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In this paper, we present a mathematical model for the 3D △×n memristor-LC circuit network in the fractional-order sense. First, the impedance of the fractional-order 3D circuit network is derived using matrix transform method and difference equation model. Moreover, we extend the concept of saturation time across the memristor to the circuit network and attempt to explore the relationship between the generalized saturation time and the direct voltage across the network in fractional-order sense. In addition, the effects of the time-varying characteristics of the memristor on the fractional-order 3D circuit network are studied. Also, we propose some issues remaining to be addressed in the near future for the network model. Furthermore, the impedance characteristics are specifically analyzed with theoretical analyses and numerical simulations, where many interesting phenomena are discussed. Finally, sensitivity analysis is provided to carefully investigate the effects of various input parameters on the output response of the fractional-order 3D circuit network. [ABSTRACT FROM AUTHOR]

This paper reports the emergence of bi-stability in a third-order memristive Wien-bridge oscillator. By transforming the parallel RC feedback network into a series resistor and capacitor (RC) feedback network in the previous non-ideal voltage-controlled memristor emulator, an improved memristor emulator is proposed and its fingerprints are exhibited. And then through introducing the proposed emulator to replace the parallel resistor in the conventional Wien-bridge oscillator, an improved memristor-based third-order Wien-bridge oscillator is constructed. Based on its mathematical model, the initial condition-dependent dynamical behaviour is revealed by theoretical analyses and numerical simulations and further verified by hardware experiments, from which the emergence of bi-stability in the memristive oscillator is well demonstrated. [ABSTRACT FROM AUTHOR]

This paper presents a numerical analysis of the migration and transformation mechanism of petroleum hydrocarbons (PHs) pollutants in soil. The mathematical model of the solute migration and plant–microbial remediation for PH polluted soil was established. The model was verified by field experimental data. Then, the software Hydrus-1D was employed to simulate the processes of diffusion, adsorption, desorption, microbial degradation, and plant adsorption of PHs in the soil–water system. The process of plant–microbial remediation for PH-contaminated soil was also simulated. The space-time change of PHs in soil was obtained, and the fate and remediation efficiency of PHs in soil were revealed in different remediation conditions. The results indicated that the Hydrus-1D model can adequately simulate the process of plant–microbial remediation. Plant–microbial remediation appears to be more efficient than the application of bacteria orSuaeda salsa. The majority of PH pollutants are degraded in the upper soil levels. For long-chain petro-alkane-contaminated soil, plant–microbial remediation is a more efficient method. A suitable moisture level in soil is important for improving the bioremediation effect of plant–microbial remediation technology. [ABSTRACT FROM AUTHOR]