Approximate symmetry reduction approach: infinite series reductions to the KdV-Burgers equation

For weak dispersion and weak dissipation cases, the (1+1)-dimensional KdV-Burgers equation is investigated in terms of approximate symmetry reduction approach. The formal coherence of similarity reduction solutions and similarity reduction equations of different orders enables series reduction solutions. For weak dissipation case, zero-order similarity solutions satisfy the Painlev\'e II, Painlev\'e I and Jacobi elliptic function equations. For weak dispersion case, zero-order similarity solutions are in the form of Kummer, Airy and hyperbolic tangent functions. Higher order similarity solutions can be obtained by solving linear ordinary differential equations.Comment: 14 pages. The original model (1) in previous version is generalized to a more extensive form and the incorrect equations (35) and (36) in previous version are correcte

Observation of Landau quantization and standing waves in HfSiS

Recently, HfSiS was found to be a new type of Dirac semimetal with a line of Dirac nodes in the band structure. Meanwhile, Rashba-split surface states are also pronounced in this compound. Here we report a systematic study of HfSiS by scanning tunneling microscopy/spectroscopy at low temperature and high magnetic field. The Rashba-split surface states are characterized by measuring Landau quantization and standing waves, which reveal a quasi-linear dispersive band structure. First-principles calculations based on density-functional theory are conducted and compared with the experimental results. Based on these investigations, the properties of the Rashba-split surface states and their interplay with defects and collective modes are discussed.Comment: 6 pages, 5 figure

The Orr mechanism in transition of parallel shear flow

The Orr mechanism is revisited to understand its precise role in the transition of plane Couette flow. By considering homogeneous shear flow and plane Couette flow, it is identified that the Orr mechanism induces a lift-up effect which significantly amplifies spanwise velocity. An optimal perturbation analysis for an individual velocity component reveals that the amplification of spanwise velocity is most active at the streamwise length comparable to the given spanwise length of the perturbation. The relevance of this mechanism to transition is subsequently examined in plane Couette flow. To this end, a set of initial conditions, which combines the optimal perturbation for spanwise velocity with the one for all the velocity components, is considered by varying their amplitudes. Two representative transition scenarios are found: oblique and streak transitions. In the former, the spanwise velocity perturbation amplified with the Orr mechanism initiates both streak amplification and breakdown, whereas in the latter, its role is limited only to the streak breakdown at the late stage of transition. As such, the oblique transition offers a route to turbulence energetically more efficient than the streak transition, at least for the cases examined in the present paper. Finally, the oblique transition is found to share many physical similarities with the transition by the minimal seed

Exact Constructions of a Family of Dense Periodic Packings of Tetrahedra

The determination of the densest packings of regular tetrahedra (one of the five Platonic solids) is attracting great attention as evidenced by the rapid pace at which packing records are being broken and the fascinating packing structures that have emerged. Here we provide the most general analytical formulation to date to construct dense periodic packings of tetrahedra with four particles per fundamental cell. This analysis results in six-parameter family of dense tetrahedron packings that includes as special cases recently discovered "dimer" packings of tetrahedra, including the densest known packings with density $\phi= 4000/4671 = 0.856347...$. This study strongly suggests that the latter set of packings are the densest among all packings with a four-particle basis. Whether they are the densest packings of tetrahedra among all packings is an open question, but we offer remarks about this issue. Moreover, we describe a procedure that provides estimates of upper bounds on the maximal density of tetrahedron packings, which could aid in assessing the packing efficiency of candidate dense packings.Comment: It contains 25 pages, 5 figures

Modeling Heterogeneous Materials via Two-Point Correlation Functions: II. Algorithmic Details and Applications

