412 research outputs found
An improved Monte Carlo method for direct calculation of the density of states
We present an efficient Monte Carlo algorithm for determining the density of
states which is based on the statistics of transition probabilities between
states. By measuring the infinite temperature transition probabilities--that
is, the probabilities associated with move proposal only--we are able to
extract excellent estimates of the density of states. When this estimator is
used in conjunction with a Wang-Landau sampling scheme [F. Wang and D. P.
Landau, Phys. Rev. Lett. 86, 2050 (2001)], we quickly achieve uniform sampling
of macrostates (e.g., energies) and systematically refine the calculated
density of states. This approach requires only potential energy evaluations,
continues to improve the statistical quality of its results as the simulation
time is extended, and is applicable to both lattice and continuum systems. We
test the algorithm on the Lennard-Jones liquid and demonstrate good statistical
convergence properties.Comment: 7 pages, 4 figures. to appear in Journal of Chemical Physic
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Exact calculations of phase and membrane equilibria for complex fluids by Monte Carlo simulation. Progress report
Objective is to develop molecular simulation techniques for phase equilibria in complex systems. The Gibbs ensemble Monte Carlo method was extended to obtain phase diagrams for highly asymmetric and ionic fluids. The modified Widom test particle technique was developed for chemical potentials of long polymeric molecules, and preliminary calculations of phase behavior of simple model homopolymers were performed
On the Wang-Landau Method for Off-Lattice Simulations in the "Uniform" Ensemble
We present a rigorous derivation for off-lattice implementations of the
so-called "random-walk" algorithm recently introduced by Wang and Landau [PRL
86, 2050 (2001)]. Originally developed for discrete systems, the algorithm
samples configurations according to their inverse density of states using
Monte-Carlo moves; the estimate for the density of states is refined at each
simulation step and is ultimately used to calculate thermodynamic properties.
We present an implementation for atomic systems based on a rigorous separation
of kinetic and configurational contributions to the density of states. By
constructing a "uniform" ensemble for configurational degrees of freedom--in
which all potential energies, volumes, and numbers of particles are equally
probable--we establish a framework for the correct implementation of simulation
acceptance criteria and calculation of thermodynamic averages in the continuum
case. To demonstrate the generality of our approach, we perform sample
calculations for the Lennard-Jones fluid using two implementation variants and
in both cases find good agreement with established literature values for the
vapor-liquid coexistence locus.Comment: 21 pages, 4 figure
Crowding of Polymer Coils and Demixing in Nanoparticle-Polymer Mixtures
The Asakura-Oosawa-Vrij (AOV) model of colloid-polymer mixtures idealizes
nonadsorbing polymers as effective spheres that are fixed in size and
impenetrable to hard particles. Real polymer coils, however, are intrinsically
polydisperse in size (radius of gyration) and may be penetrated by smaller
particles. Crowding by nanoparticles can affect the size distribution of
polymer coils, thereby modifying effective depletion interactions and
thermodynamic stability. To analyse the influence of crowding on polymer
conformations and demixing phase behaviour, we adapt the AOV model to mixtures
of nanoparticles and ideal, penetrable polymer coils that can vary in size. We
perform Gibbs ensemble Monte Carlo simulations, including trial
nanoparticle-polymer overlaps and variations in radius of gyration. Results are
compared with predictions of free-volume theory. Simulation and theory
consistently predict that ideal polymers are compressed by nanoparticles and
that compressibility and penetrability stabilise nanoparticle-polymer mixtures.Comment: 18 pages, 4 figure
Phase diagrams in the lattice RPM model: from order-disorder to gas-liquid phase transition
The phase behavior of the lattice restricted primitive model (RPM) for ionic
systems with additional short-range nearest neighbor (nn) repulsive
interactions has been studied by grand canonical Monte Carlo simulations. We
obtain a rich phase behavior as the nn strength is varied. In particular, the
phase diagram is very similar to the continuum RPM model for high nn strength.
Specifically, we have found both gas-liquid phase separation, with associated
Ising critical point, and first-order liquid-solid transition. We discuss how
the line of continuous order-disorder transitions present for the low nn
strength changes into the continuum-space behavior as one increases the nn
strength and compare our findings with recent theoretical results by Ciach and
Stell [Phys. Rev. Lett. {\bf 91}, 060601 (2003)].Comment: 7 pages, 10 figure
Universality class of criticality in the restricted primitive model electrolyte
The 1:1 equisized hard-sphere electrolyte or restricted primitive model has
been simulated via grand-canonical fine-discretization Monte Carlo. Newly
devised unbiased finite-size extrapolation methods using temperature-density,
(T, rho), loci of inflections, Q = ^2/ maxima, canonical and C_V
criticality, yield estimates of (T_c, rho_c) to +- (0.04, 3)%. Extrapolated
exponents and Q-ratio are (gamma, nu, Q_c) = [1.24(3), 0.63(3); 0.624(2)] which
support Ising (n = 1) behavior with (1.23_9, 0.630_3; 0.623_6), but exclude
classical, XY (n = 2), SAW (n = 0), and n = 1 criticality with potentials
phi(r)>Phi/r^{4.9} when r \to \infty
XY Spin Fluid in an External Magnetic Field
A method of integral equations is developed to study inhomogeneous fluids
with planar spins in an external field. As a result, the calculations for these
systems appear to be no more difficult than those for ordinary homogeneous
liquids. The approach proposed is applied to the ferromagnetic XY spin fluid in
a magnetic field using a soft mean spherical closure and the Born-Green-Yvon
equation. This provides an accurate reproduction of the complicated phase
diagram behavior obtained by cumbersome Gibbs ensemble simulation and multiple
histogram reweighting techniques.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let
Coexistence and Criticality in Size-Asymmetric Hard-Core Electrolytes
Liquid-vapor coexistence curves and critical parameters for hard-core 1:1
electrolyte models with diameter ratios lambda = sigma_{-}/\sigma_{+}=1 to 5.7
have been studied by fine-discretization Monte Carlo methods. Normalizing via
the length scale sigma_{+-}=(sigma_{+} + sigma_{-})/2 relevant for the low
densities in question, both Tc* (=kB Tc sigma_{+-}/q^2 and rhoc* (= rhoc sigma
_{+-}^{3}) decrease rapidly (from ~ 0.05 to 0.03 and 0.08 to 0.04,
respectively) as lambda increases. These trends, which unequivocally contradict
current theories, are closely mirrored by results for tightly tethered dipolar
dimers (with Tc* lower by ~ 0-11% and rhoc* greater by 37-12%).Comment: 4 pages, 5 figure
Saddles in the energy landscape: extensivity and thermodynamic formalism
We formally extend the energy landscape approach for the thermodynamics of
liquids to account for saddle points. By considering the extensive nature of
macroscopic potential energies, we derive the scaling behavior of saddles with
system size, as well as several approximations for the properties of low-order
saddles (i.e., those with only a few unstable directions). We then cast the
canonical partition function in a saddle-explicit form and develop, for the
first time, a rigorous energy landscape approach capable of reproducing trends
observed in simulations, in particular the temperature dependence of the energy
and fractional order of sampled saddles.Comment: 4 pages, 1 figur
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