Related papers: Ring polymers with topological constraints
A ring polymer is a random walk whose steps obey a single linear condition; their sum vanishes. Factoring the graph Laplacian into the product of the incidence matrix and its transpose allows us to show that for a more complicated network,…
Modeling of polymer chains has received a lot of attention in mathematics. In fact, probabilistic models that naturally arise in statistical mechanics have been widely studied by mathematicians for the very challenging and novel problems…
Circuit topology refers to the arrangement of interactions between objects belonging to a linearly ordered object set. Linearly ordered set of objects are common in nature and occur in a wide range of applications in economics, computer…
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…
We study the thermodynamics and kinetics of folding for a small peptide. Our data rely on Monte Carlo simulations where the interactions among all atoms are taken into account. Monte Carlo kinetics is used to study folding of the peptide at…
Dynamical properties of a long polymer ring in a melt of unknotted and unconcatenated rings are calculated. We re-examine and generalize the well known model of a ring confined to a lattice of topological obstacles in the light of the…
Ring polymers remain a major challenge to our current understanding of polymer dynamics. Experimental results are difficult to interpret because of the uncertainty in the purity and dispersity of the sample. Using both equilibrium and…
The HP model of protein folding, where the chain exists in a free medium, is investigated using a parallel Monte Carlo scheme based upon Wang-Landau sampling. Expanding on the work of Wust and Landau by introducing a lesser known replica…
Knots are entangled structures that cannot be untangled without a cut. Topological stability of knots is one of the many examples of their important properties that can be used in information storage and transfer. Knot dynamics is important…
The dynamics of a polymer ring enclosing a constant {\sl algebraic} area is studied. The constraint of a constant area is found to couple the dynamics of the two Cartesian components of the position vector of the polymer ring through the…
Drawing inspiration from the concept of the "primitive path" of a linear chain in melt conditions, we introduce here a numerical protocol which allows us to detect, in an unambiguous manner, the "primitive shapes" of ring polymers in…
Variational methods are used to calculate structural and thermodynamical properties of a titrating polyelectrolyte in a discrete representation. The Coulomb interactions are emulated by harmonic repulsive forces, the force constants being…
In finite-size scaling analyses of Monte Carlo simulations of second-order phase transitions one often needs an extended temperature range around the critical point. By combining the parallel tempering algorithm with cluster updates and an…
We consider the topologically constrained random walk model for topological polymers. In this model, the polymer forms an arbitrary graph whose edges are selected from an appropriate multivariate Gaussian which takes into account the…
Macromolecules can gain special properties by adopting knotted conformations, but engineering knotted macromolecules is a challenging task. Here we surprisingly observed that knotting can be very effectively produced in active polymers.…
We numerically study Turing patterns (TPs) on two-dimensional surfaces with a square boundary in ${\bf R}^3$ using a surface model for polymerized membranes. The variables used to describe the membranes correspond to two distinct degrees of…
Compact polymers are self-avoiding random walks which visit every site on a lattice. This polymer model is used widely for studying statistical problems inspired by protein folding. One difficulty with using compact polymers to perform…
Ring polymers exhibit unique flow properties due to their closed chain topology. Despite recent progress, we have not yet achieved a full understanding of the nonequilibrium flow behavior of rings in nondilute solutions where intermolecular…
We study the equilibrium shapes of prime and composite knots confined to two dimensions. Using rigorous scaling arguments we show that, due to self-avoiding effects, the topological details of prime knots are localised on a small portion of…
We address here the topological equivalence of knots through the so-called Reidemeister moves. These topology-conserving manipulations are recast into dynamical rules on the crossings of knot diagrams. This is presented in terms of a simple…