List of Functions

function ADM1sol(tspan::Tuple,u0::Vector,IV::Vector; <keyword arguments>)

Compute the solution for the given timespan, tspan; initial condition, u0; and inflow vector IV.

Also return the time (in seconds) the solution took to compute. The difference between this function and ExampleSol is that this function reads in the parameter values from a .csv file.

Optional Arguments

• alg = Rodas4P(): the ODE solver algorithm.
• tols = 1e-4: the absolute and relative tolerance of the solver method.
• tMax = 300.0: the maximum time (in seconds), that the function will run before timing out.
• saveAt = []: specific times to save the solution. If given a number n, the solver will save the solution every n timesteps

Examples

julia> u0 = initialConditions();

julia> IV = inflowvector_definition();

julia> sol, tSol = ADM1sol((0.0,200.0),u0,IV);

julia> sol
retcode: Success
Interpolation: specialized 3rd order "free" stiffness-aware interpolation
t: 146-element Vector{Float64}:
[...]

u: 146-element Vector{Vector{Float64}}:
[...]

julia> tSol

0.3854937

function ADM1sol(tspan::Tuple,u0::Vector,IV::Vector{Vector{Float64}},IVtimes::Vector{Float64}; <keyword arguments>)

Compute the solution with variable inflow for the given timespan, tspan; initial condition, u0; and variable inflow vector IV where each entry in IV corresponds to the inflow vector at the corresponding entry in IVtimes

Also return the time (in seconds) the solution took to compute.

Optional Arguments

• alg = Rodas4P(): the ODE solver algorithm.
• tols = 1e-4: the absolute and relative tolerance of the solver method.
• tMax = 300.0: the maximum time (in seconds), that the function will run before timing out.
• saveAt = []: specific times to save the solution. If given a number n, the solver will save the solution every n timesteps

Examples

julia> u0 = initialConditions();

julia> t = [i for i in 0.0:0.1:50.0];

julia> IV_temp = inflowvector_definition();

julia> IV = [IV_temp*(0.5*rand()+1.0) for i in 1:length(t)]

julia> sol,tSol = ADM1sol((0.0,50.0),u0,IV,t);

julia> sol
retcode: Success
Interpolation: specialized 3rd order "free" stiffness-aware interpolation
t: 2011-element Vector{Float64}:
[...]

u: 2011-element Vector{Vector{Float64}}:
[...]

julia> tSol

14.4643811

function MultiChamberSolution(tspan::Tuple,u0::Tuple,IV::Vector,nChambers::Int64; <keyword arguments>)

Compute the solution for a system of nChambers connected CSTRs with u0 initial conditions. The inflow of the first CSTR is given by IV, the outflow of the first CSTR becomes the inflow of second CSTR and so on.

This function reads in the parameter values from a .csv file. The names of the .csv files that contain the parameter values should be "modelparameters.csv", "modelparameters2.csv", "model_parameters3.csv", ... and so on.

Arguments

• alg = Rodas4P(): the ODE solver algorithm.
• tols = 1e-4: the absolute and relative tolerance of the solver method.
• tMax = 300.0: the maximum time (in seconds), that the function will run before timing out.
• saveAt = []: specific times to save the solution. If given a number n, the solver will save the solution every n timesteps

Examples

julia> u0 = initialConditions();

julia> IV = inflowvector_definition();

julia> sols = MultiChamberSolution((0.0,200.0),(u0,u0,u0),IV,3);
Finished Chamber 1
Finished Chamber 2
Finished Chamber 3

julia> sols[1]
retcode: Success
Interpolation: specialized 3rd order "free" stiffness-aware interpolation
t: 115-element Vector{Float64}:
[...]

u: 115-element Vector{Vector{Float64}}:
[...]

julia> sols[2]
retcode: Success
Interpolation: specialized 3rd order "free" stiffness-aware interpolation
t: 115-element Vector{Float64}:
[...]

u: 115-element Vector{Vector{Float64}}:
[...]

julia> sols[3]
retcode: Success
Interpolation: specialized 3rd order "free" stiffness-aware interpolation
t: 115-element Vector{Float64}:
[...]

u: 115-element Vector{Vector{Float64}}:
[...]

function MultiChamberSolution(tspan::Tuple,u0::Tuple,IV::Vector{Vector{Float64}},IVtimes::Vector{Float64},nChambers::Int64;<keyword arguments>)

Compute the solution for a system of nChambers connected CSTRs with u0 initial conditions. The inflow of the first CSTR is given by variable inflow vector IV where each entry in IV corresponds to the inflow vector at the corresponding entry in IVtimes, the outflow of the first CSTR becomes the inflow of second CSTR and so on.

