NDLI: On regular seven-membered loops in $${{\mathbb{R}}^3}$$ R 3 with arbitrary join angle

Content Provider	Springer Nature Link
Author	Cox, Barry J.
Copyright Year	2016
Abstract	The problem of ring molecules and macromolecules arises in a number of contexts in physical chemistry. Perhaps the simplest example of a seven-membered loop is cycloheptane $${\rm C_{7}\rm H_{14}}$$ , which is a molecule where the carbon–carbon bonds form a regular seven-membered loop. However, it is possible to envisage much more complicated arrangements of proteins in chains comprising straight rigid sections linked in ways that enforce the same angle at all of the joins. In this paper, we present a coordinate system that reduces the problem to four free variables and three constraints. We then survey the solutions numerically and find that there are families of solutions for all join angles $${\theta}$$ between $${\pi/7}$$ and $${5\pi/7}$$ with fixed planar solutions existing for $${\theta = \pi/7}$$ , $${3\pi/7}$$ and $${5\pi/7}$$ . The available families of solutions undergo a major reorganisation at the join angle $${\theta = \pi/3}$$ , where 28 intersecting solutions form a single connected network of configurations.
Ending Page	17
Page Count	17
Starting Page	1
File Format	PDF
ISSN	00442275
e-ISSN	14209039
Journal	Zeitschrift für angewandte Mathematik und Physik
Issue Number	3
Volume Number	67
Language	English
Publisher	Springer International Publishing
Publisher Date	2016-04-28
Publisher Place	Cham
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Biology, chemistry, medicine Mathematical Methods in Physics Molecular modelling Applied mathematics Cycloheptane Robot dynamics and control Theoretical and Applied Mechanics Robotics Bricard linkage
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Physics and Astronomy

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