In this paper, we discuss the Cauchy-type integral formula of hypermonogenic functions on unbounded domains in real Clifford analysis, then we extend the Plemelj formula and Cauchy–Pompeiu formula of hypermonogenic functions on bounded domains to unbounded domains. We also deal with the Green-type formula on unbounded domains and get several important corollaries. 相似文献
The weak anchoring nematic liquid crystal (NLC) cell is investigated with regard to energy. Because the Gibbs free energy of liquid crystal system used in theory does not include temperature and entropy, and because the equations and boundary conditions for δG=0 are also the mechanical equilibrium conditions of the continuum, the Gibbs free energy G is equivalent to the energy E of the liquid crystal continuum. There are multiple solutions which satisfy these equations and boundary conditions, each solution corresponding to a certain energy value. We call these discrete energy values and energy levels. Adopting a simple liquid crystal cell model, the energy levels are calculated in detail by means of analytical and numerical methods. The results show that there are three energy levels (or more in certain cases). The values and sequence of the energy levels are related to the external field and anchoring parameters. The relationships between the energy level structure and the bistable. Fréedericksz transition are disussed, together with their influence on the response time. The physical condition for the existence of more than three energy levels is also given. 相似文献
Pillararene‐containing thermoresponsive polymers are synthesized via reversible addition–fragmentation chain transfer polymerization using pillararene derivatives as the effective chain transfer agents for the first time. These polymers can self‐assemble into micelles and form vesicles after guest molecules are added. Furthermore, such functional polymers can be further applied to prepare hybrid gold nanoparticles, which integrate the thermoresponsivity of polymers and molecular recognition of pillararenes.
Titanium is a commonly used material in aviation, aerospace, and military applications, due to the outstanding mechanical properties of titanium and its alloys. However, its relatively low thermal conductivity restricts its extended usage. The use of graphene as a filler shows great potential for the enhancement of thermal conductivity in titanium-based metal-matrix composites (MMCs). We used classical molecular dynamics (MD) simulation methods to explore the thermal conductance at the titanium–graphene (Ti/Gr) interface for its thermal boundary conductance, which plays an important role in the thermal properties of Ti-based MMCs. The effects of system size, layer number, temperature, and strain were considered. The results show that the thermal boundary conductance (TBC) decreases with an increasing layer number and reaches a plateau at n = 5. TBC falls under tensile strain and, in turn, it grows with compressive strain. The variation of TBC is explained qualitatively by the interfacial atomic vibration coupling factor. Our findings also provide insights into ways to optimize future thermal management based on Ti-based MMCs materials. 相似文献