An elliptic singularly perturbed problem with two parameters I: Solution decomposition

In this paper we consider a singularly perturbed elliptic problem with two small parameters posed on the unit square. Its solution may have exponential, parabolic and corner layers. We give a decomposition of the solution into regular and layer components and derive pointwise bounds on the components and their derivatives. The estimates are obtained by the analysis of appropriate problems on unbounded domains.     

Polynomiality of primal-dual affine scaling algorithms for nonlinear complementarity problems

This paper provides an analysis of the polynomiality of primal-dual interior point algorithms for nonlinear complementarity problems using a wide neighborhood. A condition for the smoothness of the mapping is used, which is related to Zhu’s scaled Lipschitz condition, but is also applicable to mappings that are not monotone. We show that a family of primal-dual affine scaling algorithms generates an approximate solution (given a precision ε) of the nonlinear complementarity problem in a finite number of iterations whose order is a polynomial ofn, ln(1/ε) and a condition number. If the mapping is linear then the results in this paper coincide with the ones in Jansen et al., SIAM Journal on Optimization 7 (1997) 126–140. Research supported in part by Grant-in-Aids for Encouragement of Young Scientists (06750066) from the Ministry of Education, Science and Culture, Japan. Research supported by Dutch Organization for Scientific Research (NWO), grant 611-304-028     

Periodic magnetic modulation of a two-dimensional electron gas: Transport properties

Electrical transport of the two-dimensional electron gas (2DEG) is considered in the presence of a perpendicular magnetic field(B) which is modulated weakly and periodically along one direction by −B₀sin(Kx). The magnetoresistivity exhibits novel oscillations which: 1) are 90° shifted with respect to similar oscillations discovered for a 1D electrical periodic potential, and 2) their amplitude is an order of magnitude larger than for a corresponding electrical potential modulation with strength equal to .     

Toroidal momentum pinch velocity due to the coriolis drift effect on small scale instabilities in a toroidal plasma

In this Letter, the influence of the "Coriolis drift" on small scale instabilities in toroidal plasmas is shown to generate a toroidal momentum pinch velocity. Such a pinch results because the Coriolis drift generates a coupling between the density and temperature perturbations on the one hand and the perturbed parallel flow velocity on the other. A simple fluid model is used to highlight the physics mechanism and gyro-kinetic calculations are performed to accurately assess the magnitude of the pinch. The derived pinch velocity leads to a radial gradient of the toroidal velocity profile even in the absence of a torque on the plasma and is predicted to generate a peaking of the toroidal velocity profile similar to the peaking of the density profile. Finally, the pinch also affects the interpretation of current experiments.     

New Andreev-type states in superconducting nanowires

Superconducting nanowires can exhibit a spatially inhomogeneous pair condensate that leads to the formation of new Andreev-type states. Such states are mainly located beyond the regions where the order parameter is enhanced, and no normal-superconducting contact or external magnetic field is needed for their formation. Our numerical self-consistent solutions of the Bogoliubov-de Gennes equations for cylindrical nanowires, in the clean limit, demonstrate that these new Andreev-type states decrease the ratio of the energy gap to the critical temperature as compared to its bulk value. The low-lying excitations in a clean superconducting nanowire are these new Andreev-type states induced by quantum confinement of the electrons in the transverse direction.     

Electronic properties of 2H-stacking bilayer MoS2 measured by terahertz time-domain spectroscopy

Bilayer (BL) molybdenum disulfide (MoS₂) is one of the most important electronic structures not only in valleytronics but also in realizing twistronic systems on the basis of the topological mosaics in moiré superlattices. In this work, BL MoS₂ on sapphire substrate with 2H-stacking structure is fabricated. We apply the terahertz (THz) time-domain spectroscopy (TDS) for examining the basic optoelectronic properties of this kind of BL MoS₂. The optical conductivity of BL MoS₂ is obtained in temperature regime from 80 K to 280 K. Through fitting the experimental data with the theoretical formula, the key sample parameters of BL MoS₂ can be determined, such as the electron density, the electronic relaxation time and the electronic localization factor. The temperature dependence of these parameters is examined and analyzed. We find that, similar to monolayer (ML) MoS₂, BL MoS₂ with 2H-stacking can respond strongly to THz radiation field and show semiconductor-like optoelectronic features. The theoretical calculations using density functional theory (DFT) can help us to further understand why the THz optoelectronic properties of BL MoS₂ differ from those observed for ML MoS₂. The results obtained from this study indicate that the THz TDS can be applied suitably to study the optoelectronic properties of BL MoS₂ based twistronic systems for novel applications as optical and optoelectronic materials and devices.