public IonSet(List <Ion> ions)
{
foreach (Ion sourceIon in ions)
{
Ion copiedIon = new Ion(sourceIon);
this.ions.Add(copiedIon);
}
}
public void equations(double[] x, double[] f)
{
Calculate.Ljp(list, x, f, temperatureC);
for (int j = 0; j < ionCount - 2; j++)
{
Ion ion = list[j];
f[j] = (f[j] - ion.cL) / sigma[j];
}
}
public Ion(Ion ion, double c0, double cL)
{
name = ion.name;
charge = ion.charge;
conductivity = ion.conductivity;
mu = ion.mu;
this.c0 = c0;
this.cL = cL;
}
public Ion(Ion ion)
{
this.name = ion.name;
this.charge = ion.charge;
this.conductivity = ion.conductivity;
this.mu = ion.mu;
this.c0 = ion.c0;
this.cL = ion.cL;
this.phi = ion.phi;
}
private Ion IonFromMarkdownLine(String line)
{
const double K_CONDUCTANCE = 73.5;
line = line.Trim();
var parts = line.Split('|');
bool isThreeItems = (parts.Length == 3);
bool isFiveItems = (parts.Length == 5);
bool isThreeOrFiveItems = isThreeItems || isFiveItems;
if (isThreeOrFiveItems == false)
{
return(null);
}
if (parts[1].StartsWith("---") || parts[1].Contains("Charge"))
{
return(null);
}
string strCond = parts[2];
strCond = strCond.Replace(" ", "").ToUpper();
bool isNormalizedToK = false;
if (strCond.Contains("*K"))
{
strCond = strCond.Replace("*K", "");
isNormalizedToK = true;
}
try
{
string name = parts[0].Trim();
int charge = int.Parse(parts[1]);
double conductance = double.Parse(strCond) * 1E-4;
if (isNormalizedToK)
{
conductance *= K_CONDUCTANCE;
}
double c0 = (parts.Length == 5) ? double.Parse(parts[3]) : 0;
double cL = (parts.Length == 5) ? double.Parse(parts[4]) : 0;
Ion ion = new Ion(name, charge, conductance, c0, cL);
Debug.WriteLine($"Parsed ion: {ion}");
return(ion);
}
catch
{
Debug.WriteLine($"Could not parse line: {line}");
return(null);
}
}
public Ion Lookup(Ion ion)
{
foreach (Ion tableIon in ions)
{
if (string.Compare(ion.name, tableIon.name, StringComparison.OrdinalIgnoreCase) == 0)
{
return(new Ion(tableIon.name, tableIon.charge, tableIon.conductivity, ion.c0, ion.cL));
}
}
return(new Ion(ion));
}
public PhiEquations(List <Ion> list, double temperatureC)
{
this.list = list;
ionCount = list.Count;
this.temperatureC = temperatureC;
// determine smallest nonzero cL of all ions
double smallestCL = Double.PositiveInfinity;
for (int j = 0; j < ionCount; j++)
{
Ion ion = list[j];
bool ionHasCL = (ion.cL > 0);
if (ionHasCL)
{
double thisCl = Math.Abs(ion.cL);
smallestCL = Math.Min(smallestCL, thisCl);
}
}
// set sigmas to cLs (unless cL is zero, then use smallest nonzero cL)
sigma = new double[ionCount];
for (int j = 0; j < ionCount; j++)
{
Ion ion = list[j];
bool ionHasCL = (ion.cL > 0);
if (ionHasCL)
{
sigma[j] = 0.01 * Math.Abs(ion.cL);
}
else
{
sigma[j] = 0.01 * smallestCL;
}
}
}
public void Load(string filePath, bool ignoreDuplicates = false, bool sort = false)
{
ions.Clear();
foreach (string line in System.IO.File.ReadAllLines(filePath))
{
Ion ion = IonFromMarkdownLine(line);
if (ion != null)
{
if (ignoreDuplicates && Contains(ion.name))
{
continue;
}
ions.Add(ion);
}
}
if (sort)
{
var sortedIons = ions.OrderBy(ion => ion.name).ToList();
ions.Clear();
ions.AddRange(sortedIons);
}
}
// This function is balanced by the equation solver, not called directly by the user.
