Energy functions for knots: Beginning to predict physical behavior

Conference · Tue Dec 31 04:00:00 EST 1996

OSTI ID:495288

Simon, J ^[1]

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1. Univ. of Iowa, Iowa City, IA (United States)

Several definitions have been proposed for the {open_quotes}energy{close_quotes} of a knot. The intuitive goal is to define a number u(K) that somehow measures how {open_quotes}tangled{close_quotes} or {open_quotes}crumpled{close_quotes} a knot K is. Typically, one starts with the idea that a small piece of the knot somehow repels other pieces, and then adds up the contributions from all the pieces. From a purely mathematical standpoint, one may hope to define new knot-type invariants, e.g by considering the minimum of u(K) as K ranges over all the knots of a given knot-type. We also are motivated by the desire to understand and predict how knot-type affects the behavior of physically real knots, in particular DNA loops in gel electrophoresis or random knotting experiments. Despite the physical naivete of recently studied knot energies, there now is enough laboratory data on relative gel velocity, along with computer calculations of idealized knot energies, to justify the assertion that knot energies can predict relative knot behavior in physical systems. The relationships between random knot frequencies and either gel velocities or knot energies is less clear at this time. 50 refs., 8 figs., 2 tabs.

• OSTI ID: 495288
• Report Number(s): CONF-9407205--Vol.82
• Country of Publication: United States
• Language: English

Related Subjects

55 BIOLOGY AND MEDICINE
BASIC STUDIES
99 GENERAL AND MISCELLANEOUS
BEHAVIOR
COMPACTIFICATION
COMPUTER CALCULATIONS
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ELECTROPHORESIS
ENERGY
ENERGY MODELS
INVARIANCE PRINCIPLES
MATHEMATICAL MODELS
MOLECULAR BIOLOGY
MOLECULAR STRUCTURE
MOLECULES
OPTIMIZATION
PHYSICAL PROPERTIES
STRUCTURE-ACTIVITY RELATIONSHIPS
TOPOLOGY
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