Shift of Dirac points and strain induced pseudo-magnetic field in graphene

We propose that the strain induced effective pseudo-magnetic field in graphene can also be explained by a curl movement of the Dirac points, if the Dirac points can be regarded as a slowly varying function of position. We also prove that the Dirac points must be confined within two triangles, each one has 1/8 the area of the Brillouin zone.Comment: 4 pages, 5 figure

Potential-driven eddy current in rippled graphene nanoribbons

It is well known that an eddy current will be induced in a conductor subject to a varying magnetic field. Here we propose another mechanism of generating nano-scale eddy current in rippled graphene nanoribbons(GNRs), which is only driven by an electric potential. In particular, it is found that under appropriate gate voltages, a local deformation may induce some unexpected global eddy currents, which form vortices in both rippled and entire flat areas of the GNR. We will explain that these vortices in flat areas is a manifestation of the nonlocality of quantum interference.Comment: 6 pages, 5 figue

A Sharp Decay Estimate for Positive Nonlinear Waves

We consider a strictly hyperbolic, genuinely nonlinear system of conservation laws in one space dimension. A sharp decay estimate is proved for the positive waves in an entropy weak solution. The result is stated in terms of a partial ordering among positive measures, using symmetric rearrangements and a comparison with a solution of Burgers' equation with impulsive sources.Comment: 20 pages, 4 figure

Lifespan of Solution to MHD Boundary Layer Equations with Analytic Perturbation of General Shear Flow

In this paper, we consider the lifespan of solution to the MHD boundary layer system as an analytic perturbation of general shear flow. By using the cancellation mechanism in the system observed in \cite{LXY1}, the lifespan of solution is shown to have a lower bound in the order of $\varepsilon^{-2+}$ if the strength of the perturbation is of the order of $\varepsilon$. Since there is no restriction on the strength of the shear flow and the lifespan estimate is larger than the one obtained for the classical Prandtl system in this setting, it reveals the stabilizing effect of the magnetic field on the electrically conducting fluid near the boundary.Comment: 25 page

Villani conjecture on smoothing effect of the homogeneous Boltzmann equation with measure initial datum

We justify the Villani conjecture on the smoothing effect for measure value solutions to the space homogeneous Boltzmann equation of Maxwellian type cross sections. This is the first rigorous proof of the smoothing effect for any measure value initial data except the single Dirac mass, which gives the optimal description on the regularity of solutions for positive time, caused by the singularity in the cross section. The main new ingredient in the proof is the introduction of a time degenerate coercivity estimate by using the microlocal analysis.Comment: 19 pages, 6 figure

Global-in-time Stability of 2D MHD boundary Layer in the Prandtl-Hartmann Regime

In this paper, we prove global existence of solutions with analytic regularity to the 2D MHD boundary layer equations in the mixed Prandtl and Hartmann regime derived by formal multi-scale expansion in \cite{GP}. The analysis shows that the combined effect of the magnetic diffusivity and transveral magnetic field on the boundary leads to a linear damping on the tangential velocity field near the boundary. And this damping effect yields the global in time analytic norm estimate in the tangential space variable on the perturbation of the classical steady Hartmann profile.Comment: 14 page

Ill-posedness of the Prandtl equations in Sobolev spaces around a shear flow with general decay

Motivated by the paper by D. Gerard-Varet and E. Dormy [JAMS, 2010] about the linear ill-posedness for the Prandtl equations around a shear flow with exponential decay in normal variable, and the recent study of well-posedness on the Prandtl equations in Sobolev spaces, this paper aims to extend the result in \cite{GV-D} to the case when the shear flow has general decay. The key observation is to construct an approximate solution that captures the initial layer to the linearized problem motivated by the precise formulation of solutions to the inviscid Prandtl equations

Well-posedness in Gevrey function space for the three-dimensional Prandtl equations

In the paper, we study the three-dimensional Prandtl equations without any monotonicity condition on the velocity field. We prove that when one tangential component of the velocity field has a single curve of non-degenerate critical points with respect to the normal variable, the system is locally well-posed in the Gevrey function space with Gevrey index in $]1, 2].$ The proof is based on some new observation of cancellation mechanism in the three space dimensional system in addition to those in the two-dimensional setting obtained in [1,7,19,22].Comment: Enlarged version without any monotonicity assumptio

Federated Machine Learning: Concept and Applications

Today's AI still faces two major challenges. One is that in most industries, data exists in the form of isolated islands. The other is the strengthening of data privacy and security. We propose a possible solution to these challenges: secure federated learning. Beyond the federated learning framework first proposed by Google in 2016, we introduce a comprehensive secure federated learning framework, which includes horizontal federated learning, vertical federated learning and federated transfer learning. We provide definitions, architectures and applications for the federated learning framework, and provide a comprehensive survey of existing works on this subject. In addition, we propose building data networks among organizations based on federated mechanisms as an effective solution to allow knowledge to be shared without compromising user privacy

Tunable subwavelength strong absorption by graphene wrapped dielectric particles

The optical absorption properties of graphene wrapped dielectric particles have been investigated by using Mie scattering theory and exact multi-scattering method. It is shown that subwavelength strong absorption in infrared spectra can take place in such systems due to the excitation of plasmon resonance in graphene. The absorption characteristics and efficiency are tunable by varying Fermi level and damping constant of graphene, or by changing size and dielectric constant of small particles. For a cluster of these particles, the absorption characteristics are also affected by the separation distance between them. These extreme light resonances and absorptions in graphene wrapped nanostructures have great potential for opto-electronic devices