On a Degenerate Parabolic Problem in Holder Spaces

In this paper, we study some degenerate parabolic equation with Cauchy-Dirichlet boundary conditions. This problem is considered in little Holder spaces. The optimal regularity of the solution v is obtained and is specified in terms of those of the second member when some conditions upon the Holder exponent with respect to the degeneracy are satisfied. The proofs mainly use the sum theory of linear operators with or without density of domains and the results of smoothness obtained in the study of some abstract linear differential equations of elliptic type.

Microstructure and mechanical properties of slowly cooled Cu47.5Zr47.5Al5

Cu47.5Zr47.5Al5 was prepared by arc melting and solidified in situ by suction casting into 2-5-mm-diameter rods under various cooling rates (200-2000 K/s). The microstructure was investigated along the length of the rods by electron microscopy, differential scanning calorimetry and mechanical properties were investigated under compression. The microstructure of differently prepared specimens consists of macroscopic spherical shape chemically inhomogeneous regions together with a low volume fraction of randomly distributed CuZr B2 phase embedded in a 2-7 nm size clustered "glassy-martensite" matrix. The as-cast specimens show high yield strength (1721 MPa), pronounced work-hardening behavior up to 2116 MPa and large fracture strain up to 12.1-15.1%. The fracture strain decreases with increasing casting diameter. The presence of chemical inhomogenities and nanoscale "glassy-martensite" features are beneficial for improving the inherent ductility of the metallic glass.

Case Study: Influence Of Morphological Changes On Flooding In Jingjiang River

The middle reach of the Yangtze River, customarily called the Jingjiang River, together with its diversion channels and Dongting Lake, form a large complicated drainage system. In the last five decades, significant geomorphological changes have occurred in the drainage system, including the shrinkage of diversion channels, contraction of Dongting Lake, changes in the rating curve at the Luoshan station, and cutoffs of the lower Jingjiang River. These changes are believed to be the cause of the occurrence of abnormal floods in the Jingjiang River. Qualitative analyses suggest that the first three factors aggravate the flood situation in the lower Jingjiang River, while the last factor seems beneficial for flood prevention. To quantitatively evaluate these conclusions, a finite-volume numerical model was constructed. A series of numerical simulations were carried out to test the individual and combined effects of the aforementioned four factors, and these simulations showed that high flood stages in the Jingjiang River clearly are related to the geomorphological changes.

Numerical Investigation On The Flowfield Of "Swallowtail" Cavity For Supersonic Mixing Enhancement

A "swallowtail" cavity for the supersonic combustor was proposed to serve as an efficient flame holder for scramjets by enhancing the mass exchange between the cavity and the main flow. A numerical study on the "swallowtail" cavity was conducted by solving the three-dimensional Reynolds-averaged Navier-Stokes equations implemented with a k-epsilon turbulence model in a multi-block mesh. Turbulence model and numerical algorithms were validated first, and then test cases were calculated to investigate into the mechanism of cavity flows. Numerical results demonstrated that the certain mass in the supersonic main flow was sucked into the cavity and moved spirally toward the combustor walls. After that, the flow went out of the cavity at its lateral end, and finally was efficiently mixed with the main flow. The comparison between the "swallowtail" cavity and the conventional one showed that the mass exchanged between the cavity and the main flow was enhanced by the lateral flow that was induced due to the pressure gradient inside the cavity and was driven by the three-dimensional vortex ring generated from the "swallowtail" cavity structure.

Quantum path control in few-optical-cycle regime

We theoretically show that selection of a single quantum path in high-order harmonics generation can be realized in a few-optical-cycle regime with two-color schemes. We also demonstrate, in theory as well, the generation of spectrally smooth and ultrabroad extreme ultraviolet supercontinuum in argon gas which can produce single similar to 79 as pulses with currently available ultrafast laser sources. Our finding can be beneficial for generating isolated sub-100 as extreme ultraviolet pulses.