The multi-scale Gibbs–Helmholtz constrained (GHC) equation is a new predictive cubic equation of state that constrains the energy parameter in the SRK equation to satisfy the Gibbs–Helmholtz equation. It makes use of internal energies of departure calculated from NTP Monte Carlo simulations at the molecular length scale and a novel up-scaling expression to determine the energy parameter at the ...

The integrable 3rd-order Korteweg-de Vries (KdV) equation emerges uniquely at linear order in the asymptotic expansion for unidirectional shallow water waves. However, at quadratic order, this asymptotic expansion produces an entire family of shallow water wave equations that are asymptotically equivalent to each other, under a group of nonlinear, nonlocal, normal-form transformations introduce...