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Purpose: In order to ensure that vegetable seedlings (with a soil block around their roots) are planted in an upright orientation after metering in a vegetable transplanter, they need to be dropped freely from a certain height. The walkbehind hand-tractor-powered machines do not have sufficient space to drop the seedlings from that height. In the present work, a hopper-type planting device was developed for the walk-behind hand-tractor-powered vegetable transplanter to ensure that the soil block seedlings are planted in an upright orientation. Methods: Various dimensionless terms were developed based on the dimensional analysis approach, and their effect on the planting of soil block seedlings in an upright orientation (planting efficiency) was studied. The optimum design dimensions of the hopper-type planting device were identified by the Taguchi method of optimization. Results: The ratio of the height of free fall to the sliding distance of the seedling on the surface of the hopper had the highest influence on planting efficiency. The planting efficiency was highest for plants with a height 15 ± 2 cm. The plant handling Froude number, in interaction with the design of the hopper-type planting device, also significantly affected the planting efficiency. Of the hopper design factors, the length of the slide of the seedlings on the surface of the hopper was most important, and induced sufficient velocity and rotation to cause the seedling to fall in an upright orientation. An evaluation of the performance of the planting device under actual field conditions revealed that the planting efficiency of the developed planting device was more than 97.5%. Conclusions: As the seedlings were fed to the metering device manually, an increase in planting rate increased missed plantings. The planting device can be adopted for any vegetable transplanter in which the seedlings are allowed to drop freely from the metering device.

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This paper deals with the approximate design of quantum unitary gates using perturbed harmonic oscillator dynamics. The harmonic oscillator dynamics is perturbed by a small time-varying electric field which leads to time-dependent Schrödinger equation. The corresponding unitary evolution after time T is obtained by approximately solving the time-dependent Schrödinger equation. The aim of this work is to minimize the discrepancy between a given unitary gate and the gate obtained by evolving the oscillator in the weak electric field over [0, T ]. The proposed algorithm shows that the approximate design is able to realize the Hadamard gate and controlled unitary gate on three-qubit arrays with high accuracy.

This article presents formability analysis of aluminium alloy 7075 thin sheets in single point incremental forming (SPIF) through prediction of forming limit curve (FLC) and maximum formable wall angle. Deformation instability method based on tool-sheet contact and non-contact zones in incremental forming was used for the prediction of limit strains for plane strain and equi-biaxial stretching strain path. FLC of the material was also determined experimentally, after measuring limit strains for deformed sheet through groove test for the process. Further, maximum forming wall angle of the material was determined for deformed sheet in a square pyramid shape. The theoretical limit strains predicted by deformation instability approach were compared to the experimental values. Theoretically, calculated limit strains were observed to be higher for plane strain path but approximately close for equi-biaxial strain path compared to experimental limit strains. The maximum formable wall was found to be 55˚ for the material in the process.

In this article, formability of tailor laminated sheets in single point incremental forming (SPIF) is investigated using forming limit curve (FLC) and maximum formable wall angle determined theoretically and incremental sheet forming tests. Two different sheet materials namely aluminum alloy AA5083 and polycarbonate were laminated in two different configurations, that is, AA5083/PC, and AA5083/PC/AA5083. FLCs were determined for the laminated sheets using deformation instability method and compared to that of the base sheets. It was observed that formability of the laminated sheets was higher than that of the PC and AA5083 sheets for plane strain case. The maximum formable wall angle was determined by varying the wall angle till the onset of fracture through deforming the sheet into square pyramid shapes. Deformation depths at the onset of fracture for the incrementally formed laminated sheets got decreased with the increase of forming wall angle. Optical macrographs of the cross-sections of the deformed laminated sheets with maximum forming wall angles were taken, and variations of sheet thicknesses along the center line of the deformed sheets were compared for the different cases. Higher triaxiality of AA5083/PC/AA5083 sheet results in lower formability compared to AA5083/PC sheet obtained from membrane analysis. Formation of bump structure due to delamination during SPIF of laminated sheets could be avoided using proper selection of tool path.

This paper presents the design of a given quantum unitary gate by perturbing a three-dimensional (3-D) quantum harmonic oscillator with a time-varying but spatially constant electromagnetic field. The idea is based on expressing the radiationperturbed Hamiltonian as the sum of the unperturbed Hamiltonian and O(e) and O(e 2 ) perturbations and then solving the Schrödinger equation to obtain the evolution operator at time T up to O(e 2 ), and this is a linear-quadratic function of the perturbing electromagnetic field values over the time interval [0, T ]. Setting the variational derivative of the error energy with respect to the electromagnetic field values with an average electromagnetic field energy constraint leads to the optimal electromagnetic field solution, a linear integral equation. The reliability of such a gate design procedure in the presence of heat bath coupling is analysed, and finally, an example illustrating how atoms and molecules can be approximated using oscillators is presented.

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