This function reads in the parameter values from a .csv file. The names of the .csv files that contain the parameter values should be "modelparameters.csv", "modelparameters2.csv", "model_parameters3.csv", ... and so on.

Arguments

• alg = Rodas4P(): the ODE solver algorithm.
• tols = 1e-4: the absolute and relative tolerance of the solver method.
• tMax = 300.0: the maximum time (in seconds), that the function will run before timing out.
• saveAt = []: specific times to save the solution. If given a number n, the solver will save the solution every n timesteps

Examples

julia> u0 = initialConditions();

julia> t = [i for i in 0.0:0.1:50.0];

julia> IV_temp = inflowvector_definition();

julia> IV = [IV_temp*(0.5*rand()+1.0) for i in 1:length(t)];

julia> sols = MultiChamberSolution((0.0,50.0),(u0,u0,u0),IV,t,3);
Finished Chamber 1
Finished Chamber 2
Finished Chamber 3

julia> sols[1]
retcode: Success
Interpolation: specialized 3rd order "free" stiffness-aware interpolation
t: 115-element Vector{Float64}:
[...]

u: 115-element Vector{Vector{Float64}}:
[...]

julia> sols[2]
retcode: Success
Interpolation: specialized 3rd order "free" stiffness-aware interpolation
t: 115-element Vector{Float64}:
[...]

u: 115-element Vector{Vector{Float64}}:
[...]

julia> sols[3]
retcode: Success
Interpolation: specialized 3rd order "free" stiffness-aware interpolation
t: 115-element Vector{Float64}:
[...]

u: 115-element Vector{Vector{Float64}}:
[...]

  initialConditions()

Returns the default initial conditions as a Vector{Float64} of length 35.

Examples

julia> initialConditions()
35-element Vector{Float64}:
 0.012
 0.0053
 ⋮
 1.63
 0.014

  inflowvector_definition()

Returns the default inflow vector as a Vector{Float64} of length 35.

Examples

julia> inflowvector_definition()
35-element Vector{Float64}:
 0.01
 0.001
 0.001
 0.001
 ⋮
 0.02
 0.0
 0.0
 0.0

plotSols(sol;<keyword arguments>)

Plot the solutions returned by ADM1sol. The plots are split between two figures and are displayed by default. However, due to an error in Julia's Plots package, the plot's windows may overwrite eachother in some circumstances. If this occurs, use the keyword arguments to view both plots manually.

Arguments

• sol::Vector: ODESolution returned by ADM1 sol

Optional Arguments

• titleText = "Plot of Solutions": The title of the plots
• displayPlots = true: Boolean to display the plots or not.
• savePNG = false: Boolean to save pngs of the plots to the working directory as titleText(1 of 2).png and titleText(2 of 2).png
• returnPlots = false: Boolean to return the plots as a tuple so they can be displayed manually

Examples

julia> u0 = initialConditions();

julia> IV = inflowvector_definition();

julia> sol, tSol = ADM1sol((0.0,200.0),u0,IV); # compute the solution

julia> plotSols(sol); # display the plots

julia> u0 = initialConditions();

julia> IV = inflowvector_definition();

julia> sol, tSol = ADM1sol((0.0,200.0),u0,IV); # compute the solution

julia> plt1,plt2 = plotSols(sol,displayPlots=false,returnPlots=true); # return the plots

julia> display(plt1); # display the first plot

julia> display(plt2); # display the second plot

pressureOfGasses(sx,php,rp)

Compute the pressures of the gasses.

Arguments

• sx::Vector: the state vector.
• php::Vector: the physicochemical parameters.
• rp::Vector: the reactor parameters.

Examples

julia> u0 = initialConditions();

julia> rp = reactorParameterDefinition();

julia> php = physiochemicalParameterDefinition(rp);

julia> pressureOfGasses(u0,php,rp)
5-element Vector{Float64}:
    1.6333471490625e-5
    0.6525381992578124
    0.35869584449999997
    1.0669181223042932
    2695.9061152146637

monod(u, k)

Compute the monod function u/(u+k) where u is the state varible and k is the half-saturation concentration.

If u <= 0 return 0.

Examples

julia> monod(3.0,2.0) # when u is non-zero positive
0.6

julia> monod(-3.0,2.0) # when u is negative
0

RHSfun(du,u,p,t)

Return the right-hand side of the system of ODEs, this is an in-place function.

