Narrow Results

We study the critical endpoint behavior of an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. We use a two-dimensional Wang–Landau sampling method to determine the density of states for this model. An accurate density of states allowed us to map out the phase diagram accurately and observe a clear divergence of the curvature of the spectator phase boundary and of the derivative of the magnetization coexistence diameter near the critical endpoint, in agreement with previous theoretical predictions.

The honk effect is not uncommon in the real traffic and may exert great influence on the stability of traffic flow. As opposed to the linear description of the traditional one-dimensional lattice hydrodynamic model, the high-dimensional lattice hydrodynamic model is a gridded analysis of the real traffic environment, which is a generalized form of the one-dimensional lattice model. Meanwhile, the high-dimensional traffic flow exposed to the open-ended environment is more likely to be affected by the honk effect. In this paper, we propose an extension of two-dimensional triangular lattice hydrodynamic model under honk environment. The stability condition is obtained via the linear stability analysis, which shows that the stability region in the phase diagram can be effectively enlarged under the honk effect. Modified Korteweg–de Vries equations are derived through the nonlinear stability analysis method. The kink–antikink solitary wave solution is obtained by solving the equation, which can be used to describe the propagation characteristics of density waves near the critical point. Finally, the simulation example verifies the correctness of the above theoretical analysis.

We present results for the generating functions of single fully-directed walks on the triangular lattice, enumerated according to each type of step and weighted proportional to the area between the walk and the surface of a half-plane (wall), and the number of contacts made with the wall. We also give explicit formulae for total area generating functions, that is when the area is summed over all configurations with a given perimeter, and the generating function of the moments of heights above the wall (the first of which is the total area). These results generalise and summarise nearly all known results on the square lattice: all the square lattice results can be obtaining by setting one of the step weights to zero. Our results also contain as special cases those that already exist for the triangular lattice. In deriving some of the new results we utilise the Enumerating Combinatorial Objects (ECO) and marked area methods of combinatorics for obtaining functional equations in the most general cases. In several cases we give our results both in terms of ratios of infinite q-series and as continued fractions.

The c-axis charge transport of the electron doped cobaltate is investigated within the t-J model by considering the incoherent interlayer hopping. It is shown that the c-axis charge transport of the electron doped cobaltate is essentially determined by the scattering from the in-plane fluctuation. The c-axis conductivity spectrum shows a low-energy peak and the unusual broad midinfrared band, which are qualitatively consistent with these of the doped square lattice antiferromagnet.

The superconducting system in the two dimensional triangular lattice is investigated by the mean-field treatment of a simple effective model. We calculate the phase diagram of this kind of superconductor for various pairing symmetries and interactions as well as electron occupancies. It is found that the p_x+ip_y-, d+id′-, and f- wave superconducting states are stabilized in different doping regions, and there exist superconducting phase transitions by varying the carrier concentration in the system. The relevance of our results to the recently discovered superconductor, Na_xCoO₂·yH₂O, is briefly discussed.

Motivated by the controversy concerning the pairing symmetry of the superconducting sodium-doped cobalt oxide, we investigate the microscopic electronic structure of an f-wave superconductor in the vortex state by diagonalizing an effective Hamiltonian specified in the triangular lattice self-consistently. We find that the low-lying vortex core states are in essence extended for the nodal f-wave superconductors. In comparison, we find localized bound states in the vortex core of the fully-gapped (d + id')-wave superconductors.

Within the framework of kinetic-energy-driven superconductivity, the asymmetric doping dependence of superconductivity between the hole- and electron-doped triangular-lattice superconductors has been studied. It is shown that although the superconducting transition temperature has a dome-shaped doping dependence for both the hole- and electron-doped triangular-lattice superconductors, superconductivity appears over a wide range of doping in the hole-doped case, while it only exists in a narrow range of doping in the electron-doped case. Moreover, the maximum superconducting transition temperature around optimal doping in the electron-doped triangular-lattice superconductors is lower than that of the hole-doped counterparts. The theory also shows that the asymmetric doping dependence of superconductivity between the hole- and electron-doped cases may be a common feature for a doped Mott insulator.

