Mathematical Modelling for Joining Boron Nitride Graphene with Other BN Nanostructures

Alshammari, Nawa

doi:10.1155/2020/2394037

Cited by 2 publications

(2 citation statements)

References 18 publications

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“…By optimizing functionals over time, we can determine the optimal trajectory for a system while considering various constraints and variables [19]. For instance, [4] highlights its applicability in enhancing nanostructures, [20] introduces a framework for optimizing energy utilization through battery management in a cooperative environment using calculus of variations, and [27] explores its use in optimizing functional parameters of compacted modified soils for geotechnical applications. Additionally, [13] addresses uncertainty in clearing parking lots and optimizes a polynomial cost function to determine the cars that should be relocated.…”

Section: Introductionmentioning

confidence: 99%

Vacating a parking lot under uncertainty

Martínez Díaz,

Reyes Salgado,

Martínez Flores

et al. 2024

Rev. mat. (En línea)

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First-mile problems have become a major problem for the automobile industry since moving cars from production plants to selling destinations is characterized by using vehicle carriers with limited space. Although supply chain processes have automatized last-mile operations to improve productivity and increase benefits, first-mile analysis has been widely ignored. For example, in the automotive industry, cars are stored in parking lots until they are demanded, which negatively impacts delivery times and increases transportation costs. The previous issues impact the first-mile logistics of the automobile industry to the detriment of copying with delivery times and increasing the operation cost. In this paper, we deal with the previous issues by modeling the movement of cars from the parking lot to the car Carrier as an optimal control problem. Considering that not all cars should leave the parking lot, we search for conditions that guarantee the existence of a unique optimal path when the cars’ requisition is uncertain. Theoretical results provide a closed-form solution that indicates the optimal path to fill the car carrier in a time window. Such solutions allow us to study the impact of exogenous parameters (such as the parking lot size, the starting point, andmarginal costs) on the behavior and features of the optimal path.

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Section: Introductionmentioning

confidence: 99%

Vacating a parking lot under uncertainty

Martínez Díaz,

Reyes Salgado,

Martínez Flores

et al. 2024

Rev. mat. (En línea)

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“…On the other hand, because of their similarity to carbon in nanoscale structures, BN in nanoscale structures has been joined and connected using elastic energy. In detail, other studies have used elastic energy to connect and join BN nanostructures: BN nanocones to nanotubes and BN graphene to other BN nanostructures; and nanotubes to BN nanocones, as shown in [3] and [4], respectively. In this paper, the Willmore energy method is utilized to join and connect BN nanostructures.…”

Section: Introductionmentioning

confidence: 99%

Mathematical energy minimization model for joining boron nitride fullerene with several BN nanostructures

Alshammari

2021

J Mol Model

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Nanoscale materials have gained considerable interest because of their special properties and wide range of applications. Many types of boron nitride at the nanoscale have been realized, including nanotubes, nanocones, fullerenes, tori, and graphene sheets. The connection of these structures at the nanoscale leads to merged structures that have enhanced features and applications. Modeling the joining between nanostructures has been adopted by different methods. Namely, carbon nanostructures have been joined by minimizing the elastic energy in symmetric configurations. In other words, the only considerable curvature in the elastic energy is the axial curvature. Accordingly, because it has nanoscale structures similar to those in carbon, BN can also be joined and connected by using this method. On the other hand, different methods have been proposed to consider the rotational curvature because it has a similar size. Based on that argument, the Willmore energy, which depends on both curvatures, has been minimized to join carbon nanostructures. This energy is used to identify the joining region, especially for a three-dimensional structure. In this paper, we expand the use of Willmore energy to cover the joining of boron nitride nanostructures. Therefore, because catenoids are absolute minimizers of this energy, pieces of catenoids can be used to connect nanostructures. In particular, we joined boron nitride fullerene to three other BN nanostructures: nanotube, fullerene, and torus. For now, there are no experimental or simulation data for comparison with the theoretical connecting structures predicted by this study, which is some justification for the suggested simple model shown in this research. Ultimately, various nanoscale BN structures might be connected by considering the same method, which may be considered in future work.

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Mathematical Modelling for Joining Boron Nitride Graphene with Other BN Nanostructures

Cited by 2 publications

References 18 publications

Vacating a parking lot under uncertainty

Vacating a parking lot under uncertainty

Mathematical energy minimization model for joining boron nitride fullerene with several BN nanostructures

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