"Regular seven-membered loops with arbitrary join angle in R3"

Dear All,

Mathematical Soft Matter Unit (Fried Unit) would like to invite you to a Seminar by Dr. Barry Cox from University of Adelaide (Australia)

Date: Thursday, November 26th, 2015
Time: 14:00-15:00
Venue: C015, LevelC, Lab 1
 

Speaker:
Dr. Barry Cox
Senior Lecturer in Applied Mathematics
School of Mathematical Sciences
University of Adelaide, Australia

Title:
Regular seven-membered loops with arbitrary join angle in R3

Abstract:
The problem of ring molecules come up in a number of con-
texts in physical chemistry. Perhaps the simplest example of a
seven-membered ring is cycloheptane C7H14, which is a molecule
where the carbon-carbon bonds form a regular seven-membered
loop. However it is possible to envisage more complicated ar-
rangements of proteins chains comprising straight rigid sections
linked in a way that enforces the same angles at all of the joins.
This work is also applicable in the _eld of robotics where such
loops are termed Bricard linkages.
In this talk we present a coordinate system that reduces the
problem to four free variables and three constraints. We then
survey the solutions numerically and _nd that there are families
of solutions for all join angles _ between _=7 and 5_=7 with
_xed planar solutions existing for _ = _=7, 3_=7 and 5_=7.
The available families of solutions undergo an unexpected major
reorganization at the join angle _ = _=3. The nature of the
solutions available at _ = _=3 and their relation to the families
of solution available for other angles will be discussed.