Triangle Lattice Research Articles

Numerical Investigation of Octagonal Photonic Crystal Fibers with Strong Confinement Field

In this paper, the confinement loss of octagonal photonic crystal fibers (PCFs) with an isosceles triangle lattice of air-holes are numerically investigated. Taking into account the confinement loss, the mode field diameter (MFD), the effective area (A eff ) and the chromatic dispersion of octagonal PCFs are calculated, compared to conventional hexagonal PCFs. It is found from confinement loss and MFD results that the octagonal PCFs can confine the field strongly than the hexagonal PCFs due to the different air filling fraction. Moreover, it is shown that the octagonal PCFs are obtained not only positive but also negative larger dispersion values and smaller A eff values compared to the hexagonal PCFs.

In-Plane Ferromagnetism in Charge-OrderingNa0.55CoO2

The magnetic and transport properties are systematically studied on the single crystal Na(0.55)CoO2 with the resistivity divergence below 50 K. A weak ferromagnetic ordering is observed in susceptibility below 20 K with the magnetic field parallel to the Co-O plane, while no such ferromagnetic ordering is observed with the field perpendicular to the Co-O plane. It gives evidence for the existence of in-plane ferromagnetism below 20 K. The observed magnetoresistance of 30% at the field of 6 T at low temperatures indicates an unexpectedly strong spin-charge coupling in the triangle lattice NaxCoO2 system.

Electronic Raman scattering in superconductors on triangular lattices

In superconductors on triangle lattices, we show that the electronic Raman spectra in the non-resonant channel are independent of the light polarization configuration in the scattering. Therefore the light polarization configuration is no longer a judicious choice to probe the anisotropic nature of the pairing wave function (as in the case of square lattices). However, we show that the detailed energy-shift dependence of the spectrum and the effects of impurities provide useful information that can help identify the possible pairing symmetry experimentally. These results are relevant to the newly discovered Na$_x$CoO$_2\cdot y$H$_2$O superconductors.

Supercluster of Electrons in Ultrathin TaSe2Nanocrystals

pffiffiffiffiffi p supercluster based on ffiffiffi 7 pffiffiffi 7 p clusters expected in triangle lattices. This new hierarchal structure and successive clustering cannot be explained by a conventional electron clustering mechanism assisted by background lattice distortions, i.e., charge-density-wave formation mechanism based on Fermi surface nesting. We propose an alternative possible formation mechanism based on saddle-point nesting, taking into account a trigonal symmetry as well as lattice distortion energy.

Lattice-based structures for studying percolation in two-dimensional grain networks

The applicability of standard lattice percolation models to a random two-dimensional grain structure is explored. A random network based on the triangle lattice is proposed as a more appropriate model, and results in a higher percolation threshold (0.711 compared with 0.653 for the standard hexagonal lattice). The triple junction constraint inherent in grain boundary structures is subsequently applied to the new network. This results in a lowering of the percolation threshold to 0.686; this is opposite to its effect on the standard hexagonal lattice. The effect of varying the network’s ‘grain shape’ distribution on the percolation threshold is also considered.

Locally Resonant Cavity Cell Model for Electromagnetic Band Gap Structures

Mushroom-like electromagnetic band gap (EBG) structures exhibit unique electromagnetic properties that have found a wide range of electromagnetic device applications. This paper focuses on the local resonance behaviors of EBG structures, and a simply locally resonant cavity cell (LRCC) model for mushroom-like EBG structures is presented to gain insight to the physical mechanism of the EBG structures and the interaction of electromagnetic waves with EBG structures. The LRCC model proposes two kinds of main resonance modes: One is the mono-polarized mode that accurately predicts the position of the surface wave suppression bandgap, which is equivalent to the LC parallel resonance based on quasistatic assumption in principle, and the other is the cross-coupling polarized mode that exhibits some interesting resonant phenomena, which has not been observed previously. Parametric studies including the radius effect of the metal plated vias are effectively performed by using the LRCC model. Some numerical simulations and experiments of EBG structures, such as square, triangle, and hexagon lattices, are given to illustrate the applications and validation of LRCC model proposed by this paper.

