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

Recent developments of the Hierarchical Reference Theory of Fluids and its relation to the Renormalization Group

The Hierarchical Reference Theory (HRT) of fluids is a general framework for the description of phase transitions in microscopic models of classical and quantum statistical physics. The foundations of HRT are briefly reviewed in a self-consistent formulation which includes both the original sharp cut-off procedure and the smooth cut-off implementation, which has been recently investigated. The critical properties of HRT are summarized, together with the behavior of the theory at first order phase transitions. However, the emphasis of this presentation is on the close relationship between HRT and non perturbative renormalization group methods, as well as on recent generalizations of HRT to microscopic models of interest in soft matter and quantum many body physics.Comment: 17 pages, 5 figures. Review paper to appear in Molecular Physic

A model colloidal fluid with competing interactions: bulk and interfacial properties

Using a simple mean-field density functional theory theory (DFT), we investigate the structure and phase behaviour of a model colloidal fluid composed of particles interacting via a pair potential which has a hard core of diameter $\sigma$, is attractive Yukawa at intermediate separations and repulsive Yukawa at large separations. We analyse the form of the asymptotic decay of the bulk fluid correlation functions, comparing results from our DFT with those from the self consistent Ornstein-Zernike approximation (SCOZA). In both theories we find rich crossover behaviour, whereby the ultimate decay of correlation functions changes from monotonic to long-wavelength damped oscillatory decay on crossing certain lines in the phase diagram, or sometimes from oscillatory to oscillatory with a longer wavelength. For some choices of potential parameters we find, within the DFT, a $\lambda$-line at which the fluid becomes unstable with respect to periodic density fluctuations. SCOZA fails to yield solutions for state points near such a $\lambda$-line. The propensity to clustering of particles, which is reflected by the presence of a long wavelength $\gg \sigma$, slowly decaying oscillatory pair correlation function, and a structure factor that exhibits a very sharp maximum at small but non zero wavenumbers, is enhanced in states near the $\lambda$-line. We present density profiles for the planar liquid-gas interface and for fluids adsorbed at a planar hard wall. The presence of a nearby $\lambda$-transition gives rise to pronounced long-wavelength oscillations in the one-body densities at both types of interface.Comment: 14 pages, 11 figure

Model for Spreading of Liquid Monolayers

Manipulating fluids at the nanoscale within networks of channels or chemical lanes is a crucial challenge in developing small scale devices to be used in microreactors or chemical sensors. In this context, ultra-thin (i.e., monolayer) films, experimentally observed in spreading of nano-droplets or upon extraction from reservoirs in capillary rise geometries, represent an extreme limit which is of physical and technological relevance since the dynamics is governed solely by capillary forces. In this work we use kinetic Monte Carlo (KMC) simulations to analyze in detail a simple, but realistic model proposed by Burlatsky \textit{et al.} \cite{Burlatsky_prl96,Oshanin_jml} for the two-dimensional spreading on homogeneous substrates of a fluid monolayer which is extracted from a reservoir. Our simulations confirm the previously predicted time-dependence of the spreading, $X(t \to \infty) = A \sqrt t$, with $X(t)$ as the average position of the advancing edge at time $t$, and they reveal a non-trivial dependence of the prefactor $A$ on the strength $U_0$ of inter-particle attraction and on the fluid density $C_0$ at the reservoir as well as an $U_0$-dependent spatial structure of the density profile of the monolayer. The asymptotic density profile at long time and large spatial scale is carefully analyzed within the continuum limit. We show that including the effect of correlations in an effective manner into the standard mean-field description leads to predictions both for the value of the threshold interaction above which phase segregation occurs and for the density profiles in excellent agreement with KMC simulations results.Comment: 21 pages, 9 figures, submitted to Phys. Rev.

Critical behavior in colloid-polymer mixtures: theory and simulation

We extensively investigated the critical behavior of mixtures of colloids and polymers via the two-component Asakura-Oosawa model and its reduction to a one-component colloidal fluid using accurate theoretical and simulation techniques. In particular the theoretical approach, hierarchical reference theory [Adv. Phys. 44, 211 (1995)], incorporates realistically the effects of long-range fluctuations on phase separation giving exponents which differ strongly from their mean-field values, and are in good agreement with those of the three-dimensional Ising model. Computer simulations combined with finite-size scaling analysis confirm the Ising universality and the accuracy of the theory, although some discrepancy in the location of the critical point between one-component and full-mixture description remains. To assess the limit of the pair-interaction description, we compare one-component and two-component results.Comment: 15 pages, 10 figures. Submitted to Phys. Rev.

Dimer and N\'eel order-parameter fluctuations in the spin-fluid phase of the s=1/2 spin chain with first and second neighbor couplings

The dynamical properties at T=0 of the one-dimensional (1D) s=1/2 nearest-neighbor (nn) XXZ model with an additional isotropic next-nearest-neighbor (nnn) coupling are investigated by means of the recursion method in combination with techniques of continued-fraction analysis. The focus is on the dynamic structure factors S_{zz}(q,\omega) and S_{DD}(q,\omega), which describe (for q=\pi) the fluctuations of the N\'eel and dimer order parameters, respectively. We calculate (via weak-coupling continued-fraction analysis) the dependence on the exchange constants of the infrared exponent, the renormalized bandwidth of spinon excitations, and the spectral-weight distribution in S_{zz}(\pi,\omega) and S_{DD}(\pi,\omega), all in the spin-fluid phase, which is realized for planar $nn$ anisotropy and sufficiently weak nnn coupling. For some parameter values we find a discrete branch of excitations above the spinon continuum. They contribute to S_{zz}(q,\omega) but not to S_{DD}(q,\omega).Comment: RevTex file (7 pages), 8 figures (uuencoded ps file) available from author

Wave-structure interaction for long wave models in the presence of a freely moving body on the bottom

In this paper we address a particular fluid-solid interaction problem in which the solid object is lying at the bottom of a layer of fluid and moves under the forces created by waves travelling on the surface of this layer. More precisely, we consider the water waves problem in a fluid of fixed depth with a flat bottom topography and with an object lying on the bottom, allowed to move horizontally under the pressure forces created by the waves. After establishing the physical setting of the problem, namely the dynamics of the fluid and the mechanics of the solid motion, as well as analyzing the nature of the coupling, we examine in detail two particular shallow water regimes: the case of the (nonlinear) Saint-Venant system, and the (weakly nonlinear) Boussinesq system. We prove an existence and uniqueness theorem for the coupled system in both cases. Using the particular structure of the coupling terms we are able to go beyond the standard scale for the existence time of solutions to the Boussinesq system with a moving bottom.Comment: 37 pages, 1 imag