Spacetime Interpretation of Torsion in Prismatic Bodies

Domokos, G.; Gibbons, G. W.

doi:10.1007/s10659-012-9384-3

Cited by 2 publications

(2 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Non-linear model (3)-(7) can be solved analytically using the hodograph formulation. 21 A mathematical analogy of the non-linear equation of minimal surfaces with the Chaplygin gas equations [32][33][34][35][36][37] or equations describing flows of non-Newtonian fluids through porous media [38][39][40] allows one to use a rich arsenal of methods of complex analysis to obtain the explicit solution of this problem.…”

Section: Chaplygin-sokolovsky Transformationmentioning

confidence: 99%

Piercing the water surface with a blade: Singularities of the contact line

Alimov

Kornev

2016

Physics of Fluids

View full text Add to dashboard Cite

An external meniscus on a narrow blade with a slit-like cross section is studied using the hodograph formulation of the Laplace nonlinear equation of capillarity. On narrow blades, the menisci are mostly shaped by the wetting and capillary forces; gravity plays a secondary role. To describe a meniscus in this asymptotic case, the model of Alimov and Kornev ["Meniscus on a shaped fibre: Singularities and hodograph formulation," Proc. R. Soc. A 470, 20140113 (2014)] has been employed. It is shown that at the sharp edges of the blade, the contact line makes a jump. In the wetting case, the contact line sitting at each side of the blade is lifted above the points where the meniscus first meets the blade edges. In the non-wetting case, the contact line is lowered below these points. The contours of the constant height emanating from the blade edges generate unusual singularities with infinite curvatures at some points at the blade edges. The meniscus forms a unique surface made of two mirror-symmetric sheets fused together. Each sheet is supported by the contact line sitting at each side of the blade.

show abstract

Section: Chaplygin-sokolovsky Transformationmentioning

confidence: 99%

Piercing the water surface with a blade: Singularities of the contact line

Alimov

Kornev

2016

Physics of Fluids

View full text Add to dashboard Cite

show abstract

“…This formulation allows one to use the well-developed methods of fluid dynamics and complex variables to study menisci on the complex-shaped fibres. We traced a mathematical analogy of the nonlinear equation of minimal surfaces with the Chaplygin gas equations [35][36][37][38][39] or equations describing the flow of non-Newtonian fluids through porous media [40][41][42]. A hodograph transformation was introduced and illustrated on the one-dimensional meniscus on a cylindrical fibre and on the two-dimensional meniscus on a fibre with the cross section of a symmetric oval.…”

Section: Introductionmentioning

confidence: 99%

Meniscus on a shaped fibre: singularities and hodograph formulation

Alimov

Kornev

2014

Proc. R. Soc. A.

View full text Add to dashboard Cite

Using the method of matched asymptotic expansions, the problem of the capillary rise of a meniscus on the complex-shaped fibres was reduced to a nonlinear problem of determination of a minimal surface. This surface has to satisfy a special boundary condition at infinity. The proposed formulation allows one to interpret the meniscus problem as a problem of flow of a fictitious non-Newtonian fluid through a porous medium. As an example, the shape of a meniscus on a fibre of an oval cross section was analysed employing Chaplygin's hodograph transformation. It was discovered that the contact line may form singularities even if the fibre has a smooth profile: this statement was illustrated with an oval fibre profile having infinite curvature at two endpoints.

show abstract

Spacetime Interpretation of Torsion in Prismatic Bodies

Cited by 2 publications

References 10 publications

Piercing the water surface with a blade: Singularities of the contact line

Piercing the water surface with a blade: Singularities of the contact line

Meniscus on a shaped fibre: singularities and hodograph formulation

Contact Info

Product

Resources

About