Two-dimensional Riemannian and Lorentzian geometries from second order ODEs

In this note we give an alternative geometrical derivation of the results recently presented by Garcia-Godinez, Newman and Silva-Ortigoza in [1] on the class of all two-dimensional riemannian and lorentzian metrics from 2nd order ODEs which are in duality with the two dimensional Hamilton-Jacobi equation. We show that, as it happens in the Null Surface Formulation of General Relativity, the Wuschmann-like condition can be obtained as a requirement of a vanishing torsion tensor. Furthermore, from these second order ODEs we obtain the associated Cartan connections.Comment: 9 pages, final version to appear in J. Math. Phy

Molecular dynamics study of the glass transition in confined water

A molecular dynamics simulation of SPC/E water confined in a Silica pore is presented. The pore has been constructed to reproduce the average properties of a pore of Vycor glass. Due to the confinement and to the presence of a strong hydrophilic surface, the dynamic behaviour of the liquid appears to be strongly dependent on the hydration level. The approach to the glass transition of confined water is investigated on lowering hydration and on supercooling in the framework of Mode Coupling Theories. At higher hydrations two quite distinct subsets of water molecules are detectable. Those belonging to the first layer close to the substrate suffer a severe slowing down, while the remaining ones display a scenario typical of supercooled liquids approaching the kinetic glass transition.Comment: Talk presented at "International Workshop on Dynamics in Confinement", Grenoble January 2000, to be appear in J. Phys. Franc

Double dynamical regime of confined water

The Van Hove self correlation function of water confined in a silica pore is calculated from Molecular Dynamics trajectories upon supercooling. At long time in the $\alpha$ relaxation region we found that the behaviour of the real space time dependent correlators can be decomposed in a very slow, almost frozen, dynamics due to the bound water close to the substrate and a faster dynamics of the free water which resides far from the confining surface. For free water we confirm the evidences of an approach to a crossover mode coupling transition, previously found in Q space. In the short time region we found that the two dynamical regimes are overimposed and cannot be distinguished. This shows that the interplay between the slower and the faster dynamics emerges in going from early times to the $\alpha$ relaxation region, where a layer analysis of the dynamical properties can be performed.Comment: 6 pages with 9 figures. RevTeX. Accepted for pulbication in J. Phys. Cond. Mat

Slow dynamics of a confined supercooled binary mixture II: Q space analysis

We report the analysis in the wavevector space of the density correlator of a Lennard Jones binary mixture confined in a disordered matrix of soft spheres upon supercooling. In spite of the strong confining medium the behavior of the mixture is consistent with the Mode Coupling Theory predictions for bulk supercooled liquids. The relaxation times extracted from the fit of the density correlator to the stretched exponential function follow a unique power law behavior as a function of wavevector and temperature. The von Schweidler scaling properties are valid for an extended wavevector range around the peak of the structure factor. The parameters extracted in the present work are compared with the bulk values obtained in literature.Comment: 8 pages with 8 figures. RevTeX. Accepted for publication in Phys. Rev.

Glass transition and layering effects in confined water: a computer simulation study

Single particle dynamics of water confined in a nanopore is studied through Computer Molecular Dynamics. The pore is modeled to represent the average properties of a pore of Vycor glass. Dynamics is analyzed at different hydration levels and upon supercooling. At all hydration levels and all temperatures investigated a layering effect is observed due to the strong hydrophilicity of the substrate. The time density correlators show, already at ambient temperature, strong deviations from the Debye and the stretched exponential behavior. Both on decreasing hydration level and upon supercooling we find features that can be related to the cage effect typical of a supercooled liquid undergoing a kinetic glass transition. Nonetheless the behavior predicted by Mode Coupling Theory can be observed only by carrying out a proper shell analysis of the density correlators. Water molecules within the first two layers from the substrate are in a glassy state already at ambient temperature (bound water). The remaining subset of molecules (free water) undergoes a kinetic glass transition; the relaxation of the density correlators agree with the main predictions of the theory. From our data we can predict the temperature of structural arrest of free water.Comment: 14 pages, 15 figures inserted in the text, to be published in J. Chem. Phys. (2000

