Webel HelpF` options superset
HelpF`: Pull Mathematica Options[] for a function registered with addFunction
HelpF`: usageF for ::usage generation example
HelpF`: UsageF ::usage generation: Example helpClass::usage
The HelpF` & TestF` packages: General query based help
HelpF`: packageFunctionTree[$pac]: Function ::usage help and signatures within a package
HelpF`: DownValues: sigsDown[f]: Signature(s) from ExpressionTree
HelpF`: Simple function DownValues inspector GUI: gui$helpDownStrings
HelpF`: gui$helpDownStrings signature display modes
TestF`: Simple package function DownValues vs ::usage checker
TestF`: Function search by argument number/kind to aid testing automation (1)
TestF`: Function search by argument number/kind to aid testing automation (2)
The Webel HelpO`package class and method registry
HelpO`: addClass: Register an MTools class by fully qualified package name
HelpO`: addMethod: MTools method registration example for the Webel MAll class and an object
HelpO`: Part of the help registry for the Webel MAll universal MTools class and some methods
HelpO`: Find help on a method of a Webel MAll universal class object
HelpM`: Using the MFunction and MMethod helper classes with MArg & MOpt
HelpM`: Using the Webel MFunction class and MArg & MOpt with HelpF`
HelpM`: Using the Webel MMethod class and MArg & MOpt with HelpO`
HelpM`: Use MFunction and MMethod with MArg & MOpt for ::usage (and consistent with the HelpF` and HelpO` registries)
HelpM`: Using the Webel MClass helper with the MMethod helper and the HelpO` help registry
HelpM`: Using the Webel MPackage helper with MFunction and MClass and the HelpF` and HelpO` help registries
Incremental benefit through Doc`, Var`, HelpF`, HelpO`, HelpM`

SECTION: The Webel '$opt$' and '$arg$' help holder conventions for options and arguments in the Wolfram Language

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

If you want to navigate the entire section including the additional explanatory text click on the title link of the first slide to view the full slide page, then use the next links to move through the slide pages. If you just want to view the slide images only in sequence, click on any slide to view it larger in a viewer, then click again to move through each slide in this tutorial trail section.
The Webel '$opt$', 'rule$opt$', '$arg$', 'rule$arg$' and supporting '$k$' conventions for "help holders"
The Webel '$opt$' option "help holder" convention
Webel ‘$opt$grp$’ with grouping qualifier (where ‘grp$’ could be a package nickname)
Webel '$opt$' options help by function: Example: tableFunctionOptions[f]
Cleaner Options declarations!
Webel '$arg$' and '$opt$' support via the Doc` package
Functions from the W`Base`Doc` package
Make a Webel option help Rule relying on ‘$opt$’ naming conventions
Webel ‘$arg$’, ‘def$arg$’, and ‘rule$arg$’ convention
Make a Webel help Rule for a required ‘$arg$’ argument + conventions
Make a Webel argument help Rule with a default by convention OR override
Webel $arg$ convention help consistency checks
Webel ‘rule$arg$’ convention help consistency checks
Generate $doc$arg$ and $doc$opt$ Strings from Webel help Rules for use in ::usage
When to use explicit $arg$ help holders (in lower level utility packages)
Why not just generate all the '$arg$' and '$opt$' help holders (using ToExpression)?
Why not just use the Entity system for '$arg$' and '$opt$' help holders?
Association vs Class as SysML CASE: Webel $arg$ and $opt$ help
Association as SysML: CASE: Webel @RuleMap and @ArgsMap «pseudo» blocks. Very "fiddly" to represent in a SysML Block Definition Diagram!
Association as SysML: CASE: Webel @ArgMap «pseudo» block (slightly less "fiddly" as an Internal Block Diagram)
Easier ‘$arg$’ and ‘$opt$’ help Rules using the Webel MArg and MOpt helper classes and MTools for OO
Webel ‘$arg$’ help is much easier with the MArg class using MTools!
Webel ‘$opt$’ help is much easier with the MOpt class using MTools!
Webel ‘$opt$’ help even easier with makeOpt[$name] for MOpt!
HelpM`: Use Webel MOpt and MArg objects to create ‘$doc$’ Strings for ::usage help
SysML: OptionsPattern[] “Generalizations” using Join:" Example: HelpM` helper classes new functions
The AOR Map (Arguments, Options, Rules): Integrated ::usage, HelpF`/HelpO` registration, and Options[] (without MTools)
The AOR Map (Attributes, Options, Rules) Association: Example: aor$f$helpClass
The AOR Map as SysML Blocks with Rules