Numerical analysis of acoustic band gaps in two-dimensional periodic materials

Using the plane-wave expansion (PWE) method, the band gaps of the two-dimension phononic crystals composed of square, triangle and honeycomb arrays aluminum cylinders in the air are calculated numerically. The band structures of three lattices were compared and analyzed. It is concluded that the band-gap of honeycomb lattices is located at lower frequency fields, compared with square and triangle lattices. When the filling fraction is between 0.091 and 0.6046, the honeycomb lattices have larger band gaps and gain an advantage over square and triangle lattices In addition, the gap map is introduced to illustrate the influences of filling fraction on the number, the relative width and the limit frequency of the band-gap.

Exchange bias model in ferromagnetic/antiferromagnetic bilayer with L1/sub 2/-type ordered antiferromagnet

The exchange bias of the ferromagnetic (FM) and antiferromagnetic (AFM) bilayer having L1/sub 2/-type ordered structure has been investigated within the framework of Heisenberg model. The triangle lattice of magnetic atoms in the AFM layer realizes the triangular spin structure due to geometrical spin frustrations. This noncollinear spin structure can bring about an exchange bias in the FM/AFM bilayer system. Under the influence of the exchange bias, the uncompensated spin element appears in the AFM layer, resulting in a shifted loop in magnetization curves, in accord with the measured loop by X-ray magnetic circular dichroism spectroscopy for an AFM layer.

Designability of Protein Structures on the Hexagonal LatticeModel

In view of the bonding angle and the number of neighbouring sites, thehexagonal lattice model is preferred to investigate the designability ofprotein structures. Here we simulate the designable structures by thesimplified HP model in a two-dimensional hexagonal lattice with anunrestricted boundary. The result shows that the structures with a largenumber of core sites correspond to the high designability and havecircular-like profiles. The maximum and average designabilities for thehexagonal lattice model are much higher than those for the squarelattice mode, and the maximum and average designabilities for the squarelattice model are much higher than those for the triangle lattice model.

Electron correlation in the two-dimensional triangular lattice of [formula omitted] with [formula omitted

Magnetism of layered cobaltites Na x CoO 2 with x = 0.6 and 0.9 has been investigated by a positive muon spin rotation and relaxation ( μ + SR) spectroscopy together with magnetic susceptibility and specific heat measurements, using single-crystal samples in the temperature range between 250 and 1.8 K. Zero-field μ + SR measurements on Na 0.9 CoO 2 indicate a transition to an incommensurate spin density wave state at 19 K ( = T SDW ) . Since Na 0.6 CoO 2 is paramagnetic down to 1.8 K, the magnitude of T SDW is found to strongly depend on x . This behavior is explained using the Hubbard model within a mean field approximation on two-dimensional triangle lattice in the CoO 2 plane. Also, both the appearance of the IC-SDW state by the change in x and the magnitude of the electronic specific heat parameter of Na 0.6 CoO 2 indicate that Na x CoO 2 is unlikely to be a typical strongly correlated electron system.

3522 稠密三角格子サブチャンネル間の単相乱流混合量の予測(S49-3 流動,原子炉用機器(2),S49 原子炉システムおよびその要素技術)

For single-phase turbulent mixing rate between triangle tight lattice subchannels, a new prediction method was developed by modifying Sadatomi et al.'s model (1996). The method could predict well the present data as well as the data for several triangle lattice channels in literatures.

