Applications of Graph Products and Canonical Forms in Structural Mechanics: A Review

2011 ◽  
pp. 157-186
Author(s):  
A. Kaveh ◽  
H. Rahami
Keyword(s):  
Structural Mechanics ◽  
Canonical Forms ◽  
Graph Products

A hybrid flipped-learning model and a new learning-space to improve the performance of students in Structural Mechanics courses

2020 ◽  
Author(s):  
Miguel X. Rodriguez-Paz ◽  
Jorge A. Gonzalez-Mendivil ◽  
J. Asuncion Zarate-Garcia ◽  
Israel Zamora-Hernandez ◽  
Juan Arturo Nolazco-Flores
Keyword(s):  
Structural Mechanics ◽  
Learning Model ◽  
Flipped Learning ◽  
Learning Space ◽  
New Learning

scholarly journals Stringy canonical forms and binary geometries from associahedra, cyclohedra and generalized permutohedra

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Song He ◽  
Zhenjie Li ◽  
Prashanth Raman ◽  
Chi Zhang
Keyword(s):  
Large Class ◽  
Configuration Space ◽  
Moduli Space ◽  
Cluster Algebras ◽  
Configuration Spaces ◽  
Minkowski Sum ◽  
Canonical Forms ◽  
Infinite Class ◽  
Special Cases ◽  
Generalized Associahedra

Abstract Stringy canonical forms are a class of integrals that provide α′-deformations of the canonical form of any polytopes. For generalized associahedra of finite-type cluster algebras, there exist completely rigid stringy integrals, whose configuration spaces are the so-called binary geometries, and for classical types are associated with (generalized) scattering of particles and strings. In this paper, we propose a large class of rigid stringy canonical forms for another class of polytopes, generalized permutohedra, which also include associahedra and cyclohedra as special cases (type An and Bn generalized associahedra). Remarkably, we find that the configuration spaces of such integrals are also binary geometries, which were suspected to exist for generalized associahedra only. For any generalized permutohedron that can be written as Minkowski sum of coordinate simplices, we show that its rigid stringy integral factorizes into products of lower integrals for massless poles at finite α′, and the configuration space is binary although the u equations take a more general form than those “perfect” ones for cluster cases. Moreover, we provide an infinite class of examples obtained by degenerations of type An and Bn integrals, which have perfect u equations as well. Our results provide yet another family of generalizations of the usual string integral and moduli space, whose physical interpretations remain to be explored.

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