Analysis Modes

The homodyne package supports three analysis modes optimized for different experimental scenarios.

Mode Overview

Analysis Mode Comparison

Mode	Parameters	Angle Handling	Use Case	Speed	Command
Static Isotropic	3	Single dummy	Fastest, isotropic systems	⭐⭐⭐	--static-isotropic
Static Anisotropic	3	Filtering enabled	Static with angular deps	⭐⭐	--static-anisotropic
Laminar Flow	7	Full coverage	Flow & shear analysis	⭐	--laminar-flow

Static Isotropic Mode

Physical Context: Analysis of systems at equilibrium with isotropic scattering where results don’t depend on scattering angle.

Model Equation:

\[c_1(t_1,t_2) = \exp(-q^2 \int_{t_1}^{t_2} D(t) dt)\]

where there is no angular dependence in the correlation function.

Parameters (3 total):

• D₀: Effective diffusion coefficient

• α: Time exponent characterizing dynamic scaling

• D_offset: Baseline diffusion component

Key Features:

• No angle filtering: Automatically disabled regardless of configuration

• No phi_angles_file loading: Uses single dummy angle

• Fastest analysis mode: Minimal computational overhead

When to Use:

• Isotropic samples

• Quick validation runs

• Preliminary analysis

• Systems where angular effects are negligible

Example Configuration:

{
  "analysis_settings": {
    "static_mode": true,
    "static_submode": "isotropic"
  },
  "initial_parameters": {
    "parameter_names": ["D0", "alpha", "D_offset"],
    "values": [1000, -0.5, 100]
  }
}

Static Anisotropic Mode

Physical Context: Analysis of systems at equilibrium with angular dependence but no flow effects.

Parameters: D₀, α, D_offset (same as isotropic mode)

Key Features:

• Angle filtering enabled: For optimization efficiency

• phi_angles_file loaded: For angle information

• Per-angle scaling optimization: Accounts for angular variations

When to Use:

• Systems with angular dependence

• Static samples with anisotropic properties

• When isotropic mode gives poor fits

• Intermediate complexity analysis

Example Configuration:

{
  "analysis_settings": {
    "static_mode": true,
    "static_submode": "anisotropic",
    "enable_angle_filtering": true,
    "angle_filter_ranges": [[-5, 5], [175, 185]]
  },
  "file_paths": {
    "phi_angles_file": "data/phi_angles.txt"
  }
}

Laminar Flow Mode

Physical Context: Complete analysis of systems under flow conditions with both diffusion and shear contributions.

Model Equations:

The full expression combines diffusive and shear contributions:

\[c_{1,\text{total}}(t_1,t_2) = c_{1,\text{diffusion}}(t_1,t_2) \times c_{1,\text{shear}}(t_1,t_2)\]

\[c_{1,\text{shear}}(t_1,t_2) = \text{sinc}^2(\Phi)\]

Parameters (7 total):

Diffusion Parameters: - D₀: Effective diffusion coefficient - α: Time exponent for diffusion scaling - D_offset: Baseline diffusion component

Shear Parameters: - γ̇₀: Shear rate amplitude - β: Shear rate time exponent - γ̇_offset: Baseline shear rate - φ₀: Phase angle for shear/flow direction

Physical Interpretation:

The laminar flow mode captures:

• Brownian diffusion: Random thermal motion characterized by D₀, α, D_offset

• Advective shear flow: Systematic flow characterized by γ̇₀, β, γ̇_offset, φ₀

• Angular dependencies: Full angular coverage with flow direction effects

Example Configuration:

{
  "analysis_settings": {
    "static_mode": false,
    "enable_angle_filtering": true
  },
  "initial_parameters": {
    "parameter_names": ["D0", "alpha", "D_offset", "gamma_dot_t0", "beta", "gamma_dot_t_offset", "phi0"],
    "values": [1000, -0.5, 100, 10, 0.5, 1, 0],
    "active_parameters": ["D0", "alpha", "D_offset", "gamma_dot_t0"]
  }
}

When to Use:

• Systems under flow conditions

• Nonequilibrium conditions are present

• Complete transport analysis is required

• You have sufficient computational resources

Progressive Analysis Strategy

A recommended approach is to use progressive complexity:

1. Exploration: Start with isotropic mode for initial parameter estimates

2. Validation: Compare with anisotropic mode to check for angular effects

3. Full Analysis: Use laminar flow mode for complete characterization

Example Workflow:

# Step 1: Quick isotropic analysis
python run_homodyne.py --static-isotropic --method classical

# Step 2: Check for angular effects
python run_homodyne.py --static-anisotropic --method classical

# Step 3: Full flow analysis (if needed)

Mode Selection Guidelines

Choose Static Isotropic when: - System is known to be isotropic - You need quick results - Doing preliminary data validation - Angular effects are negligible

Choose Static Anisotropic when: - System shows angular dependence - No flow conditions present - Isotropic results are unsatisfactory - Need moderate complexity analysis

Choose Laminar Flow when: - System is under flow conditions - Nonequilibrium conditions are present - Complete transport analysis is required - You have sufficient computational resources

Troubleshooting

“Angle filtering enabled but static_isotropic mode detected”:

This is expected behavior - angle filtering is automatically disabled in isotropic mode.

“phi_angles_file not found” in isotropic mode:

This is normal - phi_angles_file is not used in isotropic mode.

Poor convergence with angle filtering:

Try adjusting angle_filter_ranges or disabling filtering temporarily.

Results similar to isotropic mode:

Your system may indeed be isotropic - compare chi-squared values.

Slow optimization:

Enable angle filtering for 3-5x speedup with minimal accuracy loss.