Electron correlation in the two-dimensional triangle lattice ofNaxCoO2

Magnetism of layered cobaltites ${\text{Na}}_{x}{\text{CoO}}_{2}$ with $x=0.6$ and 0.9 has been investigated by a positive muon spin rotation and relaxation $({\ensuremath{\mu}}^{+}\text{SR})$ spectroscopy together with magnetic susceptibility and specific-heat measurements, using single-crystal samples in the temperature range between 250 and $1.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$. Zero-field-(ZF-) ${\ensuremath{\mu}}^{+}\text{SR}$ measurements on ${\text{Na}}_{0.9}{\text{CoO}}_{2}$ indicate a transition from a paramagnetic to an incommensurate spin-density wave state (IC-SDW) at $19\phantom{\rule{0.3em}{0ex}}\mathrm{K}(={T}_{\text{SDW}})$. The anisotropic ZF-${\ensuremath{\mu}}^{+}\text{SR}$ spectra suggest that the oscillating moments of the IC-SDW direct along the $c$ axis. Since ${\text{Na}}_{0.6}{\text{CoO}}_{2}$ is paramagnetic down to $1.8\phantom{\rule{0.3em}{0ex}}\mathrm{K}$, the magnitude of ${T}_{\text{SDW}}$ is found to strongly depend on $x$. This behavior is well explained using the Hubbard model within a mean-field approximation on two-dimensional triangular lattice in the ${\text{CoO}}_{2}$ plane. Also, both the appearance of the IC-SDW state by the change in $x$ and the magnitude of the electronic specific-heat parameter of ${\text{Na}}_{0.6}{\text{CoO}}_{2}$ indicate that ${\text{Na}}_{x}{\text{CoO}}_{2}$ is unlikely to be a typical strongly correlated electron system.

Dynamic Monte Carlo Simulation of Polymers: Cooperative Move Algorithm

If the elementary move is carefully chosen, the Monte Carlo process can be used to simulate the dynamics of the polymers in a coarse-grained sense. It is generally believed that only local move algorithms, for example, generalized Verdier–Stockmayer algorithm and bond fluctuation method, are suitable for dynamic Monte Carlo simulation of polymer. In this work, we use a cooperative move algorithm, in which several connected segments of the polymer can move collectively, to simulate the self-avoiding walk (SAW) and random walk (RW) chains on the 2-dimensional triangle lattice. We find this cooperative move algorithm can reproduce the result of Rouse theory well, so it can be used as a dynamic Monte Carlo simulation algorithm. The cooperative move algorithm is more realistic than the conventional local move ones in that it can mimic the tensile forces in the polymer chains.

Spin wave theory for antiferromagneticXXZspin model on a triangle lattice in the presence of an external magnetic field

Spin wave theory is applied to a quantum antiferromagnetic XXZ model on a triangle lattice in the presence of an in-plane magnetic field. The effect of the field is found to enhance the quantum fluctuation and to reduce the sublattice magnetization at the intermediate field strength in the anisotropic case. The possible implication to the field driven quantum phase transition from a spin solid to a spin liquid is discussed.

Dynamics of vortex lattice formation in a rotating Bose–Einstein condensate

We study the dynamics of vortex lattice formation of a rotating trapped Bose–Einstein condensate by numerically solving the two-dimensional Gross–Pitaevskii equation with a dissipative term. The condensate trapped in a quadratic potential forms a triangle lattice of quantized vortices, following the damped elliptic oscillation of the condensate and the excitation of surface waves, which is consistent with the experimental results of an ENS group. A fast rotating condensate confined in a quadratic-plus-quartic potential generates a giant vortex absorbing all phase defects into a single density hole, where a quasi-one-dimensional circular superflow is realized.

SU(4) spin-orbital two-leg ladder, square, and triangle lattices

Based on the generalized valence bond picture, a Schwinger boson mean-field theory is applied to the symmetric SU(4) spin-orbital systems. For a two-leg SU(4) ladder, the ground state is a spin-orbital liquid with a finite energy gap, in good agreement with recent numerical calculations. In two-dimensional square and triangle lattices, the SU(4) Schwinger bosons condense at $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$ and $(\ensuremath{\pi}/3,\ensuremath{\pi}/3),$ respectively. Spin, orbital, and coupled spin-orbital static susceptibilities become singular at the wave vectors; the Bose condensation arises at twice this value. It is also demonstrated that there are spin, orbital, and coupled spin-orbital long-range orderings in the ground state.

