本文研究方程驻波的强不稳定性iu_t+△u+a|u|~(p-1)u+E_1(|u|~2)u=0,t≥0,x∈R~n,其中a0,1p(n+2)/(n+2)~+,n∈{2,3}.当1+4/n≤pn+2/(n-2)~+)时,文[Sharp threshold of global existence and instability of standing wave for a Davey-Stewartson system,Commun.Math.Phys.,2008,283:93-125]在驻波的频率满足一定假设条件下,证明了此方程驻波的强不稳定性.本文去掉这个假设,得到相同的结论. 相似文献
A free‐standing polymer brush film with tailored thicknesses based on a colorless polydopamine (PDA) thin layer is prepared and characterized. The surface‐initiated atom transfer radical polymerization (ATRP) of 2‐hydroxyethyl methacrylate (HEMA) is performed on a PDA layer with thickness of ca. 6 nm, which generated an optically transparent and colorless free‐standing PHEMA brush film (1.5 cm × 1.5 cm). Because the cross‐linked PDA layer is used as the base for the polymer brushes, the reported method does not require cross‐linking the polymer brushes. The free‐standing film thicknesses of ≈16–75 nm are controlled by simply changing the ATRP reaction time. The results show that the free‐standing PHEMA brush film transferred onto a plate exhibits a relatively smooth surface and is stable in any solvent.
An increasing trend toward integration of polymers in microelectronics and organic electronics has recently boosted research focusing in metal-polymer interfaces. These two materials differ vastly, with the former forming dense, crystalline, cohesive structures and the latter forming open structures bound together by weak van der Waals forces. As a result, there is dire need to assess their surface features (e.g., roughness) and correlate them with corresponding growth parameters, as metal-polymer interfaces are mainly determined by the preparation process. Here, we report a laboratory-based grazing-incidence small-angle x-ray scattering (GISAXS) study on distinct gold-polymer interfaces fabricated with different growth mechanisms, utilizing in-plane and oblique sputter geometries. GISAXS provided an improved analytic scheme for the buried surface in free-standing 2D gold-polymer nanosheets (with 19% porosity) revealing their fractal structure (Porod slope: ?1.71). Two quantitative approaches (Height-Height Correlation and Power Spectral Density functions) were used to describe rough surfaces characterized by Atomic Force Microscopy (AFM) in consort with GISAXS data; different correlation length dependencies on growth time were revealed for gold rough surfaces grown on bare and polymerized Si. The results are considered pertinent to interfacial nanoscience and engineering, enabling statistical data collection from large surface areas, in a fast and nondestructive manner. 相似文献
In this paper we study the existence and qualitative property of standing wave solutions for the nonlinear Schrödinger equation with being a critical frequency in the sense that We show that if the zero set of has isolated connected components such that the interior of is not empty and is smooth, has isolated zero points, , , and has critical points such that , then for small, there exists a standing wave solution which is trapped in a neighborhood of Moreover the amplitudes of the standing wave around , and are of a different order of . This type of multi-scale solution has never before been obtained.
Modulation of the intensity of light by high quality reflective micro-displays is predominantly carried out by liquid crystal over silicon (LCoS) spatial light modulator (SLM) technology for applications such as pico-projectors. Wider use of these devices, in applications such as computer-generated holography and optical correlation, is limited by their phase modulation ability and illumination polarisation state dependence. These devices rely on planar or twisted nematic liquid crystals to modulate the light, but due to their viscoelastic properties they are inherently slow. Research into the use of the polymer stabilised blue phase has already shown that it can offer high speed phase modulation. However, other chiral nematic orientations are yet to be compared in LCoS devices. In this article, we demonstrate that polymer-stabilised chiral nematic liquid crystal electro-optical effects can offer phase modulation in silicon backplane devices. The uniform standing helix and focal conic textures are shown to be independent of the input light polarisation state and the uniform lying helix is shown to be polarisation dependent. These optical responses are then compared with that of the blue phase to identify a suitable orientation for further development in LCoS technology in order to find a high-speed, full phase modulating material. 相似文献
The spinel lithium titanate oxide (Li4Ti5O12, LTO) has been extensively studied as one of the most promising alternatives to carbon materials in energy conversion and storage devices, due to its high structural and thermal stability, rate capability, and excellent cycling stability. In this study, Li4Ti5O12/multi-walled carbon nanotubes (LTO-MWCNTs) free-standing and flexible composite electrodes/buckypapers were prepared via tape casting technique and well compared with commercially available LTO. The structural, morphological, electrical and electrochemical properties of LTO-MWCNTs buckypaper as well as LTO were studied. The electrical conductivity of LTO-based buckypaper was found to be very high i. e, 4.4 × 102 Scm−1 at room temperature. Further, the buckypaper prepared by synthesized LTO showed higher specific capacity (166 mAhg−1) compared to commercially available LTO (137 mAhg−1) at 0.2 C rate. The enhanced electrochemical performance of as-synthesized LTO-based buckypaper is mainly attributed to the higher electronic conductivity and homogeneous distribution of particles with its small size which facilitates large amount of active sites for lithium insertion and also short diffusion paths. 相似文献