kawin.PopulationBalance

class kawin.PopulationBalanceModel(self, cMin = 1e-10, cMax = 1e-9, bins = 150, minBins = 100, maxBins = 200)

Class for handling particle size distributions (PSD) 
    This include time evolution, moments and graphing 
 
NOTE: more formally, the PSD is defined such that the number of particles of size R in a volume 
    is the integral of the PSD from R-1/2 to R+1/2 
    For the discrete PSD, n_i = PSD_i * (R+1/2 - R-1/2) 
    Here, we just store the PSD as the number of particles (n_i), but the formulation for  
    growth rates and moments are the same since the factor (R+1/2 - R-1/2) cancels out 
 
Parameters 
---------- 
cMin : float (optional) 
    Lower bound of PSD (defaults at 1e-10) 
cMax : float (optional) 
    Upper bound of PSD (defaults at 1e-9) 
bins : int (optional) 
    Initial number of bins (defaults at 150) 
minBins : int (optional) 
    Minimum number of bins over an order of magnitude (defaults at 100) 
maxBins : int (optional) 
    Maximum number of bins over an order of magnitude (defaults at 200) 
 
Attributes 
---------- 
originalMin : float 
    Minimum bin size initially set 
min : float 
    Current minimum bin size (this will almost always be equal to originalMin) 
originalMax : float 
    Maximum bin size initially set 
max : float 
    Current maximum bin size 
bins : int 
    Default number of bins 
minBins : int 
    Minimum number of allowed bins 
maxBins : int 
    Maximum number of allowed bins 
PSD : array 
    Particle size distribution 
PSDsize : array 
    Average radius of each PSD size class 
PSDbounds : array 
    Radius at the bounds of each size class - length of array is len(PSD)+1

kawin.PopulationBalanceModel.setAdaptiveBinSize(self, adaptive)

For Euler implementation, sets whether to change the bin size when  
the number of filled bins > maxBins or < minBins 
 
If False, the bins will still change if nucleated particles are greater than the max bin size 
and bins will still be added when the last bins starts to fill (although this will not change the bin size)

kawin.PopulationBalanceModel.setBinConstraints(self, bins = 150, minBins = 100, maxBins = 200)

Sets constraints for minimum and maxinum number of bins over an order of magnitude 
 
All bins will be overridden to an even number 
Minimum number of bins will be overridden to be at most half of maximum bins 
Default bins will be overridden to be halfway between min and max bins if out of range

kawin.PopulationBalanceModel.LoadDistribution(self, data)

Creates a particle size distribution from a set of data 
 
Parameters 
---------- 
data : array of floats 
    Array of data to be inserted into PSD

kawin.PopulationBalanceModel.LoadDistributionFunction(self, function)

Creates a particle size distribution from a function 
 
Parameters 
---------- 
function : function 
    Takes in R and returns density

kawin.PopulationBalanceModel.createBackup(self)

Stores current PSD and PSDbounds

kawin.PopulationBalanceModel.revert(self)

Reverts to previous PSD and PSDbounds

kawin.PopulationBalanceModel.reset(self, resetBounds = True)

Resets the PSD to 0 
This will remove any size classes that were added since initialization

kawin.PopulationBalanceModel.changeSizeClasses(self, cMin, cMax, bins = None, resetPSD = False)

Changes the size classes and resets the PSD 
 
Parameters 
---------- 
cMin : float 
    Lower bound of PSD 
cMax : float 
    Upper bound of PSD 
bins : int 
    Number of bins 
resetPSD : bool (optional) 
    Whether to reset the PSD (defaults to False)

kawin.PopulationBalanceModel.addSizeClasses(self, bins = 1)

Adds an additional size class to end of distribution 
 
Parameters 
---------- 
bins : int 
    Number of bins to add

kawin.PopulationBalanceModel.getDTEuler(self, currDT, growth, maxDissolution, startIndex)

Calculates time interval for Euler implementation 
    dt < dR / (2 * growth rate) 
This ensures that at most, only half of particles in one size class can go to another 
 
