User Guide: Graduate Student Learning Pathway

Welcome to the RheoJAX User Guide, structured as a 16-week graduate course in rheological analysis with JAX acceleration.

How to Use This Guide

This guide is organized progressively from fundamentals to advanced topics. Each section includes:

• Learning Objectives: What you’ll master in this section

• Key Concepts: Essential takeaways presented conceptually

• Worked Examples: Practical code demonstrations

• Self-Check Questions: Test your understanding

• Further Reading: Deep dives into mathematical details

For beginners: Start with Section 1 (Fundamentals) and progress sequentially

For experienced users: Jump directly to Section 3 (Advanced Topics) or Section 4 (Practical Guides)

For quick reference: Use the Models Handbook or API Reference

About This Guide

This User Guide emphasizes conceptual understanding and practical application over mathematical derivations. All equations and detailed theory are available in the Model Handbook and Transform Reference sections.

The guide is designed for:

• Graduate students learning rheology and computational analysis

• Researchers transitioning from commercial software to Python-based workflows

• Scientists seeking to understand rheological model selection and Bayesian inference

• Engineers applying rheology to materials characterization

Learning Pathway Overview

Section	Timeline	Focus
Fundamentals	Weeks 1-2	Core rheological concepts and terminology
Model Usage	Weeks 3-6	Practical model fitting and selection
Advanced Topics	Weeks 7-12	Bayesian inference, fractional calculus, multi-technique
Practical Guides	Weeks 13-16	Workflows, data I/O, visualization, batch processing
Appendices	Reference	Experimental design, materials database, troubleshooting

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Section 1: Fundamentals (Weeks 1-2)

Foundation in rheological concepts and terminology

Build your understanding of stress, strain, viscoelasticity, and material classification. Learn to interpret rheological parameters and understand different test modes.

• Section 1: Fundamentals (Weeks 1-2)
  • Learning Objectives
  • Section Contents
  • Section Roadmap
  • Key Concepts Summary
  • Learning Resources
  • Assessment
  • Next Steps

Key Topics:

• What is rheology and why does it matter?

• Material classification: liquids, solids, gels

• Test modes: SAOS, relaxation, creep, flow

• Physical meaning of rheological parameters

Section 2: Model Usage (Weeks 3-6)

Practical model fitting and selection strategies

Master the art of choosing appropriate models, fitting experimental data, and validating results. Learn initialization strategies and troubleshooting techniques.

• Section 2: Model Usage (Weeks 3-6)
  • Learning Objectives
  • Section Contents
  • Section Roadmap
  • Key Skills You’ll Develop
  • Learning Pathway Variations
  • Common Pitfalls and How to Avoid Them
  • Assessment
  • Resources
  • Next Steps

Key Topics:

• Getting started with model fitting

• Understanding model families (classical, fractional, flow)

• Model selection flowcharts and decision trees

• Fitting strategies and validation

Section 3: Advanced Topics (Weeks 7-12)

Deep dives into Bayesian inference, fractional viscoelasticity, and multi-technique analysis

Explore uncertainty quantification, fractional calculus applications, and simultaneous fitting of multiple experimental techniques.

• Section 3: Advanced Topics (Weeks 7-12)
  • Learning Objectives
  • Core Advanced Topics
  • Specialized Frameworks
  • Constitutive Models & Networks
  • Data Transforms
  • Key Skills Summary
  • Next Steps

Key Topics:

• Bayesian inference for parameter uncertainty

• Fractional viscoelasticity concepts and applications

• Multi-technique fitting strategies

• Time-temperature superposition

Section 4: Practical Guides (Weeks 13-16)

Workflows, data management, and production-ready analysis

Learn to build efficient analysis pipelines, manage diverse data formats, create publication-quality visualizations, and process multiple datasets in batch mode.

• Section 4: Practical Guides (Weeks 13-16)
  • Learning Objectives
  • Section Contents
  • Section Roadmap
  • Quick Examples
  • Next Steps

Key Topics:

• Pipeline API for fluent workflows

• Modular API for low-level control

• Data I/O for multiple instrument formats

• Visualization and batch processing

Section 5: Appendices

Reference materials for experimental design, material properties, and troubleshooting

Quick-reference guides consolidating best practices, material databases, and common solutions to fitting problems.

• Section 5: Appendices
  • Appendix Contents
  • Quick Access

Reference Materials:

• Experimental design guidelines

• Material property database (100+ materials)

• Troubleshooting guide

• Glossary of rheological terms

Section 6: GUI Reference

Graphical user interface for interactive analysis

Learn to use the optional RheoJAX GUI for visual data exploration, interactive model fitting, and Bayesian inference with ArviZ diagnostics.

