Description
Calculate one supplied displacement vector's squared norm.
Biophysical scalar models require explicit signal, concentration, temperature, energy and geometric conventions. Effective concentration differs from dimensionless activity, a single displacement differs from mean-square displacement, and a fluorescence yield ratio needs absorption and refractive-index corrections. Supplied model parameters do not establish that the model applies to an experiment.
Calculate one supplied displacement vector's squared norm.
When to use this tool
Use Diffusion Step Squared Displacement when you already have displacementComponents and need to calculate one supplied displacement vector's squared norm.
How to use the tool and how it works
- Enter displacementComponents. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read squaredDisplacement. Use the output convention below.
Sum squared components in order; an empty vector gives zero.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| displacementComponents | Displacement Components | Required. Array of finite number; maximum items 256. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| squaredDisplacement | Sum of squared supplied components for one step; empty components return zero, without ensemble/time averaging. | Required. Finite number. |
{
"input": {
"displacementComponents": [
3,
4
]
},
"output": {
"squaredDisplacement": 25
}
}Limitations and assumptions
- Units square with the input length. This is one displacement, not mean squared displacement, a diffusion estimate, actual trajectory or an uncertainty calculation.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use the complete physical model, calibrated measurements and uncertainty analysis. Check reference states, photon-signal bases, diffusion assumptions and binding-constant conventions before interpreting local contributions as physical measurements.
References
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