52,392 research outputs found
Crystallization and phase-separation in non-additive binary hard-sphere mixtures
We calculate for the first time the full phase-diagram of an asymmetric
non-additive hard-sphere mixture. The non-additivity strongly affects the
crystallization and the fluid-fluid phase-separation. The global topology of
the phase-diagram is controlled by an effective size-ratio y_{eff}, while the
fluid-solid coexistence scales with the depth of the effective potential well.Comment: 4 pages, 4 figures, to appear in Phys. Rev.
The structure of colloid-polymer mixtures
We investigate the structure of colloid-polymer mixtures by calculating the
structure factors for the Asakura-Oosawa model in the PY approximation. We
discuss the role of potential range, polymer concentration and polymer-polymer
interactions on the colloid-colloid structure. Our results compare reasonably
well with the recent experiments of Moussa\"{i}d et. al. for small wavenumber
, but we find that the Hansen-Verlet freezing criterion is violated when the
liquid phase becomes marginal.Comment: 7 pages, 4 figures, to appear in EuroPhys. Let
Relationship between Local Molecular Field Theory and Density Functional Theory for non-uniform liquids
The Local Molecular Field Theory (LMF) developed by Weeks and co-workers has
proved successful for treating the structure and thermodynamics of a variety of
non-uniform liquids. By reformulating LMF in terms of one-body direct
correlation functions we recast the theory in the framework of classical
Density Functional Theory (DFT). We show that the general LMF equation for the
effective reference potential phi_R follows directly from the standard
mean-field DFT treatment of attractive interatomic forces. Using an accurate
(Fundamental Measures) DFT for the non-uniform hard-sphere reference fluid we
determine phi_R for a hard-core Yukawa liquid adsorbed at a planar hard wall.
In the approach to bulk liquid-gas coexistence we find the effective potentials
exhibit rich structure that can include damped oscillations at large distances
from the wall as well as the repulsive hump near the wall required to generate
the low density 'gas' layer characteristic of complete drying. We argue that it
would be difficult to obtain the same level of detail from other (non DFT
based) implementations of LMF. LMF emphasizes the importance of making an
intelligent division of the interatomic pair potential of the full system into
a reference part and a remainder that can be treated in mean-field
approximation. We investigate different divisions for an exactly solvable one-
dimensional model where the pair potential has a hard-core plus a linear
attractive tail. Results for the structure factor and the equation of state of
the uniform fluid show that including a significant portion of the attraction
in the reference system can be much more accurate than treating the full
attractive tail in mean-field approximation. We discuss further aspects of the
relationship between LMF and DFT.Comment: 35 pages, 10 Fig
Asymptotic decay of pair correlations in a Yukawa fluid
We analyse the asymptotic decay of the total correlation
function, , for a fluid composed of particles interacting via a (point)
Yukawa pair potential. Such a potential provides a simple model for dusty
plasmas. The asymptotic decay is determined by the poles of the liquid
structure factor in the complex plane. We use the hypernetted-chain closure to
the Ornstein-Zernike equation to determine the line in the phase diagram,
well-removed from the freezing transition line, where crossover occurs in the
ultimate decay of , from monotonic to damped oscillatory. We show: i)
crossover takes place via the same mechanism (coalescence of imaginary poles)
as in the classical one-component plasma and in other models of Coulomb fluids
and ii) leading-order pole contributions provide an accurate description of
at intermediate distances as well as at long range.Comment: 5 pages, 3 figure
Time-oscillating Lyapunov modes and auto-correlation functions for quasi-one-dimensional systems
The time-dependent structure of the Lyapunov vectors corresponding to the
steps of Lyapunov spectra and their basis set representation are discussed for
a quasi-one-dimensional many-hard-disk systems. Time-oscillating behavior is
observed in two types of Lyapunov modes, one associated with the time
translational invariance and another with the spatial translational invariance,
and their phase relation is specified. It is shown that the longest period of
the Lyapunov modes is twice as long as the period of the longitudinal momentum
auto-correlation function. A simple explanation for this relation is proposed.
This result gives the first quantitative connection between the Lyapunov modes
and an experimentally accessible quantity.Comment: 4 pages, 3 figure
Coarse-graining polymers as soft colloids
We show how to coarse grain polymers in a good solvent as single particles,
interacting with density-independent or density-dependent interactions. These
interactions can be between the centres of mass, the mid-points or end-points
of the polymers. We also show how to extend these methods to polymers in poor
solvents and mixtures of polymers. Treating polymers as soft colloids can
greatly speed up the simulation of complex many-polymer systems, including
polymer-colloid mixtures.Comment: to appear in Physica A, special STATPHYS 2001 edition. Content of
invited talk by AA
Unitarity of the infinite-volume three-particle scattering amplitude arising from a finite-volume formalism
In a previous publication, two of us derived a relation between the
scattering amplitude of three identical bosons, , and a real
function referred to as the {divergence-free} K matrix and denoted . The result arose in the context of a relation between
finite-volume energies and , derived to all orders in
the perturbative expansion of a generic low-energy effective field theory. In
this work we set aside the role of the finite volume and focus on the
infinite-volume relation between and .
We show that, for any real choice of ,
satisfies the three-particle unitarity constraint to all orders. Given that
is also free of a class of kinematic divergences,
the function may provide a useful tool for parametrizing three-body scattering
data. Applications include the phenomenological analysis of experimental data
(where the connection to the finite volume is irrelevant) as well as
calculations in lattice quantum chromodynamics (where the volume plays a key
role).Comment: 19 pages, 4 figures, JLAB-THY-19-2945, CERN-TH-2019-07
Modal cut-off and the V-parameter in photonic crystal fibers
We address the long-standing unresolved problem concerning the V-parameter in
a photonic crystal fiber (PCF). Formulate the parameter appropriate for a
core-defect in a periodic structure we argue that the multi-mode cut-off occurs
at a wavelength lambda* which satisfies V_PCF(lambda*)=pi. Comparing to
numerics and recent cut-off calculations we confirm this result.Comment: 3 pages including 2 figures. Accepted for Optics Letter
Density functional theory for hard-sphere mixtures: the White-Bear version Mark II
In the spirit of the White-Bear version of fundamental measure theory we
derive a new density functional for hard-sphere mixtures which is based on a
recent mixture extension of the Carnahan-Starling equation of state. In
addition to the capability to predict inhomogeneous density distributions very
accurately, like the original White-Bear version, the new functional improves
upon consistency with an exact scaled-particle theory relation in the case of
the pure fluid. We examine consistency in detail within the context of
morphological thermodynamics. Interestingly, for the pure fluid the degree of
consistency of the new version is not only higher than for the original
White-Bear version but also higher than for Rosenfeld's original fundamental
measure theory.Comment: 16 pages, 3 figures; minor changes; J. Phys.: Condens. Matter,
accepte
- …