A route to explain water anomalies from results on an aqueous solution of salt

In this paper we investigate the possibility to detect the hypothesized liquid-liquid critical point of water in supercooled aqueous solutions of salts. Molecular dynamics computer simulations are conducted on bulk TIP4P water and on an aqueous solution of sodium chloride in TIP4P water, with concentration c = 0.67 mol/kg. The liquid-liquid critical point is found both in the bulk and in the solution. Its position in the thermodynamic plane shifts to higher temperature and lower pressure for the solution. Comparison with available experimental data allowed us to produce the phase diagrams of both bulk water and the aqueous solution as measurable in experiments. Given the position of the liquid-liquid critical point in the solution as obtained from our simulations, the experimental determination of the hypothesized liquid-liquid critical point of water in aqueous solutions of salts appears possible.Comment: 5 pages, 6 figures. Accepted for publication on the Journal of Chemical Physics (2010)

Structural Properties of High and Low Density Water in a Supercooled Aqueous Solution of Salt

We consider and compare the structural properties of bulk TIP4P water and of a sodium chloride aqueous solution in TIP4P water with concentration c = 0.67 mol/kg, in the metastable supercooled region. In a previous paper [D. Corradini, M. Rovere and P. Gallo, J. Chem. Phys. 132, 134508 (2010)] we found in both systems the presence of a liquid-liquid critical point (LLCP). The LLCP is believed to be the end point of the coexistence line between a high density liquid (HDL) and a low density liquid (LDL) phase of water. In the present paper we study the different features of water-water structure in HDL and LDL both in bulk water and in the solution. We find that the ions are able to modify the bulk LDL structure, rendering water-water structure more similar to the bulk HDL case. By the study of the hydration structure in HDL and LDL, a possible mechanism for the modification of the bulk LDL structure in the solution is identified in the substitution of the oxygen by the chloride ion in oxygen coordination shells.Comment: 10 pages, 10 figures, 2 tables. Accepted for publication on J. Phys. Chem

Mode Coupling relaxation scenario in a confined glass former

Molecular dynamics simulations of a Lennard-Jones binary mixture confined in a disordered array of soft spheres are presented. The single particle dynamical behavior of the glass former is examined upon supercooling. Predictions of mode coupling theory are satisfied by the confined liquid. Estimates of the crossover temperature are obtained by power law fit to the diffusion coefficients and relaxation times of the late $\alpha$ region. The $b$ exponent of the von Schweidler law is also evaluated. Similarly to the bulk, different values of the exponent $\gamma$ are extracted from the power law fit to the diffusion coefficients and relaxation times.Comment: 5 pages, 4 figures, changes in the text, accepted for publication on Europhysics Letter

Computer simulation of the phase diagram for a fluid confined in a fractal and disordered porous material

We present a grand canonical Monte Carlo simulation study of the phase diagram of a Lennard-Jones fluid adsorbed in a fractal and highly porous aerogel. The gel environment is generated from an off-lattice diffusion limited cluster-cluster aggregation process. Simulations have been performed with the multicanonical ensemble sampling technique. The biased sampling function has been obtained by histogram reweighting calculations. Comparing the confined and the bulk system liquid-vapor coexistence curves we observe a decrease of both the critical temperature and density in qualitative agreement with experiments and other Monte Carlo studies on Lennard-Jones fluids confined in random matrices of spheres. At variance with these numerical studies we do not observe upon confinement a peak on the liquid side of the coexistence curve associated with a liquid-liquid phase coexistence. In our case only a shouldering of the coexistence curve appears upon confinement. This shoulder can be associated with high density fluctuations in the liquid phase. The coexisting vapor and liquid phases in our system show a high degree of spatial disorder and inhomogeneity.Comment: 8 pages, 8 figures, to be published in Phys. Rev.