Even though the fundamental main structure of cellular automata (CA) is a discrete special model, the global behaviors at many iterative times and on big scales could be a close, nearly a continuous, model system. CA theory is a very rich and useful phenomena of dynamical model that focuses on the local information being relayed to the neighboring cells to produce CA global behaviors. The mathematical points of the basic model imply the computable values of the mathematical structure of CA. After modeling the CA structure, an important problem is to be able to move forwards and backwards on CA to understand their behaviors in more elegant ways. A possible case is when CA is to be a reversible one. In this paper, we investigate the structure and the reversibility of two-dimensional (2D) finite, linear, triangular von Neumann CA with null boundary case. It is considered on ternary field ${\mathbb{Z}}_3$ (i.e. 3-state). We obtain their transition rule matrices for each special case. For given special triangular information (transition) rule matrices, we prove which triangular linear 2D von Neumann CAs are reversible or not. It is known that the reversibility cases of 2D CA are generally a much challenged problem. In the present study, the reversibility problem of 2D triangular, linear von Neumann CA with null boundary is resolved completely over ternary field. As far as we know, there is no structure and reversibility study of von Neumann 2D linear CA on triangular lattice in the literature. Due to the main CA structures being sufficiently simple to investigate in mathematical ways, and also very complex to obtain in chaotic systems, it is believed that the present construction can be applied to many areas related to these CA using any other transition rules.

Predicting native conformations using computational protein models requires a large number of energy evaluations even with simplified models such as hydrophobic-hydrophilic (HP) models. Clearly, energy evaluations constitute a significant portion of computational time. We hypothesize that given the structured nature of algorithms that search for candidate conformations such as stochastic methods, energy evaluation computations can be cached and reused, thus saving computational time and effort. In this paper, we present a caching approach and apply it to 2D triangular HP lattice model. We provide theoretical analysis and prediction of the expected savings from caching as applied this model. We conduct experiments using a sophisticated evolutionary algorithm that contains elements of local search, memetic algorithms, diversity replacement, etc. in order to verify our hypothesis and demonstrate a significant level of savings in computational effort and time that caching can provide.

There is a classical correspondence between edge-signed plane graphs and link diagrams. Determining component number of links corresponding to plane graphs may be one of the first problems in studying links by using graphs. There has been several early studies in this aspect, for example, the component number of links formed from 2-dimensional square lattices (4⁴) has been determined. In this paper, we determine the component number of links corresponding to 2-dimensional triangular (3⁶) and honeycomb (6³) lattices with free or cyclic boundary condition.

We prove in this paper that the minimizer of Lennard–Jones energy per particle among Bravais lattices is a triangular lattice, i.e. composed of equilateral triangles, in ℝ² for large density of points, while it is false for sufficiently small density. We show some characterization results for the global minimizer of this energy and finally we also prove that the minimizer of the Thomas–Fermi energy per particle in ℝ² among Bravais lattices with fixed density is triangular.

We present a new family of triangular biorthogonal wavelets that is defined on a triangular lattice by introducing a new operation to generalize two-dimensional lifting, which we call twist. The resulting filters inherit several remarkable features of the early triangular biorthogonal wavelet filters such as the hexagonal symmetry of low-pass filters, symmetrical arrangement of three high-pass filters on the lattice, and that the wavelet decomposition produces uniform energy distributions over three detail components, preserving the isotropy of decomposed images. Additionally, these filters are a biorthogonal set of truly nonseparable two-dimensional wavelet filters that have much larger support, which provides much larger portions of the total energy to three detail components of decomposed images. We show that this plays a crucial role when extracting the edge structure of an image.

We report magnetic susceptibility, specific heat and muon spin relaxation (μSR) experiments on the triangular antiferromagnet La₂Ca₂MnO₇ which develops a genuine two-dimensional (2D), three-sublattice magnetic order below T_N = 2.8 K. From the susceptibility and specific heat an estimate of the exchange interaction is derived. A value for the spin-wave gap is obtained from the latter data. The analysis of a previously reported inelastic neutron scattering data yields values for the exchange and spin-wave gap compatible with the results obtained from macroscopic measurements. An appreciable entropy is still missing at 10 K that may be ascribed to intense short-range correlations. The critical paramagnetic fluctuations extend far above T_N, and can be partly understood in terms of two-dimensional spin-wave excitations. While no spontaneous μSR field is observed below T_N, persistent spin dynamics is found. Short-range correlations are detected in this temperature range. Their relation to a possible molecular spin substructure and the observed exotic spin fluctuations is discussed.

The cluster variation method is applied to the ferromagnetic six-state clock model on the triangular lattice up to the hexagonal cluster approximation. The Kosterlitz-Thouless type phase transition of the model is studied by using the coherent anomaly method (CAM).