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 $x$- and $y$-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