# properties: Common Properties with Distance, to be used with... In ReacTran: Reactive Transport Modelling in 1d, 2d and 3d

## Description

Functions that define an y-property as a function of the one-dimensional x-coordinate. These routines can be used to specify properties and parameters as a function of distance, e.g. depth in the water column or the sediment.

They make a transition from an upper (or upstream) zone, with value `y.0` to a lower zone with a value `y.inf`.

Particularly useful in combination with setup.prop.1D

• `p.exp`: exponentially decreasing transition

y=y0+(y0-yinf)*exp(-max(0,(x-x0))/xa

• `p.lin`: linearly decreasing transition

y=y0 ; y=y0-(y0-yinf)(x-xl)/xatt ; y = yinf

for 0 ≤q x ≤q x_L, x_L ≤q x ≤q x_L + x_{att} and (x ≥q x_L + x.att ) respectively.

• `p.sig`: sigmoidal decreasing transition

y=yinf+(y0-yinf)exp(-(x-xL)/(0.25xatt)) / (1+exp(-(x-xL)/(0.25xatt)))

## Usage

 ```1 2 3``` ```p.exp(x, y.0 = 1, y.inf = 0.5, x.L = 0, x.att = 1) p.lin(x, y.0 = 1, y.inf = 0.5, x.L = 0, x.att = 1) p.sig(x, y.0 = 1, y.inf = 0.5, x.L = 0, x.att = 1) ```

## Arguments

 `x ` the x-values for which the property has to be calculated. `y.0 ` the y-value at the origin `y.inf ` the y-value at infinity `x.L ` the x-coordinate where the transition zone starts; for `x <= x.0`, the value will be equal to `y.0`. For `x >> x.L + x.att` the value will tend to `y.inf` `x.att ` attenuation coefficient in exponential decrease, or the size of the transition zone in the linear and sigmoid decrease

## Details

For `p.lin`, the width of the transition zone equals `x.att` and the depth where the transition zone starts is `x.L`.

For `p.sig`, `x.L` is located the middle of the smooth transition zone of approaximate width `x.att`.

For `p.exp`, there is no clearly demarcated transition zone; there is an abrupt change at `x.L` after which the property exponentially changes from `y.0` towards `y.L` with attenuation coefficient `x.att`; the larger `x.att` the less steep the change.

## Value

the property value, estimated for each x-value.

## Author(s)

Filip Meysman <filip.meysman@nioz.nl>, Karline Soetaert <karline.soetaert@nioz.nl>

## Examples

 ```1 2 3 4 5``` ```x <- seq(0, 5, len = 100) plot(x, p.exp(x, x.L = 2), xlab = "x.coordinate", ylab = "y value", ylim = c(0, 1)) lines(x, p.lin(x, x.L = 2), col = "blue") lines(x, p.sig(x, x.L = 2), col = "red") ```

ReacTran documentation built on May 2, 2019, 9:38 a.m.