Analysis of scale-free networks based on a threshold graph with intrinsic vertex weights

Many real networks are complex and have power-law vertex degree distribution, short diameter, and high clustering. We analyze the network model based on thresholding of the summed vertex weights, which belongs to the class of networks proposed by Caldarelli et al. (2002). Power-law degree distributions, particularly with the dynamically stable scaling exponent 2, realistic clustering, and short path lengths are produced for many types of weight distributions. Thresholding mechanisms can underlie a family of real complex networks that is characterized by cooperativeness and the baseline scaling exponent 2. It contrasts with the class of growth models with preferential attachment, which is marked by competitiveness and baseline scaling exponent 3.Comment: 5 figure

Numerical comparison of pipe-column-separation models

Results comparing six column-separation numerical models for simulating localized vapor cavities and distributed vaporous cavitation in pipelines are presented. The discrete vapor-cavity model (DVCM) is shown to be quite sensitive to selected input parameters. For short pipeline systems, the maximum pressure rise following column separation can vary markedly for small changes in wave speed, friction factor, diameter, initial velocity, length of pipe, or pipe slope. Of the six numerical models, three perform consistently over a broad number of reaches. One of them, the discrete gas-cavity model, is recommended for general use as it is least sensitive to input parameters or to the selected discretization of the pipeline. Three models provide inconsistent estimates of the maximum pressure rise as the number of reaches is increased; however, these models do give consistent results provided the ratio of maximum cavity size to reach volume is kept below 10%.Angus R. Simpson and Anton Bergan

Simultaneous conduction and valence band quantisation in ultra-shallow, high density doping profiles in semiconductors

We demonstrate simultaneous quantisation of conduction band (CB) and valence band (VB) states in silicon using ultra-shallow, high density, phosphorus doping profiles (so-called Si:P $\delta$-layers). We show that, in addition to the well known quantisation of CB states within the dopant plane, the confinement of VB-derived states between the sub-surface P dopant layer and the Si surface gives rise to a simultaneous quantisation of VB states in this narrow region. We also show that the VB quantisation can be explained using a simple particle-in-a-box model, and that the number and energy separation of the quantised VB states depend on the depth of the P dopant layer beneath the Si surface. Since the quantised CB states do not show a strong dependence on the dopant depth (but rather on the dopant density), it is straightforward to exhibit control over the properties of the quantised CB and VB states independently of each other by choosing the dopant density and depth accordingly, thus offering new possibilities for engineering quantum matter.Comment: 5 pages, 2 figures and supplementary materia

On pattern structures of the N-soliton solution of the discrete KP equation over a finite field

The existence and properties of coherent pattern in the multisoliton solutions of the dKP equation over a finite field is investigated. To that end, starting with an algebro-geometric construction over a finite field, we derive a "travelling wave" formula for $N$-soliton solutions in a finite field. However, despite it having a form similar to its analogue in the complex field case, the finite field solutions produce patterns essentially different from those of classical interacting solitons.Comment: 12 pages, 3 figure

Quasideterminant solutions of a non-Abelian Hirota-Miwa equation

A non-Abelian version of the Hirota-Miwa equation is considered. In an earlier paper [Nimmo (2006) J. Phys. A: Math. Gen. \textbf{39}, 5053-5065] it was shown how solutions expressed as quasideterminants could be constructed for this system by means of Darboux transformations. In this paper we discuss these solutions from a different perspective and show that the solutions are quasi-Pl\"{u}cker coordinates and that the non-Abelian Hirota-Miwa equation may be written as a quasi-Pl\"{u}cker relation. The special case of the matrix Hirota-Miwa equation is also considered using a more traditional, bilinear approach and the techniques are compared

Quantum states and linear response in dc and electromagnetic fields for charge current and spin polarization of electrons at Bi/Si interface with giant spin-orbit coupling

An expansion of the nearly free-electron model constructed by Frantzeskakis, Pons and Grioni [Phys. Rev. B {\bf 82}, 085440 (2010)] describing quantum states at Bi/Si(111) interface with giant spin-orbit coupling is developed and applied for the band structure and spin polarization calculation, as well as for the linear response analysis for charge current and induced spin caused by dc field and by electromagnetic radiation. It is found that the large spin-orbit coupling in this system may allow resolving the spin-dependent properties even at room temperature and at realistic collision rate. The geometry of the atomic lattice combined with spin-orbit coupling leads to an anisotropic response both for current and spin components related to the orientation of the external field. The in-plane dc electric field produces only the in-plane components of spin in the sample while both the in-plane and out-of-plane spin components can be excited by normally propagating electromagnetic wave with different polarizations.Comment: 10 pages, 9 figure