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The multi-step backward difference formulas of order k (BDF-k) for 3 ≤ k ≤ 5 are proposed for solving the extended Fisher--Kolmogorov equation. Based upon the careful discrete gradient structures of the BDF-k formulas, the suggested numerical schemes are proved to preserve the energy dissipation laws at the discrete levels. The maximum norm priori estimate of the numerical solution is established by means of the energy stable property. With the help of discrete orthogonal convolution kernels techniques, the L2 norm error estimates of the implicit BDF-k schemes are established. Several numerical experiments are included to illustrate our theoretical results. [ABSTRACT FROM AUTHOR]

To overcome inadequate functional integration, irregular pits, and insufficient agricultural machinery and agronomy in tobacco seedling transplanting equipment under film, a digging transplanting integrated machine was built. The machine uses parallel four-bar mechanism. The excavation equipment uses conical spiral blades. Using the trajectory approach, the four bar mechanism's fundamental parameters can be reversed. This method meets the requirements for coordinated excavation and transplantation. Mechanical study of soil units determines upward movement characteristics. Additionally, spiral angle, spiral blade outer diameter, and spiral blade speed are quantified to affect soil movement. The range of factors is derived. Based on three factors binary regression orthogonal combination simulated optimization experiment, a discrete element analysis was performed to enhance parameters. Experimental factors optimized include a spiral angle of 19°, a spiral blade diameter of 378 mm, and a rotational speed of 258 rpm. The two optimized test indicators are: a 193 mm hole depth and 350 mm hole diameter. The improved results were verified by field validation studies using a 191 mm hole depth and 347 mm hole diameter. The simulation optimization results and field validation experiment results are very similar. This study provides a technical basis for tobacco farming concurrent drilling and transplanting research. [ABSTRACT FROM AUTHOR]

Adaptive second-order Crank--Nicolson time-stepping methods using the recent scalar auxiliary variable (SAV) approach are developed for the time-fractional molecular beam epitaxial models with Caputo's fractional derivative. Based on the piecewise linear interpolation, the Caputo's derivative is approximated by a novel second-order formula, which is naturally suitable for a general class of nonuniform meshes and essentially preserves the positive semidefinite property of the integral kernel. The resulting Crank--Nicolson SAV time-stepping schemes are unconditionally energy stable on arbitrary nonuniform time meshes. The fast algorithm and adaptive time strategy are employed to speed up the numerical computation. Ample numerical results show that our methods are computationally efficient in multiscale time simulations and appropriate for accurately resolving the intrinsically initial singularity of the solution and for efficiently capturing the fast dynamics away from the initial time. [ABSTRACT FROM AUTHOR]

In the present work, cadmium selenide (CdSe) nanoparticles are deposited directly on TiO2 film to fabricate the TiO2/CdSe interlayer by a chemical bath deposition method. The inverted organic solar cells using poly(3-hexylthiophene) (P3HT) and [6,6]-phenyl C61 butyric acid methyl ester (PCBM) bulk heterojunction as an active layer and TiO2/CdSe interlayer as an electron transport layer (ETL) are fabricated in air. A series of microstructural, photo-electronic, and electrochemical characterizations on these cells are performed. The TiO2/CdSe structure with respect to either the TiO2 layer or the CdSe layer as the ETL exhibits significantly enhanced external quantum efficiency (EQE) in the visible region. The photoluminescence (PL) measurement shows that the exciton dissociation in the TiO2/CdSe structure is more effective than that in either the TiO2 or CdSe structure. The Nyquist plots obtained from electrochemical impedance spectroscopy (EIS) implies that the charge recombination in the TiO2/CdSe structure can be suppressed with respect to that in either the CdSe or TiO2 structure. The photovoltaic performances of the cells with the TiO2/CdSe ETL are clearly improved compared with the reference cells only with the TiO2 layer or CdSe layer as the ETL. [ABSTRACT FROM AUTHOR]