A Monte Carlo analysis of percolation of line-segments on a square lattice. Abstract We study the percolative properties of bi-dimensional systems generated by a random sequential adsorption of line-segments on a square lattice. As the segment length grows, the percolation threshold decreases , goes through a minimum and then increases slowly for large segments. We explain this non-monotonic be...

Equivariant bifurcation theory has been used extensively to study pattern formation via symmetry–breaking steady state bifurcation in various physical systems modeled by E(2)– equivariant partial differential equations. Much attention has focussed on solutions that are doubly–periodic with respect to a square or hexagonal lattice, for which the bifurcation problem can be restricted to a finite–...

the purpose of this paper is the generalization of structure factor for rods by polygon section in two dimensional phononic crystals. if we use the plane wave expansion method (pwe) for the propagation of acoustic waves in 2d phononic crystals, structure factor will be an important quantity. in order to confirm the obtained relations, we have calculated the band structure for xy and z vibration...

We show that the operations of permuting columns and rows separately and independently mix a square matrix in constant time.

Self-consistent solutions to a generalized Su-Schrieffer-Heeger model on a 2-dimensional square lattice are investigated. Away from half-filling, spatially inhomogeneous phases are found. Those phases may have topological structures on the flux order, large unit cell bond order, localized bipolarons, or they are simply short-range ordered and glassy. They have an universal feature of always pos...

The Constrained-degree percolation model was introduced in de Lima et al. (2020), where it proven that this has a non-trivial phase transition on square lattice. We study the d-dimensional hypercubic lattice (Zd) and, via numerical simulations, found evidence critical time tcd(k) is monotonous not increasing constrained k if d=3,4, like when d=2. verify lowest value such system exhibits k=3 and...

By using a two-dimensional phase-field-crystal (PFC) model, the liquid crystalline growth of the plastic triangular phase is simulated with emphasis on crystal shape and topological defect formation. The equilibrium shape of a plastic triangular crystal (PTC) grown from an isotropic phase is compared with that grown from a columnar or smectic-A (CSA) phase. While the shape of a PTC nucleus in t...

The critical behavior of two-dimensional O(N) σ models with N ≤ 2 on the square, triangular, and honeycomb lattices is investigated by an analysis of the strong-coupling expansion of the two-point fundamental Green’s function G(x), calculated up to 21st order on the square lattice, 15th order on the triangular lattice, and 30th order on the honeycomb lattice. For N < 2 the critical behavior is ...

Tracer diffusion in an ordered two-dimensional lattice-gas system with square lattice symmetry is studied theoretically and by means of computer simulations. It is well known that the ordering with c 2 2 symmetry formed in the vicinity of half-filling of lattice sites is due to strong nearest neighbor repulsive interaction. In this case, the tracer migration occurs mainly by elementary displace...