public static double Ljp(List <Ion> ionList, double[] startingPhis, double[] startingCLs, double temperatureC)
{
double KT = Constants.boltzmann * (temperatureC + Constants.zeroCinK);
double cdadc = 1.0; // fine for low concentrations
int ionCount = ionList.Count;
int ionCountMinusOne = ionCount - 1;
int ionCountMinusTwo = ionCount - 2;
int indexLastIon = ionCount - 1;
int indexSecondFromLastIon = ionCount - 2;
Ion lastIon = ionList[indexLastIon];
Ion secondFromLastIon = ionList[indexSecondFromLastIon];
if (startingPhis.Length != ionCount - 2)
{
throw new ArgumentException();
}
if (startingCLs.Length != ionCount - 2)
{
throw new ArgumentException();
}
// populate charges, mus, and rhos from all ions except the last one
double[] charges = new double[ionCountMinusOne];
double[] mus = new double[ionCountMinusOne];
double[] rhos = new double[ionCountMinusOne];
for (int j = 0; j < ionCountMinusOne; j++)
{
Ion ion = ionList[j];
charges[j] = ion.charge;
mus[j] = ion.mu;
rhos[j] = ion.c0;
}
// populate phis from all ions except the last two
double[] phis = new double[ionCountMinusOne];
for (int j = 0; j < ionCountMinusTwo; j++)
{
phis[j] = startingPhis[j];
}
// second from last phi is the concentration difference
phis[indexSecondFromLastIon] = secondFromLastIon.cL - secondFromLastIon.c0;
// prepare info about second from last ion concentration difference for loop
if (secondFromLastIon.c0 == secondFromLastIon.cL)
{
throw new InvalidOperationException("second from last ion concentrations cannot be equal");
}
double KC0 = secondFromLastIon.c0;
double KCL = secondFromLastIon.cL;
double dK = (KCL - KC0) / 1000.0;
// set last ion C0 based on charges, rhos, and linear algebra
double zCl = ionList[indexLastIon].charge;
double rhoCl = -Linalg.ScalarProduct(charges, rhos) / zCl;
lastIon.c0 = rhoCl;
// cycle to determine junction voltage
double V = 0.0;
for (double rhoK = KC0; ((dK > 0) ? rhoK <= KCL : rhoK >= KCL); rhoK += dK)
{
rhoCl = -Linalg.ScalarProduct(rhos, charges) / zCl;
double DCl = lastIon.mu * KT * cdadc;
double vCl = zCl * Constants.e * lastIon.mu * rhoCl;
double[] v = new double[ionCountMinusOne];
double[,] mD = new double[ionCountMinusOne, ionCountMinusOne];
for (int j = 0; j < ionCountMinusOne; j++)
{
for (int k = 0; k < ionCountMinusOne; k++)
{
mD[j, k] = 0.0;
}
}
for (int j = 0; j < ionCountMinusOne; j++)
{
for (int k = 0; k < ionCountMinusOne; k++)
{
mD[j, k] = 0.0;
}
mD[j, j] = mus[j] * KT * cdadc;
v[j] = charges[j] * Constants.e * mus[j] * rhos[j];
}
if (Linalg.ScalarProduct(charges, v) + zCl * vCl == 0.0)
{
return(Double.NaN); // Singularity; abort calculation
}
double[,] identity = Linalg.Identity(ionCountMinusOne);
double[,] linAlgSum = Linalg.Sum(1, mD, -DCl, identity);
double[] sumCharge = Linalg.Product(linAlgSum, charges);
double chargesProd = Linalg.ScalarProduct(charges, v);
double chargesProdPlusCl = chargesProd + zCl * vCl;
double[] delta = Linalg.ScalarMultiply(sumCharge, 1.0 / chargesProdPlusCl);
double[,] mDyadic = new double[ionCountMinusOne, ionCountMinusOne];
for (int j = 0; j < ionCountMinusOne; j++)
{
for (int k = 0; k < ionCountMinusOne; k++)
{
mDyadic[j, k] = v[j] * delta[k];
}
}
double[,] mM = Linalg.Sum(1, mDyadic, -1, mD);
double[] rhop = Linalg.Solve(mM, phis);
double rhopK = rhop[indexSecondFromLastIon];
rhos = Linalg.Sum(1, rhos, dK / rhopK, rhop);
double E = Linalg.ScalarProduct(delta, rhop);
V -= E * dK / rhopK;
}
// modify CLs based on the rhos we calculated
for (int j = 0; j < ionCountMinusTwo; j++)
{
startingCLs[j] = rhos[j];
}
return(V);
}
public static LjpResult Ljp(List <Ion> ionList, double temperatureC = 25)
{
foreach (Ion ion in ionList)
{
if (ion.charge == 0)
{
throw new ArgumentException("ion charge cannot be zero");
}
if (ion.mu == 0)
{
throw new ArgumentException("ion mu cannot be zero");
}
}
LjpResult result = new LjpResult(ionList, temperatureC);
int ionCount = ionList.Count;
int ionCountMinusOne = ionCount - 1;
int ionCountMinusTwo = ionCount - 2;
Ion secondFromLastIon = ionList[ionCount - 2];
Ion LastIon = ionList[ionCount - 1];
if (secondFromLastIon.c0 == secondFromLastIon.cL)
{
throw new InvalidOperationException("second from last ion concentrations cannot be equal");
}
// phis will be solved for all ions except the last two
double[] phis = new double[ionCountMinusTwo];
// phis to solve are initialized to the concentration difference
for (int j = 0; j < phis.Length; j++)
{
Ion ion = ionList[j];
phis[j] = ion.cL - ion.c0;
}
// all phis except the last two get solved
if (ionCount > 2)
{
var phiEquations = new PhiEquations(ionList, temperatureC) as IEquationSystem;
Solver s = new Solver(phiEquations);
s.solve(phis);
}
// calculate LJP
double[] cLs = new double[phis.Length];
double ljp_V = Ljp(ionList, phis, cLs, temperatureC);
if (ljp_V == Double.NaN)
{
throw new Exception("ERROR: Singularity (calculation aborted)");
}
// update ions based on what was just calculated
for (int j = 0; j < phis.Length; j++)
{
Ion ion = ionList[j];
ion.phi = phis[j];
ion.cL = cLs[j];
}
// second from last ion phi is concentration difference
secondFromLastIon.phi = secondFromLastIon.cL - secondFromLastIon.c0;
// last ion's phi is calculated from all the phis before it
double totalChargeWeightedPhi = 0.0;
for (int j = 0; j < ionCountMinusOne; j++)
{
Ion ion = ionList[j];
totalChargeWeightedPhi += ion.phi * ion.charge;
}
LastIon.phi = -totalChargeWeightedPhi / LastIon.charge;
// last ion's cL is calculated from all the cLs before it
double totalChargeWeightedCL = 0.0;
for (int j = 0; j < ionCountMinusOne; j++)
{
Ion ion = ionList[j];
totalChargeWeightedCL += ion.cL * ion.charge;
}
LastIon.cL = -totalChargeWeightedCL / LastIon.charge;
result.Finished(ionList, ljp_V);
return(result);
}
