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.     

Two-dimensional topological gravity and intersection theory on the moduli space of holomorphic bundles

We define a two-dimensional topological Yang-Mills theory for an arbitrary compact simple Lie group. This theory is defined in terms of intersection theory on the moduli space of flat connections on a two-dimensional surface and corresponds physically to a two-dimensional reduction and truncation of four-dimensional topological Yang-Mills theory. Two-dimensional topological Yang-Mills theory defines a topological matter system and may be naturally coupled to two-dimensional topological gravity. This topological Yang-Mills theory is also closely related to Chern-Simons gauge theory in 2 + 1 dimensions. We also discuss a relation between SL (2, ) Chern-Simons theory and two-dimensional topological gravity.     

Discrete gap breathers in a two-dimensional diatomic face-centered square lattice

In this paper we study the existence and stability of two-dimensional discrete gap breathers in a two-dimensional diatomic face-centered square lattice consisting of alternating light and heavy atoms, with on-site potential and coupling potential. This study is focused on two-dimensional breathers with their frequency in the gap that separates the acoustic and optical bands of the phonon spectrum. We demonstrate the possibility of the existence of two-dimensional gap breathers by using a numerical method. Six types of two-dimensional gap breathers are obtained, i.e., symmetric, mirror-symmetric and asymmetric, whether the center of the breather is on a light or a heavy atom. The difference between one-dimensional discrete gap breathers and two-dimensional discrete gap breathers is also discussed. We use Aubry's theory to analyze the stability of discrete gap breathers in the two-dimensional diatomic face-centered square lattice.     

Two-Dimensional Discrete Gap Breathers in a Two-Dimensional Diatomic β Fermi--Pasta--Ulam Lattice

We study the existence of two-dimensional discrete breathers in a two-dimensional face-centred square lattice consisting of alternating light and heavy atoms, with nearest-neighbour coupling containing quartic soft or hardnonlinearity. This study is focused on two-dimensional breathers with frequency in the gap that separates the acoustic and optical bands of the phonon spectrum. We demonstrate the possibility of existence of two-dimensional gap breathers by using the numerical method, the local anharmonicity approximation and the rotating wave approximation. We obtain six types of two-dimensional gap breathers, i.e., symmetric, mirror-symmetric and asymmetric, no matter whether the centre of the breather is on a light or a heavy atom.     

Generalized anti-centrifugal potential

We generalize the quantum anti-centrifugal potential in the two-dimensional Euclidean plane to two-dimensional surfaces embedded in three-dimensional Euclidean space. We consider the sphere with two caps removed in some detail. We show that quantum particles in this space are “pushed” towards either of the cap boundaries. We also consider the two-dimensional Euclidean plane with an elliptic area removed and compute the quantum anti-centrifugal potential on the elliptic boundary. It is argued that a sufficiently thin electrically conducting nano-wire shaped as an ellipse will exhibit an inhomogeneous charge distribution due to this quantum potential.     

Vortex interaction and the two-dimensional dark soliton

We study vortex interaction and a two-dimensional dark soliton in the two-dimensional Gross-Pitaevskii equation. A vortex-antivortex pair propagates with a constant velocity when the initial distance is large. But complicated behaviors appear when the initial distance of two vortices becomes smaller. If the initial distance is sufficiently small, a two-dimensional dark solution is created as a result of the pair annihilation. The two-dimensional dark soliton has an anisotropic structure and propagates in a certain direction. The two-dimensional dark soliton is stable against head-on collision.     

Image processing with the radial Hilbert transform: theory and experiments

The Hilbert transform is useful for image processing because it can select which edges of an input image are enhanced and to what degree the edge enhancement occurs. However, the transform operation is one dimensional and is not applicable for arbitrarily shaped two-dimensional objects. We introduce a radially symmetric Hilbert transform that permits two-dimensional edge enhancement. We implement one-dimensional, two-dimensional, and radial Hilbert transforms with a programmable phase-only liquid-crystal spatial light modulator. Experimental results are presented.     

二维量子随机行走及其物理实现

近年来量子随机行走相关课题因其非经典的特性,已经成为越来越多科研人员的研究热点。这篇文章中我们回顾了一维经典随机行走和一维量子随机行走模型,并且在分析两种二维经典随机行走模型的基础上,我们构建二维量子随机行走模型。通过对随机行走者的位置分布标准差的计算,我们可以证明基于这种二维量子随机行走模型的算法优于其他上述随机行走。除此之外,我们提出一个利用线性光学方法的实验方案,实现这种二维量子随机行走模型。     

Reversible random sequential adsorption of dimers on a triangular lattice

We report on simulations of reversible random sequential adsorption of dimers on three different lattices: a one-dimensional lattice, a two-dimensional triangular lattice, and a two-dimensional triangular lattice with the nearest neighbors excluded. In addition to the adsorption of particles at a rate K+, we allow particles to leave the surface at a rate K-. The results from the one-dimensional lattice model agree with previous results for the continuous parking lot model. In particular, the long-time behavior is dominated by collective events involving two particles. We were able to directly confirm the importance of two-particle events in the simple two-dimensional triangular lattice. For the two-dimensional triangular lattice with the nearest neighbors excluded, the observed dynamics are consistent with this picture. The two-dimensional simulations were motivated by measurements of Ca2+ binding to Langmuir monolayers. The two cases were chosen to model the effects of changing pH in the experimental system.     

Bosonic strings and complex structures

We write the action of the bosonic string in terms of two-dimensional complex structures rather than of two-dimensional metrics. We describe in some detail the behaviour under reparametrization of the world sheet, and in particular we give an expression for the two-dimensional diffeomorphism anomaly. We describe a possible gauge-fixing procedure for the BRST quantization.     

