scholarly journals A comment on the correct boundary conditions for the Cremer impedance

2021 ◽  
Vol 1 (2) ◽  
pp. 022801
Author(s):  
Mats Åbom ◽  
Stefan Jacob
Keyword(s):  
Boundary Conditions ◽  
Correct Boundary Conditions

A Systematic Asymptotic Expansion Procedure for Slender Ships

1964 ◽  
Vol 8 (03) ◽  
pp. 15-23 ◽  
Author(s):  
E. O. Tuck
Keyword(s):  
Asymptotic Expansion ◽  
Boundary Conditions ◽  
Arbitrary Shape ◽  
Careful Consideration ◽  
Wave Resistance ◽  
Expansion Procedure ◽  
Systematic Solution ◽  
The Individual ◽  
Correct Boundary Conditions

Inner and outer expansions are used to formulate a systematic solution to the problem of the steady translation of a slender ship of arbitrary shape. Careful consideration is givien to finding the correct boundary conditions to be satisfied by successive terms in the expansions, and certain of the individual terms are determined partly or completely as functions of hull shape. Some results are given concerning the second approximations to the potential and wave resistance.

scholarly journals Boundary conditions for approximate differential equations

1992 ◽  
Vol 34 (1) ◽  
pp. 54-80 ◽  
Author(s):  
A. J. Roberts
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Initial Conditions ◽  
Higher Order ◽  
Centre Manifold ◽  
Systematic Fashion ◽  
Model Equations ◽  
Manifold Theory ◽  
Finite Domains ◽  
Correct Boundary Conditions

AbstractA large number of mathematical models are expressed as differential equations. Such models are often derived through a slowly-varying approximation under the assumption that the domain of interest is arbitrarily large; however, typical solutions and the physical problem of interest possess finite domains. The issue is: what are the correct boundary conditions to be used at the edge of the domain for such model equations? Centre manifold theory [24] and its generalisations may be used to derive these sorts of approximations, and higher-order refinements, in an appealing and systematic fashion. Furthermore, the centre manifold approach permits the derivation of appropriate initial conditions and forcing for the models [25, 7]. Here I show how to derive asymptotically-correct boundary conditions for models which are based on the slowly-varying approximation. The dominant terms in the boundary conditions typically agree with those obtained through physical arguments. However, refined models of higher order require subtle corrections to the previously-deduced boundary conditions, and also require the provision of additional boundary conditions to form a complete model.

Front propagation in laser-tweezed lipid bilayer tubules

1996 ◽  
Vol 463 ◽  
Author(s):  
Peter D. Olmsted ◽  
Fred C. Mackintosh
Keyword(s):  
Surface Tension ◽  
Boundary Conditions ◽  
Lipid Bilayer ◽  
Control Parameter ◽  
Laser Intensity ◽  
Front Propagation ◽  
Chemical Potentials ◽  
Unstable Medium ◽  
Lipid Tubules ◽  
Correct Boundary Conditions

AbstractWe study the mechanism of the ‘pearling’ instability seen recently in experiments on lipid tubules under a local applied laser intensity. We argue that the correct boundary conditions are fixed chemical potentials, or surface tensions Σ, at the laser spot and the reservoir in contact with the tubule. While most qualitative conclusions of previous studies remain the same, the ‘ramped’ control parameter (surface tension) implies several new features. We also explore some consequences of front propagation into a noisy unstable medium.

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