Section 3: Advanced Topics (Weeks 7-12)¶
Deep dives into Bayesian inference, fractional viscoelasticity, multi-technique analysis, constitutive modeling, transient networks, vitrimers, and specialized frameworks
Prerequisites
Sections 1-2 (Fundamentals and Model Usage). Timeline: Weeks 7-16 (30-40 hours).
Learning Objectives¶
By completing this section, you will be able to:
Perform Bayesian inference to quantify parameter uncertainty
Understand fractional viscoelasticity concepts and applications
Fit multiple experimental techniques simultaneously
Apply time-temperature superposition (TTS) for mastercurves
Interpret credible intervals and posterior distributions
Classify soft glassy materials using the SGR framework
Extract yield stresses and cage moduli from LAOS using SPP
Work with ODE-based constitutive models (Giesekus, IKH, Saramito)
Analyze thixotropic and yield stress materials (DMT, Fluidity, HL, STZ, EPM)
Apply transient polymer network models (TNT, VLB)
Model vitrimer and nanocomposite rheology (HVM, HVNM)
Understand dense suspension dynamics via mode-coupling theory (ITT-MCT)
Apply all 7 data transforms to experimental data
Core Advanced Topics¶
- Bayesian Inference
- Overview
- When to Use Bayesian Inference
- Quick Start
- NLSQ + NUTS Workflow
- Understanding Results
- ArviZ Diagnostic Plots
- Advanced ArviZ Integration
- Convergence Diagnostics
- Best Practices
- Common Pitfalls
- Examples
- Troubleshooting Common Issues
- Best Practices Checklist
- Model Support
- Performance Characteristics
- Further Reading
- Fractional Viscoelasticity: Mathematical Reference
- Multi-Technique Fitting Guide
- Time-Temperature Superposition (TTS)
Specialized Frameworks¶
Constitutive Models & Networks¶
- ODE-Based Constitutive Models
- Overview
- When to Use ODE-Based Models
- Theoretical Foundations
- Model Family 1: Giesekus
- Model Family 2: IKH/FIKH (Isotropic-Kinematic Hardening)
- Model Family 3: Fluidity-Saramito EVP
- Bayesian Inference for ODE Models
- Visualization and Diagnostics
- Model Selection and Comparison
- Limitations and Pitfalls
- Tutorial Notebooks
- References
- See Also
- Thixotropy and Yield Stress Analysis
- Dense Suspensions and Glassy Materials
- Transient Polymer Network Models (TNT + VLB)
- Vitrimer and Nanocomposite Models
Data Transforms¶
- Complete Guide to Data Transforms
- Overview
- When to Use Transforms
- 1. FFT (Fast Fourier Transform)
- 2. Mastercurve (Time-Temperature Superposition)
- 3. SRFS (Strain-Rate Frequency Superposition)
- 4. SPP Decomposer (Sequence of Physical Processes)
- 5. Smooth Derivative
- 6. Mutation Number
- 7. OWChirp (Optimally Windowed Chirp)
- Combining Transforms
- Transform Limitations
- References
- See Also
- Next Steps
Key Skills Summary¶
Bayesian Workflow (NLSQ -> NUTS):
from rheojax.models import Maxwell
# 1. NLSQ point estimate (fast)
model = Maxwell()
model.fit(t, G_t, test_mode='relaxation')
# 2. Bayesian inference (uncertainty quantification)
result = model.fit_bayesian(t, G_t, num_samples=2000, num_warmup=1000)
# 3. Credible intervals
intervals = model.get_credible_intervals(result.posterior_samples, credibility=0.95)
Multi-Technique Fitting:
from rheojax.pipeline import ModelComparisonPipeline
pipeline = ModelComparisonPipeline()
pipeline.fit_multi_technique(
techniques=['relaxation', 'oscillation'],
data_dict={'relaxation': (t, G_t), 'oscillation': (omega, G_star)}
)
SGR Phase Classification:
from rheojax.models import SGRConventional
model = SGRConventional()
model.fit(omega, G_star, test_mode='oscillation')
x = model.parameters.get_value('x')
print(f"x = {x:.2f}: {'Glass' if x < 1 else 'Fluid'}")
SPP Yield Stress Extraction:
from rheojax.transforms import SPPDecomposer
decomposer = SPPDecomposer(omega=1.0, gamma_0=1.0, n_harmonics=39)
result = decomposer.transform(laos_data)
spp_results = decomposer.get_results()
print(f"Cage modulus: {spp_results['G_cage']:.1f} Pa")
print(f"Static yield stress: {spp_results['sigma_sy']:.1f} Pa")
Next Steps¶
After completing advanced topics, proceed to Section 4: Practical Guides (Section 4: Practical Guides (Weeks 13-16)) for production workflows, data I/O, visualization, and batch processing.