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The initial value problem for a lumped parameter model arising from design of magneto–electromechanical device with a current-carrying conductor is analyzed. The differential equation is nonlinear because it includes the magnetic force term. The analysis for the dynamic pull-in occurring in the system is presented. The pull-in threshold is given analytically in terms of model parameters. Sufficient conditions for the existence of periodic solutions are proved analytically and verified numerically. The results can be useful for understanding and design of one-degree-of-freedom models of magnetically actuated beams.

In this paper, we investigate the existence and uniqueness of solutions for the viscous Burgers’ equation for the isothermal flow of power-law non-Newtonian fluids ρ(∂tu+u∂xu)=μ∂x∂xup−2∂xu, augmented with the initial condition u(0,x)=u0, 00, and T>0. We show that this initial boundary problem has an unique solution in the Buchner space L20,T;W01,p(0,1) for the given set of conditions. Moreover, numerical solutions to the problem are constructed by applying the modeling and simulation package COMSOL Multiphysics 6.0 at small and large Reynolds numbers to show the images of the solutions.

This work presents a high-fidelity two-way coupled Fluid-Structure Interaction (FSI) simulation framework for wind turbine blades, developed using the Arbitrary Hybrid Turbulence Modelling (AHTM) implemented through Very Large Eddy Simulation (VLES) in the DAFoam solver. By integrating VLES with the Toolkit for the Analysis of Composite Structures (TACS) structural solver via the OpenMDAO/MPhys framework, this work aims to accurately model the complex aeroelastic characteristics of wind turbines, specifically focusing on the NREL Phase VI wind turbine. The numerical model accounts for the effects of transient, turbulent, and unsteady aerodynamic loading, incorporating the impact of structural deflections. A comparison of the calculated results with experimental data demonstrates strong agreement in key performance metrics, including blade tip displacements, power output, and pressure distribution. This alignment confirms that the proposed model is effective at predicting wind turbine performance. One of the significant advantages of this study is the integration of advanced turbulence modeling with shell element structural analysis, enhancing the design and performance predictions of modern wind turbines. Although computationally intensive, this approach marks a significant advancement in accurately simulating the aeroelastic response of turbines, paving the way for optimized and more efficient wind energy systems.

Inadvertent accumulation of arsenic (As) in rice (Oryza sativa L.) is a concern for people depending on it for their subsistence, as it verily causes epigenetic alterations across the genome as well as in specific cells. To ensure food safety, certain attempts have been made to nullify this highest health hazard encompassing physiological, chemical and biological methods. Albeit, the use of mycorrhizal association along with nutrient reinforcement strategy has not been explored yet. Mechanisms of response and resistance of two rice genotypes to As with or without phosphorus (P) nutrition and Serendipita indica (S. indica; S.i) colonization were explored by root transcriptome profiling in the present study. Results revealed that the resistant genotype had higher auxin content and root plasticity, which helped in keeping the As accumulation and P starvation response to a minimum under alone As stress. However, sufficient P supply and symbiotic relationship switched the energy resources towards plant’s developmental aspects rather than excessive root proliferation. Higher As accumulating genotype (GD-6) displayed upregulation of ethylene signaling/biosynthesis, root stunting and senescence related genes under As toxicity. Antioxidant defense system and cytokinin biosynthesis/signaling of both genotypes were strengthened under As + S.i + P, while the upregulation of potassium (K) and zinc (Zn) transporters depicted underlying cross-talk with iron (Fe) and P. Differential expression of phosphate transporters, peroxidases and GSTs, metal detoxification/transport proteins, as well as phytohormonal metabolism were responsible for As detoxification. Taken together, S. indica symbiosis fortified with adequate P-fertilizer can prove to be effective in minimizing As acquisition and accumulation in rice plants.

Plants use a variety of secondary metabolites to defend themselves against herbivore insects. Methyl salicylate (MeSA) is a natural plant-derived compound that has been used as a plant defence elicitor and a herbivore repellent on several crop plants. The aim of this study was to investigate the effect of MeSA treatment of Brassica rapa subsp. chinensis (‘Hanakan’ pak choi) on its interactions with peach potato aphids, Myzus persicae, and their natural enemy, Diaeretiella rapae. For this, we selected two concentrations of MeSA (75 mg/L and 100 mg/L). Our results showed that aphid performance was significantly reduced on plants treated with MeSA (100 mg/L). In a cage bioassay, the MeSA (100 mg/L)-treated plants showed lower adult survival and larviposition. Similarly, the MeSA (100 mg/L)-treated plants had a significantly lower aphid settlement in a settlement bioassay. In contrast, the M. persicae aphids did not show any significant difference between the MeSA (75 mg/L)-treated and control plants. In a parasitoid foraging bioassay, the parasitoid D. rapae also did not show any significant difference in the time spent on MeSA-treated and control plants. A volatile analysis showed that the MeSA treatment induced a significant change in volatile emissions, as high numbers of volatile compounds were detected from the MeSA-treated plants. Our results showed that MeSA has potential to induce defence in Brassica against M. persicae and can be utilised in developing sustainable approaches for the management of peach potato aphids.

The reduced problem of the Navier–Stokes and the continuity equations, in two-dimensional Cartesian coordinates with Eulerian description, for incompressible non-Newtonian fluids, is considered. The Ladyzhenskaya model, with a non-linear velocity dependent stress tensor is adopted, and leads to the governing equation of interest. The reduction is based on a self-similar transformation as demonstrated in existing literature, for two spatial variables and one time variable, resulting in an ODE defined on a semi-infinite domain. In our search for classical solutions, existence and uniqueness will be determined depending on the signs of two parameters with physical interpretation in the equation. Illustrations are included to highlight some of the main results.

