Square Lattice Research Articles

Supercontinuum generation in all-normal dispersion regime of C7H8-core photonic crystal fibers with different lattices

We present a new design of three photonic crystal fibers (PCFs) made of fused silica glass, infiltrated with toluene (C7H8) with different lattices in cladding including circular lattice (CL), hexagonal lattice (HL) and square lattice (SL). The optimal structures that operate in the all-normal dispersion regime, were selected by investigating the dependence of the lattice parameters in the first ring surrounding the core on the PCF characteristics. In addition, we punctuate the possibility of coherent octave-wide supercontinuum (SC) generation in the wavelength range of 0.75–1.68[Formula: see text][Formula: see text]m, 0.76–1.91[Formula: see text][Formula: see text]m (1.3[Formula: see text][Formula: see text]m pump wavelength), and 0.65–1.45[Formula: see text][Formula: see text]m (1.064[Formula: see text][Formula: see text]m pump wavelength) with 90[Formula: see text]fs pulses and 30[Formula: see text]pJ of low energy in-coupled into the core of the selected PCFs. The highest SC generation efficiency is obtained with HL-PCF. The proposed fibers are good candidates for all-fiber SC sources, as a new source of SC light.

Kaleidoscopes of Hofstadter butterflies and Aharonov-Bohm caging from 2n -root topology in decorated square lattices

Square-root topology describes models whose topological properties can be revealed upon squaring the Hamiltonian, which produces their respective parent topological insulators. This concept has recently been generalized to $2^n$-root topology, characterizing models where $n$ squaring operations must be applied to the Hamiltonian in order to arrive at the topological source of the model. In this paper, we analyze the Hofstadter regime of quasi-one-dimensional (quasi-1D) and two-dimensional (2D) $2^n$-root models, the latter of which has the square lattice (SL) (known for the Hofstadter Butterfly) as the source model. We show that upon increasing the root-degree of the model, there appear multiple magnetic flux insensitive flat bands, and analytically determine corresponding eigenstates. These can be recast as compact localized states (CLSs) occupying a finite region of the lattice. For a finite flux, these CLSs correspond to different harmonics contained within the same Aharonov-Bohm (AB) cage. Furthermore, as the root-degree increases, a kaleidoscope of butterflies is seen to appear in the Hofstadter diagram, with each butterfly constituting a topologically equivalent replica of the original one of the SL. As such, the index $n$, which uniquely identifies the root-degree of the model, can be seen as an additional fractal dimension of the $2^n$-root model present in its Hofstadter diagram. We discuss how these dynamics could be realized in experiments with ultracold atoms, and measured by Bragg spectroscopy or through observing dynamics of initially localized atoms in a quantum gas microscope.

Artificial Dielectric Based on Conducting Squares with Resistive Jumpers

In this paper, we calculate the dispersion of the effective dielectric constant of the structure from the lattice of conductive squares located in a dielectric layer and connected by resistive jumpers based on the solution of the diffraction problem. Depending on the parameters of the jumpers , the dispersion of this structure was shown to be capable of varying from the relaxation type to one that corresponds to the structure of continuous resistive films. The jumpers were also shown to affect the nature of the dispersion in the long-wave part of the wave range most significantly in relation to the structure period.

Quantum phase diagram of the two-dimensional transverse-field Ising model: Unconstrained tree tensor network and mapping analysis

We investigate the ground-state phase diagram of the frustrated transverse field Ising (TFI) model on the checkerboard lattice (CL), which consists of N\'{e}el, collinear, quantum paramagnet and plaquette-valence bond solid (VBS) phases. We implement a numerical simulation that is based on the recently developed unconstrained tree tensor network (TTN) ansatz, which systematically improves the accuracy over the conventional methods as it exploits the internal gauge selections. At the highly frustrated region ($J_2=J_1$), we observe a second order phase transition from plaquette-VBS state to paramagnet phase at the critical magnetic field, $\Gamma_{c}=0.28$, with the associated critical exponents $\nu=1$ and $\gamma\simeq0.4$, which are obtained within the finite size scaling analysis on different lattice sizes $N=4\times 4, 6\times 6, 8\times8$. The stability of plaquette-VBS phase at low magnetic fields is examined by spin-spin correlation function, which verifies the presence of plaquette-VBS at $J_2=J_1$ and rules out the existence of a N\'{e}el phase. In addition, our numerical results suggest that the transition from N\'{e}el (for $J_2<J_1$) to plaquette-VBS phase is a deconfined phase transition. Moreover, we introduce a mapping, which renders the low-energy effective theory of TFI on CL to be the same model on $J_1-J_2$ square lattice (SL). We show that the plaquette-VBS phase of the highly frustrated point $J_2=J_1$ on CL is mapped to the emergent string-VBS phase on SL at $J_2=0.5J_1$.