SECTION: A brief look at the Webel W`Base` utilities for Mathematica

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

If you want to navigate the entire section including the additional explanatory text click on the title link of the first slide to view the full slide page, then use the next links to move through the slide pages. If you just want to view the slide images only in sequence, click on any slide to view it larger in a viewer, then click again to move through each slide in this tutorial trail section.
The Webel W`Base`«M:Project» and «M:Paclet»
Overview of Webel utility W`Base` packages as SysMLv1 Blocks
Overview of Webel utilities W`Base` packages as SysML Usages
Detailed overview of Webel utilities W`Base` packages with usages
Webel W`Base` vs Git repository and Wolfram Player Pro encoded version
Some Webel Devel` package functions
Diagnostic message Print output switching between Mathematica and Wolfram Player Pro
Devel` package: check Function Symbol against ::usage
Devel` functions for ExpressionTree (basic)
Some Webel Utility` package functions
The Webel ‘$pac$’ convention and DEVEL loading echo diagnostics
Utility`package: stripOpt and stripOpts Delegating subsets of Options
Some Webel Display` package functions
The Webel ManGUI` package utilities for Manipulate GUIs
The Webel ManGUI` package has some shorthand '$man$' option aliases
Some Webel ManGUI` package functions
The Webel Units` library with short-cut variables for frequently used Units and their String identifiers
Webel ManGUI` examples: man$bool and man$group$pane
The Webel W`Moo` package group: Additional utilities for the user-contributed MTools paclet for classes & object orientation
Deployment folders for projects that depend on W`Base` and MTools OO (as SysML)

SECTION: Webel coding and naming conventions for the Wolfram Language

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

If you want to navigate the entire section including the additional explanatory text click on the title link of the first slide to view the full slide page, then use the next links to move through the slide pages. If you just want to view the slide images only in sequence, click on any slide to view it larger in a viewer, then click again to move through each slide in this tutorial trail section.
DRY not WET! "Don't Repeat Yourself!"
The Webel ‘$’ prefix convention for Strings and "String similar" Wolfram Language code
The Webel $k$ prefix convention for Association String keys
The Webel ‘$pat$’ pattern helper convention for frequently used Patterns
The Webel ‘$t$’ “pseudo type” indicator String convention (for optional additional documentation only)
Webel ‘$info$f$’ prefix convention for function help holder Strings
Webel ‘def$’ DRY default capture! Applicable to arguments and options.

SECTION: Modelling the Wolfram Language in SysMLv1 and related Webel coding conventions

