5 research outputs found
Pseudospectral methods for density functional theory in bounded and unbounded domains
Classical Density Functional Theory (DFT) is a statistical-mechanical
framework to analyze fluids, which accounts for nanoscale fluid inhomogeneities
and non-local intermolecular interactions. DFT can be applied to a wide range
of interfacial phenomena, as well as problems in adsorption, colloidal science
and phase transitions in fluids. Typical DFT equations are highly non-linear,
stiff and contain several convolution terms. We propose a novel, efficient
pseudo-spectral collocation scheme for computing the non-local terms in real
space with the help of a specialized Gauss quadrature. Due to the exponential
accuracy of the quadrature and a convenient choice of collocation points near
interfaces, we can use grids with a significantly lower number of nodes than
most other reported methods. We demonstrate the capabilities of our numerical
methodology by studying equilibrium and dynamic two-dimensional test cases with
single- and multispecies hard-sphere and hard-disc particles modelled with
fundamental measure theory, with and without van der Waals attractive forces,
in bounded and unbounded physical domains. We show that our results satisfy
statistical mechanical sum rules
A Finite-Volume Method for Fluctuating Dynamical Density Functional Theory
We introduce a finite-volume numerical scheme for solving stochastic
gradient-flow equations. Such equations are of crucial importance within the
framework of fluctuating hydrodynamics and dynamic density functional theory.
Our proposed scheme deals with general free-energy functionals, including, for
instance, external fields or interaction potentials. This allows us to simulate
a range of physical phenomena where thermal fluctuations play a crucial role,
such as nucleation and other energy-barrier crossing transitions. A
positivity-preserving algorithm for the density is derived based on a hybrid
space discretization of the deterministic and the stochastic terms and
different implicit and explicit time integrators. We show through numerous
applications that not only our scheme is able to accurately reproduce the
statistical properties (structure factor and correlations) of the physical
system, but, because of the multiplicative noise, it allows us to simulate
energy barrier crossing dynamics, which cannot be captured by mean-field
approaches