An overdetermined problem for a class of anisotropic equations in a cylindrical domain

Barbu, Luminiţa; Nicolescu, Adrian Eracle

doi:10.1002/mma.6356

Cited by 3 publications

(4 citation statements)

References 18 publications

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“…Finally, we comment that using Willmore energy which depends on the axial and rotational curvatures to determine the joining between two nanostructures gives rise to similar join profiles of using elastic energy as studied in [15]. Moreover, the mathematical techniques in [16][17][18][19] have similar ideas as in this research.…”

Section: Introductionmentioning

confidence: 56%

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Mathematical Modelling for Joining Boron Nitride Graphene with Other BN Nanostructures

Alshammari

2020

Advances in Mathematical Physics

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Boron nitride (BN) nanomaterials such as boron nitride graphenes, boron nitride nanotubes, and boron nitride nanocones are attracting attention among the most promising nanomaterials due to their physical, chemical, and electronic properties when compared to other nanomaterials. BN nanomaterials suggest many exciting potential applications in various fields. Joining between BN nanostructures gives new enhanced structures with outstanding properties and potential applications for design of probes for scanning tunnelling microscopy and other nanoscale devices. This paper uses calculus of variations to model the joining between BN graphene with other BN nanostructures: BNNTs and BNNCs. Furthermore, during the joining between these BN nanostructures, this research examines two models which are depending on the curvature of the join profile. For the first case, Model I refers to when the join profile only includes positive curvature where for the second case, Model II is considered for both positive and negative curvatures. Thus, the purpose of this research is to formulate the basic underlying structure to present simple models based on joining BN graphene to other BN nanostructures.

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Section: Introductionmentioning

confidence: 56%

“…At ðx c , y c Þ, κ = 0, and by solving equation(17), we have θ c = −cos −1 ð−γ/αÞ, noting that from geometrical considerations, we have −π < θ c < −ϕ/2. By making the substitution used in equation(19) for ϕ, we have ϕ c = −π/2. By substituting ϕ c into equations (22) and (25), we can calculate x c and y c ,…”

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confidence: 99%

Mathematical Modelling for Joining Boron Nitride Graphene with Other BN Nanostructures

Alshammari

2020

Advances in Mathematical Physics

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“…Then, substituting k into equation (19), the value of β can be determined, and therefore, y 0 can be obtained from ( 15) [11]. 3 Advances in Mathematical Physics case, we follow the same process as in the last section.…”

Section: Modelmentioning

confidence: 99%

“…Finally, using Willmore energy which depends on the axial and rotational curvatures to determine the joining between nanostructures gives rise to similar joining profiles of using elastic energy as studied in [15]. Furthermore, similar techniques have been used and investigated by many researches such as in [16][17][18] and [19].…”

Section: Introductionmentioning

confidence: 99%

Joining between Boron Nitride Nanocones and Nanotubes

Alshammari

2020

Advances in Mathematical Physics

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Different nanostructures of boron nitride have been observed experimentally such as fullerenes, tubes, cones, and graphene. They have received much attention due to their physical, chemical, and electronic properties that lead them to numerous applications in many nanoscale devices. Joining between nanostructures gives rise to new structures with outstanding properties and potential applications for the design of probes for scanning tunneling microscopy and other nanoscale devices, as carriers for drug delivery and liquid separation. This paper utilizes calculus of variations to model the joining between two types of BN nanostructures, namely, BN nanotubes and BN nanocones. Based on the curvature of the join curve, the joining of these structures can be divided into two models. Model I refers to when the join profile includes positive curvature only, and Model II contains both positive and negative curvatures. The main goal here is to formulate the basic underlying structure from which any such small perturbations can be viewed as departures from an ideal model. For this scenario of joining, we successfully present simple models based on joining BN nanotubes to BN nanocones with five different angles of the cone.

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Some uniqueness results for thermoelastic materials with double porosity structure

Emin

Florea

Craciun

2020

Continuum Mech. Thermodyn.

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An overdetermined problem for a class of anisotropic equations in a cylindrical domain

Cited by 3 publications

References 18 publications

Mathematical Modelling for Joining Boron Nitride Graphene with Other BN Nanostructures

Mathematical Modelling for Joining Boron Nitride Graphene with Other BN Nanostructures

Joining between Boron Nitride Nanocones and Nanotubes

Some uniqueness results for thermoelastic materials with double porosity structure

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