The Experts below are selected from a list of 1500 Experts worldwide ranked by ideXlab platform
J. F. Davidson - One of the best experts on this subject based on the ideXlab platform.
-
the distortion of a horizontal soap film due to the impact of a falling sphere
Chemical Engineering Science, 2019Co-Authors: C.-h. Chen, A Perera, Bart Hallmark, P Jackson, J. F. DavidsonAbstract:Abstract A horizontal soap film is established in vertical tube a few centimetres in diameter. A metal sphere, 1–2 mm diameter, is dropped onto the film, whose distortion is observed by means of a high speed camera. The film wraps partly around the sphere, detaching at a circle which moves up the sphere as it falls. The shape of the film at successive radii, bigger than the radius of contact, was predicted from theory relying on the proposition that if both sides of the film are open to atmosphere, there can be no pressure difference across it. The pressure difference across a film is proportional to (surface tension)/(radius of curvature); hence it follows that the radii of curvature in two planes, perpendicular to each other and to the film surface, must be equal and opposite. This proposition gives equations predicting the shape, in reasonable agreement with experiment. This theory is compared with the theory of Catenoids, first studied by Euler in 1744. Catenoid theory gives exactly the same results as the ‘radius of curvature’ theory presented here. A simple energy conservation argument shows that the two theories are compatible and agree with a published photograph of a soap film Catenoid.
-
The distortion of a horizontal soap film due to the impact of a falling sphere
'Organisation for Economic Co-Operation and Development (OECD)', 2019Co-Authors: C.-h. Chen, Perera A, Jackson P, Hallmark Bart, J. F. DavidsonAbstract:A horizontal soap film is established in vertical tube a few centimetres in diameter. A metal sphere, 1-2mm diameter, is dropped onto the film, whose distortion is observed by means of a high speed camera. The film wraps partly around the sphere, detaching at a circle which moves up the sphere as it falls. The shape of the film at successive radii, bigger than the radius of contact, was predicted from theory relying on the proposition that if both sides of the film are open to atmosphere, there can be no pressure difference across it. The pressure difference across a film is proportional to (surface tension) / (radius of curvature); hence it follows that the radii of curvature in two planes, perpendicular to each other and to the film surface, must be equal and opposite. This proposition gives equations predicting the shape, in reasonable agreement with experiment. This theory is compared with the theory of Catenoids, first studied by Euler in 1744. Catenoid theory gives exactly the same results as the ‘radius of curvature’ theory presented here. A simple energy conservation argument shows that the two theories are compatible and agree with a published photograph of a soap film Catenoid.The work was supported by EPSRC contract number EP/N00230X/1
Yoshiroh Machigashira - One of the best experts on this subject based on the ideXlab platform.
-
An approximation of a Catenoid constructed from piecewise truncated conical minimal surfaces
Kyushu Journal of Mathematics, 2013Co-Authors: Akihito Ebisu, Yoshiroh MachigashiraAbstract:In [3], we considered an approximation of a Catenoid constructed from even truncated cones that maintains minimality in a certain sense. In this paper, we consider such an approximation consisting of odd truncated cones that maintains minimality in the same sense. Through this procedure, we obtain a discrete curve approximating a catenary by exploiting the fact that it is the function that generates a Catenoid. In this investigation, the theory of the
-
An approximation of a Catenoid constructed from piecewise truncated conical minimal surfaces
arXiv: Differential Geometry, 2012Co-Authors: Akihito Ebisu, Yoshiroh MachigashiraAbstract:We consider an appoximation of a Catenoid constructed from "odd" truncated cones that maintains minimality in a certain sense. Thorough this procedure, we obtain a discrete curve approximating a catenary by exploiting the fact that it is the function that generates a Catenoid. In this investigation, the theory of the Gauss hypergeomtric functions plays an important role. This work is a sequel to [Y.Machigashira, Piecewise truncated conical minimal surfaces and the Gauss hypergeometric functions, Journal of Math-for-Industry 4(2012), pp. 25-33 ]. The paper covers an appoximation of a Catenoid constructed from "even" truncated cones that maintains minimality in the same sense. Keywords: catenary, Catenoid, truncated cone, hypergeomtric function, Chebyshev polynomial of the third kind.
C.-h. Chen - One of the best experts on this subject based on the ideXlab platform.
