Two-Dimensional Breather Lattice Solutions and Compact-Like Discrete Breathers and Their Stability in Discrete Two-Dimensional Monatomic β-FPU Lattice

We restrict our attention to the discrete two-dimensional monatomic β-FPU lattice. We look for two- dimensional breather lattice solutions and two-dimensional compact-like discrete breathers by using trying method and analyze their stability by using Aubry＇s linearly stable theory. We obtain the conditions of existence and stability of two-dimensional breather lattice solutions and two-dimensional compact-like discrete breathers in the discrete two- dimensional monatomic β-FPU lattice.     

Existence and Stability of Two-Dimensional Compact-Like Discrete Breathers in Discrete Two-Dimensional Monatomic Square Lattices

Two-dimensional compact-like discrete breathers in discrete two-dimensional monatomic square lattices are investigated by discussing a generalized discrete two-dimensional monatomic model. It is proven that the two- dimensional compact-like discrete breathers exist not only in two-dimensional soft Φ4 potentials but also in hard two-dimensional Φ4 potentials and pure two-dimensional K4 lattices. The measurements of the two-dimensional compact-like discrete breather cores in soft and hard two-dimensional Φ4 potential are determined by coupling parameter K4, while those in pure two-dimensional K4 lattices have no coupling with parameter K4. The stabilities of the two-dimensional compact-like discrete breathers correlate closely to the coupling parameter K4 and the boundary condition of lattices.     

Photonic Band Gap Structures with Periodically Arranged Atoms in a Two-Dimensional Photonic Crystal

Linear transmission, reflection and absorption spectra for a new two-dimensional photonic crystal with periodically arranged resonant atoms are examined. Numerical results show that a twin-gap structure with forbidden bands displaced from a non-doped bandgap structure can be produced as a result of atomic polarization. The absorption spectrum is also significantly altered compared to the single atom entity.     

Band Gap and Waveguide States in Two-Dimensional Disorder Phononic Crystals

The influences of the configurational disorders on phononic band gaps and on waveguide modes are investigated for the two-dimensional phononic crystals consisting of water cylinders periodically arrayed in mercury. Two types of configurational disorders, relevant to the cylinder position and cylinder size respectively, are taken into account. It is found that the phononic band gap and the guide band are sensitive to the disorders, and generally become narrower with the increasing disorders. It is also found that the waveguide side walls without disorder can significantly prevent the guide modes in the waveguide from influence by the disorders in the crystals to a large amount.     

A Lattice Boltzmann Model for Two-Dimensional Magnetohydrodynamics

A lattice Boltzmann model （LBM） has been developed for simulating magnetohydrodynamics （MHD） along the line of Dellar [J. Comput. Phys. 179 （2002）95]. In this model the magnetic field is presented by a vector valued magnetic distribution function which obeys a vector Boltzmann equation. The truncated error of the equilibrium distribution in the present model is up to order O（u^4） in velocity u rather than the usual 0（u^3）. For verification, the model is applied to solve the shock tube problem and the main features of the flow predicted by the model are found to compare well with the corresponding results obtained with high-order semi-discrete schemes [J. Comput. Phys. 201 （2004） 261]. The numerical experiments have also shown that the present LBM model with the equilibrium distribution truncated at O（u^4） performs much better in terms of numerical stability than those truncated at O（u^3）.     

Discrete Holomorphicity at Two-Dimensional Critical Points

After a brief review of the historical role of analyticity in the study of critical phenomena, an account is given of recent discoveries of discretely holomorphic observables in critical two-dimensional lattice models. These are objects whose correlation functions satisfy a discrete version of the Cauchy-Riemann relations. Their existence appears to have a deep relation with the integrability of the model, and they are presumably the lattice versions of the truly holomorphic observables appearing in the conformal field theory (CFT) describing the continuum limit. This hypothesis sheds light on the connection between CFT and integrability, and, if verified, can also be used to prove that the scaling limit of certain discrete curves in these models is described by Schramm-Loewner evolution (SLE).     

Absolute Gap of Two-Dimensional Fractal Photonic Structure

We propose a model for two-dimensional photonic materials constructed on a kind of fractal structures. Total energy flows of the photonic materials constructed with either dielectric cylinders or air holes show that both of them possess absolute gaps for the electromagnetic waves.     

Two-Dimensional Photonic Band-Gap Defect Modes with Deformed Lattice

A numerical study of the defect modes in two-dimensional photonic crystals with deformed triangular lattice is presented by using the supercell method and the finite-difference time-domain method. We find the stretch or shrink of the lattice can bring the change not only on the frequencies of the defect modes but also on their magnetic field distributions. We obtain the separation of the doubly degenerate dipole modes with the change of the lattice and find that both the stretch and the shrink of the lattice can make the dipole modes separate large enough to realize the single-mode emission. These results may be advantageous to the manufacture of photonic crystal lasers and provide a new way to realize the single-mode operation in photonic crystal lasers.     

Waveguide Bend of 90° in Two-Dimensional Triangular Lattice Silicon Photonic Crystal Slabs

We design and realize a 90° waveguide bend in two-dimensional triangular lattice silicon photomc crystal slabs by connecting linear waveguides along the orthogonal Г - K and Г - M directions. A pass band of 70hm is realized by optimizing the geometry of the Г - M waveguide. The connection region of the waveguide bend is optimized to improve the transmission efficiency of infrared light through the two different kinds of waveguides. The transmission efficiency of an optimized single bend is about 75% in simulation and 45% in measurement.     

