Absence of bubbling phenomena for non-convex anisotropic nearly umbilical and quasi-Einstein hypersurfaces

We prove that, for every closed (not necessarily convex) hypersurface Σ in ℝ n + 1 {\mathbb{R}^{n+1}} and every p > n {p>n} , the L p {L^{p}} -norm of the trace-free part of the anisotropic second fundamental form controls from above the W 2 , p {W^{2,p}} -closeness of Σ to the Wulff shape. In the isotropic setting, we provide a simpler proof. This result is sharp since in the subcritical regime p ≤ n {p\leq n} , the lack of convexity assumptions may lead in general to bubbling phenomena. Moreover, we obtain a stability theorem for quasi-Einstein (not necessarily convex) hypersurfaces and we improve the quantitative estimates in the convex setting.

Numerical Analysis of Flow Around a Cylinder in Critical and Subcritical Regime

Modeling the wind flow around cylindrical buildings is one of the problems within urban physics. Despite the simple geometry of the cylinder, it is an interesting physical phenomenon. Partial knowledge of flow field properties can be found in the literature, but in terms of their use for practical tasks, the data are still incomplete. The authors performed a numerical analysis of the flow around the smooth cylinder in the subcritical and critical regime for Reynolds numbers in the range of Re = 2.3 × 103 to 4 × 105. Turbulent flow was solved using LES model and the numerical solution was compared with available data from experiments or standard. Analysis of the mean stream velocity showed the elongation of the core of the wake with decreasing Re. The pressure coefficient evaluation showed a big difference between its distribution in the subcritical and critical regime. In the subcritical regime, a significant increase in the minimum value and a shift of the extreme close to the axis of the cylinder is proven. The results of the drag coefficient confirm a significant decrease in the transition from subcritical to critical regime, which is indicated in the cited experiments.

Aerodynamic noise characteristics of the flow past a circular cylinder

The present study experimentally investigates the aerodynamic noise from the flow past a fixed circular cylinder. The cylinders considered for the study have the diameters (d) in the range of 6 to 25 mm while its span length (L) is constant, which is 300 mm. The free stream velocity is varied up to 50 m/s, and the corresponding Reynolds number (based on d) varies up to 8.3 104, thus maintaining the flow past the cylinder in the subcritical regime. The discrete narrowband frequency tones depicting the aeolian tones are noted in the spectra. The results showed that the aeolian tone frequency decreases with an increase in the cylinder diameter and ceases to exist beyond the diameter of 15 mm. The corresponding Strouhal number of these tones is found to be in the range of 0.18 to 0.21, which is in congruence with the vortex shedding frequency in the subcritical regime. The maximum overall sound pressure level for cylinders having tonal noise is higher by around 30 dB compared to the background noise. Directivity studies show that the noise level is higher along the perpendicular direction of the jet flow. A sixth power Mach number scaling of the acoustic spectra shows a good collapse of the acoustic tonal amplitude.

Evidence and analysis of ion/electron foreshocks for a curved shock in Subcritical regime: 2D self-consistent PIC simulations

<p>Since early 2D PIC full self-consistent quasi-perpendicular simulations of the foreshock region [Savoini et Lembege, 2001] performed for a supercritical regime, different efforts have been invested later on to analyze the foreshock region. Previous 2D PIC simulations have succeeded in recovering both the local electron distribution [Savoini and Lembege, 2001] and the ion distribution [Savoini et al., 2013] in good agreement with the in-situ experimental data. These studies have retrieved both kinds of distributions and have analyzed in detail how these local distributions vary versus (i) the local angle Θ<sub>Bn</sub> to the curved shock (defined between the normal of the shock front and the upstream interplanetary magnetic field) and (ii) the distance from the shock front, in order to identify in detail the different acceleration mechanisms at work at the curved front and supporting these local ion and electron distributions within the foreshock region [Savoini and Lembege, 2001, 2015; Savoini et al, 2013]. This last point can only be accessible to a self-consistent approach (where ion and electron scales are fully included) as in 2D PIC simulations.  </p><p>Then, the present work is an extension of the previous analyses listed above for a curved (quasi-perpendicular) shock applied now in a <strong>subcritical regime</strong>. This work is performed thanks to a new 2D parallel PIC code (SMILEI) which is highly optimized and allows much higher statistics. The main characteristics of the curved front microstructures, its time dynamics, and preliminary results on local distribution functions obtained for both electrons and ions in this new Mach regime will be presented.      </p><p>Savoini, P. and B. Lembege, « Two-dimensional simulations of a curved shock: Self-consistent formation of the electron foreshock »,  J. Geophys. Res., Vol. 106, A7, 12975-12992, <strong>2001</strong></p><p>Savoini P., B. Lembege and J. Stienlet, « On the origin of the quasi-perpendicular ion foreshock: Full-particle simulations”, J. Geophys. Res., V. 118, 1–14, doi:10.1002/jgra.50158, <strong>2013</strong><strong> </strong></p><p>Savoini P. and B. Lembege, “Production of nongyrotropic and gyrotropic backstreaming ion distributions in the quasi-perpendicular ion foreshock region”, J. Geophys. Res., V. 120, 7154–7171, doi: 10.1002/2015JA021018, <strong>2015</strong>.</p>

Exergy performance of a new ORC configuration of a solar cogeneration system using a gas ejector

In the context of sustainable development and more particularly the conversion of heat into electricity, the present work proposes a new system of cogeneration operating at low energy value. It’s an organic Rankine cycle, associated with a gas ejector and operating with different organic fluids. It should be noted that the development of the ORC technology is partly a well-adapted response to problems of energy saving and ecosystem preservation. Accordingly, this paper presents a new configuration of a cogeneration system operating at low temperature and ensuring the simultaneous production of electricity and refrigeration. The proposed system is operating under transcritical and subcritical regime using solar energy as thermal source. On the other hand, an energy and exergy study has been developed by choosing the refrigerants R124, R236fa, R1234yf and R1234ze as working fluids according to their low environmental impact and thermodynamic properties. The results of the numerical simulation carried out as part of this study have also shown the importance of integrating the ejector into the proposed machine. Indeed, we investigated the effect of the thermodynamic parameters of the ejector on the coefficient of performance and the exergy efficiency of the cogeneration system.