Parameters 
---------- 
currDT : float 
    Current time interval, will be returned if it's smaller than what's given by the contraint 
growth : array of floats 
    Growth rate, must have lenth of bins+1 (or length of PSDbounds) 
maxDissolution : float 
    Maximum volume allowed to dissolve 
startIndex : int 
    First index to look at for growth rate, all indices below startIndex will be ignored

kawin.PopulationBalanceModel.adjustSizeClassesEuler(self, checkDissolution = False)

Adds a size class if last class in PBM is filled 
Changes length of size classes based off number of allowed bins

kawin.PopulationBalanceModel.Normalize(self)

Normalizes the PSD to 1

kawin.PopulationBalanceModel.NormalizeToMoment(self, order = 0)

Normalizes the PSD with so that the moment of specified order will be 1 
 
Parameters 
---------- 
order : int (optional) 
    Order of moment that PSD will be normalized to (defaults to 0) 
    Using zeroth order will normalize the PSD so the sum of PSD will be 1

kawin.PopulationBalanceModel.Nucleate(self, amount, radius)

Adds nucleated particles to PSD given radius and amount of particles 
 
Parameters 
---------- 
amount : float 
    Amount of nucleated particles 
radius : float 
    Radius of nucleated particles

kawin.PopulationBalanceModel.UpdateEuler(self, dt, flux)

Updates PSD given the flux and any external contributions 
 
Change in the amount of particles in a given size class = d(G*n)/dx 
Where G is flux of size class, n is number of particles in size class and dx is range of size class 
 
Parameters 
---------- 
dt : float 
    Time increment 
flux : array 
    Growth rate of each particle size class 
    Array size must be (bins + 1) since this operates on bounds of size classes

kawin.PopulationBalanceModel.UpdateLagrange(self, dt, flux)

Updates bounds of size classes with given growth rate 
Fluxes of particles between size classes is d(Gn)/dx, 
however, keeping the number of particles in each size class the same, 
the bounds of the size classes can be updated by r_i = v_i * dt 
 
Parameters 
---------- 
dt : float 
    Time increment 
flux : array 
    Growth rate of each particle size class 
    Array size must be (bins + 1) since this operates on bounds of size classes

kawin.PopulationBalanceModel.Moment(self, order)

Moment of specified order 
 
Parameters 
---------- 
order : int 
    Order of moment

kawin.PopulationBalanceModel.CumulativeMoment(self, order)

Cumulative distribution using moment of specified order 
 
Parameters 
---------- 
order : int 
    Order of moment

kawin.PopulationBalanceModel.WeightedMoment(self, order, weights)

Weighted moment of specified order 
 
Parameters 
---------- 
order : int 
    Order of moment 
weights : array 
    Weights to apply to each size class 
    Array size of (bins)

kawin.PopulationBalanceModel.CumulativeWeightedMoment(self, order, weights)

Weighted moment of specified order 
 
Parameters 
---------- 
order : int 
    Order of moment 
weights : array 
    Weights to apply to each size class 
    Array size of (bins)

kawin.PopulationBalanceModel.ZeroMoment(self)

Sum of the PSD

kawin.PopulationBalanceModel.FirstMoment(self)

Length weighted moment

kawin.PopulationBalanceModel.SecondMoment(self)

Area weighted moment

kawin.PopulationBalanceModel.ThirdMoment(self)

Volume weighted moment

kawin.PopulationBalanceModel.PlotCurve(self, axes, fill = False, logX = False, logY = False, scale = 1, *args, **kwargs)

Plots the PSD as a curve 
 
Parameters 
---------- 
axes : Axes 
    Axis to plot on 
fill : bool (optional) 
    Will fill area between PSD curve and x-axis (defaults to False) 
logX : bool (optional) 
    Whether to set x-axis on log scale (defaults to False) 
logY : bool (optional) 
    Whether to set y-axis on log scale (defaults to False) 
scale : float (optional) 
    Scale factor for x-axis (defaults to 1) 
    Note: this is for grain boundary nucleation where the 
        reported precipitate radius differs from the radius 
        determined by precipitate curvature 
*args, **kwargs - extra arguments for plotting

kawin.PopulationBalanceModel.PlotDistributionDensity(self, axes, fill = False, logX = False, logY = False, scale = 1, *args, **kwargs)

