Exact solutions to Landau-Zener problems by evolution operator method

Various analytic approaches have been developed to solve the famous Landau-Zener (LZ) problem. Here, we introduce a time-evolution operator method to investigate such a problem by numerically solving the induced algebraic equations (by Runge-Kutta method). Based on these calculations, transitions between two levels driven by various time-dependent external fields can be simulated in detail, typically near the so-called avoided crossing points. Far from these points, our results reduce to the original Landau-Zener transition (LZT).     

Influence of annealing process on conductive properties of Nb-doped TiO2 polycrystalline films prepared by sol-gel method

Nb-doped TiO₂ (TNO) thin films were prepared by sol-gel dip-coating method with Nb content in a wide range of 0-20 at.%. The prepared films were preheated at 400 °C and then undertaken by two different post-annealing processes: (a) three times vacuum annealing and (b) multi-round annealing. The designed multi-round annealing was shown to be an effective way to improve the conductive properties of the films, compared to the traditional vacuum annealing process. The minimum resistivity reached approximately 0.5 Ω cm with Nb doping concentration around 12 at.%, and the carrier density increased with Nb-doping concentration until the critical point of 12 at.%, which might be the optimal doping content for our TNO films prepared by sol-gel method.     

Existence and uniqueness of solutions for singular integral equation

Using the mixed monotone method we establish existence and uniqueness results for a singular integral equation. The theorem obtained is very general and complements previous known results. The work was supported by the National Natural Science Foundation of China (No.10571021 and No.10701020) and Key Laboratory for Applied Statistics of MOE(KLAS) and Subject Foundation of Harbin University (No. HXK200714).     

A molecular dynamics simulation of the structure of ionic liquid (BMIM+/PF 6? )/rutile (110) interface

The interfacial structure between the room-temperature ionic liquid, 1-butyl-3-methyl-imidazolium hexafluorophosphate (BMIM+/PF6-) and rutile (110) surface is simulated by classical molecular dynam-ics simulation, aiming to model a crucial constituent of the electrolyte/semiconductor interface. The simulation results show several enhanced layers forming in the interfacial region, especially for the anions. A well ordered double layering structure of the ions is also observed in the interfacial region. The c...     

A study of two-term unit fraction expansions via geometric approach

In this article, we report a study of two-term unit fractionexpansions using a geometric approach. It provides us insighton how to find all two-term unit fraction expansions and identifythe property of the expansions with smallest maximal denominators,for a given unit fraction. These findings will be useful tolecturers or teachers involved in teaching history of mathematicsor elementary number theory.     

Use of stable isotopes as surrogates for radionuclides for security studies

During the past decade, interest has increased in qualifying and quantifying the threat posed to the public by the illegal use of radionuclides. In order to take investigations beyond the laboratory bench into more realistic scenarios, environmental and safety considerations dictate that these studies be performed on stable and benign surrogates. This paper discusses some of these studies, specifically the use of cerium dioxide for actinide ceramics and calcium and natural strontium ceramics for those based on ⁹⁰Sr.     

Investigation of lithium niobate composition by optical spectroscopy methods

Indirect methods of investigation of composition and defect structures of lithium niobate (LiNbO₃) single crystals with different compositions are discussed. The analysis of two methods for the determination of the Li/Nb ratio in the samples is carried out, viz., the fundamental UV absorption edge and IR vibrational spectra of the OH⁻ group defects. Intrinsic defect concentrations in lithium niobate crystals (lithium vacancies, $ V_{Li^ - } $ V_{Li^ - } and defects, $ Nb_{Li^{4 + } } $ Nb_{Li^{4 + } } ) as a function of the Li/Nb ratio in the samples are given. The results obtained can serve as an effective way of express non-destructive composition analysis in a mass production of parallel-plane plates.