Change of evaporation rate of single monocomponent droplet with temperature using time-resolved phase rainbow refractometry

Droplet evaporation characterization, although of great significance, is still challenging. The recently developed phase rainbow refractometry (PRR) is proposed as an approach to measuring the droplet temperature, size as well as evaporation rate simultaneously, and is applied to a single flowing n-heptane droplet produced by a droplet-on-demand generator. The changes of droplet temperature and evaporation rate after a transient spark heating are reflected in the time-resolved PRR image. Results show that droplet evaporation rate increases with temperature, from ?1.28$\times {10}^{?8}$ m²/s at atmospheric 293 K to a range of (?1.5, ?8)$\times {10}^{?8}$ m²/s when heated to (294, 315) K, agreeing well with the Maxwell and Stefan–Fuchs model predictions. Uncertainty analysis suggests that the main source is the indeterminate gradient inside droplet, resulting in an underestimation of droplet temperature and evaporation rate. With the demonstration on simultaneous measurements of droplet refractive index as well as droplet transient and local evaporation rate in this work, PRR is a promising tool to investigate single droplet evaporation in real engine conditions.     

Automorphisms with only infinite orbits on non-algebraic elements

 This paper generalizes results of F. K?rner from [4] where she established the existence of maximal automorphisms (i.e. automorphisms moving all non-algebraic elements). An ω-maximal automorphism is an automorphism whose powers are maximal automorphisms. We prove that any structure has an elementary extension with an ω-maximal automorphism. We also show the existence of ω-maximal automorphisms in all countable arithmetically saturated structures. Further we describe the pairs of tuples (ˉa,ˉb) for which there is an ω-maximal automorphism mapping ˉa to ˉb. Received: 12 December 2001 / Published online: 10 October 2002 Supported by the ``Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture' Mathematics Subject Classification (2000): Primary: 03C50; Secondary: 03C57 Key words or phrases: Automorphism – Recursively saturated structure     

Almost global existence for Hamiltonian semilinear Klein‐Gordon equations with small Cauchy data on Zoll manifolds

This paper is devoted to the proof of almost global existence results for Klein‐Gordon equations on Zoll manifolds (e.g., spheres of arbitrary dimension) with Hamiltonian nonlinearities, when the Cauchy data are smooth and small. The proof relies on Birkhoff normal form methods and on the specific distribution of eigenvalues of the Laplacian perturbed by a potential on Zoll manifolds. © 2007 Wiley Periodicals, Inc.     

Numerical solution of the Monge–Ampère equation by a Newton's algorithm

We solve numerically the Monge–Ampère equation with periodic boundary condition using a Newton's algorithm. We prove convergence of the algorithm, and present some numerical examples, for which a good approximation is obtained in 10 iterations. To cite this article: G. Loeper, F. Rapetti, C. R. Acad. Sci. Paris, Ser. I 340 (2005).     

On the ordering in [(C2H5)4N]2CuCl4 crystal: an X-ray study and theoretical considerations

The crystal structure [(C₂H₅)₄N]₂CuCl₄ has been determined by X-ray diffraction at 243K. The room temperature phase (phase I) belongs to the space group P4₂/nm [1] whereas the low temperature phase (phase II) is orthorhombic and belongs to the space group Pnna. The phase transition at T_c=258K is of improper ferroelastic type and it is associated with the ordering of the CuCl₄ ^2? and a partial ordering of the [(C₂H₅)₄N]⁺ ions which are disordered in the high temperature tetragonal phase. At lower temperature, there occurs another instability which could correspond to a complete ordering in the crystal.