Performance Comparison of Cognitive Radio Sensor Networks for Industrial IoT With Different Deployment Patterns

Square lattice (SL), triangle lattice (TL), and hexagon lattice (HL) are widely used regular deployment patterns for industrial Internet of Things (IoT). However, the performance of cognitive-radio-based access with these three deployment patterns has not been explored yet. This paper first designs a transmission scheduling method named cognitive access for regular topology (CART) in cognitive radio sensor networks (CRSNs) with minimal occupation of channels and high transmission efficiency. CART consists of a timeslot-and-channel allocation scheme, a cooperative spectrum-sensing scheme, and a scheme for reporting spectrum-sensing results (SSRs) in SL, TL, and HL. This paper also analyzes CART’s cooperative spectrum-sensing performance, reception bandwidth, and transmission delay for different transmission interference range and coverage patterns. Based on numerical analysis and simulation, this paper makes comparison between CART and optimal transmission scheduling method for single channel, and that among these three deployment patterns. Results show the following insights for efficient deployment of CRSN: 1) TL yields the optimal cooperative spectrum-sensing performance among three patterns by data fusion rule of 3-out-of-7; 2) under the same conditions and area for deployment, SL provides the optimal reception bandwidth; 3) SL and TL lead to low transmission delay for critical complete coverage; 4) SL leads to the lowest transmission delay for critical multiple coverage; 5) the false alarm (FA) probability of individual node has little influence on transmission delay, while the probability of primary user’s (PU) occurrence has noticeably influence on it; and 6) increasing the ratio of transmission timeslot to spectrum-sensing timeslot may decrease transmission delay

Design rules of nanostructured transparent conductive electrodes for light trapping in hematite photoanodes

Hematite is an appealing material for photoelectrochemical water splitting due to nearly ideal bandgap and Earth abundance. However, its short-distance hole transport has so far hindered exploiting its full potential. Two nanostructured transparent electrodes coated with a thin hematite layer are studied using full-field electromagnetic modeling. One structure comprises an ordered array of stripes of a transparent conductive oxide (TCO) and the other is composed of a square-lattice array of TCO nanorods. We find that height and filling ratio (FR) of the nanostructured elements constitutes the most crucial design parameter where the tall nanostructures with small FR constitute the ideal design for a nanostructured electrode with resonant-size elements. The simulations show that current densities up to 10.4 mA cm−2 can be obtained in a 20-nm thick hematite layer uniformly coated onto a properly designed nanostructured transparent conductive scaffold. Practical permittivity data are used in the simulation and the results show that these structures are quite robust against irregularities that might occur during the fabrications process.

Phase Transitions in Equilibrium and Non-Equilibrium Models on Some Topologies

On some regular and non-regular topologies, we studied the critical properties of models that present up-down symmetry, like the equilibrium Ising model and the nonequilibrium majority vote model. These are investigated on networks, like Apollonian (AN), Barabási–Albert (BA), small-worlds (SW), Voronoi–Delaunay (VD) and Erdös–Rényi (ER) random graphs. The review here is on phase transitions, critical points, exponents and universality classes that are compared to the results obtained for these models on regular square lattices (SL).

The square lattice shuffle, correction

The square lattice shuffle, correction

Wideband Grating-Lobe Suppression by Rotation of the Phased Array Stations in the SKA Low-Frequency Sparse Aperture Array

A simple cost-effective technique of wideband grating-lobe (GL) suppression by rotation of the phased array antennas is developed for application in a system of low-frequency sparse aperture array (LF-SAA) antennas of the square kilometer array (SKA) radio-telescope. The technique implies using of equal sparse planar circular antennas with the well-tried square lattice (SqL) distribution of the station antenna array sensors, which is known as the best in terms of production costs and maintenance charges. The peak levels of residual GLs in the fringe pattern of most pairs of the rotated antenna array stations do not exceed value of -17 dB over frequencies ranged from 70 to 450 MHz in the case of uniform antenna array element weighting, whereas the maximum levels of residual GLs are reduced to -25 dB when the Hamming weight tapering is applied.

