7,179 research outputs found
Coping with Poorly Understood Domains: the Example of Internet Trust
The notion of trust, as required for secure operations over the Internet, is important for ascertaining the source of received messages. How can we measure the degree of trust in authenticating the source? Knowledge in the domain is not established, so knowledge engineering becomes knowledge generation rather than mere acquisition. Special techniques are required, and special features of KBS software become more important than in conventional domains. This paper generalizes from experience with Internet trust to discuss some techniques and software features that are important for poorly understood domains
Solvent fluctuations around solvophobic, solvophilic and patchy nanostructures and the accompanying solvent mediated interactions
Using classical density functional theory (DFT) we calculate the density
profile and local compressibility of a
simple liquid solvent in which a pair of blocks with (microscopic) rectangular
cross-section are immersed. We consider blocks that are solvophobic,
solvophilic and also ones that have both solvophobic and solvophilic patches.
Large values of correspond to regions in space where the
liquid density is fluctuating most strongly. We seek to elucidate how enhanced
density fluctuations correlate with the solvent mediated force between the
blocks, as the distance between the blocks and the chemical potential of the
liquid reservoir vary. For sufficiently solvophobic blocks, at small block
separations and small deviations from bulk gas-liquid coexistence, we observe a
strongly attractive (near constant) force, stemming from capillary evaporation
to form a low density gas-like intrusion between the blocks. The accompanying
exhibits structure which reflects the incipient gas-liquid
interfaces that develop. We argue that our model system provides a means to
understanding the basic physics of solvent mediated interactions between
nanostructures, and between objects such as proteins in water, that possess
hydrophobic and hydrophilic patches.Comment: 19 pages, 21 figure
The standard mean-field treatment of inter-particle attraction in classical DFT is better than one might expect
In classical density functional theory (DFT) the part of the Helmholtz free
energy functional arising from attractive inter-particle interactions is often
treated in a mean-field or van der Waals approximation. On the face of it, this
is a somewhat crude treatment as the resulting functional generates the simple
random phase approximation (RPA) for the bulk fluid pair direct correlation
function. We explain why using standard mean-field DFT to describe
inhomogeneous fluid structure and thermodynamics is more accurate than one
might expect based on this observation. By considering the pair correlation
function and structure factor of a one-dimensional model fluid,
for which exact results are available, we show that the mean-field DFT,
employed within the test-particle procedure, yields results much superior to
those from the RPA closure of the bulk Ornstein-Zernike equation. We argue that
one should not judge the quality of a DFT based solely on the approximation it
generates for the bulk pair direct correlation function.Comment: 9 pages, 3 figure
Sedimentation of a two-dimensional colloidal mixture exhibiting liquid-liquid and gas-liquid phase separation: a dynamical density functional theory study
We present dynamical density functional theory results for the time evolution
of the density distribution of a sedimenting model two-dimensional binary
mixture of colloids. The interplay between the bulk phase behaviour of the
mixture, its interfacial properties at the confining walls, and the
gravitational field gives rise to a rich variety of equilibrium and
non-equilibrium morphologies. In the fluid state, the system exhibits both
liquid-liquid and gas-liquid phase separation. As the system sediments, the
phase separation significantly affects the dynamics and we explore situations
where the final state is a coexistence of up to three different phases. Solving
the dynamical equations in two-dimensions, we find that in certain situations
the final density profiles of the two species have a symmetry that is different
from that of the external potentials, which is perhaps surprising, given the
statistical mechanics origin of the theory. The paper concludes with a
discussion on this
Solvent mediated interactions between model colloids and interfaces: A microscopic approach
We determine the solvent mediated contribution to the effective potentials
for model colloidal or nano- particles dispersed in a binary solvent that
exhibits fluid-fluid phase separation. Using a simple density functional theory
we calculate the density profiles of both solvent species in the presence of
the `colloids', which are treated as external potentials, and determine the
solvent mediated (SM) potentials. Specifically, we calculate SM potentials
between (i) two colloids, (ii) a colloid and a planar fluid-fluid interface,
and (iii) a colloid and a planar wall with an adsorbed wetting film. We
consider three different types of colloidal particles: colloid A which prefers
the bulk solvent phase rich in species 2, colloid C which prefers the solvent
phase rich in species 1, and `neutral' colloid B which has no strong preference
for either phase, i.e. the free energies to insert the colloid into either of
