Description
Return an isotropic diffusion displacement scale.
A dimensionless time-step ratio, free-diffusion scale or sampling weight assumes a particular model and data basis. Local bounds and factors can help diagnose a method, but accuracy, stability and statistical uncertainty depend on the complete algorithm and its assumptions.
Return an isotropic diffusion displacement scale.
When to use this tool
Use Diffusion Length One Timestep Factor when checking the stated local stability, diffusion or sampling convention.
How to use the tool and how it works
- Enter diffusivity, step, dimensions. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read meanSquareDisplacement, rmsDisplacement. Use the output convention below.
Return an isotropic diffusion displacement scale. Require diffusivity/step >= 0 and whole dimensions >= 1; meanSquareDisplacement = 2*d*D*t, rmsDisplacement is its square root.1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| diffusivity | Diffusivity | Required. Finite number; minimum 0. |
| step | Step duration or increment under the stated convention. | Required. Finite number; minimum 0. |
| dimensions | Dimensions | Required. Safe integer; minimum 1. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| meanSquareDisplacement | Mean Square Displacement | Required. Finite number. |
| rmsDisplacement | sqrt(2*dimensions*diffusivity*step); ensemble magnitude scale, not a simulated path. | Required. Finite number. |
{
"input": {
"diffusivity": 2,
"step": 1,
"dimensions": 1
},
"output": {
"meanSquareDisplacement": 4,
"rmsDisplacement": 2
}
}Limitations and assumptions
- Use length²/time and matching time; this is an ensemble free-diffusion scale, not a sampled displacement or confined-system prediction.
- 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
Analyze the full numerical or stochastic method, its support and error behavior before treating a local factor as a reliability guarantee.
References
Similar or alternative tools
- Grid Diffusion Stability Ratio
Return a grid diffusion number and explicit-Euler limit ratio.
- Numerical Cell Peclet Term
Return signed and absolute cell Peclet numbers.