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Physical and numerical models in knot theory : including applications to the life sciences /

The physical properties of knotted and linked configurations in space have long been of interest to mathematicians. More recently, these properties have become significant to biologists, physicists, and engineers among others. Their depth of importance and breadth of application are now widely appre...

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Други автори: Calvo, Jorge Alberto, 1971-
Формат: Електронна книга
Език: English
Публикувано: Hackensack, N.J. : World Scientific, ℗♭2005.
Серия: K & E series on knots and everything ; v. 36.
Предмети:
Knot theory.
N¿“uds, Theorie des.
MATHEMATICS > Topology.
Electronic books.
Онлайн достъп: http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=174667
Подобни документи: Print version:: Physical and numerical models in knot theory.
Съдържание:
  • Cover
  • Contents
  • Preface
  • Chapter 1 On the Theory of Solid Knots Otto Krotenheerdt and Sigrid Veit (translated by Ted Ashton)
  • 1. Problem Statement and Results
  • 2. A Lemma about Polygonal Knots
  • 3. Solid Knots Made of Congruent Components
  • 4. Solid Knots of Uniform Thickness d
  • References
  • Chapter 2 A Tutorial on Knot Energies E.J. Janse van Rensburg
  • 1. Introduction to Knot Energies
  • 2. Examples of Knot Energies
  • 3. Properties of Knot Energies: Polygonal Knots
  • 4. Thickness Energies
  • 5. Conclusions
  • References
  • Chapter 3 Universal Energy Spectrum of Tight Knots and Links in Physics Roman V. Buniy and Thomas W. Kephart
  • 1. Introduction
  • 2. Review of previous physical results on tight knots and links
  • 3. Exact calculations
  • 4. Plasma physics
  • 4.1. Magnetic relaxation
  • 4.2. Abelian helicity
  • 4.3. Non-abelian helicity
  • 4.4. "Freeze-in8221; condition
  • 5. QCD and Glueballs
  • 5.1. QCD
  • 5.2. Knot energies
  • 5.3. Model
  • 6. Discussion and conclusions
  • References
  • Chapter 4 Knot Dynamics in a Driven Hanging Chain: Experimental Results Andrew Belmonte
  • 1. Introduction
  • 2. Our Experimental System
  • 2.1. Spontaneous Knots
  • 3. How Long is a Knot?
  • 3.1. Previous Work
  • 3.2. Open Knot Length in Our Chain
  • 4. Untying Dynamics: Dependence on Knot Type
  • 5. Conclusions
  • Acknowledgments
  • References
  • Chapter 5 Biarcs, Global Radius of Curvature, and the Computation of Ideal Knot Shapes (4 color plates) M. Carlen, B. Laurie, J.H. Maddocks and J. Smutny
  • 1. Introduction
  • 2. Criteria for the assessment of closeness to ideality
  • 3. Why compute with Biarcs?
  • 4. Simulated annealing with biarcs
  • 5 . Results for the 3.1-knot
  • 5.1. The numbers
  • 5.2. The shape
  • 5.3. The contact sets
  • 6. Results for the 4.1-knot
  • 6.1. The numbers
  • 6.2. The shape
  • 6.3. The contact sets
  • 7. Discussion
  • References
  • Chapter 6 Knotted Umbilical Cords (2 color plates) Alain Goriely
  • 1. Introduction
  • 2. Description
  • 3. Knots
  • 4. History
  • 5. Knotting frequency
  • 6. Contributing factors
  • 7. A simple model
  • 8. Clinical significance
  • 9. Complex and multiple knots
  • 10. Handedness and perversion
  • 11. Conclusions
  • Acknowledgments
  • References
  • Chapter 7 Modelling DNA as a Flexible Thick Polymer: DNA Elasticity and Packaging Thermodynamics Cristian Micheletti and Davide Marenduzzo
  • 1. Introduction
  • 2. The model
  • 3. Persistence length & Stretching curves
  • 4. Loading curves & DNA packaging
  • 5. Perspectives and Conclusions
  • Acknowledgments
  • References
  • Chapter 8 Monte-Carlo Simulations of Gel-Electrophoresis of DNA Knots C. Weber, M. Fleurant, P. De Los Rios and G. Dietler
  • 1. Introduction
  • 2. Methods
  • 3. Results
  • 4. Conclusion
  • Acknowledgments
  • References
  • Chapter 9 Atomic Force Microscopy of Complex DNA Knots F. Valle, M. Favre, J . Roca and G. Dietler
  • 1. Introduction
  • 2. Methods
  • 3. Characterization of the conformation of a DNA molecule bound to a surface
  • 4. Images of knotted DNA
  • Acknowledgments
  • References
  • Chapter 10 Protein Folds, Knots and Tangles William R. Taylor
  • 1. Introduction
  • 2. The 'Topol.

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