A variational principle for two-fluid models

A variational principle for two-fluid mixtures is proposed. The Lagrangian is constructed as the difference between the kinetic energy of the mixture and a thermodynamic potential conjugated to the internal energy with respect to the relative velocity of phases. The equations of motion and a set of Rankine-Hugoniot conditions are obtained. It is proved also that the convexity of the internal energy guarantees the hyperbolicity of the one-dimensional equations of motion linearized at rest.Comment: 7 page

Los cementerios de la Gran Guerra de Sir Edwin Lutyens

Already in 1917, the British architect sir Edwin Lutyens was asked to make designs for warcemeteries on the continent. In the end this resulted in almost 1000 cemeteries and monuments designed by Lutyens and other architects in Belgium, Northern France and other locations in Asia. Under leadership of the director of the British Museum, the architects have chosen for a common style, with the freedom to make individual variations for each cemetery related to the site. As a result of two opposing ideas there are two main elements on each cemetery, the War Stone designed by Lutyens and the Cross of Sacrifice by Blomfield. For the soldiers which were not found huge monuments were erected with their names on walls as their only surviving memory. The smaller cemeteries were designed by young architects who were in the army during the war. There are headstones instead of crosses for each grave due to the different religious background of the soldiers. For Lutyens the concept of a cemetery was based on the idea of green cathedral, a church in the open air, surrounded by trees as columns. For this idea he took advice from the well-known landscape architect Getrude Jekyll. Because of the maintenance by de Commonwealth War Graves Commission Still the cemeteries are still in perfect state and play an important role in the remembrance of the First World War.En 1917 se le encargó al arquitecto británico sir Edwin Lutyens que hiciera diseños para los cementerios de guerra en el continente. El resultado fue casi 1000 cementerios y monumentos diseñados por Lutyens y otros arquitectos en Bélgica, norte de Francia y varios lugares de Asia. Bajo el liderazgo del director del Museo Británico, los arquitectos optaron por un estilo común, con la libertad de hacer variaciones individuales para cada cementerio relacionado con su contexto. Como resultado de estas dos ideas opuestas, hay dos elementos principales en cada cementerio, la ‘Piedra de Guerra’ diseñada por Lutyens y la Cruz del Sacrificio de Blomfield. Para los soldados desaparecidos, se erigieron enormes monumentos con sus nom- bres en las paredes como único recuerdo. Los cementerios más pequeños fueron diseñados por jóvenes arquitectos que estuvieron en el ejército durante la guerra. Hay lápidas en lugar de cruces para cada tumba según las diferentes condiciones religiosas de los soldados. Para Lutyens, el concepto de cementerio se basaba en la idea de una catedral verde, una iglesia al aire libre, rodeada de árboles como columnas. Esta idea se inspiró en la conocida arquitecta paisajista Getrude Jekyll. Gracias al mantenimiento por parte de la Commonwealth War Graves Commission, los cementerios todavía están en perfecto estado y juegan un papel importante en el recuerdo de la Primera Guerra Mundial

Vortex density waves and high-frequency second sound in superfluid turbulence hydrodynamics

In this paper we show that a recent hydrodynamical model of superfluid turbulence describes vortex density waves and their effects on the speed of high-frequency second sound. In this frequency regime, the vortex dynamics is not purely diffusive, as for low frequencies, but exhibits ondulatory features, whose influence on the second sound is here explored.Comment: 8 page

Mixture of Fluids involving Entropy Gradients and Acceleration Waves in Interfacial Layers

Through an Hamiltonian action we write down the system of equations of motions for a mixture of thermocapillary fluids under the assumption that the internal energy is a function not only of the gradient of the densities but also of the gradient of the entropies of each component. A Lagrangian associated with the kinetic energy and the internal energy allows to obtain the equations of momentum for each component and for the barycentric motion of the mixture. We obtain also the balance of energy and we prove that the equations are compatible with the second law of thermodynamics. Though the system is of parabolic type, we prove that there exist two tangential acceleration waves that characterize the interfacial motion. The dependence of the internal energy of the entropy gradients is mandatory for the existence of this kind of waves. The differential system is non-linear but the waves propagate without distortion due to the fact that they are linearly degenerate (exceptional waves).Comment: 30 page

Turbulent superfluid profiles in a counterflow channel

We have developed a two-dimensional model of quantised vortices in helium II moving under the influence of applied normal fluid and superfluid in a counterflow channel. We predict superfluid and vortex-line density profiles which could be experimentally tested using recently developed visualization techniques.Comment: 3 double figures, 9 page

Electrodynamics in Superconductors Explained by Proca Equations

A fully consistent model to study electrodynamics for superconductors in the stationary and non-stationary regime has been developed based on Proca equations and a massive photon. In particular, this approach has been applied to study the electric field penetration depth in superconductors. The model shows a deviation from the charge contribution to an internal electric field compared to previous approaches.Comment: Accepted for publication in Phys. Lett.

Rotating Superconductors and the Frame-independent London Equation

A frame-independent, thermodynamically exact London equation is presented, which is especially valid for rotating superconductors. A direct result is the unexpectedly high accuracy ($\sim10^{-10}$) for the usual expression of the London moment.Comment: 4 pages, 0 figure

Water hammer with column separation: A historical review

Column separation refers to the breaking of liquid columns in fully filled pipelines. This may occur in a water-hammer event when the pressure in a pipeline drops to the vapor pressure at specific locations such as closed ends, high points or knees (changes in pipe slope). The liquid columns are separated by a vapor cavity that grows and diminishes according to the dynamics of the system. The collision of two liquid columns, or of one liquid column with a closed end, may cause a large and nearly instantaneous rise in pressure. This pressure rise travels through the entire pipeline and forms a severe load for hydraulic machinery, individual pipes and supporting structures. The situation is even worse: in one water-hammer event many repetitions of cavity formation and collapse may occur. This paper reviews water hammer with column separation from the discovery of the phenomenon in the late 19th century, the recognition of its danger in the 1930s, the development of numerical methods in the 1960s and 1970s, to the standard models used in commercial software packages in the late 20th century. A comprehensive survey of laboratory tests and field measurements is given. The review focuses on transient vaporous cavitation. Gaseous cavitation and steam condensation are beyond the scope of the paper. © 2005 Elsevier Ltd. All rights reserved.A. Bergant, A.R. Simpson, and A.S. Tijsselinghttp://www.elsevier.com/wps/find/journaldescription.cws_home/622877/description#descriptio