The J1-J2Model on the Anisotropic Triangular and the Square Lattice: Similarities and Differences

The J₁-J₂Model on the Anisotropic Triangular and the Square Lattice: Similarities and Differences

Binder Cumulant for Bond Diluted Ising Model

The fourth order Binder cumulant U and the critical Binder cumulant U* of bond-diluted Ising model on a square lattice are studied using Monte Carlo techniques. The values of the transition temperature Tc obtained from U* for different probabilities of bond dilution p are discussed. When p is no too large (p 0.35, things are not so clear and our results show that the determination of Tc from U is questionable

MAJORITY-VOTE MODEL WITH HETEROGENEOUS AGENTS ON SQUARE LATTICE

We study a nonequilibrium model with up-down symmetry and a noise parameter q known as majority-vote model (MVM) of [M. J. Oliveira, J. Stat. Phys.66, 273 (1992)] with heterogeneous agents on square lattice (SL). By Monte Carlo (MC) simulations and finite-size scaling relations, the critical exponents β∕ν, γ∕ν and 1∕ν and points qc and U* are obtained. After extensive simulations, we obtain β∕ν = 0.35(1), γ∕ν = 1.23(8) and 1∕ν = 1.05(5). The calculated values of the critical noise parameter and Binder cumulant are qc = 0.1589(4) and U* = 0.604(7). Within the error bars, the exponents obey the relation 2β∕ν + γ∕ν = 2 and the results presented here demonstrate that the MVM heterogeneous agents belongs to a different universality class than the nonequilibrium MVM with homogeneous agents on SL.

Tunnel Magnetoresistance of M^(+)@C(subscript 60) (M = Cs, Li, and Na) Molecular Junctions

In this research, a theoretical study of spin-polarized quantum transport has been reported through a M^(+)@C(subscript 60) (M = Cs, Li, Na) molecule attached to two square lattice FM electrodes with finite cross sections. The effects of dimerization bond, the contact types, the ion positions into cage and ion types on the transmission coefficient, the spin-injection factor, and the TMR ratio have been investigated using the Keldysh nonequilibrium Green's function formalism. The results indicate that the spin-injection factor can reach to as large as 100% with the proper selection of the contact types, the ion positions and types. When the Li atom locates at 2 A distance from the cage center, the TMR ratio in the Li^(+)@C(subscript 60) molecule varies from 100% to -80% corresponding to the contact types.

TAX EVASION AND NONEQUILIBRIUM MODEL ON APOLLONIAN NETWORKS

The Zaklan model had been proposed and studied recently using the equilibrium Ising model on square lattices (SLs) by [G. Zaklan, F. Westerhoff and D. Stauffer, J. Econ. Interact. Coord.4, 1 (2008), arXiv:0801.2980; G. Zaklan, F. W. S. Lima and F. Westerhoff, Physica A387, 5857 (2008)], near the critical temperature of the Ising model presenting a well-defined phase transition; but on normal and modified Apollonian networks (ANs), [J. S. Andrade, Jr., H. J. Herrmann, R. F. S. Andrade, and L. R. da Silva, Phys. Rev. Lett.94, 018702 (2005); R. F. S. Andrade, J. S. Andrade Jr. and H. J. Herrmann, Phys. Rev. E79, 036105 (2009)] studied the equilibrium Ising model. They showed the equilibrium Ising model not to present on ANs a phase transition of the type for the 2D Ising model. Here, using agent-based Monte Carlo simulations, we study the Zaklan model with the well-known majority-vote model (MVM) with noise and apply it to tax evasion on ANs, to show that differently from the Ising model the MVM on ANs presents a well-defined phase transition. To control the tax evasion in the economics model proposed by Zaklan et al., MVM is applied in the neighborhood of the critical noise qc to the Zaklan model. Here we show that the Zaklan model is robust because this can also be studied, besides using equilibrium dynamics of Ising model, through the nonequilibrium MVM and on various topologies giving the same behavior regardless of dynamic or topology used here.

