7,984 research outputs found
Self-diffusion in a monatomic glassforming liquid embedded in the hyperbolic plane
We study by Molecular Dynamics simulation the slowing down of particle motion
in a two-dimensional monatomic model: a Lennard-Jones liquid on the hyperbolic
plane. The negative curvature of the embedding space frustrates the long-range
extension of the local hexagonal order. As a result, the liquid avoids
crystallization and forms a glass. We show that, as temperature decreases, the
single particle motion displays the canonical features seen in real
glassforming liquids: the emergence of a "plateau" at intermediate times in the
mean square displacement and a decoupling between the local relaxation time and
the (hyperbolic) diffusion constant.Comment: Article for the "11th International Workshop on Complex Systems
The smooth cut-off Hierarchical Reference Theory of fluids
We provide a comprehensive presentation of the Hierarchical Reference Theory
(HRT) in the smooth cut-off formulation. A simple and self-consistent
derivation of the hierarchy of differential equations is supplemented by a
comparison with the known sharp cut-off HRT. Then, the theory is applied to a
hard core Yukawa fluid (HCYF): a closure, based on a mean spherical
approximation ansatz, is studied in detail and its intriguing relationship to
the self consistent Ornstein-Zernike approximation is discussed. The asymptotic
properties, close to the critical point are investigated and compared to the
renormalization group results both above and below the critical temperature.
The HRT free energy is always a convex function of the density, leading to flat
isotherms in the two-phase region with a finite compressibility at coexistence.
This makes HRT the sole liquid-state theory able to obtain directly fluid-fluid
phase equilibrium without resorting to the Maxwell construction. The way the
mean field free energy is modified due to the inclusion of density fluctuations
suggests how to identify the spinodal curve. Thermodynamic properties and
correlation functions of the HCYF are investigated for three values of the
inverse Yukawa range: z=1.8, z=4 and z=7 where Monte Carlo simulations are
available. The stability of the liquid-vapor critical point with respect to
freezing is also studied.Comment: 23 pages, 15 figures, 1 tabl
On the interplay between sedimentation and phase separation phenomena in two-dimensional colloidal fluids
Colloidal particles that are confined to an interface effectively form a
two-dimensional fluid. We examine the dynamics of such colloids when they are
subject to a constant external force, which drives them in a particular
direction over the surface. Such a situation occurs, for example, for colloidal
particles that have settled to the bottom of their container, when the
container is tilted at an angle, so that they `sediment' to the lower edge of
the surface. We focus in particular on the case when there are attractive
forces between the colloids which causes them to phase separate into regions of
high density and low density and we study the influence of this phase
separation on the sedimentation process. We model the colloids as Brownian
particles and use both Brownian dynamics computer simulations and dynamical
density functional theory (DDFT) to obtain the time evolution of the ensemble
average one-body density profiles of the colloids. We consider situations where
the external potential varies only in one direction so that the ensemble
average density profiles vary only in this direction. We solve the DDFT in
one-dimension, by assuming that the density profile only varies in one
direction. However, we also solve the DDFT in two-dimensions, allowing the
fluid density profile to vary in both the - and -directions. We find that
in certain situations the two-dimensional DDFT is clearly superior to its
one-dimensional counterpart when compared with the simulations and we discuss
this issue.Comment: 17 pages, 10 figures, submitted to Molecular Physic
Liquid-vapor coexistence in square-well fluids: an RHNC study
We investigate the ability of the reference hypernetted-chain integral
equation to describe the phase diagram of square-well fluids with four
different ranges of attraction. Comparison of our results with simulation data
shows that the theory is able to reproduce with fairly good accuracy a
significant part of the coexistence curve, provided an extrapolation procedure
is used to circumvent the well-known pathologies of the pseudo-spinodal line,
which are more severe at reduced width of the attractive well. The method
provides a useful approach for a quick assessment of the location of the
liquid-vapor coexistence curve in this kind of fluid and serves as a check for
the more complex problem of anisotropic "patchy" square-well molecules
Charged Magnetic Brane Solutions in AdS_5 and the fate of the third law of thermodynamics
We construct asymptotically AdS_5 solutions to 5-dimensional Einstein-Maxwell
theory with Chern-Simons term which are dual to 4-dimensional gauge theories,
including N=4 SYM theory, in the presence of a constant background magnetic
field B and a uniform electric charge density \rho. For the solutions
corresponding to supersymmetric gauge theories, we find numerically that a
small magnetic field causes a drastic decrease in the entropy at low
temperatures. The near-horizon AdS_2 \times R^3 geometry of the purely
electrically charged brane thus appears to be unstable under the addition of a
small magnetic field. Based on this observation, we propose a formulation of
the third law of thermodynamics (or Nernst theorem) that can be applied to
black holes in the AdS/CFT context.
