Higher-order Dirac solitons in binary waveguide arrays

We study optical analogues of higher-order Dirac solitons (HODSs) in binary waveguide arrays. Like higher-order solitons obtained from the well-known nonlinear Schrödinger equation governing the pulse propagation in an optical fiber, these HODSs have amplitude profiles which are numerically shown to be periodic over large propagation distances. At the same time, HODSs possess some unique features. Firstly, the period of a HODS depends on its order parameter. Secondly, the discrete nature in binary waveguide arrays imposes the upper limit on the order parameter of HODSs. Thirdly, the order parameter of HODSs can vary continuously in a certain range.     

Dynamics of a powered disk in clay soil

Experiments were conducted with a single powered disk in a laboratory soil bin containing Bangkok clay soil with an average moisture content of 18% (db) and 1100 kPa cone index. The disk was 510 cm in diameter and 560 mm in radius of concavity. During the tests the disk angle was varied from 20° to 35°, ground speed from 1 to 3 km/h and rotational speed from 60 to 140 rpm. The working depth was kept constant at 12 cm. The vertical, horizontal and lateral reactions of the soil were measured by force transducers. The forward and rotational speeds were recorded. It was observed that disk angle, rotational speed and ground speed had significant effects on soil reactive forces and power requirement. With a small disk angle, low ground speed, and high rotational speed, the soil longitudinal reactive force was a pushing force and became a resistive one at larger disk angles and ground speeds. The soil transverse reactive force increased with an increase of rotational and ground speed but decreased with the increase of disk angle, whereas the vertical relative force increased only with the increase of ground speed but decreased with the increase of rotational speed and disk angle. It was found that the powered disk required the least power at a disk angle of 30° and rotational speed between 80 and 100 rpm. Increase in ground speed from 1 to 3 km/h increased the total power requirement by 31.8%. Upon driving the disk forward, the draft reduced considerably compared to that of the free-rolling disk. By driving the disk in the reverse direction, the draft reduced slightly. At a disk angle of 30°, rotational speed of 100 rpm, and ground speed of 3 km/h, the total power requirement of the forward-driven disk was 65% higher than that of the free-rolling disk. The predicted engine power of the forward-driven disk, however, was only 21% higher than that of the free-rolling one owing to the more efficient power transmission through the PTO, as opposed to the drawbar. The effects of reverse driving and free rolling of the disk were also studied.     

Ondes adhérence–glissement–décollement sous contact unilatéral frottantStick–slip–separation waves in unilateral and frictional contact

A numerical study on the dynamic response of a mechanical system composed of two coaxial cylinders in relative rotation and unilateral contact with Coulomb friction is presented. This discussion complements the semi-analytical results on stick–slip waves given in Moirot, Nguyen, C. R. Acad. Sci. Paris Sér. IIb 328 (2000) 663–669, by some numerical simulations on the dynamic transition of the system from a given initial state to a surface wave. The case of stick–slip–separation waves is considered. To cite this article: A. Oueslati et al., C. R. Mecanique 331 (2003).     

Nouvelle approche numerique des solutions de la couche limite laminaire incompressible en regime non-stationnaire autour d'une paroi cylindrique elliptique mise en impulsion brutale

The equations of the unsteady incompressible laminar boundary layers about circular and elliptic cylinders started impulsively from rest are solved, after an original coordinate transformation, with the help of a semi-implicit difference scheme linearly stable without conditions. The knowledge of the phenomenon results only from that of the flow characteristics at the initial time; this makes mandatory the use of an analytical method of the Blasius type. When the ratio of the semi-axes of the elliptic cylinder becomes infinite, the present method gives the solution of the stagnation flow.When the flow presents a separation point in the steady state (circular cylinder), a criterion for stopping computation is proposed. It may be noted that to obtain the stagnation flow, we can continue the computations as far as possible and a steady solution is found with excellent accuracy.     

Unsteadiness of Flow Separation and End-Effects Regime in a Thrust-Optimized Contour Rocket Nozzle

Turbulent flow separation in over-expanded rocket nozzles is investigated experimentally in a sub-scale model nozzle fed with cold air and having a thrust-optimized contour. Depending upon the pressure ratio either a free shock separation (FSS) or a restricted shock separation (RSS) is observed with a significant hysteresis between these two flow regimes. It is shown that the RSS configuration may involve several separated regions. Analysis of wall pressure fluctuations give quantitative information on the fluctuating pressure field directly connected with the occurrence of significant side loads. Direct measurements of the evolution of the side loads with respect to the pressure ratio show the occurrence of three distinct peaks which are explained by the wall pressure fluctuations measurements.     

The Mach reflection of shock waves in converging,cylindrical channels

Shock waves impinging on axisymmetric converging passages of moderate wall angle undergo cyclical Mach reflection processes which are generally not self-similar during progression through the contraction. This paper presents the results of shock tube experiments in air where shocks of moderate strength are incident on cones having a range of wall angles of 10° to 30°. Mach reflection is maintained as the dominant reflection process throughout this range but the number of cycles decreases as wall angle increases. A ray-shock approach, used to calculate the triple-point trajectories gives good agreement with the experimental locations of their intersections with the centreline and wall.     

Experimental and numerical investigation of thermal chaotic mixing in a T-shaped microchannel

In this paper, thermal chaotic mixing characteristics of two miscible fluids in a T-shaped microchannel are investigated experimentally and numerically. In the experiments, fluorescent dye Acid Yellow and Rhodamine B was employed to show the mass mixing behavior and temperature field, respectively. Power input and flow rate were studied to investigate the thermal mixing characteristics in the microchannel. The mixing efficiency increases with increasing power input, while decreases with increasing flow rate. A numerical simulation of conjugate forced convection-conduction heat and mass transfer was employed to investigate the thermal chaotic mixing processes in the T-shaped microchannel. The measured mixing efficiency versus applied voltage and flow rate were compared with numerical simulation results, which showed reasonably agreement.     

Calculus rules of the generalized contingent derivative and applications to set-valued optimization

Positivity - In the paper, we develop sum and chain rules of the generalized contingent derivative for set-valued mappings. Then, their applications to sensitivity analysis and optimality...     

Some characterizations of magnetic Sobolev spaces

ABSTRACT

The aim of this note is to survey recent results contained in Nguyen H-M, Squassina M. [On anisotropic Sobolev spaces. Commun Contemp Math, to appear. DOI:10.1142/S0219199718500177]; Nguyen H-M, Pinamonti A, Squassina M, et al. [New characterizations of magnetic Sobolev spaces. Adv Nonlinear Anal. 2018;7(2):227–245]; Pinamonti A, Squassina M, Vecchi E. [Magnetic BV functions and the Bourgain-Brezis-Mironescu formula. Adv Calc Var, to appear. DOI:10.1515/acv-2017-0019]; Pinamonti A, Squassina M, Vecchi E. [The Maz'ya-Shaposhnikova limit in the magnetic setting. J Math Anal Appl. 2017;449:1152–1159] and Squassina M, Volzone B. [Bourgain-Brezis-Mironescu formula for magnetic operators. C R Math Acad Sci Paris. 2016;354:825–831], where the authors extended to the magnetic setting several characterizations of Sobolev and BV functions.