Fabrication of two-dimensional elliptic photonic lattices in photorefractive crystal by optical induction method

We fabricate two-dimensional elliptic photonic lattices in iron-doped lithium niobate photorefractive crystal for the first time with optical induction method. The experimental setup of our method is very simple and flexible without complicated optical adjustment system. We analyze and verify the two-dimensional elliptic photonic lattices by plane wave guiding, far field diffraction pattern imaging, and Brillouin-zone spectroscopy. Induced elliptic photonic lattices can stably exist for a long time in the iron-doped lithium niobate crystal. The induced two-dimensional elliptic photonic lattices might offer an easy method to study generic band gap phenomena in anisotropic periodic structures.     

Two-dimensional model for mixtures of enantiomers,bent hard needles: a Monte Carlo simulation

We study the statistical mechanical conditions under which segregation of racemic mixtures of chiral molecules is possible in a two-dimensional fluid model. Motivated by experimental evidence indicating that chiral hydrophilic heads of amphiphilic molecules lying in a monolayer can crystallize undergoing a chiral phase separation, we propose a two-dimensional system to model the projection of the chiral head of amphiphilic molecules in a monolayer. The molecules of our model are infinitely hard and infinitely thin. We consider interactions with only a repulsive contribution where molecules have no effective area (two-dimensional volume). As a consequence all effects found are due to excluded area. The Monte Carlo Gibbs ensemble is used to study phase separation whereas constant pressure simulations are performed to obtain equations of state of pure and racemic systems. We find that for this simple model segregation is generally possible in the very high density regime.     

Absence of skew scattering in two-dimensional systems: testing the origins of the anomalous Hall effect

We study the anomalous Hall conductivity in spin-polarized, asymmetrically confined two-dimensional electron and hole systems, taking into account the intrinsic, side-jump, and skew-scattering contributions to the transport. We find that the skew scattering, principally responsible for the extrinsic contribution to the anomalous Hall effect, vanishes for the two-dimensional electron system if both chiral Rashba subbands are partially occupied, and vanishes always for the two-dimensional hole gas studied here, regardless of the band filling. Our prediction can be tested with the proposed coplanar two-dimensional electron-hole gas device and can be used as a benchmark to understand the crossover from the intrinsic to the extrinsic anomalous Hall effect.     

Reaction-diffusion fronts in periodically layered media

We compute the effective wavefront speeds of reaction-diffusion equations in periodically layered media with coefficients that have small-amplitude oscillations around a uniform mean state. We compare them with the corresponding wavefront speeds in the uniform state. We analyze a one-dimensional model where wave propagation is along the layering direction of the medium and a two-dimensional shear flow model where wave propagation is othogonal to the layering direction. We find that the effective wave speed is smaller in the one-dimensional model and is larger in the two-dimensional model for both bistable cubic and quadratic nonlinearities of the Kolmogorov-Petrovskii-Piskunov form. We derive approximate expressions for the wave speeds in the bistable case.Dedicated to Jerry Percus on the occasion of his 65th birthday.     

Melting of mesoscopic lattices of magnetic fluid thin film subjected to perpendicular fields

Applying a magnetic field on the magnetic fluid thin film perpendicularly, leads a phase separation that is concentrated in particles separating from a dilute phase. The concentrated phase forms cylindrical columns that construct two-dimensional lattices. This kind of artificial lattice is a novel mesoscopic system and has been explored with optical microscope, CCD, and digital imaging analysis. We explore the ordering evolution of the two-dimensional extraordinary lattice by varying the applied field. The ordering of these lattices is analyzed in terms of translational and bond-orientation correlation functions to address the two-dimensional melting.     

Low-energy modes and Debye behavior in a colloidal crystal

We study the vibrational spectrum and the low-energy modes of a three-dimensional colloidal crystal using confocal microscopy. This is done in a two-dimensional cut through a three-dimensional crystal. We find that the observed density of states is incompatible with the standard Debye form in either two or three dimensions. These results are confirmed by numerical simulations. We show that an effective theory for the projections of the modes onto the two-dimensional cut describes the experimental and simulation data in a satisfactory way.     

Hot-electron effects in two-dimensional hopping with a large localization length

We have studied nonlinear effects in the resistance of a two-dimensional system with a large localization length on both sides of the crossover from weak to strong localization. It is shown that nonlinearity in the hopping regime is due to electron overheating rather than the field effects. This qualitatively new behavior is a signature of a two-dimensional hopping transport with a large localization length.     

Spin susceptibility of two-dimensional electrons in narrow AlAs quantum wells

We report measurements of the spin susceptibility in dilute two-dimensional electrons confined to a 45 A wide AlAs quantum well. The electrons in this well occupy an out-of-plane conduction-band valley, rendering a system similar to two-dimensional electrons in Si-MOSFETs but with only one valley occupied. We observe an enhancement of the spin susceptibility over the band value that increases as the density is decreased, following closely the prediction of quantum Monte Carlo calculations and continuing at finite values through the metal-insulator transition.     

Complete determination of the stress tensor of a polarization-maintaining fiber by photoelastic tomography

The use of photoelastic tomography to obtain the two-dimensional axial stress profile of a polarization-maintaining (PM) fiber with high resolution and accuracy is described. We illustrate, for what is believed to be the first time, the two-dimensional distribution of the local principal axes of the fiber's cross section, which is directly related to the fiber's PM ability. We demonstrate that the stress-induced anisotropy as well as all the stress tensor components of the fiber can be fully determined.