Fractional Square Functions and Potential Spaces, Ⅱ

In this paper, we study fractional square functions associated with the Poisson semigroup for SchrSdinger operators. We characterize the potential spaces in the SchrSdinger setting by using vertical, area and gλ, fractional square functions.

Fast Measurement of Dielectric Conductivity for Space Application by Surface Potential Decay Method

Surface potential decay of polymers for electrical insulation can help to determine the dark conductivity for spacecraft charging analysis. Due to the existence of radiation-induced conductivity, it decays fast in the first few hours after irradiation and exponentially slowly for the remaining time. The measurement of dark conductivity with this method usually takes the slow part and needs a couple of days. Integrating the Fowler formula into the deep dielectric charging equations, we obtain a new expression for the fast decay part. The experimental data of different materials, dose rates and temperatures are fitted by the new expression. Both the dark conductivity and the radiation-induced conductivity are derived and compared with other methods. The result shows a good estimation of dark conductivity and radiation-induced conductivity in high-resistivity polymers, which enables a fast measurement of dielectric conductivity within about 600 rain after irradiation.

Automatic emissive probe apparatus for accurate plasma and vacuum space potential measurements

We have developed an automatic emissive probe apparatus based on the improved inflection point method of the emissive probe for accurate measurements of both plasma potential and vacuum space potential.The apparatus consists of a computer controlled data acquisition card,a working circuit composed by a biasing unit and a heating unit,as well as an emissive probe.With the set parameters of the probe scanning bias,the probe heating current and the fitting range,the apparatus can automatically execute the improved inflection point method and give the measured result.The validity of the automatic emissive probe apparatus is demonstrated in a test measurement of vacuum potential distribution between two parallel plates,showing an excellent accuracy of 0.1 V.Plasma potential was also measured,exhibiting high efficiency and convenient use of the apparatus for space potential measurements.

Space Charges Effect of Static Induction Transistor

The space charge effect (SCE) of static induction transistor (SIT) that occurs in high current region is systematically studied.The I V equations are deduced and well agree with experimental results.Two kinds of barriers are presented in SIT,corresponding to channel voltage barrier control (CVBC) mechanism and space charge limited control (SCLC) mechanism respectively.With the increase of drain voltage,the gradual transferring of operational mechanism from CVBC to SCLC is demonstrated.It points out that CVBC mechanism and its contest relationship with space charge barrier makes the SIT distinctly differentiated from JFET and triode devices,etc.The contest relationship of the two potential barriers also results in three different working regions,which are distinctly marked and analyzed.Furthermore,the extreme importance of grid voltage on SCE is illustrated.

Pseudo-Differential Operators on Sobolev and Lipschitz Spaces

In this paper, by discovering a new fact that the Lebesgue boundedness of a class of pseudo- differential operators implies the Sobolev boundedness of another related class of pseudo-differential operators, the authors establish the boundedness of pseudo-differential operators with symbols in Sρ,δ^m on Sobolev spaces, where ∈ R, ρ≤ 1 and δ≤ 1. As its applications, the boundedness of commutators generated by pseudo-differential operators on Sobolev and Bessel potential spaces is deduced. Moreover, the boundedness of pseudo-differential operators on Lipschitz spaces is also obtained.

Towards an L^p Potential Theory for Sub-Markovian Semigroups:Kernels and Capacities

We study in fairly general measure spaces （X,μ） the （non-linear） potential theory of L^p sub-Markovian semigroups which are given by kernels having a density with respect to the underlying measure. In terms of mapping properties of the operators we provide sufficient conditions for the existence （and regularity） of such densities. We give various （dual） representations for several associated capacities and, in the corresponding abstract Bessel potential spaces, we study the role of the truncation property. Examples are discussed in the case of R^n where abstract Bessel potential spaces can be identified with concrete function spaces.

Investigation of Fermions in Non-commutative Space by Considering Kratzer Potential

The two-dimensional Dirac equation for a fermion moving under Kratzer potential in the presence of an external magnetic field is analytically being solved for the energy eigenvalues and eigenfunctions. Subsequently, we have obtained the Wigner function corresponding to the eigenfunctions.

Study on rare earth electrolyte of SDC

The grain boundaries of polycrystalline oxygen ion conductors presented a blocking effect on the oxygen ionic transport across them. It was found that the apparent specific grain boundary conductivity was 2-3 orders of magnitude lower than the bulk conductivity in the temperature range of 200-500 °C for normal purity Ce0.85Sm0.15O1.925 (SDC) with an average grain size of 320-580 nm. The apparent specific grain boundary conductivity increased with decreasing average grain size. It was found that the space charge potential was nearly independent of grain size, and the reason was analyzed. The increase of the conduction path width was responsible for the increase in the apparent specific grain boundary conductivity.

Influence of mechanical damage generated by small space debris on electrostatic discharge

Recent studies have indicated that hypervelocity impacts by meteoroids and space debris can induce spacecraft anomalies. However, the basic physical process through which space debris impacts cause anomalies is not entirely clear. Currently, impact-generated plasma is thought to be the primary cause of electrical spacecraft anomalies, while the effects of impact-generated mechanical damage have rarely been researched. This paper presents new evidence showing that impact-generated mechanical damage strongly influences electrostatic discharge. Hypervelocity impact experiments were conducted in a plasma drag particle accelerator, using particles with diameters of 200–500 ?m and velocities of 2–7 km/s. The impact-generated mechanical damage on a specimen surface was measured by a stereoscopic microscope and 3D Profilometer and it indicated that microscopic irregularities around the impact crater could be responsible for local electric field enhancement. Furthermore, the influence of impact-generated mechanical damage on electrostatic discharge was simulated in an inverted potential gradient situation. The experimental results show that the electrostatic discharge voltage threshold was significantly reduced after the specimen was impacted by particles.