We present recent simulations on charged polymers in poor solvent in the dilute concentration range, with and without imposed extension constraints. The resulting pearl-necklace polymer conformations are analyzed in detail. We find strong pearl number and size fluctuations leading only to minimal signatures in the form factor and the force-extension relation. We see no sign of instability of th...

A one-dimensional assembly of cadmium sulfide (CdS) nanoparticles was prepared by using functionalized polymers with pendant Fréchet-type dendritic wedges of different generation. The novel dendronized polymers acted as both nanoreactors for the formation of CdS nanoparticles and a template to arrange the nanoparticles into a necklace. The polymers of different dendron generation were applied t...

We study a hierarchical approach for modeling deformable necklaces. A recent paper by Guibas et al. [5] introduced two hierarchies, wrapped and layered. They proved that the wrapped hierarchy admits a separating family of size O(n2−2/d). The main result of this paper is that the same bound holds for the layered hierarchy. The layered hierarchy has some advantages compared with wrapped hierarchy...

We show that wetting properties crucially control the patterns in two-phase flows of immiscible fluids in microchannels. Ordered patterns, continuously entrained by the flow, are obtained when one phase completely wets the walls, while disordered patterns, intermittently adhering to the channel walls, are unavoidably produced when wetting is partial. A lower limit for the channel sizes capable ...

We introduce novel classes of higher-order spatial optical solitons in analogy with Laguerre-Gaussian and Hermite-Gaussian linear eigenmodes. We reveal that stable higher-order optical solitons can exist in nonlocal nonlinear media in the various forms of soliton necklaces and soliton matrices. Modulational instability can lead to nontrivial transformations between energetically close solitons ...

Given a length m string f over a k-ary alphabet and a positive integer n, we develop eecient algorithms to generate (a) all k-ary strings of length n that have no substring equal to f, (b) all k-ary circular strings of length n that have no substring equal to f, and (c) all k-ary necklaces of length n that have no substring equal to f, where f is an aperiodic necklace. Each of the algorithms ru...

The notion of polytopal map between two polytopal complexes is defined. Surprisingly, this definition is quite simple and extends naturally those of simplicial and cubical maps. It is then possible to define an induced chain map between the associated chain complexes. Finally, we use this new tool to give the first combinatorial proof of the splitting necklace theorem of Alon. The paper ends wi...

Abstract. We discuss a pair of isoperimetric problems which at a glance seem to be unrelated. The first one is classical: one places N identical point charges at a closed curve Γ at the same arc-length distances and asks about the energy minimum, i.e. which shape does the loop take if left by itself. The second problem comes from quantum mechanics: we take a Schrödinger operator in L(R), d = 2,...