Related papers: Cyclic Bonds in Branched Polymers
The formation mechanism of ice banding in the system of freezing colloidal suspensions, which is of significance in frost heaving, ice-templating porous materials and biological materials, still remains a mystery. Recently, the theory of…
The mechanics of single-chain stretching and rupture are central to understanding the resilience of biological polymers and designing strong and tough soft materials such as double-network gels and multi-network elastomers. In this work, we…
To establish the bond-site duality of explosive percolations in 2 dimension, the site and bond explosive percolation models are carefully defined on a square lattice. By studying the cluster distribution function and the behavior of the…
We analyze the fragmentation behavior of random clusters on the lattice under a process where bonds between neighboring sites are successively broken. Modeling such structures by configurations of a generalized Potts or random-cluster model…
Bonded knots arise naturally in topological protein modeling, where intramolecular interactions such as disulfide bridges stabilize folded configurations. These structures extend classical knot theory by incorporating embedded graphs, and…
This article discusses recent attempts to provide a deeper understanding of the thermoreversible "gel" state of colloidal matter and to unravel the analogies between gels at the colloidal level and gels at the molecular level, commonly…
In this chapter, a study of the glass transitions in colloidal systems is presented, in connection with gelation, mainly from theoretical and simulation results. Mode Coupling Theory, which anticipated the existence of attraction driven…
Message passing, also known as belief propagation, is a versatile framework for analyzing models defined on graphs. Its most prototypical application is percolation; yet, the interpretation of the message passing formulation of percolation…
We exhibit two instances of the cyclic sieving phenomenon - one on dissections of a polygon of a fixed type and one on triangulations of a once-punctured polygon. We use these results to give refined enumerations of certain families of…
We adopt the point of view that analysis of the stability of the protein folding process is central to understanding the underlying physics of folding. Stability of the folding process means that many perturbations do not disrupt the…
The art of tying knots is exploited in nature and occurs in multiple applications ranging from being an essential part of scouting programs to engineering molecular knots. Biomolecular knots, such as knotted proteins, bear various cellular…
We study the spontaneous nucleation and crystallization of linear and cyclic chains of flexibly connected hard spheres using extensive molecular dynamics simulations. To this end, we present a novel event-driven molecular dynamics…
We perform computer simulations of mechanically linked (poly[2]catenanes, PC) and chemically bonded (bonded rings, BR) pairs of self-avoiding ring polymers in steady shear. We find that BR's develop a novel motif, termed gradient tumbling,…
Percolation in complex networks is viewed as both: a process that mimics network degradation and a tool that reveals peculiarities of the underlying network structure. During the course of percolation, networks undergo non-trivial…
The prototypical Hydrogen bond in water dimer and Hydrogen bonds in the protonated water dimer, in other small molecules, in water cyclic clusters, and in ice, covering a wide range of bond strengths, are theoretically investigated by…
Ring, or cyclic, polymers have unique properties compared to linear polymers, due to their topologically closed structure that has no beginning or end. Experimental measurements on molecular ring polymers are challenging due to their…
We introduce a theory of chemical bond with a corpuscular picture of electrons. It employs a minimal set of localized electron wave packets with 'floating and breathing' degrees of freedom and the spin-coupling of non-orthogonal…
The importance of nonlinearities in material constitutive relations has long been appreciated in the continuum mechanics of macroscopic rods. Although the moment (torque) response to bending is almost universally linear for small deflection…
The random-cluster model, a correlated bond percolation model, unifies a range of important models of statistical mechanics in one description, including independent bond percolation, the Potts model and uniform spanning trees. By…
The addition of enough non-adsorbing polymer to an otherwise stable colloidal suspension gives rise to a variety of phase behavior and kinetic arrest due to the depletion attraction induced between the colloids by the polymers. We report a…