We also find interesting behavior for smaller, non-supersymmetric, values of
the Chern-Simons coupling k. For k=1 we exhibit exact solutions corresponding
to warped AdS_3 black holes, and show that these can be connected to
asymptotically AdS_5 spacetime. For k\leq 1 the entropy appears to go to a
finite value at extremality, but the solutions still exhibit a mild singularity
at strictly zero temperature. In addition to our numerics, we carry out a
complete perturbative analysis valid to order B^2, and find that this
corroborates our numerical results insofar as they overlap.Comment: 45 pages v2: added note about subsequent results found in
arXiv:1003.130
Smectic and columnar ordering in length-polydisperse fluids of parallel hard cylinders
We apply a recently proposed density functional for mixtures of parallel hard
cylinders, based on Rosenfeld's fundamental measure theory, to study the effect
of length-polydispersity on the relative stability between the smectic and
columnar liquid crystal phases.To this purpose we derive from this functional
an expression for the direct correlation function and use it to perform a
bifurcation analysis. We compare the results with those obtained with a second
and a third virial approximation of this function. All three approximations
lead to the same conclusion: there is a terminal polydispersity beyond which
the smectic phase is less stable than the columnar phase. This result is in
agreement with previous Monte Carlo simulations conducted on a freely rotating
length-polydisperse hard spherocylinder fluid, although the theories always
overestimate the terminal polydispersity because the nematic-columnar phase
transition is first order and exhibits a wide coexistence gap. Both, the
fundamental-measure functional and the third virial approximation, predict a
metastable nematic-nematic demixing. Conversely, according to second virial
approximation this demixing might be stable at high values of the
polydispersity, something that is observed neither in simulations nor in
experiments. The results of the fundamental-measure functional are
quantitatively superior to those obtained from the other two approximations.
Thus this functional provides a promising route to map out the full phase
diagram of this system.Comment: 7 pages, 2 figure
Dynamics on the Way to Forming Glass: Bubbles in Space-time
We review a theoretical perspective of the dynamics of glass forming liquids
and the glass transition. It is a perspective we have developed with our
collaborators during this decade. It is based upon the structure of trajectory
space. This structure emerges from spatial correlations of dynamics that appear
in disordered systems as they approach non-ergodic or jammed states. It is
characterized in terms of dynamical heterogeneity, facilitation and excitation
lines. These features are associated with a newly discovered class of
non-equilibrium phase transitions. Equilibrium properties have little if
anything to do with it. The broken symmetries of these transitions are obscure
or absent in spatial structures, but they are vivid in space-time (i.e.,
trajectory space). In our view, the glass transition is an example of this
class of transitions. The basic ideas and principles we review were originally
developed through the analysis of idealized and abstract models. Nevertheless,
the central ideas are easily illustrated with reference to molecular dynamics
of more realistic atomistic models, and we use that illustrative approach here.Comment: 21 pages, 8 figures. Submitted to Annu. Rev. Phys. Che
New mean field theories for the liquid-vapor transition of charged hard spheres
The phase behavior of the primitive model of electrolytes is studied in the
framework of various mean field approximations obtained recently by means of
methods pertaining to statistical field theory (CAILLOL, J.-M., 2004,
\textit{J. Stat. Phys.}, \textbf{115}, 1461). The role of the regularization of
the Coulomb potential at short distances is discussed in details and the link
with more traditional approximations of the theory of liquids is discussed. The
values computed for the critical temperatures, chemical potentials, and
densities are compared with available Monte Carlo data and other theoretical
predictions.Comment: 17 pages, 4 figures, 3 table
Synchrotron imaging assessment of bone quality
Bone is a complex hierarchical structure and its principal function is to resist mechanical forces and fracture. Bone strength depends not only on the quantity of bone tissue but also on the shape and hierarchical structure. The hierarchical levels are interrelated, especially the micro-architecture, collagen and mineral components; hence analysis of their specific roles in bone strength and stiffness is difficult. Synchrotron imaging technologies including micro-CT and small/wide angle X-Ray scattering/diffraction are becoming increasingly popular for studying bone because the images can resolve deformations in the micro-architecture and collagen-mineral matrix under in situ mechanical loading. Synchrotron cannot be directly applied in-vivo due to the high radiation dose but will allow researchers to carry out systematic multifaceted studies of bone ex-vivo. Identifying characteristics of aging and disease will underpin future efforts to generate novel devices and interventional therapies for assessing and promoting healthy aging. With our own research work as examples, this paper introduces how synchrotron imaging technology can be used with in-situ testing in bone research
Empirical likelihood estimation of the spatial quantile regression
The spatial quantile regression model is a useful and flexible model for analysis of empirical problems with spatial dimension. This paper introduces an alternative estimator for this model. The properties of the proposed estimator are discussed in a comparative perspective with regard to the other available estimators. Simulation evidence on the small sample properties of the proposed estimator is provided. The proposed estimator is feasible and preferable when the model contains multiple spatial weighting matrices. Furthermore, a version of the proposed estimator based on the exponentially tilted empirical likelihood could be beneficial if model misspecification is suspect
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