Simple pair potentials are constructed which give hexagonal-or square-lattice ground states in two dimensions, depending on the value of a single parameter controlling the width of the potential well. Molecular dynamics calculations for free clusters of a few hundred particles are used to examine a structural transition from the square lattice, at low temperatures, to the hexagonal lattice at h...

The Taylor series expansionand least-square-based Lattice Boltzmann method (TLLBM) is a flexible Lattice Boltzmann approach capable of simulating incompressible viscous flows with arbitrary geometry. The method is based on the standard Lattice Boltzmann equation (LBE), Taylor series expansion and the least square optimisation. The final formulation is an algebraic form and essentially has no li...

Based on rigorous theoretical findings, we present a proof-of-concept design for a structured square cloak enclosing a void in an elastic lattice. We implement high-precision fabrication and experimental testing of an elastic invisibility cloak for flexural waves in a mechanical lattice. This is accompanied by verifications and numerical modelling performed through finite element simulations. T...

In this paper, the study of bond percolation on the square lattice is explored. In particular, the probability at which there exist infinite clusters on an inhomogeneous model of the square lattice is proven from the basics used to prove the model with equal probabilities.

We study the conformal spectra of the critical square lattice Ising model on the Klein bottle andMöbius strip using Yang-Baxter techniques and the solution of functional equations. In particular, we obtain expressions for the finitized conformal partition functions in terms of finitized Virasoro characters. This demonstrates that Yang-Baxter techniques and functional equations can be used to st...

The square and kagome lattices with nearest-neighbor springs of spring constant k are isostatic with a number of zero-frequency modes that scale with their perimeter. We analytically study the approach to this isostatic limit as the spring constant k' for next-nearest-neighbor bonds vanishes. We identify a characteristic frequency omega* approximately square root of k' and length l* approximate...

I show that the cluster variation method, long used as a powerful hierarchy of approximations for discrete (Ising-like) two-dimensional lattice models, yields exact results on the disorder varieties which appear when competitive interactions are put into these models. I consider, as an example, the plaquette approximation of the cluster variation method for the square lattice Ising model with n...

Covering a graph or a lattice with nonoverlapping dimers is a problem that has received considerable interest in areas, such as discrete mathematics, statistical physics, chemistry, and materials science. Yet, the problem of percolation on dimer-covered lattices has received little attention. In particular, percolation on lattices that are fully covered by nonoverlapping dimers has not evidentl...

in this paper we investigate the effect of a random transverse field, distributed according to a trimodal distribution, on the phase diagram and magnetic properties of a two-dimensional lattice (square with z=4),  ferromagnetic ising system consisting of magnetic atoms with spin-1. this study is done using the effectivefield theory (eft) with correlations method. the equations are derived using...