Optical properties of monolayer lattice and three-dimensional photonic crystals using dielectric spheres

The transmittance spectra for the monolayer triangle lattice using millimeter-sized ${\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ spheres are measured and calculated at various incident angles of electromagnetic waves. From the results, the dispersion of photonic bands for the monolayer triangle lattice is obtained. Furthermore, the transmittance spectra of three-dimensional layered photonic crystals are measured for different layer numbers and different air gaps. Theoretical analysis shows that the photonic band gaps refer to the anticrossing between heavy photon bands and light photon bands. Finally, we discuss the future prospect of the photonic crystals using dielectric spheres.

Change of Surface Structures of Ba Deposited on Mo(110) Surface

The change of the surface structures of barium (Ba) deposited on a Mo(110) surface has been investigated by means of a reflection high-energy electron diffraction (RHEED) apparatus. Based on our RHEED observation, it has been clarified that the surface atomic density of Ba increased continuously in proportion to the increase of the film thickness, and there are no critical film thicknesses related to the structural phase transition. This means that the surface structures which appear in the Ba/Mo(110) system do not exhibit any drastic phase transition at any film thickness. The change of the surface structures of the Ba/Mo(110) system occurs in two steps and results in the c(2×2), (1.6×2) and (1.5×1.8) structures that form a boundary. In either of the two steps, surface structures appear in the balance between the energetic stability of the coherency with the atomic arrangement of the Mo substrate and the energetic stability achieved by surface structures themselves forming triangle lattices.

Triangle lattice Green functions for vector fields

All the identities and integral theorems of vector calculus are contained in the calculus of differential forms. The analogy between the exterior calculus of forms and the homology theory of a cell complex yields discrete lattice models for an array of interesting physical phenomena. These models, based on arbitrary combinations of coupled scalar and polar or axial vector field quantities, can be manipulated as conveniently as the standard scalar tight-binding models. We develop Green functions (GFs) for an infinite hierarchy of such models expressed using the four fundamental operators of the triangle lattice. The triangle lattice is distinguished among two-dimensional grid types for having the highest possible isotropy. Closed formulae are derived for GFs of the scalar and vector models that belong to a hierarchy generated by the four fundamental operators of the triangle family of lattices. The particular example of lattice electromagnetism coupled to an elastic distortion field is treated in detail. Topological properties not dependent upon symmetry split the response functions into plasmon- and polariton-like parts. Since the fundamental vector operators of the triangle lattice are related simply to adjacency matrices of the Kagome lattice, scalar GFs for this lattice are found also as a byproduct.

Polymer Dispersed Liquid Crystals as Mesoscale 2D and 3D Lattices

AbstractWe introduce and explore two- and three-dimensional lattices formed in Holographic-Polymer Dispersed Liquid Crystals (H-PDLC) materials, which exhibit an electrically controllable index modulation in multiple dimensions. As electro-optically active holograms, these materials exhibit fast dynamic switching phenomena (~100 microseconds), and are simple to fabricate. While many applications have been proposed for these materials, almost all are based on one-dimensional index modulations in various grating regimes. However, constraints in additional dimensions lead to a much greater sensitivity of the polymer morphology to monomer functionality, exposure irradiance, and grating pitch. In an effort to begin to understand this relationship, two-dimensional triangle lattices were created using two monomeric blends exposed over a range of powers. Final diffraction efficiency (Bragg regime), saturation voltage, and polymer morphology were examined from the resulting triangle lattices. Three- dimensional lattices are discussed and a six-beam holographic method is proposed. Photonic crystal applications are envisioned where the pseudo-bandgap can be electrically controlled.