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

Local-in-time well-posedness for Compressible MHD boundary layer

In this paper, we are concerned with the motion of electrically conducting fluid governed by the two-dimensional non-isentropic viscous compressible MHD system on the half plane, with no-slip condition for velocity field, perfect conducting condition for magnetic field and Dirichlet boundary condition for temperature on the boundary. When the viscosity, heat conductivity and magnetic diffusivity coefficients tend to zero in the same rate, there is a boundary layer that is described by a Prandtl-type system. By applying a coordinate transformation in terms of stream function as motivated by the recent work \cite{liu2016mhdboundarylayer} on the incompressible MHD system, under the non-degeneracy condition on the tangential magnetic field, we obtain the local-in-time well-posedness of the boundary layer system in weighted Sobolev spaces.Comment: 29p

Justification of Prandtl Ansatz for MHD boundary layer

As a continuation of \cite{LXY}, the paper aims to justify the high Reynolds numbers limit for the MHD system with Prandtl boundary layer expansion when no-slip boundary condition is imposed on velocity field and perfect conducting boundary condition on magnetic field. Under the assumption that the viscosity and resistivity coefficients are of the same order and the initial tangential magnetic field on the boundary is not degenerate, we justify the validity of the Prandtl boundary layer expansion and give a $L^\infty$ estimate on the error by multi-scale analysis.Comment: 34 page

Effects of biaxial strain on the electronic structures and band topologies of group-V elemental monolayers

Using first-principles calculations, we systematically investigate the electronic structures and band topologies of four kinds of group-V elemental (P, As, Sb and Bi) monolayers with buckled honeycomb structure. It is found that all these monolayers can change from semiconducting to semimetallic under compressive strain. If a tensile strain is however applied, the P, As and Sb monolayers undergo phase transition from topologically trivial to non-trivial regime, whereas the topological insulating nature of Bi monolayer remains unchanged. With tunability of the band gaps and band topologies, it can be expected that these elemental monolayers could be promising candidates for future optoelectronic and spintronic applications

A well-posedness theory for the Prandtl equations in three space variables

The well-posedness of the three space dimensional Prandtl equations is studied under some constraint on its flow structure. It reveals that the classical Burgers equation plays an important role in determining this type of flow with special structure, that avoids the appearance of the complicated secondary flow in the three-dimensional Prandtl boundary layers. And the sufficiency of the monotonicity condition on the tangential velocity field for the existence of solutions to the Prandtl boundary layer equations is illustrated in the three dimensional setting. Moreover, it is shown that this structured flow is linearly stable for any three-dimensional perturbation.Comment: 40 page

On the origin of the Extreme-Ultraviolet late phase of solar flares

Solar flares typically have an impulsive phase that followed by a gradual phase as best seen in soft X-ray emissions. A recent discovery based on the EUV Variability Experiment (EVE) observations onboard the Solar Dynamics Observatory (SDO) reveals that some flares exhibit a second large peak separated from the first main phase peak by tens of minutes to hours, which is coined as the flare's EUV late phase. In this paper, we address the origin of the EUV late phase by analyzing in detail two late phase flares, an M2.9 flare on 2010 October 16 and an M1.4 flare on 2011 February 18, using multi-passband imaging observations from the Atmospheric Imaing Assembly (AIA) onboard SDO. We find that: (1) the late phase emission originates from a different magnetic loop system, which is much larger and higher than the main phase loop system. (2) The two loop systems have different thermal evolution. While the late phase loop arcade reaches its peak brightness progressively at a later time spanning for more than one hour from high to low temperatures, the main phase loop arcade reaches its peak brightness at almost the same time (within several minutes) in all temperatures. (3) Nevertheless, the two loop systems seem to be connected magnetically, forming an asymmetric magnetic quadruple configuration. (4) Further, the footpoint brightenings in UV wavelengths show a systematic delay of about one minute from the main flare region to the remote footpoint of the late phase arcade system. We argue that the EUV late phase is the result of a long-lasting cooling process in the larger magnetic arcade system.Comment: 12 figure

Spinor Field Realizations of W2,6W_{2,6} String and W6W_{6} String

In this paper the spinor field BRST charges of the W2,6 string and W6 string are constructed, where the BRST charges are graded.Comment: 8 pages, no figure

Extremely Large EUV Late Phase of Solar Flares

The second peak in the Fe XVI 33.5 nm line irradiance observed during solar flares by Extreme ultraviolet Variability Experiment (EVE) is known as Extreme UltraViolet (EUV) late phase. Our previous paper (Liu et al. 2013) found that the main emissions in the late phase are originated from large-scale loop arcades that are closely connected to but different from the post flare loops (PFLs), and we also proposed that a long cooling process without additional heating could explain the late phase. In this paper, we define the extremely large late phase because it not only has a bigger peak in the warm 33.5 irradiance profile, but also releases more EUV radiative energy than the main phase. Through detailedly inspecting the EUV images from three point-of-view, it is found that, besides the later phase loop arcades, the more contribution of the extremely large late phase is from a hot structure that fails to erupt. This hot structure is identified as a flux rope, which is quickly energized by the flare reconnection and later on continuously produces the thermal energy during the gradual phase. Together with the late-phase loop arcades, the fail to erupt flux rope with the additional heating create the extremely large EUV late phase.Comment: 9 figure

Norm-Range Partition: A Universal Catalyst for LSH based Maximum Inner Product Search (MIPS)

Recently, locality sensitive hashing (LSH) was shown to be effective for MIPS and several algorithms including $L_2$-ALSH, Sign-ALSH and Simple-LSH have been proposed. In this paper, we introduce the norm-range partition technique, which partitions the original dataset into sub-datasets containing items with similar 2-norms and builds hash index independently for each sub-dataset. We prove that norm-range partition reduces the query processing complexity for all existing LSH based MIPS algorithms under mild conditions. The key to performance improvement is that norm-range partition allows to use smaller normalization factor most sub-datasets. For efficient query processing, we also formulate a unified framework to rank the buckets from the hash indexes of different sub-datasets. Experiments on real datasets show that norm-range partition significantly reduces the number of probed for LSH based MIPS algorithms when achieving the same recall

Perfect charge compensation in extremely large magnetoresistance materials LaSb and LaBi revealed by the first-principles calculations

By the first-principles electronic structure calculations, we have systematically studied the electronic structures of recently discovered extremely large magnetoresistance (XMR) materials LaSb and LaBi. We find that both LaSb and LaBi are semimetals with the electron and hole carriers in perfect balance. The calculated carrier densities in the order of $10^{20}$ cm$^{-3}$ are in good agreement with the experimental values, implying long mean free time of carriers and thus high carrier mobilities. With a semiclassical two-band model, the perfect charge compensation and high carrier mobilities naturally explain (i) the XMR observed in LaSb and LaBi; (ii) the non-saturating quadratic dependence of XMR on external magnetic field; and (iii) the resistivity plateau in the turn-on temperature behavior at very low temperatures. The explanation of these features without resorting to the topological effect indicates that they should be the common characteristics of all perfectly electron-hole compensated semimetals.Comment: 7 pages, 7 figures, 1 tabl