Delta-shocks and vacuum states in the vanishing pressure limit of solutions to the isentropic Euler equations for modified Chaplygin gas

The phenomena of concentration and cavitation and the formation of δ-shocks and vacuum states in solutions to the isentropic Euler equations for a modified Chaplygin gas are analyzed as the double parameter pressure vanishes. Firstly, the Riemann problem of the isentropic Euler equations for a modified Chaplygin gas is solved analytically. Secondly, it is rigorously shown that, as the pressure vanishes, any two-shock Riemann solution to the isentropic Euler equations for a modified Chaplygin gas tends to a δ-shock solution to the transport equations, and the intermediate density between the two shocks tends to a weighted δ-measure that forms the δ-shock; any two-rarefaction-wave Riemann solution to the isentropic Euler equations for a modified Chaplygin gas tends to a two-contact-discontinuity solution to the transport equations, the nonvacuum intermediate state between the two rarefaction waves tends to a vacuum state. Finally, some numerical results exhibiting the formation of δ-shocks and vacuum states are presented as the pressure decreases.     

Bi-velocity transport processes. Single-component liquid and gaseous continua

The present contribution supplements the previous findings regarding the need for two independent velocities rather than one when quantifying mass, momentum and energy transport phenomena in fluid continua. Explicitly, for the case of single-component fluids the present paper furnishes detailed expressions for the phenomenological coefficients appearing in the constitutive equations governing these bi-velocity transport processes. Whereas prior analyses furnished coefficient values only for the case of dilute monatomic gases using data from Burnett’s solution of the Boltzmann equation, the present study furnishes values applicable to all fluids, liquids as well as dense gases. Moreover, whereas prior coefficient calculations derived these values (for dilute monatomic gases) from Burnett’s solution of Boltzmann’s gas-kinetic equation, the latter a molecular theory, the present analysis derives the liquid- and gas-phase values from purely macroscopic data requiring knowledge only of the fluid’s coefficients of thermal expansion, isothermal compressibility, and thermometric diffusivity. In the dilute monatomic gas case common to both levels of analysis, the respective molecularly and macroscopically derived phenomenological coefficients are found to be in excellent agreement, confirming the credibility of both bi-velocity theory and the theory establishing the values of the phenomenological coefficients appearing in the constitutive relations derived therefrom. Whereas the preceding macroscopic calculations invoked Onsager’s reciprocal theorem relating coupled phenomenological coefficients, an alternative scheme is presented at the conclusion of the paper, one that reverses the usual order of things, at least in the present single-component fluid case. This alternate scheme enables Onsager’s nonequilibrium reciprocal relation, originally derived by him using molecular arguments, to be derived using purely macroscopic arguments originating from knowledge of Maxwell’s equilibrium reciprocal relations, the latter fundamental to equilibrium thermodynamics.     

Similitude généralisée et modélisation géométrique à complexité réduiteGeneral similitude solutions and low-complexity geometric models

We present low complexity models for the transport of passive scalars for environmental applications. The model uses partial observations assimilation. Similitude solutions are proposed in a non symmetric metric based on travel times. The approach does not require the solution of any PDE and is mesh free. Also, the solution can be computed in one point only without computing the whole solution. To cite this article: B. Mohammadi, J.-M. Brun, C. R. Mecanique 334 (2006).     

Estimation of Jc(B) dependence from self-field alternating current (AC) losses measured on Bi-2223/Ag tapes

Transport AC losses measured in self-field conditions on multifilamentary Bi-2223 tapes are often found to be lower than those calculated within the framework of the critical state model for a bulk wire with elliptical cross section, though generally higher than predicted for a strip. This effect is sometimes ascribed to the non-ideal geometry of the tapes, which does not exactly reproduce either shape. Here we propose an alternative explanation assuming that the critical current density of superconducting material depends on magnetic field. In practice, we analyzed the AC loss curve and deduced different I_c values for the individual data points, using the standard Norris equation for elliptical conductor. This gives the relation between ‘calculated' I_c and the self-field associated to AC transport current, which can be regarded as an alternative way to qualify the dependence of J_c on magnetic field. Important is that this procedure covers the range of fields below the self-field at I_c where the measurement in background DC field can not be used to determine J_c(B).     

Modeling of chemical tracer transport in the atmospheric environment and its impact on the global climate

Continental regions are experiencing rapid environmental changes due to expansion of industrial activities and land uses in different types of agricultural productions, burning of fossil fuels, etc., which lead to the emanation of huge amount of smog aerosol particulates and chemicals in the atmosphere. Information about these chemical tracers has been found from Indian Ocean Experiment (INDOEX), Intergovernmental Panel for Climate Change (IPCC) assessment reports as well as from other sources. The results of these computations may be interpreted by the chemical tracer transport model. In this paper, we have used a global atmospheric model in which the optical properties and the concentrations of the chemical tracers and aerosols have been incorporated. The aerosols and chemicals are transported in the atmospheric environment by the model cumulus convection and through the model semi-Lagrangian advection process . Thus, they are globally distributed along with the wind flow. The model has been used in studying the impact of the tropospheric chemical perturbations on the global environment.     

Observation of a sharp lambda peak in the third harmonic voltage response of high-T superconductor thin films

In this paper, we report on the sharp peak observed in the third harmonic voltage response generated by a bias sinusoidal current applied to several strips patterned in a YBa₂Cu₃O _{7 - δ} thin film and in two La_2-xSr_xCuO₄ thin films, when the temperature is close to the normal-superconductor transition. The lambda-shaped temperature dependence of the third harmonic signal on the current characteristics is studied. Several physical mechanisms of third harmonic generation are examined. Received 13 November 2002 / Received in final form 21 February 2003 Published online 7 May 2003