In the first part of this series of two papers, we proposed a theoretical formalism that enables one to model and categorize heterogeneous materials (media) via two-point correlation functions S2 and introduced an efficient heterogeneous-medium (re)construction algorithm called the "lattice-point" algorithm. Here we discuss the algorithmic details of the lattice-point procedure and an algorithm modification using surface optimization to further speed up the (re)construction process. The importance of the error tolerance, which indicates to what accuracy the media are (re)constructed, is also emphasized and discussed. We apply the algorithm to generate three-dimensional digitized realizations of a Fontainebleau sandstone and a boron carbide/aluminum composite from the two- dimensional tomographic images of their slices through the materials. To ascertain whether the information contained in S2 is sufficient to capture the salient structural features, we compute the two-point cluster functions of the media, which are superior signatures of the micro-structure because they incorporate the connectedness information. We also study the reconstruction of a binary laser-speckle pattern in two dimensions, in which the algorithm fails to reproduce the pattern accurately. We conclude that in general reconstructions using S2 only work well for heterogeneous materials with single-scale structures. However, two-point information via S2 is not sufficient to accurately model multi-scale media. Moreover, we construct realizations of hypothetical materials with desired structural characteristics obtained by manipulating their two-point correlation functions.Comment: 35 pages, 19 figure

An immune system based genetic algorithm using permutation-based dualism for dynamic traveling salesman problems

Copyright @ Springer-Verlag Berlin Heidelberg 2009.In recent years, optimization in dynamic environments has attracted a growing interest from the genetic algorithm community due to the importance and practicability in real world applications. This paper proposes a new genetic algorithm, based on the inspiration from biological immune systems, to address dynamic traveling salesman problems. Within the proposed algorithm, a permutation-based dualism is introduced in the course of clone process to promote the population diversity. In addition, a memory-based vaccination scheme is presented to further improve its tracking ability in dynamic environments. The experimental results show that the proposed diversification and memory enhancement methods can greatly improve the adaptability of genetic algorithms for dynamic traveling salesman problems.This work was supported by the Key Program of National Natural Science Foundation (NNSF) of China under Grant No. 70431003 and Grant No. 70671020, the Science Fund for Creative Research Group of NNSF of China under GrantNo. 60521003, the National Science and Technology Support Plan of China under Grant No. 2006BAH02A09 and the Engineering and Physical Sciences Research Council (EPSRC) of UK under Grant No. EP/E060722/1

Approximate perturbed direct homotopy reduction method: infinite series reductions to two perturbed mKdV equations

An approximate perturbed direct homotopy reduction method is proposed and applied to two perturbed modified Korteweg-de Vries (mKdV) equations with fourth order dispersion and second order dissipation. The similarity reduction equations are derived to arbitrary orders. The method is valid not only for single soliton solution but also for the Painlev\'e II waves and periodic waves expressed by Jacobi elliptic functions for both fourth order dispersion and second order dissipation. The method is valid also for strong perturbations.Comment: 8 pages, 1 figur

Magnetic structure of superconducting Eu(Fe0.82Co0.18)2As2 as revealed by single-crystal neutron diffraction

The magnetic structure of superconducting Eu(Fe0.82Co0.18)2As2 is unambiguously determined by single-crystal neutron diffraction. A long-range ferromagnetic order of the Eu2+ moments along the c-direction is revealed below the magnetic phase transition temperature Tc = 17 K. In addition, the antiferromagnetism of the Fe2+ moments still survives and the tetragonal-to-orthorhombic structural phase transition is also observed, although the transition temperatures of the Fe-spin density wave (SDW) order and the structural phase transition are significantly suppressed to Tn = 70 K and Ts = 90 K, respectively, compared to the parent compound EuFe2As2.We present the microscopic evidences for the coexistence of the Eu-ferromagnetism (FM) and the Fe-SDW in the superconducting crystal. The superconductivity (SC) competes with the Fe-SDW in Eu(Fe0.82Co0.18)2As2.Moreover, the comparison between Eu(Fe1-xCox)2As2 and Ba(Fe1-xCox)2As2 indicates a considerable influence of the rare-earth element Eu on the magnetism of the Fe sublattice.Comment: 7 pages, 7 figures, accepted for publication in Physical Review