This implementation accounts for:
effects of ammonia and phosphate concentrations in the feed (X_Nr, X_Pr),
throughput rates (h) and temperature (T).
These environmental parameters are taken to be constant in the
present implementation, but it is not difficult to let them vary in
time. Limitations by light, carbon and other can be implemented as well.
Two other nutrients can be substituted for ammonia and phosphate.
Organic compounds (that make up the alga):
V = structure, EN = N-reserve, EP = P-reserve,
Mineral compounds:
C = carbon dioxide, H = water, O = dioxygen,
N = ammonia, P = phosphate,
DN = excreted N-reserve, DP = excreted P-reserve
Uptake is proportional to surface area, which is taken to be proportional to the structural volume: V1-morph. This removes the distinction between the individual and the population level.
The simplification k_J = k_M*(1 - kap)/kap is implemented,
which makes this energy-structured model also size-structured
The alga divides when the structural mass exceeds a threshold value
Example of use after (optionally) editing file "pars.m": alga
fig 1
Ammonia (blue, drawn) and excreted N-reserve (blue, stippled) in Molar
fig 2
Phosphate (red, drawn) and excreted P-reserve (red, stippled) in Molar
fig 3
Structure (green, drawn) in Molar
fig 4
N-reserve density (blue, drawn) and P-reserve density (red, drawn) in mol/mol
Example of use after editing "pars.m": clear; pars;
shbatch in Octave, or clear all; pars; shbatch in
Matlab.
The command clear; pars; shbatch (4) will
only plot fig 4.
fig 1
Ammonia (blue, drawn) and excreted N-reserve (blue, stippled) in Molar.
Most parameter settings result in a practical absence of
excreted reserves.
fig 2
Phosphate (red, drawn) and excreted P-reserve (red, stippled) in Molar
Most parameter settings result in a practical absence of
excreted reserves.
fig 3
Structure (green, drawn) in Molar. Note the difference with shbatch1;
the structure does not decline after reaching a ceiling.
fig 4
N-reserve density (blue, drawn) and P-reserve density (red, drawn) in mol/mol
Example of use after editing "pars.m": clear; pars;
shbatch1 in Octave, or clear all; pars; shbatch1
in Matlab.
The command clear; pars; shbatch1 (4) will
only plot fig 4.
fig 1
Ammonia (blue, drawn) and excreted N-reserve (blue, stippled) in Molar
fig 2
Phosphate (red, drawn) and excreted P-reserve (red, stippled) in Molar
fig 3
Total ammonia (blue, drawn) and phosphate (red, drawn) in Molar
fig 4
Structure (green, drawn) in Molar
fig 5
N-reserve density (blue, drawn) and P-reserve density (red, drawn) in mol/mol
fig 6
N/C ratio (blue, drawn) and P/C ratio (red, drawn) in biomass (mol/mol).
Usually looks similar to fig 5, because N and P in structure contribute little.
Example of use after editing "pars.m": clear; pars;
shchemclear; pars; shbatch1 in Octave, or
clear all; pars; shbatch1 in Matlab.
The command
clear; pars; shchem (5) will only plot fig 5.
fig 1
Ammonia (blue, drawn) and excreted N-reserve (blue, stippled) in Molar;
Note that there is hardly any excreted N-reserve at low throughput rates
(compare with shchem)
fig 2
Phosphate (red, drawn) and excreted P-reserve (red, stippled) in Molar
Note that there is hardly any excreted P-reserve at low throughput rates
(compare with shchem)
fig 3
Total ammonia (blue, drawn) and phosphate (red, drawn) in Molar
fig 4
Structure (green, drawn) in Molar; Note the difference with shchem;
the biomass is still high at small throughput rates.
fig 5
N-reserve density (blue, drawn) and P-reserve density (red, drawn) in mol/mol
fig 6
N/C ratio (blue, drawn) and P/C ratio (red, drawn) in biomass (mol/mol).
Usually looks similar to fig 5, because N and P in structure contribute little.
Example of use after editing "pars.m": clear; pars;
shchem in Octave, or clear all; pars; shchem in
Matlab.
The command clear; pars; shchem (5) will only
plot fig 5.
fig 1
Nutrient N (blue) and P (red) as functions of time.
fig 2
Reserve densities for nutrient N (blue) and P
(red) as functions of time for each specified reserve turnover rate.
fig 3
The logarithm of structure as a function of time
for each specified reserve turnover rate. The structure for the first
reserve turnover rate is plotted in blue, for the last value in red,
the rest in green.
Example of use after editing "pars_cycle.m": clear;
shcycle in Octave, or clear all; shcycle in
Matlab.
The command clear; shcycle (3) will only
plot fig 3.
shmcn. The function
shmcn_lm also shows the leak and the Morel model, which
has two maximum assimilation parameters for each nutrient.
fig 1
DIC (red), DIN (blue) and light (green) as functions of time.
fig 2
Reserve densities for carbohydrate (red) and
nitrogen (blue) as functions of time.
fig 3
Excretion rate of carbohydrates (red), and
nitrogen (blue) as functions of time.
fig 4
Specific growth rate as function of time.
Example of use after editing "shmcn.m": clear;
shmcn in Octave, or clear all; shmcn in
Matlab.
The command clear; shmcn(3) will only
plot fig 3.
Inputs :
Output: vector with optical densities of the batch culture.
The scriptfile mydata_clim sets data and the parameters
and shows how the biomass develops in the batch culture.
Inputs :
Routine shcnplim shows how the biomass develops; the data and the
parameters are set in mydata_cnplim.
sgr have the same structure, and the
input/output is presented for sgri where i
takes values 1, 2, 3 of 4.
Inputs:
Outputs:
An example of use is given in mydata_sgr