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Abstract This paper investigates the manipulation of induced torque on a four-level tripod atom system through the interaction with two vortex probe beams featuring spatial inhomogeneity, along with a non-vortex control beam. The study explores both the linear and nonlinear regimes of torque induction. In the linear regime, where the intensity of the vortex beams is weaker than that of the control field, effective control over the induced torque is demonstrated by adjusting parameters such as magnetic field strength, control field intensity, detuning, and dephasing terms between relevant atomic levels. The analysis highlights the significant contribution of the Zeeman shift-induced magnetic field, which enhances the torque and exhibits a distinct sharp peak. Furthermore, higher-order contributions to the induced torque are discussed as the intensity of the probe fields approaches that of the control field, resulting in further enhancement of the induced torque. These findings offer opportunities for precise control over the rotational motion of atoms within the system, with potential applications in precision measurement, quantum information processing, and quantum control.

Regarding the long-term toxic effects of Pb (II) ions on human health and its bioaccumulation property, taking measures for its reduction in the environment is necessary. The MMT-K10 (montmorillonite-k10) nanoclay was characterized by XRD, XRF, BET, FESEM, and FTIR. The effects of pH, initial concentrations, reaction time, and adsorbent dosage were studied. The experimental design study was carried out with RSM-BBD method. Results prediction and optimization were investigated with RSM and artificial neural network (ANN)-genetic algorithm (GA) respectively. The RSM results showed that the experimental data followed the quadratic model with the highest regression coefficient value (R2 = 0.9903) and insignificant lack of fit (0.2426) showing the validity of the Quadratic model. The optimal adsorption conditions were obtained at pH 5.44, adsorbent = 0.98 g/l, concentration of Pb (II) ions = 25 mg/L, and reaction time = 68 min. Similar optimization results were observed by RSM and artificial neural network-genetic algorithm methods. The experimental data revealed that the process followed the Langmuir isotherm and the maximum adsorption capacity was 40.86 mg/g. Besides, the kinetic data indicated that the results fitted with the pseudo-second-order model. Hence, the MMT-K10 nanoclay can be a suitable adsorbent due to having a natural source, simple and inexpensive preparation, and high adsorption capacity. [ABSTRACT FROM AUTHOR]