Description
Return exponential morphogen decay length and concentration.
Morphogen models distinguish amount flow, concentration and spatial decay. A steady exponential profile or local flux balance requires explicit geometry, reaction assumptions and compatible units; it is not a fitted mechanism.
Return exponential morphogen decay length and concentration.
When to use this tool
Use Morphogen Exponential Decay Length Term when checking a supplied morphogen-domain or balance term.
How to use the tool and how it works
- Enter diffusivity, decayRate, sourceConcentration, distance. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read decayLength, concentration. Use the output convention below.
Return exponential morphogen decay length and concentration. Require positive diffusivity/decayRate and nonnegative source concentration/distance; decayLength = sqrt(D/k), concentration = source*exp(-distance/length).1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| diffusivity | Positive diffusivity, in length²/time. | Required. Finite number; strictly above 0. |
| decayRate | Positive first-order decay rate, in reciprocal matching time. | Required. Finite number; strictly above 0. |
| sourceConcentration | Source Concentration | Required. Finite number; minimum 0. |
| distance | Distance | Required. Finite number; minimum 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| decayLength | sqrt(diffusivity/decayRate), in the distance unit. | Required. Finite number. |
| concentration | Concentration | Required. Finite number. |
{
"input": {
"diffusivity": 4,
"decayRate": 1,
"sourceConcentration": 100,
"distance": 2
},
"output": {
"decayLength": 2,
"concentration": 36.787944117144235
}
}Limitations and assumptions
- This steady one-dimensional linear diffusion-decay profile assumes fixed source conditions and coherent units.
- 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 suitable concentration measurements, boundary conditions and a full transport/reaction model when inferring developmental mechanisms.
References
Similar or alternative tools
- Morphogen Source Sink Flux Balance
Return net morphogen amount and concentration rates.
- Morphogen Domain Edge Token
Classify position within a supplied closed-or-open domain.