• Journal for History of Mathematics
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• v.21 no.3
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• pp.1-30
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• 2008

The success of Newton's Gravitational Theory has influenced the theory of capillarity, beginning in the early nineteenth century, by providing a major model of molecular attraction. He used the equation of the attraction of spheroids, which is expressed by second order partial differential equations, to utilize this analogy as the same kind of a particle's force, between gravitational, refractive force of light, and capillarity. The solution of the differential equation corresponds to the geometrical figure of the vessel and the contact angle which is made by the fluid. Unknown abstract functions $\varphi(f)$ represent interaction forces between molecules, giving their potential functions. By conducting several kinds of experimental conditions, it was found that the height of the ascending fluid in the tube is inversely proportional to the rayon of the tube or the distance of the plate. This model is an essential element in the theory of capillarity. Laplace has brought Newtonian mechanics to completion, which relates to the standard model of gravitational theory. Laplace-Young's equation of capillarity is applicable to minimal surfaces in mathematics, to surface tensional phenomena in physics, and to soap bubble experiments.

• Journal of Mechanical Science and Technology
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• v.19 no.2
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• pp.625-633
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• 2005

A finite element vibration analysis of thin-walled cylindrical shells conveying fluid with uniform velocity is presented. The dynamic behavior of thin-walled shell is based on the Sanders' theory and the fluid in cylindrical shell is considered as inviscid and incompressible so that it satisfies the Laplace's equation. A beam-like shell element is used to reduce the number of degrees-of-freedom by restricting to the circumferential modes of cylindrical shell. An estimation of frequency response function of the pipe considering of the coupled effects of the internal fluid is presented. A dynamic coupling condition of the interface between the fluid and the structure is used. The effective thickness of fluid according to circumferential modes is also discussed. The influence of fluid velocity on the frequency response function is illustrated and discussed. The results by this method are compared with published results and those by commercial tools.

• Advances in concrete construction
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• v.15 no.3
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• pp.171-178
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• 2023

Cytoskeleton components play key role in maintaining cell structure and in giving shape to the cell. These components include microtubules, microfilaments and intermediate filaments. Among these filaments intermediate filaments are the most rigid and bear large compressive force. Actually, these filaments are surrounded by other filaments like microtubules and microfilaments. This network of filaments makes a layer as a surface on intermediate filaments that have great impact on buckling behavior of intermediate filaments. In the present article, buckling behavior of intermediate filaments is studied by taking into account the effects of surface by using Euler Bernoulli and Timoshenko beam theories. It is found that effects of surface greatly affect the critical buckling force of intermediate filaments. Further, it is observed that the critical buckling force is inversely proportional to the length of filament. Such types of observations are helpful for further analysis of nanofibrous in their actual environments within the cell.

• Journal of Ocean Engineering and Technology
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• v.23 no.1
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• pp.16-23
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• 2009

The three-dimensional ship motion with forward speed was solved by a finite element method in the time domain. A boundary value problem was described in the frame of a fixed-body reference, and the problem was formulated according to Double-Body and Neumann-Kelvin linearizations. Laplace's equation with boundary conditions was solved by a classical finite element method based on the weak formulation. Chebyshev filtering was used to get rid of an unwanted saw-tooth wave and a wave damping zone was adopted to impose a numerical radiation condition. The time marching of the free surface was performed by the 4th order Adams-Bashforth-Moulton method. Wigley I and Wigely III models were considered for numerical validation. The hydrodynamic coefficients and wave exciting forces were validated by a comparison with experimental data and the numerical results of the Wigley I. The effects of the linearization are also discussed. The motion RAO was also checked with a Wigley III model through mono-chromatic and multi-chromatic regular waves.