Arguments

• du::Vector: the rate change of the state vector (required since the function is defined in-place).
• u::Vector: the state vector.
• p::Vector: all of the model parameters.
• t: the timestep, usually a Float64.

RHSfunInflowVaried(du,u,p,t)

Return the right-hand side of the system of ODEs, this is an in-place function.

Arguments

• du::Vector: the rate change of the state vector (required since the function is defined in-place).
• u::Vector: the state vector.
• p::Vector: all of the model parameters.
• t: the timestep, usually a Float64.

transportmatrix_definition(rp,pressures)

Transport matrix

```

reactionrates(bp,rp,php,pressures,sx,NREAC::Int)

Compute and return the vector of reaction rates.

Arguments

• bp::Vector: the biochemical parameters.
• rp::Vector: the reactor parameters.
• php::Vector: the physiochemical parameters.
• pressures::Vector: the gas pressures.
• sx::Vector: the state vector.
• NREAC::Integer: the number of reaction rates.

Examples

julia> u0 = initialConditions();

julia> bp = biochemicalparameter_definition();

julia> rp = reactorParameterDefinition();

julia> php = physiochemicalParameterDefinition(rp);

julia> pressures = pressureOfGasses(u0,php,rp);

julia> NREAC = 29;

julia> reactionrates(bp,rp,php,pressures,u0,NREAC)
29-element Vector{Real}:
 0.155
 0.28
 1.0
 0.29000000000000004
 0.2950855111452082
 ⋮
 0.0
 7.402547081085608e-6
 1.295220255437568

 0.052518812965057435

petersenmatrixtranspose_definition(rp,bp,sp,cc)

Transpose of the Petersen matrix

individualSolutions(sol)

Rearranges the ODESolution returned by ADM1sol into a 1D array containing vectors of each solution over time.

i.e. A[i] is a vector containing the values of the ith solution for all times.

So, if we say t is a vector containing the timesteps, then plot(t,A[i]) will plot the ith solution vs time.

Arguments

• sol::Vector: ODESolution returned by ADM1 sol

Examples

julia> u0 = initialConditions();

julia> IV = inflowvector_definition();

julia> sol, tSol = ADM1sol((0.0,200.0),u0,IV); # compute the solution

julia> indSols = individualSolutions(sol)
35-element Vector{Vector{Float64}}:
 [0.012, 0.011999986305998722, 0.011999977102201841, 0.01199997267285494, 0.011999969386113186, 0.011999967149464337, 0.011999965091000644, 0.011999963258166062, 0.01199996178749697, 0.011999961662742068  …  0.01195750330094027, 0.011957024281388772, 0.01195654102848209, 0.011955980109704207, 0.011955371939386264, 0.011955036272014314, 0.011954879037458292, 0.011954836213455822, 0.011954830158706282, 0.011954829810563401]
 [0.0053, 0.005299528080754454, 0.005299211849244109, 0.005299059933102669, 0.005298947319276687, 0.005298870740171685, 0.005298800301401363, 0.005298737615364131, 0.005298687337685513, 0.005298683073531872  …  0.00531290262808903, 0.005313145376836529, 0.005313458937485294, 0.00531386295705003, 0.0053143158605383585, 0.0053145727297110815, 0.005314697865111298, 0.00531473416356305, 0.0053147398286552405, 0.0053147401832121036]
 ⋮
 [1.63, 1.6300010043803432, 1.630003893522008, 1.6300064891566448, 1.6300090584027846, 1.630011157417349, 1.630013359837308, 1.6300155516628245, 1.6300174749013072, 1.6300176449752604  …  1.6258740229661408, 1.6256583127128807, 1.6256250660754588, 1.625621749084325, 1.625620443499663, 1.6256197935003422, 1.6256194976733636, 1.6256194164919724, 1.6256194045086088, 1.6256194037384155]
 [0.014, 0.013987846051651676, 0.01395723325778608, 0.013936637777305555, 0.013919032066060481, 0.013905958298756526, 0.01389316476641871, 0.013881173393149072, 0.013871152739877324, 0.013870287064082722  …  0.01414633009687048, 0.014149764848711631, 0.01415028486767014, 0.014150328062007254, 0.01415033918241631, 0.014150344102072282, 0.014150346161797715, 0.014150346675181056, 0.014150346741486993, 0.014150346745679485]

 julia> indSols[1] # Solution vector for the first state variable (S_su)
 115-element Vector{Float64}:
 0.012
 0.011999986305998722
 ⋮
 0.011954830158706282
 0.011954829810563401