SEC.Models.SdmMonoPore

SEC.Models.SdmMonoPore#

SEC.Models.SdmMonoPore.py

sdm_monopore_cf(w, npi, tpi, N0, t0)#
sdm_monopore_pdf(x, npi, tpi, N0, t0, timescale=0.25)#

PDF of the SDM (Standard Dispersive Model) for a monoporous stationary phase.

Uses FFT-based characteristic function inversion via FftInvPdf.

Parameters:

  • x (array_like) – Time array (physical time units).

  • npi (float) – Mean number of pore entries (Poisson parameter of the compound-Poisson process). Physical mapping: npi ≈ F * a (phase ratio × Henry coefficient).

  • tpi (float) – Mean pore residence time per visit (scale of the exponential distribution). Physical mapping: tpi ≈ t0 / npi in the k → ∞ LKM limit.

  • N0 (float) – Mobile-phase plate count (controls Gaussian peak width; σ_mobile ≈ t0/√N0).

  • t0 (float) – Mean mobile-phase transit time (dead time). Fix at the known dead time when fitting; do not use as a free parameter unless the dead time is unknown.

  • timescale (float, optional) –

    Time rescaling factor for the internal FFT grid (default 0.25). The FFT grid spans [0, 1024) in scaled coordinates. The peak should land well within [10, 900] on the scaled grid to avoid edge artefacts. Rule of thumb: timescale ≈ 80 / t_R

    • SEC-SAXS data (t_R ~ 0.2–2 s): default 0.25 is appropriate.

    • General chromatography (t_R ~ 8): use timescale=10.0.

Returns:

Normalised PDF evaluated at each point in x (integral ≈ 1). Multiply by the pulse area (cinj × t_inj) to obtain absolute concentration units.

Return type:

ndarray

Notes

Non-identifiability of npi and tpi

Only the product npi * tpi (= mean total pore retention time ≈ F*a*t0) is tightly constrained by the peak position. The individual values affect peak shape (variance and skewness), but many (npi, tpi) pairs with the same product give nearly indistinguishable peaks for typical chromatographic data. When fitting, report npi * tpi as the physically meaningful quantity rather than npi or tpi individually.

sdm_monopore_gamma_cf(w, npi, k, theta, N0, t0)#

Gamma-distributed residence times with mobile phase dispersion.

Parameters:#

warray

Frequency array

npifloat

Mean number of pore entries (Poisson parameter)

kfloat

Gamma shape parameter (k=1 recovers exponential)

thetafloat

Gamma scale parameter (mean residence = k*theta)

N0float

Plate number (mobile phase dispersion)

t0float

Mean mobile phase time

Returns:#

CFcomplex array

Characteristic function

Notes:#

  • Exponential: CF = 1/(1 - iω*τ)

  • Gamma: CF = (1 - iω*θ)^(-k)

  • For k=1, θ=τ: Gamma → Exponential

sdm_monopore_gamma_pdf(x, npi, k, theta, N0, t0, timescale=0.25)#

Wrapper with timescale normalization