Complexity of commuting Hamiltonians on a square lattice of qubits

We consider the computational complexity of Hamiltonians which are sums of commuting terms acting on plaquettes in a square lattice of qubits, and we show that deciding whether the ground state min...

Structural optimization of arranged carbon nanotubes for hydrogen storage by grand canonical Monte Carlo simulation

We revealed the arrangement of single-wall carbon nanotube (SWNT) which is suitable for the adsorption of hydrogen by means of grand canonical Monte Carlo (GCMC) simulation with simple cylindrical model. Here, we calculated the amount of adsorbed hydrogen with triangular lattice (TL) and square lattice (SL) model for the bundle structure with various kinds of tube diameters ( D) and inter-axis distances ( R a). Our results indicate that any arrangements having smaller R a are not suitable for the storage of hydrogen and the adsorption amount of hydrogen can be achieved the target value (6 wt.% and 45 kg m −3) proposed by Department of Energy (DOE) in United States by SWNTs having larger R a at 77 K and 1 MPa. Furthermore, these results show that the best arrangement of SWNTs for the adsorption of hydrogen at this condition is TL structure having R a = 2.159 nm and D = 1.227 nm.

Optical and electro-optical properties of photonic crystals based on polymer-dispersed liquid crystals

Two-dimensional (2-D) square lattice (SL) photonic crystals (PCs) are fabricated, and their optical/electro-optical properties are studied. The PCs are based on polymer-dispersed liquid crystals (PDLC) that are formed using two-beam interference with double exposures. The PC structure that is observed using a scanning electron microscope matches with the calculated interference pattern. The results of optical/electro-optical studies demonstrate that superprism and negative refraction effects occur at certain incident angles over a range of frequencies and are consistent with the simulated ones. Moreover, the negative refraction efficiency is electrically controllable.

Bond percolation for homogeneous two-dimensional lattices

Abstract Bond percolation is studied for the three homogeneous two-dimensional lattices: square lattice (SL), triangular lattice (TL) and honeycomb lattice (HL). An expanding cell technique is used to obtain percolation thresholds and other relevant information for different cell sizes. We extend the analysis as to include slightly asymmetric cells in addition to the usual symmetric cells to get more points in the scaling analysis. Exact percolation functions are obtained for each size. Then, the percolation threshold is obtained by means of two complementary methods: one based on the well-known renormalization techniques and the other one introduced here which is based upon determining the inflection point of the percolation curves. A comparison of the results obtained by these two methods is performed. The study includes iterations to extrapolate numerical results towards the thermodynamic limit. Critical exponents ν , β and γ are obtained. Values are compared with numerical results and expected theoretical estimations; present results show agreement and even improvement (in the case of γ ) with respect to some numeric values available in the literature. Comparison tables are provided.

Properties of the Ut 2-electrons in two dimensions using the hubbard model

We examine the behaviour of 2 electrons on a 2 x 2 square lattice sites. The Hubbard model was used to model the system and was diagonalized using the configuration interaction method which is a variational method. The variations of the ground state energy ground state double occupied sites D, and the ground state kinetic energy with the interaction strength (u 0) were examined. The functions and were found to be parabolic functions of. This suggests that superconductivity is driven by both electron and hole doping. Key words: Hubbard model, Superconductivity, Configuration interaction and Electron correlation.

Tuning of band gaps for a two-dimensional piezoelectric phononic crystal with a rectangular lattice

In this paper, the elastic wave propagation in a two-dimensional piezoelectric phononic crystal is studied by considering the mechanic–electric coupling. The generalized eigenvalue equation is obtained by the relation of the mechanic and electric fields as well as the Bloch–Floquet theorem. The band structures of both the in-plane and anti-plane modes are calculated for a rectangular lattice by the plane-wave expansion method. The effects of the lattice constant ratio and the piezoelectricity with different filling fractions are analyzed. The results show that the largest gap width is not always obtained for a square lattice. In some situations, a rectangular lattice may generate larger gaps. The band gap characteristics are influenced obviously by the piezoelectricity with the larger lattice constant ratios and the filling fractions.