Analysing chaos in fractional-order systems with the harmonic balance method

In this paper, the fractional-order Genesio-Tesi system showing chaotic behaviours is introduced, and the corresponding one in an integer-order form is studied intensively. Based on the harmonic balance principle, which is widely used in the frequency analysis of nonlinear control systems, a theoretical approach is used to investigate the conditions of system parameters under which this fractional-order system can give rise to a chaotic attractor. Finally, the numerical simulation is used to verify the validity of the theoretical results.

Detailed balance limit efficiency of silicon intermediate band solar cells

The detailed balance method is used to study the potential of the intermediate band solar cell （IBSC）, which can improve the efficiency of the gi-based solar cell with a bandgap between 1.1 eV to 1.7 eV. It shows that a crystalline silicon solar ceil with an intermediate band located at 0.36 eV below the conduction band or above the valence band can reach a limiting efficiency of 54% at the maximum light concentration, improving greatly than 40.7% of the Shoekley-Queisser limit for the single junction Si solar cell. The simulation also shows that the limiting efficiency of the silicon-based solar cell increases as the bandgap increases from 1.1 eV to 1.7 eV, and the amorphous Si solar cell with a bandgap of 1.7 eV exhibits a radiative limiting efficiency of 62.47070, having a better potential.

Spatio-temporal variation of water conservation and its impact factors on the southern slope of Qilian Mountains

The ecology of Qilian Mountains has been seriously threatened by uncontrolled grazing and wasteland reclamation. This study examined the ecological changes on the southern slope of Qilian Mountains in China from the perspective of water conservation by classifying different clusters of water conservation functional areas to efficiently use limited human resources to tackle the water conservation protection problem. In this study, we used Integrate Valuation of Ecosystem Services and Tradeoffs(InVEST) model to estimate water conservation and analyzed the factors that influence the function. The results of this study include:(1) from 2000 to 2015, the water conservation of the southern slope of Qilian Mountains generally showed an increasing trend, and the total water conservation in 2015 increased by 42.18% compared with that in 2000.(2) Rainfall, fractional vegetation cover(FVC), and evapotranspiration have the most significant influence on the water conservation of the study area. Among them, water conservation is positively correlated with rainfall and FVC(P<0.05) and negatively correlated with evapotranspiration(P<0.05).(3) The importance level of water conservation functional areas gradually increases from northwest to southeast, and the region surrounding Menyuan Hui Autonomous County in the southeast of the southern slope of Qilian Mountains is the core water conservation functional area. And(4) the study area was divided into five clusters(Cluster Ⅰ–Cluster Ⅴ) of water conservation, with the areas of Clusters Ⅰ through Ⅴ accounting for 0.58%, 13.74%, 41.23%, 32.43%, and 12.01% of the whole study area, respectively.

Compositions,Proportions,and Equilibrium Temperature of Coexisting Two-feldspar in Crystalline Rocks

Compositions, proportions, and equilibrium temperature of coexisting two-feldspar in crystalline rocks are of great importance to classification in petrography and interpretation of petrogenesis. Crystalline rocks are usually composed of 4-6 minerals （phases）, depending on their independent chemical components and the equilibrium temperature of crystallizations. In general, number of mineral phases can be determined by the ＂Phase Rule＂. According to the mass balance principle, bulk composition of coexisting two-feldspar could be evaluated from the bulk chemistry of a rock, provided that the compositions of the coexisting mafic mineral phases containing calcium, sodium, and potassium oxides are determined, e.g., by microprobe analysis. The compositions, proportions, and temperature of two-feldspar in equilibrium can thus be simultaneously resolved numerically from bulk composition of the rock, by incorporating the activity/composition relations of the ternary feldspars with the mass balance constraints. Upon the numerical approximation method presented in this paper, better-quality, internally consistent data on feldspar group could usually be obtained, which would be expected more realistic and accurate in consideration of thermodynamic equilibria in the system of crystalline rocks, as well as bulk chemistry of a rock and the composing minerals.

A Simplified Hirota Method and Its Application

By means of the homogeneous balance principle, a nonlinear transformation to the well known breaking soliton equation with physical interest was given. The original equation was turned into a homogeneity differential equation with this nonlinear transformation. By solving the homogeneity equation via the simplified Hirota method and applying the nonlinear transformation, one soliton, two soliton and three soliton solutions as well as some other types of explicit solutions to the breaking soliton equation were obtained with the assistance of Maple.