5 papers
Application of a two-length scale field theory to the solvation of charged molecules: I. Hydrophobic effect revisited
G. Sitnikov, S. Nechaev, M. Taran +1
On a basis of a two-length scale description of hydrophobic interactions we develop a continuous self-consistent theory of solute-water interactions which allows to determine a hyd…
Topological percolation on a square lattice
S. K. Nechaev, O. A. Vasilyev
We investigate the formation of an infinite cluster of entangled threads in a (2+1)-dimensional system. We demonstrate that topological percolation belongs to the universality clas…
Topological correlations in trivial knots: new arguments in support of the crumpled polymer globule
Sergei Nechaev, Oleg Vasilyev
We prove the fractal crumpled structure of collapsed unknotted polymer ring. In this state the polymer chain forms a system of densely packed folds, mutually separated in all scale…
Random walks on hyperbolic groups and their Riemann surfaces
Sergei Nechaev, Raphael Voituriez
We investigate invariants for random elements of different hyperbolic groups. We provide a method, using Cayley graphs of groups, to compute the probability distribution of the min…
Statistics of knots and entangled random walks
Sergei Nechaev
The lectures review the state of affairs in modern branch of mathematical physics called probabilistic topology. In particular we consider the following problems: (i) We estimate t…