Spontaneous Magnetization, A Generalized Square Lattice

The square lattice shuffle

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

Inhibited Spontaneous Emission by Photonic Band Gaps in a Square Lattice of Periodic Dielectric Medium

Spontaneous magnetization and anomalous Hall effect in an emergent Dice lattice

Ultracold atoms in optical lattices serve as a tool to model different physical phenomena appearing originally in condensed matter. To study magnetic phenomena one needs to engineer synthetic fields as atoms are neutral. Appropriately shaped optical potentials force atoms to mimic charged particles moving in a given field. We present the realization of artificial gauge fields for the observatio...

Numerical Simulation of Fluid Flow Past a Square Cylinder Using a Lattice Boltzmann Method

The method of lattice boltzmann equation(LBE) is a kinetic-based approach for fluid flow computations. In the last decade, minimal kinetic models, and primarily the LBE, have met with significant success in the simulation of complex hydrodynamic phenomena, ranging from slow flows in grossly irregular geometries to fully developed turbulence, to flow with dynamic phase transitions. In the presen...

Coincidence isometries of a shifted square lattice

We consider the coincidence problem for the square lattice that is translated by an arbitrary vector. General results are obtained about the set of coincidence isometries and the coincidence site lattices of a shifted square lattice by identifying the square lattice with the ring of Gaussian integers. To illustrate them, we calculate the set of coincidence isometries, as well as generating func...