857 research outputs found
The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method
The recently proposed full configuration interaction quantum Monte Carlo
method allows access to essentially exact ground-state energies of systems of
interacting fermions substantially larger than previously tractable without
knowledge of the nodal structure of the ground-state wave function. We
investigate the nature of the sign problem in this method and how its severity
depends on the system studied. We explain how cancelation of the positive and
negative particles sampling the wave function ensures convergence to a
stochastic representation of the many-fermion ground state and accounts for the
characteristic population dynamics observed in simulations.Comment: 11 pages. 6 figure
Open-source development experiences in scientific software: the HANDE quantum Monte Carlo project
The HANDE quantum Monte Carlo project offers accessible stochastic algorithms
for general use for scientists in the field of quantum chemistry. HANDE is an
ambitious and general high-performance code developed by a
geographically-dispersed team with a variety of backgrounds in computational
science. In the course of preparing a public, open-source release, we have
taken this opportunity to step back and look at what we have done and what we
hope to do in the future. We pay particular attention to development processes,
the approach taken to train students joining the project, and how a flat
hierarchical structure aids communicationComment: 6 pages. Submission to WSSSPE
Accurate exchange-correlation energies for the warm dense electron gas
Density matrix quantum Monte Carlo (DMQMC) is used to sample exact-on-average
-body density matrices for uniform electron gas systems of up to 10
matrix elements via a stochastic solution of the Bloch equation. The results of
these calculations resolve a current debate over the accuracy of the data used
to parametrize finite-temperature density functionals. Exchange-correlation
energies calculated using the real-space restricted path-integral formalism and
the -space configuration path-integral formalism disagree by up to
\% at certain reduced temperatures and densities . Our calculations confirm the accuracy of the configuration
path-integral Monte Carlo results available at high density and bridge the gap
to lower densities, providing trustworthy data in the regime typical of
planetary interiors and solids subject to laser irradiation. We demonstrate
that DMQMC can calculate free energies directly and present exact free energies
for and .Comment: Accepted version: added free energy data and restructured text. Now
includes supplementary materia
Reconstruction of three-dimensional porous media using generative adversarial neural networks
To evaluate the variability of multi-phase flow properties of porous media at
the pore scale, it is necessary to acquire a number of representative samples
of the void-solid structure. While modern x-ray computer tomography has made it
possible to extract three-dimensional images of the pore space, assessment of
the variability in the inherent material properties is often experimentally not
feasible. We present a novel method to reconstruct the solid-void structure of
porous media by applying a generative neural network that allows an implicit
description of the probability distribution represented by three-dimensional
image datasets. We show, by using an adversarial learning approach for neural
networks, that this method of unsupervised learning is able to generate
representative samples of porous media that honor their statistics. We
successfully compare measures of pore morphology, such as the Euler
characteristic, two-point statistics and directional single-phase permeability
of synthetic realizations with the calculated properties of a bead pack, Berea
sandstone, and Ketton limestone. Results show that GANs can be used to
reconstruct high-resolution three-dimensional images of porous media at
different scales that are representative of the morphology of the images used
to train the neural network. The fully convolutional nature of the trained
neural network allows the generation of large samples while maintaining
computational efficiency. Compared to classical stochastic methods of image
reconstruction, the implicit representation of the learned data distribution
can be stored and reused to generate multiple realizations of the pore
structure very rapidly.Comment: 21 pages, 20 figure
Macroscopic Equations of Motion for Two Phase Flow in Porous Media
The established macroscopic equations of motion for two phase immiscible
displacement in porous media are known to be physically incomplete because they
do not contain the surface tension and surface areas governing capillary
phenomena. Therefore a more general system of macroscopic equations is derived
here which incorporates the spatiotemporal variation of interfacial energies.
These equations are based on the theory of mixtures in macroscopic continuum
mechanics. They include wetting phenomena through surface tensions instead of
the traditional use of capillary pressure functions. Relative permeabilities
can be identified in this approach which exhibit a complex dependence on the
state variables. A capillary pressure function can be identified in equilibrium
which shows the qualitative saturation dependence known from experiment. In
addition the new equations allow to describe the spatiotemporal changes of
residual saturations during immiscible displacement.Comment: 15 pages, Phys. Rev. E (1998), in prin
Broken symmetry and the variation of critical properties in the phase behaviour of supramolecular rhombus tilings
The degree of randomness, or partial order, present in two-dimensional
supramolecular arrays of isophthalate tetracarboxylic acids is shown to vary
due to subtle chemical changes such as the choice of solvent or small
differences in molecular dimensions. This variation may be quantified using an
order parameter and reveals a novel phase behaviour including random tiling
with varying critical properties as well as ordered phases dominated by either
parallel or non-parallel alignment of neighbouring molecules, consistent with
long-standing theoretical studies. The balance between order and randomness is
driven by small differences in the intermolecular interaction energies, which
we show, using numerical simulations, can be related to the measured order
parameter. Significant variations occur even when the energy difference is much
less than the thermal energy highlighting the delicate balance between entropic
and energetic effects in complex self-assembly processes
Simulating temporal evolution of pressure in two-phase flow in porous media
We have simulated the temporal evolution of pressure due to capillary and
viscous forces in two-phase drainage in porous media. We analyze our result in
light of macroscopic flow equations for two-phase flow. We also investigate the
effect of the trapped clusters on the pressure evolution and on the effective
permeability of the system. We find that the capillary forces play an important
role during the displacements for both fast and slow injection rates and both
when the invading fluid is more or less viscous than the defending fluid. The
simulations are based on a network simulator modeling two-phase drainage
displacements on a two-dimensional lattice of tubes.Comment: 12 pages, LaTeX, 14 figures, Postscrip
Critical point network for drainage between rough surfaces
In this paper, we present a network method for computing two-phase flows between two rough surfaces with significant contact areas. Low-capillary number drainage is investigated here since one-phase flows have been previously investigated in other contributions. An invasion percolation algorithm is presented for modeling slow displacement of a wetting fluid by a non wetting one between two rough surfaces. Short-correlated Gaussian process is used to model random rough surfaces.The algorithm is based on a network description of the fracture aperture field. The network is constructed from the identification of critical points (saddles and maxima) of the aperture field. The invasion potential is determined from examining drainage process in a flat mini-channel. A direct comparison between numerical prediction and experimental visualizations on an identical geometry has been performed for one realization of an artificial fracture with a moderate fractional contact area of about 0.3. A good agreement is found between predictions and observations
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