the coexisting bulk phases are almost equal. When a colloid which has a
preference for one of the two solvent phases is inserted into the disfavored
phase at statepoints close to coexistence a thick adsorbed `wetting' film of
the preferred phase may form around the colloids. The presence of the adsorbed
film has a profound influence on the form of the SM potentials.Comment: 17 Pages, 13 Figures. Accepted for publication in Journal of Chemical
Physic
Liquid drops on a surface: using density functional theory to calculate the binding potential and drop profiles and comparing with results from mesoscopic modelling
The contribution to the free energy for a film of liquid of thickness on
a solid surface, due to the interactions between the solid-liquid and
liquid-gas interfaces is given by the binding potential, . The precise
form of determines whether or not the liquid wets the surface. Note that
differentiating gives the Derjaguin or disjoining pressure. We develop a
microscopic density functional theory (DFT) based method for calculating
, allowing us to relate the form of to the nature of the molecular
interactions in the system. We present results based on using a simple lattice
gas model, to demonstrate the procedure. In order to describe the static and
dynamic behaviour of non-uniform liquid films and drops on surfaces, a
mesoscopic free energy based on is often used. We calculate such
equilibrium film height profiles and also directly calculate using DFT the
corresponding density profiles for liquid drops on surfaces. Comparing
quantities such as the contact angle and also the shape of the drops, we find
good agreement between the two methods. We also study in detail the effect on
of truncating the range of the dispersion forces, both those between the
fluid molecules and those between the fluid and wall. We find that truncating
can have a significant effect on and the associated wetting behaviour of
the fluid.Comment: 16 pages, 13 fig
Functional programming framework for GRworkbench
The software tool GRworkbench is an ongoing project in visual, numerical
General Relativity at The Australian National University. Recently, the
numerical differential geometric engine of GRworkbench has been rewritten using
functional programming techniques. By allowing functions to be directly
represented as program variables in C++ code, the functional framework enables
the mathematical formalism of Differential Geometry to be more closely
reflected in GRworkbench . The powerful technique of `automatic
differentiation' has replaced numerical differentiation of the metric
components, resulting in more accurate derivatives and an order-of-magnitude
performance increase for operations relying on differentiation
Two-dimensional colloidal fluids exhibiting pattern formation
Fluids with competing short range attraction and long range repulsive
interactions between the particles can exhibit a variety of microphase
separated structures. We develop a lattice-gas (generalised Ising) model and
analyse the phase diagram using Monte Carlo computer simulations and also with
density functional theory (DFT). The DFT predictions for the structures formed
are in good agreement with the results from the simulations, which occur in the
portion of the phase diagram where the theory predicts the uniform fluid to be
linearly unstable. However, the mean-field DFT does not correctly describe the
transitions between the different morphologies, which the simulations show to
be analogous to micelle formation. We determine how the heat capacity varies as
the model parameters are changed. There are peaks in the heat capacity at state
points where the morphology changes occur. We also map the lattice model onto a
continuum DFT that facilitates a simplification of the stability analysis of
the uniform fluid.Comment: 13 pages, 15 figure
The van Hove distribution function for Brownian hard spheres: dynamical test particle theory and computer simulations for bulk dynamics
We describe a test particle approach based on dynamical density functional
theory (DDFT) for studying the correlated time evolution of the particles that
constitute a fluid. Our theory provides a means of calculating the van Hove
distribution function by treating its self and distinct parts as the two
components of a binary fluid mixture, with the `self' component having only one
particle, the `distinct' component consisting of all the other particles, and
using DDFT to calculate the time evolution of the density profiles for the two
components. We apply this approach to a bulk fluid of Brownian hard spheres and
compare to results for the van Hove function and the intermediate scattering
function from Brownian dynamics computer simulations. We find good agreement at
low and intermediate densities using the very simple Ramakrishnan-Yussouff
[Phys. Rev. B 19, 2775 (1979)] approximation for the excess free energy
functional. Since the DDFT is based on the equilibrium Helmholtz free energy
functional, we can probe a free energy landscape that underlies the dynamics.
Within the mean-field approximation we find that as the particle density
increases, this landscape develops a minimum, while an exact treatment of a
model confined situation shows that for an ergodic fluid this landscape should
be monotonic. We discuss possible implications for slow, glassy and arrested
dynamics at high densities.Comment: Submitted to Journal of Chemical Physic
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