The nonlinear Brinkman-Forchheimer-Darcy equation is used to model some porous medium flow in chemical reactors of packed bed type. The results concerning the existence and uniqueness of a weak solution are presented for nonlinear convective flows in medium with variable porosity and for small data. Furthermore, the finite element approximations to the flow profiles in the fixed bed reactor are presented for several Reynolds numbers at the non-Darcy’s range.

The use of coat-hanger dies is prevalent in the plastic film and sheet extrusion industry. The product quality and the power of the extrusion machine depend on the uniformities of the fluid velocity at the exit and the pressure drop. Die manufacturers face the challenge of producing coat-hanger dies that can extrude materials uniformly and with a minimal pressure drop. Previous studies have analyzed the die outlet’s flow homogeneity and pressure drop using various numerical simulations. However, the combination of the scheme programming language together with the Adjoint Method of Optimization has yet to be attempted. The adjoint optimization method has been demonstrated to be beneficial in addressing issues related to shape optimization problems and it may also be beneficial in optimizing the design of dies used in polymer melt extrusion. In this study, the proposed innovations involve incorporating both the Scheme programming language and Adjoint solver to examine and optimize the coat hanger’s flow homogeneity and pressure drop. Before optimization, the outlet velocity was almost 10 times higher at the die center than at the edges but after optimization, it became more uniform. The proposed optimized coat-hanger die geometry results in more uniform melt flow as demonstrated by the velocity contour plot and the outlet velocity graph in the die slit area, reducing the deviation value from 0.097 to 0.015. Additionally, the mass flux variance across the die outlet decreased by 71.6% from 0.015069 kg m−2 s−1 to 0.004281 kg m−2 s−1. Therefore, using this method reduces the amount of time wasted on trial and error or other optimization techniques that may be limited by design constraints.

To evaluate novel turbine designs, the wind energy sector extensively depends on computational fluid dynamics (CFD). To use CFD in the design optimization process, where lower-fidelity approaches such as blade element momentum (BEM) are more popular, new tools to increase the accuracy must be developed as the latest wind turbines are larger and the aerodynamics and structural dynamics become more complex. In the present study, a new concurrent aerodynamic shape optimization approach towards multidisciplinary design optimization (MDO) that uses a Reynolds-averaged Navier–Stokes solver in conjunction with a numerical optimization methodology is introduced. A multidisciplinary design optimization tool called DAFoam is used for the NREL phase VI turbine as a baseline geometry. Aerodynamic design optimizations in terms of five different schemes, namely, cross-sectional shape, pitch angle, twist, chord length, and dihedral optimization are conducted. Pointwise, a commercial mesh generator is used to create the numerical meshes. As the adjoint approach is strongly reliant on the mesh quality, up to 17.8 million mesh cells were employed during the mesh convergence and result validation processes, whereas 2.65 million mesh cells were used throughout the design optimization due to the computational cost. The Sparse Nonlinear OPTimizer (SNOPT) is used for the optimization process in the adjoint solver. The torque in the tangential direction is the optimization’s merit function and excellent results are achieved, which shows the promising prospect of applying this approach for transient MDO. This work represents the first attempt to implement DAFoam for wind turbine aerodynamic design optimization.

Excessive industrialization and the usage of pesticides plague the farming soils with heavy metals, reducing the quality of arable land. Assessing phytoavailability of cadmium (Cd) from growth medium to plant system is crucial and necessitates precise and timely monitoring of Cd to ensure food safety. Zinc (Zn) and silicon (Si) have singularly demonstrated the potential to ameliorate Cd toxicity and are important for agricultural production, human health, and environment in general. However, Zn-Si interaction on Cd toxicity alleviation, their effects and underlying mechanisms are still fragmentarily understood. Seven treatments were devised besides control to evaluate the single and combined effects of Zn and Si on the physio-biochemical attributes and ultrastructural fingerprints of Cd-treated rice genotypes, i.e., Cd tolerant “Xiushui-110” and Cd sensitive “HIPJ-1”. Supplementation of both Zn and Si promoted plant biomass, photosynthetic parameters, ionic balance, and improved chloroplast ultrastructure with minimized Cd uptake and malondialdehyde (MDA) content due to the activation of antioxidant enzymes in Cd stressed plants. The combined effects of 10 μM Zn and 15 μM Si on 15 μM Cd displayed a greater reduction in Cd uptake and root-leaf MDA content, while enhancing photosynthetic activity, superoxide dismutase (SOD) activity and root-leaf ultrastructure particularly in HIPJ-1, whilst Xiushui-110 had an overall higher leaf catalase (CAT) activity and a higher root length and shoot height was observed in both genotypes compared to the Cd 15 µM treatment. Alone and combined Zn and Si alleviation treatments reduced Cd translocation from the root to the stem for HIPJ-1 but not for Xiushui-110. Our results confer that Zn and Si singularly and in combination are highly effective in reducing tissue Cd content in both genotypes, the mechanism behind which could be the dilution effect of Cd due to improved biomass and competitive nature of Zn and Si, culminating in Cd toxicity alleviation. This study could open new avenues for characterizing interactive effects of simultaneously augmented nutrients in crops and provide a bench mark for crop scientists and farmers to improve Cd tolerance in rice.