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

If you want to navigate the entire section including the additional explanatory text click on the title link of the first slide to view the full slide page, then use the next links to move through the slide pages. If you just want to view the slide images only in sequence, click on any slide to view it larger in a viewer, then click again to move through each slide in this tutorial trail section.
Modelling the Wolfram Language in SysML and SysML-friendly coding conventions.
Basic SysMLv1 example: The HelpM` package MTools classes as Blocks
SysML Stereotypes and icons used for Mathematica and Wolfram technologies
Wolfram Language vs SysMLv1
Parameter types in most SysML tools
Explicit vs implicit representation of expressions in SysML4Mathematica
Webel SysML4Mathematica: Some Wolfram Language Heads as SysMLv1 Blocks and ValueTypes
Concise {} for List and <||> for Association
Frequently used typed {} Lists
Frequently used String pair Lists
Association <||> vs Rule
Typed Association example: <||>$* maps String to any expression
“Active” OpaqueBehaviors corresponding to block Heads: Used in CallBehaviorActions
“Chained” Head and OpaqueBehavior Convenient for frequently used combinations
Example: Representation of a Webel MAll class MTools method as a SysML Activity Diagram
SysML Activities as function networks (simple contrived Real maths example)
SysML/UML ExpansionRegion for iteration (as adapted for use with Mathematica)
SysML Activity with @pseudo functions capturing Wolfram Language logic
The sigsUp/Down functions as a SysML BDD: With Options Block and pseudo functional indicators
The sigsUp function with OptionsPattern modelled as a SysML Activity (and with "pseudo functional" representation)
Extract Options from an OptionsPattern[] in a SysML Activity (1)
Extract Options from an OptionsPattern[] in a SysML Activity (2) DETAILED
About «pseudo» blocks (always prefixed with ‘@’)

SECTION: The Webel Mathematica libraries - INTRODUCTION - And the role of SysML

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

Slides in this section

If you want to navigate the entire section including the additional explanatory text click on the title link of the first slide to view the full slide page, then use the next links to move through the slide pages. If you just want to view the slide images only in sequence, click on any slide to view it larger in a viewer, then click again to move through each slide in this tutorial trail section.
DISCLAIMERS & CONCERNING TRADEMARKS
About the author
About this slide set
About use of Wolfram Language code
About use of SysML Diagrams
A word on classes and object orientation for Mathematica
Representing the SysMLv1 Block and SysMLv2 Part Def in Mathematica requires classes and object orientation (OO)
SysMLv1 vs SysMLv2
Main topics & sections
HOW not WHAT!
It’s rather technical!

[TECHNICAL SLIDE TRAIL] The Webel libraries for Wolfram Mathematica: With SysMLv1 models.

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DISCLAIMERS & CONCERNING TRADEMARKS
SECTION: The Webel Mathematica libraries - INTRODUCTION - And the role of SysML
SECTION: Modelling the Wolfram Language in SysMLv1 and related Webel coding conventions
SECTION: Webel coding and naming conventions for the Wolfram Language
SECTION: The Webel '$opt$' and '$arg$' help holder conventions for options and arguments in the Wolfram Language
SECTION: A brief look at the Webel W`Base` utilities for Mathematica
SECTION: The Webel Doc` package and the HelpF, HelpO`& HelpM` help registry packages
SECTION: The Webel Var` package Entity-based variable registry
SECTION: The Webel MAll & MOptsSet classes MTools extensions (with SysMLv1 models)
SECTION: The Webel Abstract Data Type (ADT) stateless pseudo-classes with inheritance (with SysMLv1 models)
SECTION: Webel ADT case study: Extracting structured data from unstructured Open XML spreadsheet data
SECTION: CASE STUDY: Applications of the Webel MTools class extensions to Psychrometrics (humid air physics). With SysMLv1 models.
SECTION: Miscellaneous examples of applications of Webel libraries for Mathematica to air conditioners and heat exchangers. With SysMLv1 models.
[PUBLIC VERSION PENDING] SECTION: CASE STUDY: Applications of the Webel MTools class extensions to air conditioners and heat exchangers. With SysMLv1 models.

The Webel Recipe for SysML-friendly Wolfram Language coding in Mathematica

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As part of a long term project developed, initially during work for a client, Webel IT Australia in partnership with GreenSoft Pty Ltd is developing a very complex Mathematica application with substantial SysML modelling support.

Service: Wolfram Mathematica: Modelling, data analysis, mapping, transformation, and visualisation, including end-user GUIs

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Webel IT Australia are experts in applications of the powerful  Wolfram Mathematica technical computing system to symbolic algebra, equation analysis, numerical analysis, physics and engineering simulations, data analysis and transformation, plotting, generative graphics, 3D modelling, animation, image processing, and rapid desktop GUI development for end users for deployment to Wolfram Player Pro<

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