The dip effect under integer quantized Hall conditions

In this work we investigate an unusual transport phenomenon observed in two-dimensional electron gas under integer quantum Hall effect conditions. Our calculations are based on the screening theory, using a semi-analytical model. The transport anomalies are dip and overshoot effects, where the Hall resistance decreases (or increases) unexpectedly at the quantized resistance plateaus intervals. We report on our numerical findings of the dip effect in the Hall resistance, considering GaAs/AlGaAs heterostructures in which we investigated the effect under different experimental conditions. We show that, similar to overshoot, the amplitude of the dip effect is strongly influenced by the edge reconstruction due to electrostatics. It is observed that the steep potential variation close to the physical boundaries of the sample results in narrower incompressible strips, hence, the experimental observation of the dip effect is limited by the properties of these current carrying strips. By performing standard Hall resistance measurements on gate defined narrow samples, we demonstrate that the predictions of the screening theory is in well agreement with our experimental findings.     

Optimal shape design for fluid flow using topological perturbation technique

This paper is concerned with an optimal shape design problem in fluid mechanics. The fluid flow is governed by the Stokes equations. The theoretical analysis and the numerical simulation are discussed in two and three-dimensional cases. The proposed approach is based on a sensitivity analysis of a design function with respect to the insertion of a small obstacle in the fluid flow domain. An asymptotic expansion is derived for a large class of cost functions using small topological perturbation technique. A fast and accurate numerical algorithm is proposed. The efficiency of the method is illustrated by some numerical examples.     

Crystal structure,ionic conductivity and dielectric relaxation studies in the (C5H10N)2BiBr5 compound

The synthesis and crystal structure of the bis (3-dimethylammonium-1-propyne) pentabromobismuthate(III) salt are given in the present paper. After an X-ray investigation, it has been shown that the title compound crystallizes at 298 K in a centrosymmetric monoclinic system, in the space group C₂/c with the following lattice parameters a=12.9034(3) Å, b=19.4505(6) Å, c=8.5188(2) Å, β=102.449(2). Not only were the impedance spectroscopy measurements of (C₅H₁₀N)₂BiBr₅ carried out from 209 Hz to 5 MHz over the temperature range of 318 K–373 K, but also its ac conductivity evaluated. Besides, the dielectric relaxation was examined using the modulus formalism. Actually, the near values of activation energies obtained from the impedance and modulus spectra confirms that the transport is of an ion hopping mechanism, dominated by the motion of the H⁺ ions in the structure of the investigated material.     

Long-Time Instability of the Couette Flow in Low Gevrey Spaces

We prove the instability of the Couette flow if the disturbances is less smooth than the Gevrey space of class 2. This shows that this is the critical regularity for this problem since it was proved in [5] that stability and inviscid damping hold for disturbances which are smoother than the Gevrey space of class 2. A big novelty is that this critical space is due to an instability mechanism which is completely nonlinear and is due to some energy cascade. © 2023 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.