30 research outputs found
Dynamical density functional theory for colloidal particles with arbitrary shape
Starting from the many-particle Smoluchowski equation, we derive dynamical
density functional theory for Brownian particles with an arbitrary shape. Both
passive and active (self-propelled) particles are considered. The resulting
theory constitutes a microscopic framework to explore the collective dynamical
behavior of biaxial particles in nonequilibrium. For spherical and uniaxial
particles, earlier derived dynamical density functional theories are recovered
as special cases. Our study is motivated by recent experimental progress in
preparing colloidal particles with many different biaxial shapes.Comment: 9 pages, 1 figur
Transport coefficients for inelastic Maxwell mixtures
The Boltzmann equation for inelastic Maxwell models is used to determine the
Navier-Stokes transport coefficients of a granular binary mixture in
dimensions. The Chapman-Enskog method is applied to solve the Boltzmann
equation for states near the (local) homogeneous cooling state. The mass, heat,
and momentum fluxes are obtained to first order in the spatial gradients of the
hydrodynamic fields, and the corresponding transport coefficients are
identified. There are seven relevant transport coefficients: the mutual
diffusion, the pressure diffusion, the thermal diffusion, the shear viscosity,
the Dufour coefficient, the pressure energy coefficient, and the thermal
conductivity. All these coefficients are {\em exactly} obtained in terms of the
coefficients of restitution and the ratios of mass, concentration, and particle
sizes. The results are compared with known transport coefficients of inelastic
hard spheres obtained analytically in the leading Sonine approximation and by
means of Monte Carlo simulations. The comparison shows a reasonably good
agreement between both interaction models for not too strong dissipation,
especially in the case of the transport coefficients associated with the mass
flux.Comment: 9 figures, to be published in J. Stat. Phy
Geometry dominated fluid adsorption on sculptured substrates
Experimental methods allow the shape and chemical composition of solid
surfaces to be controlled at a mesoscopic level. Exposing such structured
substrates to a gas close to coexistence with its liquid can produce quite
distinct adsorption characteristics compared to that occuring for planar
systems, which may well play an important role in developing technologies such
as super-repellent surfaces or micro-fluidics. Recent studies have concentrated
on adsorption of liquids at rough and heterogeneous substrates and the
characterisation of nanoscopic liquid films. However, the fundamental effect of
geometry has hardly been addressed. Here we show that varying the shape of the
substrate can exert a profound influence on the adsorption isotherms allowing
us to smoothly connect wetting and capillary condensation through a number of
novel and distinct examples of fluid interfacial phenomena. This opens the
possibility of tailoring the adsorption properties of solid substrates by
sculpturing their surface shape.Comment: 6 pages, 4 figure
Beyond forcing scenarios: predicting climate change through response operators in a coupled general circulation model
Global Climate Models are key tools for predicting the future response of the climate system to a variety of natural and anthropogenic forcings. Here we show how to use statistical mechanics to construct operators able to flexibly predict climate change for a variety of climatic variables of interest. We perform our study on a fully coupled model - MPI-ESM v.1.2 - and for the first time we prove the effectiveness of response theory in predicting future climate response to CO2 increase on a vast range of temporal scales, from inter-annual to centennial, and for very diverse climatic quantities. We investigate within a unified perspective the transient climate response and the equilibrium climate sensitivity and assess the role of fast and slow processes. The prediction of the ocean heat uptake highlights the very slow relaxation to a newly established steady state. The change in the Atlantic Meridional Overturning Circulation (AMOC) and of the Antarctic Circumpolar Current (ACC) is accurately predicted. The AMOC strength is initially reduced and then undergoes a slow and only partial recovery. The ACC strength initially increases as a result of changes in the wind stress, then undergoes a slowdown, followed by a recovery leading to a overshoot with respect to the initial value. Finally, we are able to predict accurately the temperature change in the Northern Atlantic
Dynamical density functional theory for orientable colloids including inertia and hydrodynamic interactions
Over the last few decades, classical density-functional theory (DFT) and its
dynamic extensions (DDFTs) have become powerful tools in the study of colloidal
fluids. Recently, previous DDFTs for spherically-symmetric particles have been
generalised to take into account both inertia and hydrodynamic interactions,
two effects which strongly influence non-equilibrium properties. The present
work further generalises this framework to systems of anisotropic particles.
Starting from the Liouville equation and utilising Zwanzig's
projection-operator techniques, we derive the kinetic equation for the Brownian
particle distribution function, and by averaging over all but one particle, a
DDFT equation is obtained. Whilst this equation has some similarities with
DDFTs for spherically-symmetric colloids, it involves a
translational-rotational coupling which affects the diffusivity of the
(asymmetric) particles. We further show that, in the overdamped (high friction)
limit, the DDFT is considerably simplified and is in agreement with a previous
DDFT for colloids with arbitrary shape particles.Comment: dynamical density functional theory ; colloidal fluids ;
arbitrary-shape particles ; orientable colloid
O(N) model for charge density waves
We generalize the Fukuyama, Lee, Rice model for pinned charge density waves to the case of an O(N) vector order parameter and exactly solve the large-N limit. A second order field induced phase transition is observed, from a pinned to a conducting phase, analogously to the scalar case. The pinned region displays an infinite number of metastable equilibrium states while, above threshold, the system has a periodic solution. The model subject to a time dependent external field shows interesting analogies with some features observed in real materials such as the field cooled and the pulse sign memory effects
Coarsening in diluted systems
We investigate domain growth after a quench to the unstable region of the phase diagram on a lattice lacking translational invariance due to the presence of voids. The dynamical process is analyzed using a Ginzburg-Landau model with Langevin dynamics: studied numerically by means of a cell dynamical simulation in d = 2 for conserved order parameter at T-F = 0. We find that for short times ordering proceeds as on compact substrates (L(t) similar to t(1/3)); later on, when L(t) becomes comparable to the typical distance separating voids, coarsening occurs only via activated processes and for T-F = 0 the system Freezes out of equilibrium
Active Fluids Within the Unified Coloured Noise Approximation
Active matter is made of active particles which are able to convert energy from the environment into directed persistent motion. They can be modelled by stochastic differential equations subject to persistent noise. Run and tumble and active Brownian particle (ABP) models have been first proposed and still are considered closer to experimental observations but do not allow for much analytical progress. The Gaussian coloured noise (GCN) model, introduced as a time coarse-grained version of the ABP can be tuned to have the same variance of the active force as the ABP, which leads to a simpler analytical treatment. Finally, the UCNA can be considered as a Markovian reduction of the GCN. We give a simple derivation of the governing equation and analyse some of its recent applications ranging from the study of the swim pressure, its relation to the mobility, to the state induced by a moving object