Finiteness effects for spherical boundary conditions: An illustrative calculation

A group-theoretical technique is described whereby a linear system of tensor field equations of arbitrary rank and form, but with spherical or almost spherical boundary conditions, can be represented by an infinite-dimensional matrix equation. The matrix elements are in general radial operators, and formulae are given which enable them to be calculated explicitly. Particular reference is made to geophysical systems, where boundary perturbations, parameter fields and forcing fields may be expressed in terms of convergent series of spherical harmonics, and a truncated matrix of an appropriate finite dimension will represent the system to the desired accuracy.

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Moving and reactive boundary conditions in moving-mesh hydrodynamics

Monthly Notices of the Royal Astronomical Society ◽

10.1093/mnras/staa1031 ◽

2020 ◽

Vol 494 (4) ◽

pp. 4616-4626 ◽

Cited By ~ 2

Author(s):

Logan J Prust

Keyword(s):

Boundary Conditions ◽

Moving Boundary ◽

Initial Conditions ◽

Moving Boundaries ◽

Moving Mesh ◽

Test Cases ◽

Conserved Quantities ◽

Common Envelope ◽

Gravitational Forces ◽

Spherical Boundary

ABSTRACT We outline the methodology of implementing moving boundary conditions into the moving-mesh code manga. The motion of our boundaries is reactive to hydrodynamic and gravitational forces. We discuss the hydrodynamics of a moving boundary as well as the modifications to our hydrodynamic and gravity solvers. Appropriate initial conditions to accurately produce a boundary of arbitrary shape are also discussed. Our code is applied to several test cases, including a Sod shock tube, a Sedov–Taylor blast wave, and a supersonic wind on a sphere. We show the convergence of conserved quantities in our simulations. We demonstrate the use of moving boundaries in astrophysical settings by simulating a common envelope phase in a binary system, in which the companion object is modelled by a spherical boundary. We conclude that our methodology is suitable to simulate astrophysical systems using moving and reactive boundary conditions.

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Use of the Magnetostatic Analogue In Electromagnetic Lens Engineering

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100068795 ◽

1970 ◽

Vol 28 ◽

pp. 360-361

Author(s):

John W. Coleman

Keyword(s):

Boundary Conditions ◽

High Performance ◽

Force Fields ◽

Optical Design ◽

Direct Conversion ◽

Design Engineering ◽

Design Data ◽

Scalar Potentials ◽

Geometric Elements ◽

At Will

In the design engineering of high performance electromagnetic lenses, the direct conversion of electron optical design data into drawings for reliable hardware is oftentimes difficult, especially in terms of how to mount parts to each other, how to tolerance dimensions, and how to specify finishes. An answer to this is in the use of magnetostatic analytics, corresponding to boundary conditions for the optical design. With such models, the magnetostatic force on a test pole along the axis may be examined, and in this way one may obtain priority listings for holding dimensions, relieving stresses, etc..The development of magnetostatic models most easily proceeds from the derivation of scalar potentials of separate geometric elements. These potentials can then be conbined at will because of the superposition characteristic of conservative force fields.

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