相关论文: Conservation of polymer winding states: a combinat…
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…
We extend classical Flory-Rehner theory for the expansion and compression of porous materials such as cross-linked polymer networks. The theory includes volume exclusion, affinity with the solvent, and finite stretching of the polymer…
We study a model of two polymers confined to a slit with sticky walls. More precisely, we find and analyse the exact solution of two directed friendly walks in such a geometry on the square lattice. We compare the infinite slit limit, in…
We study the conformational properties of complex Gaussian polymers containing $f_c$ linear branches and $f_r$ closed loops, periodically tethered at $n$ branching points to either a linear polymer backbone (generalized bottlebrush…
Polymers exposed to shear flow exhibit a rich tumbling dynamics. While rigid rods rotate on Jeffery orbits, flexible polymers stretch and coil up during tumbling. Theoretical results show that in both of these asymptotic regimes the…
We study the interplay between entropy and topological constraints for a polymer chain in which sliding rings (slip-links) enforce pair contacts between monomers. These slip-links divide a closed ring polymer into a number of sub-loops…
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,…
The winding number is a concept in complex analysis which has, in the presence of chiral symmetry, a physics interpretation as the topological index belonging to gapped phases of fermions. We study statistical properties of this topological…
The viscous flow of polymer chains in dense melts is dominated by topological constraints whenever the single chain contour length, N, becomes larger than the characteristic scale Ne, defining comprehensively the macroscopic rheological…
Polymer entanglements lead to complicated topological constraints and interactions between neighbouring chains in a dense solution or melt. Entanglements can be treated in a mean field approach, within the famous reptation model, since they…
We develop a continuum theory to model low energy excitations of a generic four-band time reversal invariant electronic system with boundaries. We propose a variational energy functional for the wavefunctions which allows us derive natural…
It is nontrivial whether the average size of a ring polymer should become smaller or larger under a topological constraint. Making use of some knot invariants, we evaluate numerically the mean square radius of gyration for ring polymers…
In this paper, we consider local moves on classical and welded diagrams of string links, and the notion of welded extension of a classical move. Such extensions being non-unique in general, the idea is to find a topological criterion which…
We present experimental and theoretical results addressing the Reynolds number (Re) dependence of drag reduction by sufficiently large concentrations of rod-like polymers in turbulent wall-bounded flows. It is shown that when Re is small…
I show that random distributions of vortex-antivortex pairs (rather than of individual vortices) lead to scaling of typical winding numbers W trapped inside a loop of circumference C with the square root of C when the expected winding…
It has been shown that under high cylindrical confinement, two ring polymers with excluded volume interactions between monomers, segregate to two halves of the cylinder to maximize their entropy. In contrast, two ring polymers remain mixed…
When injected through a contraction, high molecular weight polymer solutions exhibit a sharp increase of apparent viscosity which originates from stretching polymer chains above a critical extension rate. This chain stretching can also…
We study the computational problem of rigorously describing the asymptotic behaviour of topological dynamical systems up to a finite but arbitrarily small pre-specified error. More precisely, we consider the limit set of a typical orbit,…
Elucidating the physics of a concentrated suspension of ring polymers, or of an ensemble of ring polymers in a complex environment, is an important outstanding question in polymer physics. Many of the characteristic features of these…
We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be…