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61.
We study laser cooling of atomic gases by collisional redistribution, a technique applicable to ultradense atomic ensembles at a pressure of a few hundred bars. Frequent collisions of an optically active atom with a buffer gas shift atoms into resonance with a far red detuned laser beam, while spontaneous decay occurs close to the unperturbed resonance frequency. In such an excitation cycle, a kinetic energy of the order of the thermal energy k B T is extracted from the sample. Here we report of recent experiments investigating the cooling of a potassium?Cargon gas mixture, which compared to a rubidium?Cargon mixture investigated in earlier experiments has a smaller fine structure of the optically active alkali atoms. We observe a relative cooling of the potassium?Cargon gas mixture by 120?K. 相似文献
62.
Mohamed Saïdi 《Mathematische Zeitschrift》2014,277(1-2):361-372
We show the existence of group-theoretic sections of the “étale-by-geometrically abelian” quotient of the arithmetic fundamental group of hyperbolic curves over $p$ -adic local fields relative to a proper and flat model which are non-geometric, i.e., which do not arise from rational points. 相似文献
63.
Simon Štampar Saša Sokolič Gorazd Karer Alenka Žnidaršič Igor Škrjanc 《Mathematical and Computer Modelling》2011,53(5-6):637-645
This paper deals with the development of a batch-reactor model with a theoretical and a locally affine fuzzy model. The batch reactor is used in the pharmaceutical industry for the production of drugs, where a rapid and precise temperature control is necessary. The model has to be built to include all the main features necessary for the purposes of modelling. The development of the model for the reactor is designed for further control development and simulation purposes, without doing any further experiments on the real process. In our case we use the model for simulating the reactor’s jacket temperature and the reactor’s core temperature. The theoretical model describes all the nonlinearities of the process of heating and cooling the content of the batch reactor. The main contribution of the theoretical model is in the modelling of the heat transfer between the reactor’s jacket and the reactor’s core, mainly caused by the change in the overall heat transfer, which also covers the main nonlinearity. Because of the complexity of the theoretical model a locally affine fuzzy model is also developed. 相似文献
64.
65.
The unsteady incompressible Navier-Stokes equations have been accurately solved for the laminar flow past a circular cylinder in the Reynolds number range 50–200. A direct elliptic solver called the SEVP is used to rapidly advance the streamfunction in time, facilitating the overall convergence to the fully periodic or quasi-steady state. A new integral-series method is developed for the far-field streamfunction condition on a finite two-dimensional computational domain. The use of fourth-order Hermitian relations for the convection terms in the conservation-form vorticity transport equation has also contributed to the good comparison of the present results with the earlier experimental data. The vortex-shedding patterns visualized by the experimentalist are numerically reproduced here in the given Reynolds number range. Discussions that may be helpful in interpreting the behaviour of the shedding frequency are presented in the main text. 相似文献
66.
Let $M$ be a compact immersed submanifold of the Euclidean space, the hyperbolic space or the standard sphere. For any continuous
potential q on M, we give a sharp upper bound for the second eigenvalue of the operator −Δ+q in terms of the total mean curvature of M and the mean value of q. Moreover, we analyze the case where this bound is achieved. As a consequence of this result we obtain an alternative proof
for the Alikakos–Fusco conjecture concerning the stability of the interface in the Allen–Cahn reaction diffusion model.
Received: 18 June 1999 / Accepted: 6 July 1999 相似文献
67.
Mohammed Boutat Yves DAngelo Sa?d Hilout Véronique Lods 《Comptes Rendus Mathematique》2003,337(8):549-552
In this Note, we are interested in the evolution of a surface of a crystal structure, constituted by an elastic substrate and a thin film. If the crystal is constrained, some morphological instabilities may appear. To study these instabilities, we made use of the model developped in Phys. Rev. B 47 (1993) 9760–9777. There, the map f of the free surface of the film satisfies a parabolic partial differential equation, depending on the elastic displacement of the substrate. For simplicity, the substrate is assumed to be linearly elastic and the structure to be infinite in one direction. Then, under some formal asymptotic assumptions, a formal expansion of the displacement can be determined after some appropriate scalings, allowing to derive a simplified parabolic nonlinear equation as in Lods et al. (Asymptotic Anal. 33 (2003) 67–91). We give here some results about the finite-time blow-up and the existence and uniqueness of the solution in an appropriate space. To validate the theoretical results, we also performed some numerical simulations using a pseudo-spectral method and also compute the initial-profile dependent critical value of the parameter θ involved in the nonlinear equation. To cite this article: M. Boutat et al., C. R. Acad. Sci. Paris, Ser. I 337 (2003). 相似文献
68.
The convective instability of a horizontal liquid layer confined in an annular Hele–Shaw cell subject to a constant rotation and submitted to a centrifugal gradient of temperature is investigated. Using a linear stability analysis, we study the effects of both Coriolis forces and curvature aspect on the stationary convective threshold when the Prandtl number is of the order of unity or larger than unity. We show that the Coriolis forces have a stabilizing effect, and the wave number is independent of these forces. However, a multicellular regime in the radial direction is observed for small Ekman numbers. The results related to the influence of the curvature are also shown. To cite this article: S. Ramezani et al., C. R. Mecanique 330 (2002) 633–640. 相似文献
69.
70.
As alternative to the usual assumptions of Boussinesq, we propose, for heated gases, a new approximation called polytropic approximation. With this approximation the quantities of corresponding state are related by a polytropic law of exponent χ of which we neglect the variability in space-time derivations in the equations governing the flow considered. As application, we used this new proposition to solve numerically a heated gas flow in an annular cavity of rotor-stator type. We expose here the numerical method and some results of the polytropic approximation with comparison to results of Boussinesq approximations. To cite this article: S. Benjeddou et al., C. R. Mecanique 332 (2003). 相似文献