-
the distortion of a horizontal soap film due to the impact of a falling sphere
Chemical Engineering Science, 2019Co-Authors: C.-h. Chen, A Perera, Bart Hallmark, P Jackson, J. F. DavidsonAbstract:Abstract A horizontal soap film is established in vertical tube a few centimetres in diameter. A metal sphere, 1–2 mm diameter, is dropped onto the film, whose distortion is observed by means of a high speed camera. The film wraps partly around the sphere, detaching at a circle which moves up the sphere as it falls. The shape of the film at successive radii, bigger than the radius of contact, was predicted from theory relying on the proposition that if both sides of the film are open to atmosphere, there can be no pressure difference across it. The pressure difference across a film is proportional to (surface tension)/(radius of curvature); hence it follows that the radii of curvature in two planes, perpendicular to each other and to the film surface, must be equal and opposite. This proposition gives equations predicting the shape, in reasonable agreement with experiment. This theory is compared with the theory of Catenoids, first studied by Euler in 1744. Catenoid theory gives exactly the same results as the ‘radius of curvature’ theory presented here. A simple energy conservation argument shows that the two theories are compatible and agree with a published photograph of a soap film Catenoid.
-
The distortion of a horizontal soap film due to the impact of a falling sphere
'Organisation for Economic Co-Operation and Development (OECD)', 2019Co-Authors: C.-h. Chen, Perera A, Jackson P, Hallmark Bart, J. F. DavidsonAbstract:A horizontal soap film is established in vertical tube a few centimetres in diameter. A metal sphere, 1-2mm diameter, is dropped onto the film, whose distortion is observed by means of a high speed camera. The film wraps partly around the sphere, detaching at a circle which moves up the sphere as it falls. The shape of the film at successive radii, bigger than the radius of contact, was predicted from theory relying on the proposition that if both sides of the film are open to atmosphere, there can be no pressure difference across it. The pressure difference across a film is proportional to (surface tension) / (radius of curvature); hence it follows that the radii of curvature in two planes, perpendicular to each other and to the film surface, must be equal and opposite. This proposition gives equations predicting the shape, in reasonable agreement with experiment. This theory is compared with the theory of Catenoids, first studied by Euler in 1744. Catenoid theory gives exactly the same results as the ‘radius of curvature’ theory presented here. A simple energy conservation argument shows that the two theories are compatible and agree with a published photograph of a soap film Catenoid.The work was supported by EPSRC contract number EP/N00230X/1
Ralf Stannarius - One of the best experts on this subject based on the ideXlab platform.
-
Collapse of Catenoid-shaped smectic films
Europhysics Letters (EPL), 2006Co-Authors: Frank Müller, Ralf StannariusAbstract:We report an experimental study of the collapse dynamics of smectic Catenoids. It is shown that in dependence on the thickness of the smectic films, different rupture scenarios take place. The change of the film thickness during the collapse process is monitored using an interference technique. We separate influences of inertia and viscosity of the smectic film material and inertia and viscosity of the air enclosed by the Catenoid by performing experiments at different pressures. At low pressure, the collapse of thin (submicrometer) membranes is considerably accelerated, while for thick (several micrometers) membranes, the dynamics is practically unchanged.
Taku Sato - One of the best experts on this subject based on the ideXlab platform.
-
In situ observation of a soap-film Catenoid-a simple educational physics experiment
European Journal of Physics, 2010Co-Authors: Masato Ito, Taku SatoAbstract:The solution to the Euler–Lagrange equation is an extremal functional. To understand that the functional is stationary at local extrema (maxima or minima), we propose a physics experiment that involves using a soap film to form a Catenoid. A Catenoid is a surface that is formed between two coaxial circular rings and is classified mathematically as a minimal surface. Using the soap film, we create Catenoids between two rings and characterize the Catenoid in situ while varying the distance between the rings. The shape of the soap film is very interesting and can be explained using dynamic mechanics. By observing the Catenoid, physics students can observe local extrema phenomena. We stress that in situ observation of soap-film Catenoids is an appropriate physics experiment that combines theory and experimentation.
-
In-situ observation of a soap film Catenoid - a simple educational physics experiment
arXiv: Classical Physics, 2007Co-Authors: Masato Ito, Taku SatoAbstract:The solution to the Euler-Lagrange equation is an extremal functional.To understand that the functional is stationary at local extrema (maxima or minima), we propose a physics experiment that involves using soap film to form a Catenoid. A Catenoid is a surface that is formed between two coaxial circular rings and is classified mathematically as a minimal surface.Using soap film, we create Catenoids between two rings and characterize the Catenoid in-situ while varying distance between rings. The shape of the soap film is very interesting and can be explained using dynamic mechanics. By observing Catenoid, physics students can observe local extrema phenomena. We stress that in-situ observation of soap film Catenoids is an appropriate physics experiment that combines theory and experimentation.