An Explicit Determination of the Non-self-adjoint Wave Equations that Satisfy Huygens’ Principle on Petrov Type III Background Space-times

1997 ◽  
Vol 16 (1) ◽  
pp. 37-58
Author(s):  
W.G. Anderson ◽  
R.G. McLenaghan ◽  
Tom Walton
Keyword(s):  
Wave Equations ◽  
Petrov Type ◽  
Type Iii ◽  
Background Space ◽  
Huygens Principle ◽  
Explicit Determination

An explicit determination of the empty space-times on which the wave equation satisfies Huygens' principle

1969 ◽  
Vol 65 (1) ◽  
pp. 139-155 ◽  
Author(s):  
R. G. McLenaghan
Keyword(s):  
Wave Equation ◽  
Wave Equations ◽  
Empty Space ◽  
Space Time ◽  
Necessary Condition ◽  
Scalar Wave ◽  
Wave Space ◽  
Huygens Principle ◽  
Necessary And Sufficient

AbstractThe validity of Huygens' principle in the sense of Hadamard's ‘minor premise’ is investigated for scalar wave equations on curved space-time. A new necessary condition for its validity in empty space-time is derived from Hadamard's necessary and sufficient condition using a covariant Taylor expansion in normal coordinates. A two component spinor calculus is then employed to show that this necessary condition implies that the plane wave space-times and Minkowski space are the only empty space-times on which the scalar wave equation satisfies Huygens' principle.

A Hybrid Highly Parallelizable Algorithm for the Dynamics of Rigid Body Chain Systems

1999 ◽  
Author(s):  
Shanzhong Duan ◽  
Kurt S. Anderson
Keyword(s):  
Rigid Body ◽  
Degrees Of Freedom ◽  
High Efficiency ◽  
Equations Of Motion ◽  
Constraint Forces ◽  
Dynamics Of Rigid Body ◽  
A Chain ◽  
Explicit Determination ◽  
Order Algorithm

Abstract The paper presents a new hybrid parallelizable low order algorithm for modeling the dynamic behavior of multi-rigid-body chain systems. The method is based on cutting certain system interbody joints so that largely independent multibody subchain systems are formed. These subchains interact with one another through associated unknown constraint forces f¯c at the cut joints. The increased parallelism is obtainable through cutting the joints and the explicit determination of associated constraint loads combined with a sequential O(n) procedure. In other words, sequential O(n) procedures are performed to form and solve equations of motion within subchains and parallel strategies are used to form and solve constraint equations between subchains in parallel. The algorithm can easily accommodate the available number of processors while maintaining high efficiency. An O[(n+m)Np+m(1+γ)Np+mγlog2Np](0<γ<1) performance will be achieved with Np processors for a chain system with n degrees of freedom and m constraints due to cutting of interbody joints.

Two new measurement methods for explicit determination of complex permittivity

1998 ◽  
Vol 46 (11) ◽  
pp. 1614-1619 ◽  
Author(s):  
C. Wan ◽  
B. Nauwelaers ◽  
W. De Raedt ◽  
M. Van Rossum
Keyword(s):  
Complex Permittivity ◽  
Measurement Methods ◽  
Explicit Determination
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