The model under consideration is an asymmetric two-dimensional Coulomb gas of positively (q1 = +1) and negatively (q2 = −1/2) charged pointlike particles, interacting via a logarithmic potential. This continuous system is stable against collapse of positive-negative pairs of charges for the dimensionless coupling constant (inverse temperature) β < 4. The mapping of the Coulomb gas is made onto ...

Successful synthesis of the stable metal-free two-dimensional polymer graphitic carbon-nitride with remarkable properties has made it as one of the most promising nanostructures in many novel nanodevices, especially photocatalytic ones. Understanding the mechanical properties of nanostructures is of crucial importance. Thus, this study employs density functional theory (DFT) to obtain the mecha...

We study the Ginzburg-Landau energy of superconductors with high , put in a prescribed external eld h ex , for h ex varying between the two critical elds H c 1 and H c 2. As ! +1, we give the leading term in the asymptotic expansion of the minimal energy and show that energy minimizers have vortices whose density tends to be uniform and equal to h ex. In this paper, we study minimizers of the G...

For an integer s1, s2, s3 > 0, let Ns1,s2,s3 denote the graph obtained by identifying each vertex of a K3 with an end vertex of three disjoint paths Ps1+1, Ps2+1, Ps3+1 of length s1, s2, and s3, respectively. We determine a family F of graphs such that, every 3-connected (K1,3, Ns1,s2,1)-free graph Γ with s1 + s2 + 1 ≤ 10 is hamiltonian if and only if the closure of Γ is L(G) for some graph G /...

In 1906 Axel Thue showed how to construct an infinite non-repetitive (or squarefree) word on an alphabet of size 3. Since then this result has been rediscovered many times and extended in many ways. We present a two-dimensional version of this result. We show how to construct a rectangular tiling of the plane using 5 symbols which has the property that lines of tiles which are horizontal, verti...