Topological winding properties of spin edge states in Kane-Mele graphene model

We study the spin edge states in the quantum spin-Hall (QSH) effect on a single-atomic layer graphene ribbon system with both intrinsic and Rashba spin-orbit couplings. The Harper equation for solving the energies of the spin edge states is derived. The results show that in the QSH phase, there are always two pairs of gapless spin-filtered edge states in the bulk energy gap, corresponding to two pairs of zero points of the Bloch function on the complex-energy Riemann surface (RS). The topological aspect of the QSH phase can be distinguished by the difference of the winding numbers of the spin edge states with different polarized directions cross the holes of the RS, which is equivalent to the Z2 topological invariance proposed by Kane and Mele [Phys. Rev. Lett. 95, 146802 (2005)].Comment: 9 pages, 10 figure

A transient solution for vesicle electrodeformation and relaxation

A transient analysis for vesicle deformation under DC electric fields is developed. The theory extends from a droplet model, with the additional consideration of a lipid membrane separating two fluids of arbitrary properties. For the latter, both a membrane-charging and a membrane-mechanical model are supplied. The vesicle is assumed to remain spheroidal in shape for all times. The main result is an ODE governing the evolution of the vesicle aspect ratio. The effects of initial membrane tension and pulse length are examined. The model prediction is extensively compared with experimental data, and is shown to accurately capture the system behavior in the regime of no or weak electroporation. More importantly, the comparison reveals that vesicle relaxation obeys a universal behavior regardless of the means of deformation. The process is governed by a single timescale that is a function of the vesicle initial radius, the fluid viscosity, and the initial membrane tension. This universal scaling law can be used to calculate membrane properties from experimental data

Fractional quantum Hall states in two-dimensional electron systems with anisotropic interactions

We study the anisotropic effect of the Coulomb interaction on a 1/3-filling fractional quantum Hall system by using an exact diagonalization method on small systems in torus geometry. For weak anisotropy the system remains to be an incompressible quantum liquid, although anisotropy manifests itself in density correlation functions and excitation spectra. When the strength of anisotropy increases, we find the system develops a Hall-smectic-like phase with a one-dimensional charge density wave order and is unstable towards the one-dimensional crystal in the strong anisotropy limit. In all three phases of the Laughlin liquid, Hall-smectic-like, and crystal phases the ground state of the anisotropic Coulomb system can be well described by a family of model wave functions generated by an anisotropic projection Hamiltonian. We discuss the relevance of the results to the geometrical description of fractional quantum Hall states proposed by Haldane [ Phys. Rev. Lett. 107 116801 (2011)].Comment: 8 pages, 8 figure

Topological edge states and quantum Hall effect in the Haldane model

We study the topological edge states of the Haldane's graphene model with zigzag/armchair lattice edges. The Harper equation for solving the energies of the edge states is derived. The results show that there are two edge states in the bulk energy gap, corresponding to the two zero points of the Bloch function on the complex-energy Riemann surface. The edge-state energy loops move around the hole of the Riemann surface in appropriate system parameter regimes. The quantized Hall conductance can be expressed by the winding numbers of the edge states, which reflects the topological feature of the Haldane model.Comment: 5 pages, 6 figure

A method for describing large rotations with a combination of axial and transverse Euler vectors

In order to overcome the problem of “singular points”, a method has been developed for the kinematically accurate separation of a large rotation into an axial Euler vector and a transverse Euler vector. The proposal is based on the fact that in the problems of the rotor dynamics of machines consisting of shafts, gears, bearings, etc., the transverse rotation never reaches a value of 2π (a critical value for the Euler vector). The axial rotation is not limited in any way. A numerical dynamics example illustrating the method is presented. The result of the dynamics problem is checked by observing the law of conservation of total energy

Additive manufacturing: A framework for implementation

As mass production has migrated to developing countries, European and US companies are forced to rapidly switch towards low volume production of more innovative, customised and sustainable products with high added value. To compete in this turbulent environment, manufacturers have sought new fabrication techniques to provide the necessary tools to support the need for increased flexibility and enable economic low volume production. One such emerging technique is Additive Manufacturing (AM). AM is a method of manufacture which involves the joining of materials, usually layer-upon-layer, to create objects from 3D model data. The benefits of this methodology include new design freedom, removal of tooling requirements, and economic low volumes. AM consists various technologies to process versatile materials, and for many years its dominant application has been the manufacture of prototypes, or Rapid Prototyping. However, the recent growth in applications for direct part manufacture, or Rapid Manufacturing, has resulted in much research effort focusing on development of new processes and materials. This study focuses on the implementation process of AM and is motivated by the lack of socio-technical studies in this area. It addresses the need for existing and potential future AM project managers to have an implementation framework to guide their efforts in adopting this new and potentially disruptive technology class to produce high value products and generate new business opportunities. Based on a review of prior works and through qualitative case study analysis, we construct and test a normative structural model of implementation factors related to AM technology, supply chain, organisation, operations and strategy

Stability of Strutinsky Shell Correction Energy in Relativistic Mean Field Theory

The single-particle spectrum obtained from the relativistic mean field (RMF) theory is used to extract the shell correction energy with the Strutinsky method. Considering the delicate balance between the plateau condition in the Strutinsky smoothing procedure and the convergence for the total binding energy, the proper space sizes used in solving the RMF equations are investigated in detail by taking 208Pb as an example. With the proper space sizes, almost the same shell correction energies are obtained by solving the RMF equations either on basis space or in coordinate space.Comment: 9 pages, 4 figure

Understanding the white-light flare on 2012 March 9 : Evidence of a two-step magnetic reconnection

We attempt to understand the white-light flare (WLF) that was observed on 2012 March 9 with a newly constructed multi-wavelength solar telescope called the Optical and Near-infrared Solar Eruption Tracer (ONSET). We analyzed WLF observations in radio, H-alpha, white-light, ultraviolet, and X-ray bands. We also studied the magnetic configuration of the flare via the nonlinear force-free field (NLFFF) extrapolation and the vector magnetic field observed by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO). Continuum emission enhancement clearly appeared at the 3600 angstrom and 4250 angstrom bands, with peak contrasts of 25% and 12%, respectively. The continuum emission enhancement closely coincided with the impulsive increase in the hard X-ray emission and a microwave type III burst at 03:40 UT. We find that the WLF appeared at one end of either the sheared or twisted field lines or both. There was also a long-lasting phase in the H-alpha and soft X-ray bands after the white-light emission peak. In particular, a second, yet stronger, peak appeared at 03:56 UT in the microwave band. This event shows clear evidence that the white-light emission was caused by energetic particles bombarding the lower solar atmosphere. A two-step magnetic reconnection scenario is proposed to explain the entire process of flare evolution, i.e., the first-step magnetic reconnection between the field lines that are highly sheared or twisted or both, and the second-step one in the current sheet, which is stretched by the erupting flux rope. The WLF is supposed to be triggered in the first-step magnetic reconnection at a relatively low altitude.Comment: 4 pages, 4 figures, published in A&A Lette

Solving the Dirac equation with nonlocal potential by Imaginary Time Step method

The Imaginary Time Step (ITS) method is applied to solve the Dirac equation with the nonlocal potential in coordinate space by the ITS evolution for the corresponding Schr\"odinger-like equation for the upper component. It is demonstrated that the ITS evolution can be equivalently performed for the Schr\"odinger-like equation with or without localization. The latter algorithm is recommended in the application for the reason of simplicity and efficiency. The feasibility and reliability of this algorithm are also illustrated by taking the nucleus $^{16}$O as an example, where the same results as the shooting method for the Dirac equation with localized effective potentials are obtained