It is well known that the Lyndon words of length n can be used to construct a basis for the n-th homogeneous component of the free Lie algebra. We develop an algorithm that uses a dynamic programming table to efficiently generate the standard bracketing for all Lyndon words of length n, thus constructing a basis for the n-th homogeneous component of the free Lie algebra. The algorithm runs in l...

A coarse-graining strategy for dilute and semi-dilute solutions of interacting polymers, and of colloid–polymer mixtures, is briefly described. Monomer degrees of freedom are traced out to derive an effective, state-dependent pair potential between the polymer centres of mass. The cross-over between good and poor solvent conditions is discussed within a scaling analysis. The method is extended ...

Host-stabilized charge-transfer (CT) interactions and supramolecular assemblies built with these interactions are described. A variety of supramolecular assemblies including polyrotaxanes, molecular necklaces, and rotaxane dendrimers were synthesized through the intramolecular or intermolecular host-stabilized CT complex formation using cucurbit[8]uril (CB[8]) and D-A molecules having both elec...

We have analyzed the equilibrium response of chain molecules to stretching. For a homogeneous sequence of monomers, the induced transition from compact globule to extended coil below the θ-temperature is predicted to be sharp. For random sequences, however, the transition may be smoothed by a prevalence of necklace-like structures, in which globular regions and coil regions coexist in a single ...

If many micelles adsorb onto the same polymer molecule then they are said to form a necklace. A minimal model of such a necklace is proposed and shown to be almost equivalent to a 1-dimensional fluid with nearest-neighbour interactions. The thermodynamic functions of this fluid are obtained and then used to predict the change in the critical micellar concentration of the surfactant in the prese...