23 research outputs found
A proof of Jarzynski's non-equilibrium work theorem for dynamical systems that conserve the canonical distribution
We present a derivation of the Jarzynski identity and the Crooks fluctuation
theorem for systems governed by deterministic dynamics that conserves the
canonical distribution such as Hamiltonian dynamics, Nose-Hoover dynamics,
Nose-Hoover chains and Gaussian isokinetic dynamics. The proof is based on a
relation between the heat absorbed by the system during the non-equilibrium
process and the Jacobian of the phase flow generated by the dynamics.Comment: 12 page
Liquid-vapor transition of systems with mean field universality class
We have considered a system where the interaction, v(r) = v_IS(r) + xi^2
v_MF(r), is given as a linear combination of two potentials, each of which
being characterized with a well-defined critical behavior: for v_IS(r) we have
chosen the potential of the restricted primitive model which is known to belong
to the Ising 3D (IS) universality class, while for v_MF(r) we have considered a
long-range interaction in the Kac-limit, displaying mean field (MF) behavior.
We study the performance of two theoretical approaches and of computer
simulations in the critical region for this particular system and give a
detailed comparison between theories and simulation of the critical region and
the location of the critical point. Both, theory and simulation give evidence
that the system belongs to the MF universality class for any positive value of
xi and that it shows only non-classical behavior for xi=0. While in this
limiting case theoretical approaches are known to fail, we find good agreement
for the critical properties between the theoretical approaches and the
simulations for xi^2 larger than 0.05.Comment: 9 pages, 11 figures, 3 table
A numerical study of a binary Yukawa model in regimes characteristic of globular proteins in solutions
The main goal of this paper is to assess the limits of validity, in the
regime of low concentration and strong Coulomb coupling (high molecular
charges), for a simple perturbative approximation to the radial distribution
functions (RDF), based upon a low-density expansion of the potential of mean
force and proposed to describe protein-protein interactions in a recent
Small-Angle-Scattering (SAS) experimental study. A highly simplified Yukawa
(screened Coulomb) model of monomers and dimers of a charged globular protein
(-lactoglobulin) in solution is considered. We test the accuracy of the
RDF approximation, as a necessary complementary part of the previous
experimental investigation, by comparison with the fluid structure predicted by
approximate integral equations and exact Monte Carlo (MC) simulations. In the
MC calculations, an Ewald construction for Yukawa potentials has been used to
take into account the long-range part of the interactions in the weakly
screened cases. Our results confirm that the perturbative first-order
approximation is valid for this system even at strong Coulomb coupling,
provided that the screening is not too weak (i.e., for Debye length smaller
than monomer radius). A comparison of the MC results with integral equation
calculations shows that both the hypernetted-chain (HNC) and the Percus-Yevick
(PY) closures have a satisfactory behavior under these regimes, with the HNC
being superior throughout. The relevance of our findings for interpreting SAS
results is also discussed.Comment: Physical Review E, in press (2005
Transient State Work Fluctuation Theorem for a Driven Classical System
We derive the nonequilibrium transient state work fluctuation theorem and
also the Jarzynski equality for a classical harmonic oscillator linearly
coupled to a harmonic heat bath, which is dragged by an external agent.
Coupling with the bath makes the dynamics not only dissipative but also
non-Markovian in general. Since we do not assume anything about the spectral
nature of the harmonic bath the derivation is not only restricted to the
Markovian bath rather it is more general, for a non-Markovian bath
Theoretical description of phase coexistence in model C60
We have investigated the phase diagram of the Girifalco model of C60
fullerene in the framework provided by the MHNC and the SCOZA liquid state
theories, and by a Perturbation Theory (PT), for the free energy of the solid
phase. We present an extended assessment of such theories as set against a
recent Monte Carlo study of the same model [D. Costa et al, J. Chem. Phys.
118:304 (2003)]. We have compared the theoretical predictions with the
corresponding simulation results for several thermodynamic properties. Then we
have determined the phase diagram of the model, by using either the SCOZA, or
the MHNC, or the PT predictions for one of the coexisting phases, and the
simulation data for the other phase, in order to separately ascertain the
accuracy of each theory. It turns out that the overall appearance of the phase
portrait is reproduced fairly well by all theories, with remarkable accuracy as
for the melting line and the solid-vapor equilibrium. The MHNC and SCOZA
results for the liquid-vapor coexistence, as well as for the corresponding
critical points, are quite accurate. All results are discussed in terms of the
basic assumptions underlying each theory. We have selected the MHNC for the
fluid and the first-order PT for the solid phase, as the most accurate tools to
investigate the phase behavior of the model in terms of purely theoretical
approaches. The overall results appear as a robust benchmark for further
theoretical investigations on higher order C(n>60) fullerenes, as well as on
other fullerene-related materials, whose description can be based on a
modelization similar to that adopted in this work.Comment: RevTeX4, 15 pages, 7 figures; submitted to Phys. Rev.
Continuous demixing at liquid-vapor coexistence in a symmetrical binary fluid mixture
We report a Monte Carlo finite-size scaling study of the demixing transition
of a symmetrical Lennard-Jones binary fluid mixture. For equal concentration of
species, and for a choice of the unlike-to-like interaction ratio delta=0.7,
this transition is found to be continuous at liquid-vapor coexistence. The
associated critical end point exhibits Ising-like universality. These findings
confirm those of earlier smaller scale simulation studies of the same model,
but contradict the findings of recent integral equation and hierarchical
reference theory investigations.Comment: 7 pages, 6 figure
Effect of Polydispersity and Anisotropy in Colloidal and Protein Solutions: an Integral Equation Approach
Application of integral equation theory to complex fluids is reviewed, with
particular emphasis to the effects of polydispersity and anisotropy on their
structural and thermodynamic properties. Both analytical and numerical
solutions of integral equations are discussed within the context of a set of
minimal potential models that have been widely used in the literature. While
other popular theoretical tools, such as numerical simulations and density
functional theory, are superior for quantitative and accurate predictions, we
argue that integral equation theory still provides, as in simple fluids, an
invaluable technique that is able to capture the main essential features of a
complex system, at a much lower computational cost. In addition, it can provide
a detailed description of the angular dependence in arbitrary frame, unlike
numerical simulations where this information is frequently hampered by
insufficient statistics. Applications to colloidal mixtures, globular proteins
and patchy colloids are discussed, within a unified framework.Comment: 17 pages, 7 figures, to appear in Interdiscip. Sci. Comput. Life Sci.
(2011), special issue dedicated to Prof. Lesser Blu
Accurate determination of the phase diagram of model fullerenes
It is by now well established that the self-consistent
Ornstein-Zernike approximation (SCOZA) is able to provide accurate
data for the location of the liquid-vapour coexistence curve and
for the critical point of simple fluids. However, up to now
applications of the SCOZA were restricted only to a rather small
variety of interatomic potentials. In this contribution we
present an extension of the SCOZA which offers access to a
considerably larger class of systems. As an example, we present
results for model fullerenes \chem{C} (characterised
by the sphericalized Girifalco potentials) and thus contribute to
the still open question on the existence of the liquid phase and
on the size of the liquid pocket in the phase diagram of
fullerenes