Total Curvature and Total Torsion of Knotted Polymers
نویسندگان
چکیده
منابع مشابه
Total Curvature and Total Torsion of Knotted Polymers
Previous work on radius of gyration and average crossing number has demonstrated that polymers with fixed topology show a different scaling behavior with respect to these characteristics than polymers with unrestricted topology. Using numerical simulations, we show here that the difference in the scaling behavior between polymers with restricted and unrestricted topology also applies to the tot...
متن کاملThe Total Curvature of a Knotted Curve
1. We are indebted to W. Fenchel [5] for a theorem which is a left closed curve (in ordinary space) has total curvature ≥ 2π. Recently, K. Borsuk [3] gave a new proof of this theorem that applies to curves in R. In a note at the end of this paper, Borsuk asked the question wheter the total curvature of a left knotted curve is always ≥ 4π. The primary purpose of this note is to give an affirmati...
متن کاملRegular Homotopy and Total Curvature
We consider properties of the total absolute geodesic curvature functional on circle immersions into a Riemann surface. In particular, we study its behavior under regular homotopies, its infima in regular homotopy classes, and the homotopy types of spaces of its local minima. We also consider the total curvature functional on the space of 2-sphere immersions into 3-space in a similar spirit. We...
متن کاملCurves, Knots, and Total Curvature
Charles Evans We present an exposition of various results dealing with the total curvature of curves in Euclidean 3-space. There are two primary results: Fenchel’s theorem and the theorem of Fary and Milnor. Fenchel’s theorem states that the total curvature of a simple closed curve is greater than or equal to 2π, with equality if and only if the curve is planar convex. The Fary-Milnor theorem s...
متن کاملTotal Curvature and Packing of Knots
We establish a new fundamental relationship between total curvature of knots and crossing number. If K is a smooth knot in R3, R the cross-section radius of a uniform tube neighborhood K, L the arclength of K, and κ the total curvature of K, then (up to some coefficient), crossing number of K ≤ L R κ . The proof generalizes to show that for smooth knots in R3, the crossing number, writhe, Möbiu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Macromolecules
سال: 2007
ISSN: 0024-9297,1520-5835
DOI: 10.1021/ma0627673