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In this article, we construct a numerical method to solve a two-parameter singularly perturbed problem in two dimensions on a tensor product mesh of two exponentially graded mesh. The finite difference scheme is proved to be second-order uniformly convergent when μ 2 / ε → 0 as ε → 0. Numerical experiments validate the obtained error estimates. [ABSTRACT FROM AUTHOR]

We study the topological properties of the generalized two-dimensional (2D) Su-Schrieffer-Heeger (SSH) models. We show that a pair of Dirac points appear in the Brillouin zone (BZ), consisting a semimetallic phase. Interestingly, the locations of these Dirac points are not pinned to any high-symmetry points of the BZ but tunable by model parameters. Moreover, the merging of two Dirac points undergoes a novel topological phase transition, which leads to either a weak topological insulator or a nodal-line metallic phase. We demonstrate these properties by constructing two specific models, which we referred as type-I and type-II 2D SSH models. The feasible experimental platforms to realize our models are also discussed.

Using a 2D ion crystal for quantum simulation and computation has been pursued for a long time. The coherent manipulation of a stationary 2D crystal in the Paul trap may be hampered by the micromotion synchronous with the oscillating electric field. Here, a simple Paul trap that stably confines over 20 171Yb+ions in a stationary 2D crystal is presented. The disturbance of the micromotion in coherent operations is mitigated by making the direction of micromotion perpendicular to the transverse direction of the 2D crystal. To achieve the condition of perpendicularity, the structure of the trap electrodes is comprehensively designed, which also provides the controllability of rotating principal axes. The transverse vibrational modes by Raman laser‐beams are addressed and coherent evolution of sideband transitions on these modes observed. Moreover, this trap allows for optical access with a 0.86 numerical aperture which facilitates applying individually addressing laser‐beams. This work can be an example of realizing a 2D‐trapped‐ion based quantum simulator and computer in a Paul trap. [ABSTRACT FROM AUTHOR]

The Poisson equation is used to calculate the drift velocity in the two-dimensional diffusion couple. This approach is based on the bi-velocity (Darken) method which combines the Darken and Brenner concepts that the volume velocity is essential in defining the local material velocity in multicomponent mixture at non-equilibrium. As an example the arbitrary binary system is considered. It is shown that (1) the two dimensional calculations should be applied with the stochastization method and (2) the drift term in mass conservation law does not affect the calculations. [ABSTRACT FROM AUTHOR]

Within the BCS theory of superconductivity we calculate the superconducting gap at a zero-temperature for metallic hydrogen–graphene system in order to estimate the superconducting critical temperature of quasi-two-dimensional highly oriented pyrolytic graphite. The obtained results are given as a function of the hydrogen-induced density of carriers n and their effective mass m ⋆. The obtained gap shows a Maxwell-like distribution with a maximum of ∼60 K at n∼3×1014 cm−2 and m ⋆/ m=1. The theoretical results are discussed taking into account recent experimental evidence for granular superconductivity in graphite. [ABSTRACT FROM AUTHOR]

We show the insulating region of the metal-insulator transition phenomena in disordered two-dimensional electron systems contains new information about the quantum critical dynamics at low T because the insulating region and the quantum critical region are two aspects of the localized phase. [ABSTRACT FROM AUTHOR]

The three-dimensional physiological tooth movement synchronized with heartbeat, periodontal pulsation, has already been demonstrated by previous researchers. The purpose of this study was to estimate physiological tooth movements within clinically normal periodontal tissues, thus establishing periodontal pulsation standards. The measuring device consisted of an amorphous sensor and a small magnet, which could detect tooth displacement without coming into contact with the tooth surface. The samples consisted of the left maxillary central incisors of 23 adult subjects. Three points on the labial surface were used as reference points to measure the labial-lingual movement range, and a point on the incisal edge was used for measuring the incisal-apical movement range. Periodontal pulsation and electrocardiogram measurements were recorded simultaneously for six minutes. The results showed that the mean amplitude of periodontal pulsation concerning the labial-lingual movement range was equal at the three labial points (0.59 µm) and tended to the smaller than that of the incisal-apical movement range (0.87 µm). There were no significant differences in the mean amplitude of periodontal pulsation at any of the four reference points. Significant correlations of the amplitude of periodontal pulsation existed among the three labial points. Though most teeth pulsated uniformly to the labial direction, some teeth moved in a complex manner including rotation with an axis among the three labial points. These results suggest that the values of periodontal pulsation amplitude which were recorded employing the amorphous sensor device are reliable standards of periodontal pulsation within clinically normal periodontal issues. [ABSTRACT FROM AUTHOR]

The ground state energy per particle of a dilute, homogeneous, two-dimensional Bose gas, in the thermodynamic limit is shown rigorously to be E0/N=(2πℏ2ρ/m)|ln(ρa2)|−1, to leading order, with a relative error at most O(|ln(ρa2)|−1/5). Here N is the number of particles, ρ=N/V is the particle density and a is the scattering length of the two-body potential. We assume that the two-body potential is short range and nonnegative. The amusing feature of this result is that, in contrast to the three-dimensional case, the energy, E0 is not simply N(N−1)/2 times the energy of two particles in a large box of volume (area, really) V. It is much larger. [ABSTRACT FROM AUTHOR]

• 2D split-ring resonator array with resonant frequency disorder. • Localized modes and magnetic transport for uncorrelated and correlated disorder in 2D. • Correlated disorder can create sub-diffusive propagation. We study the effect of a resonant frequency disorder on the eigenstates and the transport of magnetic energy in a two-dimensional (square) array of split-ring resonators (SRRs). In the absence of disorder, we find the dispersion relation of magneto-inductive waves and the mean square displacement (MSD) in closed form, showing that at long times the MSD is ballistic. When disorder is present, we consider two types: the usual Anderson distribution (uncorrelated monomers) and 2 × 2 units assigned at random to lattice sites (correlated tetramers). This is a direct extension to two dimensions of the one-dimensional random dimer model (RDM). For the uncorrelated case, we see saturation of the MSD for all disorder widths, while for the correlated case we find a disorder window, inside which the MSD does not saturate at long times, with an asymptotic sub-diffusive behavior M S D ∼ t 0.26. Outside this disorder window, the MSD shows the same kind of saturation as in the monomer case. We conjecture that the sub-diffusive behavior is a remanent of a weak resonant transmission of a 2D plane wave across a tetramer unit. [ABSTRACT FROM AUTHOR]

• Some two dimensional Schrödinger equations have solutions for which the amplitudes and phases can be interchanged. • This only occurs when the Bohm potential vanishes, and for negative potentials. • These solutions represent particles with equal energy but different momenta, evolving in the same potential. • Exact solutions for physical systems, as repulsive harmonic oscillator or hydrogen atom, are found. • This system has a correspondence with optics, which implies that dual solutions can be studied in analogue optical systems. It is shown that the Schrödinger equation for a large family of pairs of two–dimensional quantum potentials possess wavefunctions for which the amplitude and the phase are interchangeable, producing two different solutions which are dual to each other. This is a property of solutions with vanishing Böhm potential. These solutions can be extended to three–dimensional systems. We explicitly calculate dual solutions for physical systems, such as the repulsive harmonic oscillator and the two–dimensional hydrogen atom. These dual wavefunctions are also solutions of an analogue optical system in the eikonal limit. In this case, the potential is related to the refractive index, allowing the study of this two–dimensional dual wavefunction solutions with an optical (analogue) system. [ABSTRACT FROM AUTHOR]