Differential geometry of polymer models: worm-like chains, ribbons and Fourier knots

Semiflexible Chains at Surfaces: Worm-Like Chains and beyond

We give an extended review of recent numerical and analytical studies on semiflexible chains near surfaces undertaken at Institut Charles Sadron (sometimes in collaboration) with a focus on static properties. The statistical physics of thin confined layers, strict two-dimensional (2D) layers and adsorption layers (both at equilibrium with the dilute bath and from irreversible chemisorption) are...

Organized condensation of worm-like chains

We present results relevant to the equilibrium organization of DNA strands of arbitrary length interacting with a spherical organizing center, suggestive of DNA-histone complexation in nucleosomes. We obtain a rich phase diagram in which a wrapping state is transformed into a complex multi-leafed structure as the adhesion energy is reduced. The statistical mechanics of the “melting” of a rosett...

Fourier Knots

This paper introduces the concept of Fourier knot. A Fourier knot is a knot that is represented by a parametrized curve in three dimensional space such that the three coordinate functions of the curve are each finite Fourier series in the parameter. That is, the knot can be regarded as the result of independent vibrations in each of the coordinate directions with each of these vibrations being ...

Worm-like carbon shell chains produced from wood

Coset Models and Differential Geometry *

String propagation on a curved background defines an embedding problem of surfaces in differential geometry. Using this, we show that in a wide class of backgrounds the classical dynamics of the physical degrees of freedom of the string involves 2–dim σ–models corresponding to coset conformal field theories. Contribution to the proceedings of the Conference on Gauge Theories, Applied Supersymme...