Dynamical density functional theory: phase separation in a cavity and the influence of symmetry

Consider a fluid composed of two species of particles, where the interparticle pair potentials $u_{11} = u_{22} \neq u_{12}$. On confining an equal number of particles from each species in a cavity, one finds that the average one body density profiles of each species are constrained to be exactly the same due to the symmetry, when both external cavity potentials are the same. For a binary fluid of Brownian particles interacting via repulsive Gaussian pair potentials that exhibits phase separation, we study the dynamics of the fluid one body density profiles on breaking the symmetry of the external potentials, using the dynamical density functional theory of Marconi and Tarazona [{\it J. Chem. Phys.}, {\bf 110}, 8032 (1999)]. On breaking the symmetry we see that the fluid one body density profiles can then show the phase separation that is present.Comment: 7 pages, 4 figures. Accepted for the proceedings of the Liquid Matter conference 2005, to be publication in J. Phys.: Condens. Matte

Dynamical density functional theory for molecular and colloidal fluids: a microscopic approach to fluid mechanics

In recent years, a number of dynamical density functional theories (DDFTs) have been developed for describing the dynamics of the one-body density of both colloidal and atomic fluids. In the colloidal case, the particles are assumed to have stochastic equations of motion and theories exist for both the case when the particle motion is over-damped and also in the regime where inertial effects are relevant. In this paper we extend the theory and explore the connections between the microscopic DDFT and the equations of motion from continuum fluid mechanics. In particular, starting from the Kramers equation which governs the dynamics of the phase space probability distribution function for the system, we show that one may obtain an approximate DDFT that is a generalisation of the Euler equation. This DDFT is capable of describing the dynamics of the fluid density profile down to the scale of the individual particles. As with previous DDFTs, the dynamical equations require as input the Helmholtz free energy functional from equilibrium density functional theory (DFT). For an equilibrium system, the theory predicts the same fluid one-body density profile as one would obtain from DFT. Making further approximations, we show that the theory may be used to obtain the mode coupling theory that is widely used for describing the transition from a liquid to a glassy state.Comment: 11 pages, accepted for publication in J. Chem. Phy

The human value of scientific investigations of the origin and evolution of the solar system

The value of space exploration in relation to such earth bound problems as poverty, hunger, overpopulation, pollution, disease, and urban blight is discussed

Dynamical density functional theory and its application to spinodal decomposition

We present an alternative derivation of the dynamical density functional theory for the one body density profile of a classical fluid developed by Marconi and Tarazona [J. Chem. Phys., 110, 8032 (1999)]. Our derivation elucidates further some of the physical assumptions inherent in the theory and shows that it is not restricted to fluids composed of particles interacting solely via pair potentials; rather it applies to general, multi-body interactions. The starting point for our derivation is the Smoluchowski equation and the theory is therefore one for Brownian particles and as such is applicable to colloidal fluids. In the second part of this paper we use the dynamical density functional theory to derive a theory for spinodal decomposition that is applicable at both early and intermediate times. For early stages of spinodal decomposition our non-linear theory is equivalent to the (generalised) linear Cahn-Hilliard theory, but for later times it incorporates coupling between different Fourier components of the density fluctuations (modes) and therefore goes beyond Cahn-Hilliard theory. We describe the results of calculations for a model (Yukawa) fluid which show that the coupling leads to the growth of a second maximum in the density fluctuations, at a wavenumber larger than that of the main peak.Comment: 23 pages, 3 figure

Pair correlation functions and phase separation in a two component point Yukawa fluid

We investigate the structure of a binary mixture of particles interacting via purely repulsive (point) Yukawa pair potentials with a common inverse screening length $\lambda$. Using the hyper-netted chain closure to the Ornstein-Zernike equations, we find that for a system with `ideal' (Berthelot mixing rule) pair potential parameters for the interaction between unlike species, the asymptotic decay of the total correlation functions crosses over from monotonic to damped oscillatory on increasing the fluid total density at fixed composition. This gives rise to a Kirkwood line in the phase diagram. We also consider a `non-ideal' system, in which the Berthelot mixing rule is multiplied by a factor $(1+\delta)$. For any $\delta>0$ the system exhibits fluid-fluid phase separation and remarkably the ultimate decay of the correlation functions is now monotonic for all (mixture) state points. Only in the limit of vanishing concentration of either species does one find oscillatory decay extending to $r = \infty$. In the non-ideal case the simple random phase approximation provides a good description of the phase separation and the accompanying Lifshitz line.Comment: 11 pages, 6 figures. Accepted for publication in J. Chem. Phy

Redundant electronic circuit provides fail-safe control

Circuit using dual control amplifiers and dual position demand potentiometers powered from separate sources is used for reliable hydraulic valve controller that prevents closure of valve when control circuits fail, and maintains valve control to close tolerance for more common modes of controller failure

User community development for the space transportation system/Skylab

The New User Function plan for identifying beneficial uses of space is described. Critical issues such as funding, manpower, and protection of user proprietary rights are discussed along with common barriers which impede the development of a user community. Studies for developing methodologies of identifying new users and uses of the space transportation system are included

Selectivity in binary fluid mixtures: static and dynamical properties

Selectivity of particles in a region of space can be achieved by applying external potentials to influence the particles in that region. We investigate static and dynamical properties of size selectivity in binary fluid mixtures of two particles sizes. We find that by applying an external potential that is attractive to both kinds of particles, due to crowding effects, this can lead to one species of particles being expelled from that region, whilst the other species is attracted into the region where the potential is applied. This selectivity of one species of particle over the other in a localized region of space depends on the density and composition of the fluid mixture. Applying an external potential that repels both kinds of particles leads to selectivity of the opposite species of particles to the selectivity with attractive potentials. We use equilibrium and dynamical density functional theory to describe and understand the static and dynamical properties of this striking phenomenon. Selectivity by some ion-channels is believed to be due to this effect.Comment: 11 pages, 9 figure

Improved analytic longitudinal response analysis for axisymmetric launch vehicles. Volume I - Linear analytic model

Improved analytic longitudinal response analysis for axisymmetric launch vehicles - linear mode