Torsion of a Shaft with a Toroidal Cavity

  title={Torsion of a Shaft with a Toroidal Cavity},
  author={George Weiss and Lawrence Edward Payne},
  journal={Journal of Applied Physics},
This paper gives the solution to the torsion problem for a near‐cylindrical shaft of circular section having a toroidal cavity. Since the interpretation of the axially symmetric problem as a flow problem in 5 dimensions is well known, the first part of the paper is devoted to developing a method for handling the flow problem about an n dimensional ring‐shaped body of general cross section. In the second part of the paper this method is applied to the case of an n dimensional torus ring. The… 
Three Part Boundary Value Problems in Potential and Axially Symmetric Generalised Potential Theories with Some Applications in Elasticity and Fluid Dynamics. II
Three part and generalised three part boundary value problems in potential theories and related problems are considered for the case of an annular spherical cap shaped lamina when the difference
Hydrodynamic friction and the capacitance of arbitrarily shaped objects.
  • Douglas, Zhou, Hubbard
  • Physics
    Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
  • 1994
The translational friction coefficient and the capacitance of a variety of objects are calculated with a probabilistic method involving hitting the ``probed'' objects with random walks launched from
Singularity Methods in Mathematical Physics
By considering suitable distributions of the Dirac delta function and its derivatives on lines and curves, solutions are obtained in closed form for various boundary value problems in mathematical
A first-passage algorithm for the hydrodynamic friction and diffusion-limited reaction rate of macromolecules
This paper introduces a first-passage algorithm (FPA) that uses certain exact Green’s functions, or propagators, for the Laplace equation to eliminate the need to construct explicitly those portions of a diffusing particle's trajectory that are not near an absorbing object.
The iterated equation of generalized axially symmetric potential theory. V. Generalized weinstein correspondence principle
Solutions of the iterated equation of generalized axially symmetric potential theory [1] where the operator L k is defined by will be denoted by except that when n = 1, f k will be written instead of
Hyperspherical caps in generalised axially symmetric potential theory (I)
RésuméLe problème du potentiel généralisé axisymétrique d'un secteur d'une sphère àn dimensions est formulé comme une équation intégrale. Cette équation est résolue par deux applications de la


Theory of elasticity
This book is designed for use by students and teachers in the field of applied mechanics and mathematics, and for practitioners in civil and mechanical engineering. Since tensor calculus is an
Virtual mass and polarization
In this paper we deal with two classical problems of Potential Theory arising in Hydrodynamics and in the Theory of Electricity, respectively. They are the problems of virtual mass and polarization.
The Theory of Spherical and Ellipsoidal Harmonics
Preface 1. The transformation of Laplaces's equation 2. The solution of Laplace's equation in polar coordinates 3. The Legendres associated functions 4. Spherical harmonics 5. Spherical harmonics of
On axially symmetric flow and the method of generalized electrostatics
Scarborough, 2nd edition, pp. 99-103, the mistake arising from identification of two ^-values in the interval which may be distinct.) Consider the given data / (J) — j for j = 0, 1, • • • , n, for