Preface ......................................................... v
Chapter 1 Ideal Knots and Their Relation to the Physics of
Real Knots ........................................... 1
(6 colour plates)
A. Stasiak, J. Dubochet, V. Katritch and
P. Pieranski
Chapter 2 In Search of Ideal Knots ............................ 20
P. Pieranski
Chapter 3 Annealing Ideal Knots and Links: Methods and
Pitfalls ............................................ 42
(2 colour plates)
B. Laurie
Chapter 4 Knots with Minimal Energies ......................... 52
Y. Diao, C. Ernst and E.J. Janse van Rensburg
Chapter 5 The Writhe of Knots and Links ....................... 70
E.J. Janse van Rensburg, D.W. Summers and
S.G. Whittington
Chapter 6 Minimal Lattice Knots ............................... 88
E.J. Janse van Rensburg
Chapter 7 Minimal Edge Piecewise Linear Knots ................ 107
J.A. Calvo and К.C. Millett
Chapter 8 Entropy of a Knot: Simple Arguments About
Difficult Problem .................................. 129
A.Yu. Grosberg
Chapter 9 Approximating the Thickness of a Knot .............. 143
(4 colour plates)
E.J. Rawdon
Chapter 10 Energy Functions for Knots: Beginning to Predict
Physical Behaviour ................................. 151
(2 colour plates)
J. Simon
Chapter 11 Physically-Based Stochastic Simplification of
Mathematical Knots ................................. 183
R.P. Grzeszczuk, M. Huang and L.H. Kauffman
Colour Plates ................................................. 207
Chapter 12 Knots and Fluid Dynamics ........................... 223
H.K. Moffatt
Chapter 13 Knots in Bistable Reacting Systems ................. 234
(1 colour plate)
A. Malevanets and R. Kapral
Chapter 14 New Developments in Topological Fluid Mechanics:
From Kelvin's Vortex Knots to Magnetic Knots ....... 255
R.L. Ricca
Chapter 15 Hamiltonian Approach to Knotted Solitons ........... 274
A.J. Niemi
Chapter 16 Energy of Knots .................................... 288
J. O'Hara
Chapter 17 Möbius-Invariant Knot Energies ..................... 315
R.B. Kusner and J.M. Sullivan
Chapter 18 An Introduction to Harmonic Knots .................. 353
A.K. Trautwein
Chapter 19 Fourier Knots ...................................... 364
L.H. Kauffman
Chapter 20 Symmetric Knots and Billiard Knots ................. 374
J. Przytycki
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