Explicit Determination in $$\mathbb {R} ^{N}$$RN of $$(N-1)$$(N-1)-Dimensional Area Minimizing Surfaces with Arbitrary Boundaries

2019 ◽  
Vol 30 (1) ◽  
pp. 601-616
Author(s):  
Harold R. Parks ◽  
Jon T. Pitts
Keyword(s):  
Area Minimizing ◽  
Explicit Determination

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.

Discs area-minimizing in mean convex Riemannian n-manifolds

2021 ◽  
pp. 1-22
Author(s):  
Ezequiel Barbosa ◽  
Franciele Conrado
Keyword(s):  
Scalar Curvature ◽  
Mean Curvature ◽  
Higher Dimensions ◽  
Dimensional Torus ◽  
Rigidity Result ◽  
Equality Case ◽  
Totally Geodesic ◽  
Zero Degree ◽  
Area Minimizing ◽  
Mean Convex

In this work, we consider oriented compact manifolds which possess convex mean curvature boundary, positive scalar curvature and admit a map to $\mathbb {D}^{2}\times T^{n}$ with non-zero degree, where $\mathbb {D}^{2}$ is a disc and $T^{n}$ is an $n$ -dimensional torus. We prove the validity of an inequality involving a mean of the area and the length of the boundary of immersed discs whose boundaries are homotopically non-trivial curves. We also prove a rigidity result for the equality case when the boundary is strongly totally geodesic. This can be viewed as a partial generalization of a result due to Lucas Ambrózio in (2015, J. Geom. Anal., 25, 1001–1017) to higher dimensions.

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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