Nucleation in a Fermi liquid at negative pressure

Experimental investigation of cavitation in liquid helium 3 has revealed a singular behaviour in the degenerate region at low temperature. As the temperature decreases below 80 mK, the cavitation pressure becomes significantly more negative. To investigate this, we have extrapolated the Fermi parameters in the negative pressure region. This allowed us to calculate the zero sound velocity, which we found to remain finite at the spinodal limit where the first sound velocity vanishes. We discuss the impact on the nucleation of the gas phase in terms of a quantum stiffness of the Fermi liquid. As a result we predict a cavitation pressure which is nearer to the spinodal line than previously thought.Comment: 6 pages, 2 figures. To be published in Journal of Low Temperature Physics, Proceedings of the International Symposium on Quantum Fluids and Solids QFS200

Effects of compressibility and wetting on the liquid-vapor transition in a confined fluid

When a fluid is constrained to a fixed, finite volume, the conditions for liquid-vapor equilibrium are different from the infinite volume or constant pressure cases. There is even a range of densities for which no bubble can form, and the liquid at a pressure below the bulk saturated vapor pressure remains indefinitely stable. As fluid density in mineral inclusions is often derived from the temperature of bubble disappearance, a correction for the finite volume effect is required. Previous works explained these phenomena, and proposed a numerical procedure to compute the correction for pure water in a container completely wet by the liquid phase. Here we revisit these works, and provide an analytic formulation valid for any fluid and including the case of partial wetting. We introduce the Berthelot-Laplace length $\lambda=2\gamma\kappa/3$, which combines the liquid isothermal compressibility $\kappa$ and its surface tension $\gamma$. The quantitative effects are fully captured by a single, non-dimensional parameter: the ratio of $\lambda$ to the container size.Comment: 13 pages, 13 figure

Non-linear effects and shock formation in the focusing of a spherical acoustic wave : Numerical simulations and experiments in liquid helium

The focusing of acoustic waves is used to study nucleation phenomena in liquids. At large amplitude, non-linear effects are important so that the magnitude of pressure or density oscillations is difficult to predict. We present a calculation of these oscillations in a spherical geometry. We show that the main source of non-linearities is the shape of the equation of state of the liquid, enhanced by the spherical geometry. We also show that the formation of shocks cannot be ignored beyond a certain oscillation amplitude. The shock length is estimated by an analytic calculation based on the characteristics method. In our numerical simulations, we have treated the shocks with a WENO scheme. We obtain a very good agreement with experimental measurements which were recently performed in liquid helium. The comparison between numerical and experimental results allows in particular to calibrate the vibration of the ceramics used to produce the wave, as a function of the applied voltage.Comment: 20 pages, 26 figures. Submitted to The European Physical Journal

Minimal microscopic model for liquid polyamorphism and water-like anomalies

Liquid polyamorphism is the intriguing possibility for a single component substance to exist in multiple liquid phases. We propose a minimal model for this phenomenon. Starting with a binary lattice model with critical azeotropy and liquid-liquid demixing, we allow interconversion of the two species, turning the system into a single-component fluid with two states differing in energy and entropy. Unveiling the phase diagram of the non-interconverting binary mixture gives unprecedented insight on the phase behaviors accessible to the interconverting fluid, such as a liquid-liquid transition with a critical point, or a singularity-free scenario, exhibiting thermodynamic anomalies without polyamorphism. The model provides a unified theoretical framework to describe supercooled water and a variety of polyamorphic liquids with water-like anomalies.Comment: 15 pages, 11 figure

Compressibility anomalies in stretched water and their interplay with density anomalies

Water keeps puzzling scientists because of its numerous properties which behave oppositely to usual liquids: for instance, water expands upon cooling, and liquid water is denser than ice. To explain this anomalous behaviour, several theories have been proposed, with different predictions for the properties of supercooled water (liquid at conditions where ice is more stable). However, discriminating between those theories with experiments has remained elusive because of spontaneous ice nucleation. Here we measure the sound velocity in liquid water stretched to negative pressure, and derive an experimental equation of state, which reveals compressibility anomalies. We show by rigorous thermodynamic relations how these anomalies are intricately linked with the density anomaly. Some features we observe are necessary conditions for the validity of two theories of water.Comment: 17 pages, 3 figures, 24 reference

Politique d'ouverture commerciale et instabilité de la croissance économique : Le cas des pays du Moyen Orient et d’Afrique du Nord

This paper studies the impact of trade openness policy on economic growth volatility in Middle Eastern and North African countries. The observed trade openness is divided into natural openness and trade openness policy. Natural openness is determined by a country’s structural and geographical characteristics while trade openness policy depends on policy makers’ decisions. First, a specific indicator is elaborated for the trade openness policy. Then, the impact of trade openness policy is econometrically tested on 13 countries of the Middle East and North Africa over 1960-1999. The results show that countries with a more open trade policy are less volatile.Middle East and North Africa., economic growth volatility, Trade openness policy