Plots the distribution density as a curve 
Defined as N_i / (R_i+1/2 - R_i-1/2) 
 
Parameters 
---------- 
axes : Axes 
    Axis to plot on 
fill : bool (optional) 
    Will fill area between PSD curve and x-axis (defaults to False) 
logX : bool (optional) 
    Whether to set x-axis on log scale (defaults to False) 
logY : bool (optional) 
    Whether to set y-axis on log scale (defaults to False) 
scale : float (optional) 
    Scale factor for x-axis (defaults to 1) 
    Note: this is for grain boundary nucleation where the 
        reported precipitate radius differs from the radius 
        determined by precipitate curvature 
*args, **kwargs - extra arguments for plotting

kawin.PopulationBalanceModel.PlotKDE(self, axes, bw_method = None, fill = False, logX = False, logY = False, scale = 1, *args, **kwargs)

Plots the kernel density estimation (KDE) 
 
Parameters 
---------- 
axes : Axes 
    Axis to plot on 
bw_method : str (optional) 
    Method to estimate bandwidth ('scott', 'silverman' or a scalar) 
    Defaults to scipy's default for KDE 
fill : bool (optional) 
    Will fill area between PSD curve and x-axis (defaults to False) 
logX : bool (optional) 
    Whether to set x-axis on log scale (defaults to False) 
logY : bool (optional) 
    Whether to set y-axis on log scale (defaults to False) 
scale : float (optional) 
    Scale factor for x-axis (defaults to 1) 
    Note: this is for grain boundary nucleation where the 
        reported precipitate radius differs from the radius 
        determined by precipitate curvature 
*args, **kwargs - extra arguments for plotting

kawin.PopulationBalanceModel.PlotHistogram(self, axes, outline = ‘outline bins’, fill = True, logX = False, logY = False, scale = 1, *args, **kwargs)

Plots the PSD as a histogram 
 
Parameters 
---------- 
axes : Axes 
    Axis to plot on 
outline : str (optional) 
    How to outline the bins ('no outline', 'outline bins', 'outline top') 
    Defaults to 'outline bins' 
fill : bool (optional) 
    Will fill area between PSD curve and x-axis (defaults to False) 
logX : bool (optional) 
    Whether to set x-axis on log scale (defaults to False) 
logY : bool (optional) 
    Whether to set y-axis on log scale (defaults to False) 
scale : float (optional) 
    Scale factor for x-axis (defaults to 1) 
    Note: this is for grain boundary nucleation where the 
        reported precipitate radius differs from the radius 
        determined by precipitate curvature 
*args, **kwargs - extra arguments for plotting

kawin.PopulationBalanceModel.PlotCDF(self, axes, logX = False, scale = 1, order = 0, *args, **kwargs)

Plots cumulative size distribution 
 
Parameters 
---------- 
axes : Axes 
    Axis to plot on 
logX : bool (optional) 
    Whether to set x-axis on log scale (defaults to False) 
scale : float (optional) 
    Scale factor for x-axis (defaults to 1) 
    Note: this is for grain boundary nucleation where the 
        reported precipitate radius differs from the radius 
        determined by precipitate curvature 
order : int (optional) 
    Moment of specified order 
*args, **kwargs - extra arguments for plotting

kawin.PopulationBalanceModel.setAxes(self, axes, scale = 1, logX = False, logY = False)

Sets x- and y-axis to linear or log scale 
 
Parameters 
---------- 
axes : Axis 
    Axis to plot on 
logX : bool (optional) 
    Whether to set x-axis on log scale (defaults to False) 
logY : bool (optional) 
    Whether to set y-axis on log scale (defaults to False)
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