Impact of perturbations on watersheds

We find that watersheds in real and artificial landscapes can be strongly affected by small, local perturbations like landslides or tectonic motions. We observe power-law scaling behavior for both the distribution of areas enclosed by the original and the displaced watershed as well as the probability density to induce, after perturbation, a change at a given distance. Scaling exponents for real and artificial landscapes are determined, where in the latter case the exponents depend linearly on the Hurst exponent of the applied fractional Brownian noise. The obtained power laws are shown to be independent on the strength of perturbation. Theoretical arguments relate our scaling laws for uncorrelated landscapes to properties of invasion percolation.     

One-dimensionality effects in quasi-one-dimensional conductors

The electrophysical properties of quasi-one-dimensional conductors with a charge-density wave change qualitatively upon a decrease in their transverse sizes. The temperature and electric-field dependences of the conductivities of thin samples are governed by the laws expected for one-dimensional electron systems. The results of studying these effects and the present-day knowledge of their origin are presented.     

Nonlinear theory of transverse perturbations of quasi-one-dimensional solitons

An averaged variational principle is applied to analyze the nonlinear effect of transverse perturbations (including diffraction) on quasi-one-dimensional soliton propagation governed by various wave equations. It is shown that parameters of the spatiotemporal solitons described by the cubic Schrödinger equation and the Yajima-Oikawa model of interaction between long-and short-wavelength waves satisfy the spatial quintic nonlinear Schrödinger equation for a complex-valued function composed of the amplitude and eikonal of the soliton. Three-dimensional solutions are found for two-component “bullets” having long-and short-wavelength components. Vortex and hole-vortex structures are found for envelope solitons and for two-component solitons in the regime of resonant long/short-wave coupling. Weakly nonlinear behavior of transverse perturbations of one-dimensional soliton solutions in a self-defocusing medium is described by the Kadomtsev-Petviashvili equation. The corresponding rationally localized “lump” solutions can be considered as secondary solitons propagating along the phase fronts of the primary solitons. This conclusion holds for primary solitons described by a broad class of nonlinear wave equations.     

Magnetic properties of a mixed spin- 1/2 and spin- 3/2 transverse Ising model in a longitudinal magnetic field

The mixed spin- 1/2 and spin- 3/2 transverse Ising model in a longitudinal magnetic field is studied within the framework of the effective-field theory with correlations. In this approach the effective-field equations are derived by using a probability distribution method based on the generalized but approximated van der Waerden identities. The total longitudinal and transverse magnetizations, the transverse susceptibility and longitudinal susceptibility and the critical temperatures are obtained. We find a number of interesting phenomena in these quantities, due to the applied transverse field and the longitudinal field.     

Chemical reactivity of Ni-Rh nanowires

The properties of bimetallic Ni-Rh nanowires, fabricated by decorating the steps of vicinal Rh(111) surfaces by stripes of self-assembled Ni adatoms, have been probed by STM, photoemission, and ab initio density functional theory calculations. These Ni-Rh nanowires have specific electronic properties that lead to a significantly enhanced chemical reactivity towards oxygen. As a result, the Ni-Rh nanowires can be oxidized exclusively, generating novel quasi-one-dimensional oxide structures.     

Segment Motion in the Reptation Model of Polymer Dynamics. I. Analytical Investigation

We analyze the motion of individual beads of a polymer chain using a discrete version of De Gennes' reptation model that describes the motion of a polymer through an ordered lattice of obstacles. The motion within the tube can be evaluated rigorously; tube renewal is taken into account in an approximation motivated by random walk theory. We find microstructure effects to be present for remarkably large times and long chains, affecting essentially all present-day computer experiments. The various asymptotic power laws commonly considered as typical for reptation hold only for extremely long chains. Furthermore, for an arbitrary segment even in a very long chain, we find a rich variety of fairly broad crossovers, which for practicably accessible chain lengths overlap and smear out the asymptotic power laws. Our analysis suggests observables specifically adapted to distinguish reptation from motions dominated by disorder of the environment.     