Microstructure of a Spark Discharge in Air in a Point–Plane Gap

A microchannel structure of a spark discharge initiated in atmospheric-pressure air in a point–plane gap has been discovered by shadow photography. The structure has been observed since the onset of the discharge glow. The evolution of the microstructure over times from several nanoseconds to several tens of nanoseconds has been traced. Specifically, the development of microchannels from the point into the discharge gap, expansion of the microchannels, and their interaction have been observed. A correlation has been found between the microstructure of the spark channel in the discharge gap and its autograph on the surface of the plane electrode.     

Anderson Localization in a Two-Dimensional Electron–Hole System

JETP Letters - Anderson localization is discovered in a highly disordered two-dimensional electron–hole system in a HgTe quantum well. The behavior of this localization is fundamentally...     

Negative Resistance in a Two-Dimensional System with Entropic Barrier

A phenomenon of negative resistance is found in two-dimensional bistable and periodic potentials via Langevin simulation, where output quantities for noise and signal driven system, such as the power-spectrum density modulus and the signal power amplification, can become minima at finite temperatures. In such a system, the curvature of the potential along non-transport degree of freedom at the barrier is larger than that at the local minima. The temperature-dependent effective barrier, i.e. entropic barrier, is introduced via integration over the non-transport variables. The system shows the negative resistance because of the competence between the signal and the entropic barrier.     

Two-Dimensional Gap Solitons in Parity-Time Symmetry Moiré Optical Lattices with Rydberg–Rydberg Interaction

Realizing single light solitons that are stable in high dimensions is a long-standing goal in research of nonlinear optical physics.Here,we address a scheme to generate stable two-dimensional solitons in a cold Rydberg atomic system with a parity-time(PT) symmetric moiré optical lattice.We uncover the formation,properties,and their dynamics of fundamental and two-pole gap solitons as well as vortical ones.The PT symmetry,lattice strength,and the degrees of local and nonlocal nonlinearity are tun...     

Observation of Two-Dimensional Mott Insulator and π-Superfluid Quantum Phase Transition in Shaking Optical Lattice

The Mott insulator and superfluid phase transition is one of the most prominent phenomena in ultracold atoms. We report the observation of a novel 2D quantum phase transition between the Mott insulator and πsuperfluid in a shaking optical lattice. In the deep optical lattice regime, the lowest S band can be tuned to Mott phase, while the higher Px,y bands are itinerant for having larger bandwidth. Through a shaking technique coupling the s-orbital to px,y-orbital states, we experimentally observ...     

Nonlinear Waves in Two-Dimensional （2D） Square Lattice Frenkel-Kontorova （FK） System

A 2D square lattice is studied. By using the continuum approximation, we set up the differential equations of motion for an arbitrary particle in the square lattice which subjects to an external periodic substrate potential. The exact solitary waves of the system are found for special cases. We conclude that the adhesive force f and the angle between propagation directions of upper and lower layers can affect these waves.     

A Positronium Molecule Confined in a Two-Dimensional Space Under a Magnetic Field

Making use of hyperspherical coordinates, we investigate the qualitative features of the ground and lowlying states of a positronium molecule confined in a two-dimensional (2D) space under a magnetic field. We find that a positronium molecule has more bound states in 2D than in 3D. With the increase of the magnetic field, the second bound state experiences a transition in angular momentum. The result shows that symmetry plays an essential role in the energy spectrum of low-lying states.     

Explicit Solutions for a （2＋1）-Dimensional Toda Lattice with Two Discrete Variables

An integrable （2＋1）-dimensional Toda lattice with two discrete variables is investigated again, which is produced from a compatible condition of the Lax triad. The Darboux transformation for its spectral problems is found. As an application, explicit solutions of the （2＋1）-dimensional Toda equation with two discrete variables are obtained.     

An Effective Method on Two-Dimensional Lattice Boltzmann Simulations with Moving Boundaries

We propose a lattice Boltzmann scheme for two-dimensional complex boundaries moving in fluid flow. The hydrodynamic forces exerting on the moving boundaries are calculated based on a stress-integration method proposed before, but the extrapolation procedure is avoided, and the stability of this model is improved. The accuracy and robustness are demonstrated by numerical simulations of a circular particle settling in a twodimensional vertical channel. The numerical convergence is studied by varying the time-step and the dimensionless particle sizes.     

Finite-Difference Lattice Boltzmann Scheme for High-Speed Compressible Flow： Two-Dimensional Case

Lattice Boltzmann （LB） modeling of high-speed compressible flows has long been attempted by various authors. One common weakness of most of previous models is the instability problem when the Mach number of the flow is large. In this paper we present a finite-difference LB model, which works for flows with flexible ratios of specific heats and a wide range of Mach number, from 0 to 30 or higher. Besides the discrete-velocity-model by Watari [Physica A 382 （2007） 502], a modified Lax Wendroff finite difference scheme and an artificial viscosity are introduced. The combination of the finite-difference scheme and the adding of artificial viscosity must find a balance of numerical stability versus accuracy. The proposed model is validated by recovering results of some well-known benchmark tests： shock tubes and shock reflections. The new model may be used to track shock waves and/or to study the non-equilibrium procedure in the transition between the regular and Mach reflections of shock waves, etc.