Transforms

The Transform page provides data transformation tools for rheological analysis.

Available Transforms

Mastercurve (Time-Temperature Superposition)

Shift multi-temperature data to a reference temperature:

Usage:

  1. Load datasets at different temperatures

  2. Select Mastercurve transform

  3. Set reference temperature

  4. Choose shift method (auto or manual)

  5. Apply transform

Parameters:

  • Reference Temperature: T_ref in °C or K

  • Auto Shift: Automatic shift factor calculation

  • Manual Shifts: Enter known shift factors

Output:

  • Mastercurve at T_ref

  • Shift factors (a_T)

  • Williams-Landel-Ferry (WLF) fit (if applicable)

FFT (Fourier Transform)

Convert between time and frequency domains:

Usage:

  1. Select time-domain dataset

  2. Choose FFT transform

  3. Configure window and padding

  4. Apply transform

Parameters:

  • Window: Hanning, Hamming, Blackman, None

  • Zero Padding: Extend data for resolution

  • Nyquist Warning: Alert for aliasing

Output:

  • Frequency-domain G*(ω)

  • \(G'(\omega)\) and \(G''(\omega)\)

IFFT (Inverse Fourier Transform)

Convert frequency to time domain:

Usage:

  1. Select frequency-domain dataset

  2. Choose IFFT transform

  3. Apply transform

Output:

  • Time-domain G(t)

Derivatives

Numerical differentiation:

Usage:

  1. Select dataset

  2. Choose Derivative transform

  3. Select order (1st or 2nd)

  4. Choose method

Parameters:

  • Order: 1 (first derivative), 2 (second derivative)

  • Method: Central difference, Savitzky-Golay

  • Smoothing: Window size for noise reduction

Output:

  • dG/dt or d²G/dt²

SRFS (Strain-Rate Frequency Superposition)

Collapse flow curves at different shear rates:

Usage:

  1. Load datasets at different shear rates

  2. Select SRFS transform

  3. Set reference shear rate

  4. Apply transform

Parameters:

  • Reference Rate: γ̇_ref

  • Power Law Exponent: For scaling

Output:

  • Master flow curve

  • Shift factors

Using Transforms

Basic Workflow

  1. Navigate to Transform page

  2. Select source dataset from dropdown

  3. Choose transform from list

  4. Configure parameters

  5. Click Apply Transform

  6. Review result in preview

  7. Accept to add as new dataset

Transform Preview

Before accepting:

  • View transformed data plot

  • Check data ranges

  • Verify expected behavior

  • Adjust parameters if needed

Transform History

All transforms are tracked:

  • Source dataset

  • Transform type

  • Parameters used

  • Timestamp

  • Random seed (if applicable)

This enables reproducibility and audit trails.

Chaining Transforms

Apply multiple transforms sequentially:

  1. Apply first transform

  2. Accept result as new dataset

  3. Select new dataset

  4. Apply next transform

  5. Repeat as needed

Transform Parameters

Mastercurve Settings

Shift Method:

  • Auto WLF: Automatic WLF fit

  • Auto Arrhenius: Automatic Arrhenius fit

  • Manual: User-specified shift factors

Overlap Region:

  • Minimum overlap decades for shifting

  • Default: 0.5 decades

Optimization:

  • JAX-accelerated shift optimization

  • Multi-start for robustness

FFT Settings

Windowing:

  • Reduces spectral leakage

  • Hanning recommended for most cases

Padding:

  • Zero-padding increases frequency resolution

  • Powers of 2 for efficiency

Detrending:

  • Remove DC offset

  • Linear detrend option

Derivative Settings

Method Comparison:

  • Central Difference: Fast, sensitive to noise

  • Savitzky-Golay: Smoother, preserves features

Window Size:

  • Larger = smoother, less detail

  • Smaller = noisier, more detail

  • Odd numbers only

Output Handling

New Dataset

Transforms create new datasets:

  • Original preserved

  • Transform result added to dataset list

  • Naming: original_name_transform

Metadata

Transformed datasets include:

  • Source dataset reference

  • Transform parameters

  • Provenance chain

Export

Export transformed data:

  1. Select transformed dataset

  2. Go to Export page

  3. Choose format

Tips and Best Practices

Mastercurve

  1. Ensure sufficient temperature range

  2. Check for thermorheological simplicity

  3. Use auto-shift first, then refine

  4. Validate WLF parameters against literature

FFT

  1. Use windowing to reduce artifacts

  2. Ensure time data is evenly spaced

  3. Check Nyquist frequency

  4. Zero-pad for smooth spectra

Derivatives

  1. Always smooth noisy data first

  2. Start with larger windows

  3. Compare methods on same data

  4. Validate against known solutions

SRFS

  1. Verify power-law scaling behavior

  2. Check for shear banding (discontinuities)

  3. Use consistent strain amplitudes