Magnetization process of a quasi-one-dimensional ising antiferromagnet with an applied transverse field

The effects of an applied field perpendicular to the spin direction for the zero field on the magnetization and the transition temperature are investigated in a quasi-one-dimensional Ising antiferromagnet, using the new correlated effective-field theory. We find some interesting behavior for the quantities in the applied transverse field. Theoretically, the present formulation does not lead to the appearance of an anti-Néel point, although the standard cluster theories suffer from the familiar defect.     

Localization-delocalization transition in non-hermitian disordered systems

Using the supersymmetry technique, we study the localization-delocalization transition in quasi-one-dimensional non-Hermitian systems with a direction. In contrast to chains, our model captures the diffusive character of carriers' motion at short distances. We calculate the joint probability of complex eigenvalues and some other correlation functions. We find that the transition is abrupt and it is due to an interplay between two saddle points in the free energy functional.     

Betweenness centrality in finite components of complex networks

We use generating function formalism to obtain an exact formula of the betweenness centrality in finite components of random networks with arbitrary degree distributions. The formula is obtained as a function of the degree and the component size, and is confirmed by simulations for Poisson, exponential, and power-law degree distributions. We find that the betweenness centralities for the three distributions are asymptotically power laws with an exponent 1.5 and are invariant to the particular distribution parameters.     

Theoretical model for the evolution of the linguistic diversity

Here we describe how some important scaling laws observed in the distribution of languages on Earth can emerge from a simple computer simulation. The proposed language dynamics includes processes of selective geographic colonization, linguistic anomalous diffusion and mutation, and interaction among populations that occupy different regions. It is found that the dependence of the linguistic diversity on the area after colonization displays two power law regimes, both described by critical exponents which are dependent on the mutation probability. Most importantly for the future prospect of world's population, our results show that the linguistic diversity always decrease to an asymptotic very small value if large areas and sufficiently long times of interaction among populations are considered.     

矩形波导中超短脉冲电子束的相干同步辐射

考虑了当射频调制的超短脉冲电子束径向长度远小于辐射波长时，将其理想化为δ时间函数，提出了用波导本往模展开的方法来计算矩形波导中超短脉冲电子束的相干同步辐射及其频率特性。结果表明：（１）当谐振频率等于调制电子束微脉冲时间隔的射频的整数倍时，辐射模式表现为“纯”的波导本征模。（２）波导效应使得超短脉冲电子束在两个频率处发生相干同步辐射，而且低频支的辐射功率高于高频支的。最后指出波导自由电子激光器单横模     

虚时间分裂算符方法研究溶剂电子转移动力学

在Sumi-Marcus理论中，采用虚时间分裂算符方法研究电子转移动力学．此方法具体应用于计算嗪-1和N,N-二甲基苯胺分子之间的电子转移速率常数．通过计算得到的两种反应物态的平均速率常数和一个长时间的速率常数，揭示了不同的sink函数时的电子转移动力学．在数值模拟过程中还发现了一些新的电子转移特性．     

A Monte Carlo study of the thermodynamic properties of a quasi-one-dimensional organic polymer ferromagnet

The thermodynamic properties of a quasi-one-dimensional organic ferromagnet at different temperatures and in different applied magnetic fields have been investigated by means of the Heisenberg model combined with the Monte Carlo method. The results indicate that a peak in the magnetic susceptibility is obtained at low temperatures. Furthermore, the effect of dimerization on the magnetic properties has also been studied. We find that the dimerization suppresses the magnetization in this model. The ferromagnetic couplings between the side-free radicals stabilize the ferromagnetism and increase the apparent Curie temperature.     

Transverse dynamics and bunch-to-bunch energy exchange in a dielectric-filled accelerating structure

The self-consistent transverse dynamics of high-current relativistic electron bunches used for generating wakefields in multiple-bunch schemes of wakefield acceleration, which are applied in dielectric-filled structures, is studied. The flight range of the electron bunch under no-focusing conditions and the energy transferred to the bunch being accelerated in schemes with profiled (nonuniform) and uniform distributions of the charge over a sequence of generator bunches are determined. Requirements are formulated for a focusing system in which the profiled distribution offers an advantage over the uniform distribution for the efficiency of energy transfer from generator bunches to that being accelerated.     

