scholarly journals Periodic Rigidity on a Variable Torus Using Inductive Constructions

10.37236/2212 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Anthony Nixon ◽  
Elissa Ross
Keyword(s):  
Rigidity Theory ◽  
Periodic Graph ◽  
Gain Graphs ◽  
Generic Rigidity ◽  
Periodic Frameworks

In this paper we prove a recursive characterisation of generic rigidity for frameworks periodic with respect to a partially variable lattice. We follow the approach of modelling periodic frameworks as frameworks on a torus and use the language of gain graphs for the finite counterpart of a periodic graph. In this setting we employ variants of the Henneberg operations used frequently in rigidity theory.

Glossary of Signed and Gain Graphs

10.37236/31 ◽  
2002 ◽  
Vol 1000 ◽  
Author(s):  
Thomas Zaslavsky
Keyword(s):  
Gain Graphs

A glossary to accompany DS8.

Hybrid rigidity theory with signed constraints and its application to formation shape control in 2-D space

2020 ◽  
Author(s):  
Seong-Ho Kwon ◽  
Zhiyong Sun ◽  
Brian D. O. Anderson ◽  
Hyo-Sung Ahn
Keyword(s):  
Shape Control ◽  
Rigidity Theory

A New Split Charge Equilibration Model and REPEAT Electrostatic Potential Fitted Charges for Periodic Frameworks with a Net Charge

2017 ◽  
Vol 13 (6) ◽  
pp. 2858-2869 ◽  
Author(s):  
Mykhaylo Krykunov ◽  
Christopher Demone ◽  
Jason W.-H. Lo ◽  
Tom K. Woo
Keyword(s):  
Electrostatic Potential ◽  
Net Charge ◽  
Charge Equilibration ◽  
Periodic Frameworks ◽  
Equilibration Model

Predicting Protein Hinge Motions and Allostery Using Rigidity Theory

2011 ◽  
Author(s):  
Adnan Sljoka ◽  
Alexandr Bezginov ◽  
Ilias Kotsireas ◽  
Roderick Melnik ◽  
Brian West
Keyword(s):  
Rigidity Theory

scholarly journals Geometric auxetics

2015 ◽  
Vol 471 (2184) ◽  
pp. 20150033 ◽  
Author(s):  
Ciprian Borcea ◽  
Ileana Streinu
Keyword(s):  
Computer Simulations ◽  
Mathematical Theory ◽  
Three Dimensional ◽  
Numerical Approximations ◽  
Periodic Frameworks ◽  
Infinite Supply

We formulate a mathematical theory of auxetic behaviour based on one-parameter deformations of periodic frameworks. Our approach is purely geome- tric, relies on the evolution of the periodicity lattice and works in any dimension. We demonstrate its usefulness by predicting or recognizing, without experiment, computer simulations or numerical approximations, the auxetic capabilities of several well-known structures available in the literature. We propose new principles of auxetic design and rely on the stronger notion of expansive behaviour to provide an infinite supply of planar auxetic mechanisms and several new three-dimensional structures.

scholarly journals Irreducibility of the Fermi surface for planar periodic graph operators

2020 ◽  
Vol 110 (9) ◽  
pp. 2543-2572
Author(s):  
Wei Li ◽  
Stephen P. Shipman
Keyword(s):  
Fermi Surface ◽  
Periodic Graph

On Generic Rigidity in the Plane

1982 ◽  
Vol 3 (1) ◽  
pp. 91-98 ◽  
Author(s):  
L. Lovász ◽  
Y. Yemini
Keyword(s):  
Generic Rigidity

scholarly journals Criteria for Balance in Abelian Gain Graphs, with Applications to Piecewise-Linear Geometry

2005 ◽  
Vol 34 (2) ◽  
pp. 251-268 ◽  
Author(s):  
Konstantin Rybnikov ◽  
Thomas Zaslavsky
Keyword(s):  
Piecewise Linear ◽  
Gain Graphs ◽  
Linear Geometry

scholarly journals A group representation approach to balance of gain graphs

2020 ◽  
Author(s):  
Matteo Cavaleri ◽  
Daniele D’Angeli ◽  
Alfredo Donno
Keyword(s):  
Group Representation ◽  
Gain Graphs
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