Dynamics of simulated water under pressure

We present molecular dynamics simulations of the SPC/E model of water to probe the dynamic properties at temperatures from 350 K down to 190 K and pressures from 2.5GPa (25kbar) down to -300MPa (-3kbar). We compare our results with those obtained experimentally, both of which show a diffusivity maximum as a function of pressure. We find that our simulation results are consistent with the predictions of the mode-coupling theory (MCT) for the dynamics of weakly supercooled liquids -- strongly supporting the hypothesis that the apparent divergences of {\it dynamic} properties observed experimentally may be independent of a possible thermodynamic singularity at low temperature. The dramatic change in water's dynamic and structural properties as a function of pressure allows us to confirm the predictions of MCT over a much broader range of the von Schweidler exponent values than has been studied for simple atomic liquids. We also show how structural changes are reflected in the wave-vector dependence of dynamic properties of the liquid along a path of nearly constant diffusivity. For temperatures below the crossover temperature of MCT (where the predictions of MCT are expected to fail), we find tentative evidence for a crossover of the temperature dependence of the diffusivity from power-law to Arrhenius behavior, with an activation energy typical of a strong liquid.Comment: 14 pages, 15 figure

Parallel-tempering cluster algorithm for computer simulations of critical phenomena

In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature range around the critical point. By combining the parallel tempering algorithm with cluster updates and an adaptive routine to find the temperature window of interest, we introduce a flexible and powerful method for systematic investigations of critical phenomena. As a result, we gain one to two orders of magnitude in the performance for 2D and 3D Ising models in comparison with the recently proposed Wang-Landau recursion for cluster algorithms based on the multibondic algorithm, which is already a great improvement over the standard multicanonical variant.Comment: pages, 5 figures, and 2 table

Towards a unification of HRT and SCOZA. Analysis of exactly solvable mean-spherical and generalized mean-spherical models

The hierarchical reference theory (HRT) and the self-consistent Ornstein-Zernike approximation (SCOZA) are two liquid state theories that both furnish a largely satisfactory description of the critical region as well as the phase coexistence and equation of state in general. Furthermore, there are a number of similarities that suggest the possibility of a unification of both theories. Earlier in this respect we have studied consistency between the internal energy and free energy routes. As a next step toward this goal we here consider consistency with the compressibility route too, but we restrict explicit evaluations to a model whose exact solution is known showing that a unification works in that case. The model in question is the mean spherical model (MSM) which we here extend to a generalized MSM (GMSM). For this case, we show that the correct solutions can be recovered from suitable boundary conditions through either of SCOZA or HRT alone as well as by the combined theory. Furthermore, the relation between the HRT-SCOZA equations and those of SCOZA and HRT becomes transparent.Comment: Minimal correction of some typos found during proof reading. Accepted for publication in Phys. Rev.

Supercooled Water: Dynamics, Structure and Thermodynamics

The anomalous properties of water in the supercooled state are numerous and well-known. Particularly striking are the strong changes in dynamic properties that appear to display divergences at temperatures close to -- but beyond -- the lowest temperatures attainable either experimentally or in computer simulations. Recent work on slow or glassy dynamics in water suggests analogies with simple liquids not previously appreciated, and at the same time highlights some aspects that remain peculiar to water. A comparison of the behavior of water with normal liquids, with respect to its dynamic, thermodynamic and structural changes in the supercooled regime is made by analyzing, via computer simulations, the properties of local potential energy minima sampled by water in supercooled temperatures and pressures.Comment: Submitted to DAE(India) Solid State Physics Symposium. 4 pages, Revtex (two column), 6 figures (eps

Entropy and Long range correlations in literary English

Recently long range correlations were detected in nucleotide sequences and in human writings by several authors. We undertake here a systematic investigation of two books, Moby Dick by H. Melville and Grimm's tales, with respect to the existence of long range correlations. The analysis is based on the calculation of entropy like quantities as the mutual information for pairs of letters and the entropy, the mean uncertainty, per letter. We further estimate the number of different subwords of a given length $n$. Filtering out the contributions due to the effects of the finite length of the texts, we find correlations ranging to a few hundred letters. Scaling laws for the mutual information (decay with a power law), for the entropy per letter (decay with the inverse square root of $n$) and for the word numbers (stretched exponential growth with $n$ and with a power law of the text length) were found.Comment: 8 page

Fragile to strong crossover coupled to liquid-liquid transition in hydrophobic solutions

Using discrete molecular dynamics simulations we study the relation between the thermodynamic and diffusive behaviors of a primitive model of aqueous solutions of hydrophobic solutes consisting of hard spheres in the Jagla particles solvent, close to the liquid-liquid critical point of the solvent. We find that the fragile-to-strong dynamic transition in the diffusive behavior is always coupled to the low-density/high-density liquid transition. Above the liquid-liquid critical pressure, the diffusivity crossover occurs at the Widom line, the line along which the thermodynamic response functions show maxima. Below the liquid-liquid critical pressure, the diffusivity crossover occurs when the limit of mechanical stability lines are crossed, as indicated by the hysteresis observed when going from high to low temperature and vice versa. These findings show that the strong connection between dynamics and thermodynamics found in bulk water persists in hydrophobic solutions for concentrations from low to moderate, indicating that experiments measuring the relaxation time in aqueous solutions represent a viable route for solving the open questions in the field of supercooled water.Comment: 6 pages, 4 figures. Accepted for publication on Physical Review