35 research outputs found
Vortex distribution in a confining potential
We study a model of interacting vortices in a type II superconductor. In the
weak coupling limit, we constructed a mean-field theory which allows us to
accurately calculate the vortex density distribution inside a confining
potential. In the strong coupling limit, the correlations between the particles
become important and the mean-field theory fails. Contrary to recent
suggestions, this does not imply failure of the Boltzmann-Gibbs statistical
mechanics, as we clearly demonstrate by comparing the results of Molecular
Dynamics and Monte Carlo simulations
Lattice Model of an Ionic Liquid at an Electrified Interface
We study ionic liquids interacting with electrified interfaces. The ionic
fluid is modeled as a Coulomb lattice gas. We compare the ionic density
profiles calculated using a popular modified Poisson-Boltzmann equation with
the explicit Monte Carlo simulations. The modified Poisson-Boltzmann theory
fails to capture the structural features of the double layer and is also unable
to correctly predict the ionic density at the electrified interface. The
lattice Monte Carlo simulations qualitatively capture the coarse-grained
structure of the double layer in the continuum. We propose a convolution
relation that semiquantitatively relates the ionic density profiles of a
continuum ionic liquid and its lattice counterpart near an electrified
interface
Reply to 'Comment on "Vortex distribution in a confining potential"
We argue that contrary to recent suggestions, non-extensive statistical
mechanics has no relevance for inhomogeneous systems of particles interacting
by short-range potentials. We show that these systems are perfectly well
described by the usual Boltzmann-Gibbs statistical mechanics
Simulations of Coulomb systems with slab geometry using an efficient 3D Ewald summation method
We present a new approach to efficiently simulate electrolytes confined between infinite charged walls using a 3d Ewald summation method. The optimal performance is achieved by separating the electrostatic potential produced by the charged walls from the electrostatic potential of electrolyte. The electric field produced by the 3d periodic images of the walls is constant inside the simulation cell, with the field produced by the transverse images of the charged plates canceling out. The non-neutral confined electrolyte in an external potential can be simulated using 3d Ewald summation with a suitable renormalization of the electrostatic energy, to remove a divergence, and a correction that accounts for the conditional convergence of the resulting lattice sum. The new algorithm is at least an order of magnitude more rapid than the usual simulation methods for the slab geometry and can be further sped up by adopting a particle–particle particle–mesh approach
Yukawa particles in a confining potential
We study the density distribution of repulsive Yukawa particles confined by
an external potential. In the weak coupling limit, we show that the mean-field
theory is able to accurately account for the particle distribution. In the
strong coupling limit, the correlations between the particles become important
and the mean-field theory fails. For strongly correlated systems, we construct
a density functional theory which provides an excellent description of the
particle distribution, without any adjustable parameters.Comment: Submitte
Lattice model of ionic liquid confined by metal electrodes
We study, using Monte Carlo simulations, the density profiles and differential capacitance of ionic liquids confined by metal electrodes. To compute the electrostatic energy, we use the recently developed approach based on periodic Green’s functions. The method also allows us to easily calculate the induced charge on the electrodes permitting an efficient implementation of simulations in a constant electrostatic potential ensemble. To speed up the simulations further, we model the ionic liquid as a lattice Coulomb gas and precalculate the interaction potential between the ions. We show that the lattice model captures the transition between camel-shaped and bell-shaped capacitance curves—the latter characteristic of ionic liquids (strong coupling limit) and the former of electrolytes (weak coupling). We observe the appearance of a second peak in the differential capacitance at ≈0.5 V for 2:1 ionic liquids, as the packing fraction is increased. Finally, we show that ionic size asymmetry decreases substantially the capacitance maximum, when all other parameters are kept fixed
Simulations of Coulomb systems confined by polarizable surfaces using periodic Green functions
We present an efficient approach for simulating Coulomb systems confined by
planar polarizable surfaces. The method is based on the solution of the
Poisson equation using periodic Green functions. It is shown that the
electrostatic energy arising from the surface polarization can be decoupled
from the energy due to the direct Coulomb interaction between the ions. This
allows us to combine an efficient Ewald summation method, or any other fast
method for summing over the replicas, with the polarization contribution
calculated using Green function techniques. We apply the method to calculate
density profiles of ions confined between the charged dielectric and metal
surfaces
Simulations of electrolyte between charged metal surfaces
We present a new method for simulating ungrounded charged metal slabs inside an electrolyte solution. The ions are free to move between the interior and exterior regions of the slab–electrolyte system. This leads to polarization of both sides of each slab, with a distinct surface charge induced on each surface. Our simulation method is based on the exact solution of the Poisson equation using periodic Green functions. To efficiently perform the calculations, we decouple the electrostatic energy due to surface polarization from that of purely Coulomb interaction between the ions. This allows us to combine a fast 3D Ewald summation technique with an equally fast calculation of polarization. As a demonstration of the method, we calculate ionic density profiles inside an electrolyte solution and explore charge neutrality violation in between charged metal slabs