Evolving laws of human cooperative behaviour

In this study, we improve Lvy walk model, and make it suitable for simulating the collective behaviours of humans. Here we show how rescuers find missing persons by collective cooperative search in a natural background. In the search process, the search strategy represents an optimal algorithm which is used to maximize the success rates for finding missing persons. We simulate the rescuer's movement pattern, and find some basic laws governing the rescuer's cooperative search. For example, the probability that each rescuer finds missing persons shows a power law distribution.     

椭圆孔光子晶体光纤的本地正交函数模型

提出了一种用于分析椭圆孔光子晶体光纤的正交函数模型.发展了一种新型超格子的构造方法，将光子晶体光纤的横向介电常数表示为两种周期性结构叠加，这两种周期性结构分别用余弦函数展开；同时将横向电场以Hermite-Gaussian函数展开.利用正交函数的性质，将全矢量波动方程转化为矩阵本征值问题，求得两偏振模式传输常数.利用此模型可以研究圆孔及椭圆孔光子晶体光纤的模式特性、色散特性、偏振特性等. 关键词： 光子晶体光纤 超格子 正交函数 本征值问题     

双轴棱锥产生长距离近似无衍射光的新技术

提出了一种利用会聚透镜、轴棱锥等简单光学元件产生长距离近似无衍射光的新技术. 分别利用几何光学和衍射理论分析了该方法产生长距离近似无衍射光束的原理, 通过软件模拟了长距离近似无衍射光束的形成过程,得出了该光束在不同距离处的横向光强分布. 模拟结果显示该光束在较长距离处的横向光强分布满足Bessel分布. 从实验上获得了传播距离长达80 m、中心光斑发散角约为0.12 mrad的近似无衍射光束, 相比于国外学者最近的研究成果(Belyi et al. 2010 Opt. Exp. 18 1966)将传播距离延长了50多米,而光束发散角压缩了22倍.实验中, 对光束沿光轴传播时在不同距离处的光斑进行了拍摄,所得实验结果与理论分析基本符合.     

Non-Classical Behavior of Atoms in an Interferometer

Using the time-dependent wave function we have studied the properties of the atomic transverse motion in an interferometer, and the cause of the non-classical behavior of atoms reported by Kurtsiefer, Pfau, and Mlynek [Nature 386, 150 (1997)]. The transverse wave function is derived from the solution of the two-dimensional Schrödinger's equation, written in the form of the Fresnel–Kirchhoff diffraction integral. It is assumed that the longitudinal motion is classical. Comparing data of the space distribution and of the transverse momentum distribution in interferometers with one and two open slits, it follows that the atomic motion is influenced by the atomic matter wave and violates the laws of classical mechanics. However, the negative values of Wigner's function should not be taken as evidence that the atoms in an interferometer violate the classical statistical law of the addition of positive probabilities. This inference follows from the comparison of properties of Wigner's function and of the de Broglian probability density in phase space.     

A simple,analytic solution of the semiclassical Rabi model in the red-detuned regime

We consider the semiclassical Rabi model in the large, red-detuned regime. Using the method of multiple-scales we obtain a simple, analytic, and approximate solution that describes the evolution of the system accurately for long times and for arbitrary values of the qubit-field coupling. It is used to characterize the probability to find the qubit in the excited state and the trajectory of the associated Bloch vector. Finally, we present physical situations where the results can be applied.     

Area Distribution for Directed Random Walks

We study the probability distribution for the area under a directed random walk in the plane. The walk can serve as a simple model for avalanches based on the idea that the front of an avalanche can be described by a random walk and the size is given by the area enclosed. This model captures some of the qualitative features of earthquakes, avalanches, and other self-organized critical phenomena in one dimension. By finding nonlinear functional relations for the generating functions we calculate directly the exponent in the size distribution law and find it to be 4/3.