Equation Patterns

YamDB.jl uses a two-layer equation design:

Equation patterns — generic mathematical functions (this page)
Paper-name wrappers — functions named after publications that call a pattern with specific coefficients

All patterns are defined in src/equations/patterns.jl and are internal to the package.

Constant and Linear

Pattern	Formula
`constant(val)`	$val$
`linear(T, a, b)`	$a + bT$
`linear_tref(T, a, b, T_{ref})`	$a - b(T - T_{ref})$

Polynomials in T

Pattern	Formula
`poly2(T, a, b, c)`	$a + bT + cT^2$
`poly3(T, a, b, c, d)`	$a + bT + cT^2 + dT^3$
`poly4(T, a, b, c, d, e)`	$a + bT + cT^2 + dT^3 + eT^4$
`poly5(T, a, b, c, d, e, f)`	$a + bT + cT^2 + dT^3 + eT^4 + fT^5$

Polynomials with Reference Temperature

Pattern	Formula
`poly2_tref(T, T_{ref}, a, b, c)`	$a + b(T - T_{ref}) + c(T - T_{ref})^2$
`poly3_tref(T, T_{ref}, a, b, c, d)`	$a + b(T - T_{ref}) + c(T - T_{ref})^2 + d(T - T_{ref})^3$

Polynomial in τ = T/1000

Pattern	Formula
`poly_tau(T, a)`	$\sum_{i=0}^{n} a_i \tau^i$ where $\tau = T/1000$

The coefficient vector a can have arbitrary length.

Arrhenius Type

Pattern	Formula
`arrhenius(T, A, B, R)`	$A \exp(B / RT)$
`arrhenius_shifted(T, A, B, R, T_0)`	$A \exp(B / R(T - T_0))$

Exponential Types

Pattern	Formula
`exp_linear(T, a, b)`	$\exp(a + bT)$
`exp_linear_tref(T, a, b, T_{ref})`	$a \exp(b(T - T_{ref}))$
`exp_BT_CT2(T, A, B, C)`	$A \exp(B/T + C/T^2)$

Power-Exponential

Pattern	Formula
`power_exp(T, a, b, c)`	$a T^b \exp(c/T)$

Logarithmic Types

Pattern	Formula
`log_poly(T, a, b, c)`	$\exp(a + b \ln T + c/T)$
`log10_linear(T, a, b)`	$10^{-a + b/T}$
`log10_poly3(T, a, b, c, d)`	$a + b \log_{10} T + c (\log_{10} T)^2 + d (\log_{10} T)^3$

Concentration Polynomials

Temperature-independent polynomials in concentration $C$ (mol%):

Pattern	Formula
`conc_poly1(C, a, b)`	$a + bC$
`conc_poly2(C, a, b, c)`	$a + bC + cC^2$
`conc_poly3(C, a, b, c, d)`	$a + bC + cC^2 + dC^3$
`conc_poly4(C, a, b, c, d, e)`	$a + bC + cC^2 + dC^3 + eC^4$

Mixed Temperature-Concentration Patterns

Pattern	Formula
`tc_linear(T, x, a, b, c, d)`	$a + bT + cx + dx^2$
`tc_cross(T, x, a, b, c, d, e)`	$a + bT + cx + dx^2 T + exT^2$

Special Patterns

Pattern	Formula
`reciprocal_linear(T, a, T_{ref})`	$1 / (a - T)$
`molar_volume_to_density(T, a, b, M, T_{ref})`	$M / V_m$ where $V_m = [a(T - T_{ref}) + b] \times 10^{-6}$

Vapour Pressure

Pattern	Formula
`vapour_pressure_iaea(T, a, b, c, d)`	$\exp(a + b/T + c \ln T + dT)$
`vapour_pressure_kelley(T, A, B, C, R)`	$\exp(-\Delta F / RT)$ where $\Delta F = A + BT \log_{10} T - CT$
`vapour_pressure_iida(T, A, B, C)`	$10^{A + B/T + C \log_{10} T}$

Heat Capacity

Pattern	Formula
`heat_capacity_polynomial_molar(T, c_{p,0}, a, b, c, M)`	$(c_{p,0} + aT + bT^2 + cT^{-2}) / M$