• GUI Reference Guide
  • Getting Started
  • Data Loading
  • Model Fitting
  • Bayesian Inference
  • Diagnostics
  • Transforms
  • Exporting
  • Menu Reference
  • Keyboard Shortcuts
  • Overview
  • Installation
  • Launching the GUI
  • Architecture
  • Performance

GUI Topics:

• Getting started with the GUI

• Data loading and visualization

• Interactive model fitting

• Bayesian inference and diagnostics

• Transforms and exporting

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Alternative Learning Paths

Not following the 16-week course? Choose a path that matches your goals:

Rapid Onboarding (1 week)

For experienced rheologists familiar with commercial software:

1. Getting Started with Model Fitting — RheoJAX basics

2. Model Selection Guide — Choose the right model

3. Pipeline API Tutorial — Build workflows

4. Data I/O Guide — Import your data

Bayesian Focus (4 weeks)

For researchers interested in uncertainty quantification:

1. Section 1: Fundamentals (Weeks 1-2) — Core concepts

2. Getting Started with Model Fitting — Basic fitting

3. Bayesian Inference — Bayesian workflow

4. Visualization Guide — Posterior diagnostics

Fractional Viscoelasticity (6 weeks)

For advanced users studying complex materials:

1. Material Classification — Material types

2. Model Families Overview — Model overview

3. Fractional Viscoelasticity: Mathematical Reference — Fractional calculus

4. Fitting Strategies and Troubleshooting — Initialization and validation

High-Throughput Analysis (2 weeks)

For labs processing many samples:

1. Data I/O Guide — Auto-detect file formats

2. Pipeline API Tutorial — Automated workflows

3. Batch Processing — Process multiple datasets

4. Troubleshooting Guide — Handle edge cases

Soft Glassy & LAOS Analysis (4 weeks)

For researchers working with yield stress fluids, gels, and nonlinear rheology:

1. Material Classification — Understanding soft materials

2. Soft Glassy Rheology (SGR) Analysis — SGR framework for soft glassy materials

3. Sequence of Physical Processes (SPP) — SPP for LAOS yield stress extraction

4. Bayesian Inference — Uncertainty in SGR/SPP parameters

Thixotropy & Yield Stress (4 weeks)

For researchers working with drilling muds, waxy oils, emulsions, and structured fluids:

1. Material Classification — Material behavior fundamentals

2. Thixotropy and Yield Stress Analysis — DMT, Fluidity, HL, STZ, EPM models

3. ODE-Based Constitutive Models — IKH/FIKH kinematic hardening

4. Bayesian Inference — Uncertainty quantification

Polymer Network Theory (4 weeks)

For researchers studying associative polymers, wormlike micelles, and biological gels:

1. Getting Started with Model Fitting — Basic fitting workflow

2. ODE-Based Constitutive Models — Giesekus nonlinear viscoelasticity

3. Transient Polymer Network Models (TNT + VLB) — TNT and VLB frameworks

4. Vitrimer and Nanocomposite Models — HVM/HVNM for covalent adaptable networks

Smart Materials & Nanocomposites (3 weeks)

For researchers working with vitrimers, nanocomposites, and adaptive materials:

1. Transient Polymer Network Models (TNT + VLB) — VLB distribution tensor foundations

2. Vitrimer and Nanocomposite Models — HVM and HVNM models

3. Bayesian Inference — Bayesian parameter estimation

DMTA / DMA Analysis (2 weeks)

For researchers analyzing tensile, bending, or compression oscillatory data:

1. Test Modes in Rheology — DMTA as a test mode (E* vs G*)

2. Model Capabilities — DMTA-compatible models (41 of 53)

3. DMTA / DMA Analysis — Modulus conversion theory and workflows

4. Bayesian Inference — Uncertainty quantification for DMTA fits

Dense Suspensions & Glasses (4 weeks)

For researchers studying colloidal glasses, metallic glasses, and amorphous solids:

1. Soft Glassy Rheology (SGR) Analysis — SGR soft glassy framework

2. Dense Suspensions and Glassy Materials — ITT-MCT mode-coupling theory

3. Thixotropy and Yield Stress Analysis — STZ and EPM for amorphous solids

4. Bayesian Inference — Phase classification with uncertainty

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Related Documentation

• Quickstart Guide — 5-minute installation and first fit

• Models Handbook — Comprehensive Model Handbook (53 models, all equations and theory)

• Transforms — Transform Reference (11 transforms, mathematical details)

• API Reference — Complete API documentation

• Tutorial Notebooks — 240+ example notebooks across all model families

Getting Help

• Troubleshooting Guide: Troubleshooting Guide

• Glossary: Glossary of Rheological Terms

• GitHub Issues: Report bugs or request features

• Examples: Tutorial Notebooks — 240+ worked notebooks across all model families

Next Steps

Begin your learning journey:

• New to rheology? Start with What is Rheology?

• Ready to fit models? Jump to Getting Started with Model Fitting

• Need quick reference? Check Section 5: Appendices