Description
Return a ratio of diffusive time scales.
Diffusive and thermal scales depend on dimensionality, geometry, drag and compatible energy/time units. A local displacement correction or ideal spherical diffusivity is distinct from fitting a stochastic trajectory or establishing that a measured system satisfies the model.
Return a ratio of diffusive time scales.
When to use this tool
Use Diffusion Time Scale Ratio when checking the stated diffusion, drift, work or thermal-energy convention.
How to use the tool and how it works
- Enter firstLength, firstDiffusivity, secondLength, secondDiffusivity. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read timeScaleRatio. Use the output convention below.
Return a ratio of diffusive time scales. Require firstLength >= 0 and secondLength/both diffusivities > 0; timeScaleRatio = (firstLength/secondLength)²*secondDiffusivity/firstDiffusivity.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| firstLength | First Length | Required. Finite number; minimum 0. |
| firstDiffusivity | First Diffusivity | Required. Finite number; strictly above 0. |
| secondLength | Second Length | Required. Finite number; strictly above 0. |
| secondDiffusivity | Second Diffusivity | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| timeScaleRatio | Time Scale Ratio | Required. Finite number. |
{
"input": {
"firstLength": 2,
"firstDiffusivity": 1,
"secondLength": 1,
"secondDiffusivity": 2
},
"output": {
"timeScaleRatio": 8
}
}Limitations and assumptions
- The same length-squared/diffusivity convention is assumed for both systems; no geometry-specific first-passage time is solved.
- 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 calibrated trajectories and an appropriate geometry/noise/transport model for fitted diffusion parameters, uncertainty or molecular mechanisms.
References
Similar or alternative tools
- Diffusion Stokes Einstein Radius Factor
Return spherical translational Stokes-Einstein diffusivity.
- Rotational Diffusion Viscosity Radius Term
Return spherical rotational diffusivity and second-rank correlation time.