Fractality and degree correlations in scale-free networks

Fractal scale-free networks are empirically known to exhibit disassortative degree mixing. It is, however, not obvious whether a negative degree correlation between nearest neighbor nodes makes a scale-free network fractal. Here we examine the possibility that disassortativity in complex networks is the origin of fractality. To this end, maximally disassortative (MD) networks are prepared by rewiring edges while keeping the degree sequence of an initial uncorrelated scale-free network. We show that there are many MD networks with different topologies if the degree sequence is the same with that of the (u,v)-flower but most of them are not fractal. These results demonstrate that disassortativity does not cause the fractal property of networks. In addition, we suggest that fractality of scale-free networks requires a long-range repulsive correlation, in the sense of the shortest path distance, in similar degrees.     

Local Thermodynamic Equilibrium for some Stochastic Models of Hamiltonian Origin

We consider a class of 1-D stochastic models that are realizations of Hamiltonian models of heat conduction and prove that in the infinite volume limit local thermodynamic equilibrium is attained with linear energy profile.     

The <Emphasis Type="Italic">q</Emphasis>-Analogues of Squeezed States and Some Properties

In this paper we shall introduce two q-analogues of the squeezed states in terms of the technique of integration within an ordered product of operators and the properties of the inverses of q-deformed annihilation and creation operators, and some nonclassical properties of the states are examined. Furthermore, we obtain some new completeness relations composed of the bra and ket which are not mutually Hermitian conjugate. PACS numbers: 03.65.-w; 45.50.Ct. Work supported by the National Natural Science Foundation of China under Grant 10574060 and the Natural Science Foundation of Shandong Province of China under Grant Y2004A09.     

Fast reproducible identification and large-scale databasing of individual functional cognitive networks

Background  

Although cognitive processes such as reading and calculation are associated with reproducible cerebral networks, inter-individual variability is considerable. Understanding the origins of this variability will require the elaboration of large multimodal databases compiling behavioral, anatomical, genetic and functional neuroimaging data over hundreds of subjects. With this goal in mind, we designed a simple and fast acquisition procedure based on a 5-minute functional magnetic resonance imaging (fMRI) sequence that can be run as easily and as systematically as an anatomical scan, and is therefore used in every subject undergoing fMRI in our laboratory. This protocol captures the cerebral bases of auditory and visual perception, motor actions, reading, language comprehension and mental calculation at an individual level.     

A Higher Dimensional Stationary Rotating Black Hole Must be Axisymmetric

A key result in the proof of black hole uniqueness in 4-dimensions is that a stationary black hole that is “rotating”—i.e., is such that the stationary Killing field is not everywhere normal to the horizon—must be axisymmetric. The proof of this result in 4-dimensions relies on the fact that the orbits of the stationary Killing field on the horizon have the property that they must return to the same null geodesic generator of the horizon after a certain period, P. This latter property follows, in turn, from the fact that the cross-sections of the horizon are two-dimensional spheres. However, in spacetimes of dimension greater than 4, it is no longer true that the orbits of the stationary Killing field on the horizon must return to the same null geodesic generator. In this paper, we prove that, nevertheless, a higher dimensional stationary black hole that is rotating must be axisymmetric. No assumptions are made concerning the topology of the horizon cross-sections other than that they are compact. However, we assume that the horizon is non-degenerate and, as in the 4-dimensional proof, that the spacetime is analytic.     

Semiconductor quantum dots in high magnetic fields

We review and extend the composite fermion theory for semiconductor quantum dots in high magnetic fields. The mean-field model of composite fermions is unsatisfactory for the qualitative physics at high angular momenta. Extensive numerical calculations demonstrate that the microscopic CF theory, which incorporates interactions between composite fermions, provides an excellent qualitative and quantitative account of the quantum dot ground state down to the largest angular momenta studied, and allows systematic improvements by inclusion of mixing between composite fermion Landau levels (called Λ levels).     

Transient thermal characterization of micro/submicroscale polyacrylonitrile wires

In this work, the thermal diffusivity of single polyacrylonitrile (PAN) wires with diameters from 4.62 μm down to 324 nm is measured by using our recently developed transient electro-thermal technique. The wires span from 23 μm to 126.2 μm in our measurement. Since PAN wires are dielectric, a thin Au film is coated on the surface of the wires to make them conductive. In the experiment, a step current (with ∼2 μs rising time) is fed to the sample. The sample is heated and takes a certain time to reach its steady thermal state. The temperature rising response of the sample is sensed by measuring the resistance change of the thin Au coating. From the average temperature evolution of the sample, the thermal diffusivity can be extracted. Three PAN wires with different diameters are synthesized using the electro-spinning technique and are measured to obtain their thermal diffusivities (around 1.53×10^-7 m²/s), which are slightly smaller than the bulk value. PACS 65.80.+n; 66.30.Xj; 44.10.+i     

Simple Analog Complementary Metal Oxide Semiconductor Circuit for Generating Motion Signal

We proposed in this study a novel analog complementary metal oxide semiconductor (CMOS) circuit for generating a motion signal when an object moves, which is a simple structure. The proposed unit circuit was constructed using a previously proposed edge detection circuit and a novel proposed circuit for generating a motion signal which accepts an edge signal. The part for generating the motion signal was constructed using six metal oxide semiconductor (MOS) transistors and one capacitor. Results obtained by the simulation program with integrated circuit emphasis (SPICE) and the measured results of a test circuit constructed with discrete MOS transistors and the test circuit fabricated with a 1.2 μm CMOS process showed that the proposed unit circuit can output pulsed current (motion signal) when an object moves on the circuit. It was clarified from the SPICE results that the two-dimensional network constructed with proposed unit circuits can output motion signals. The size of the novel unit circuit is expected to be about 110 × 110μm² obtained by the 1.2 μm CMOS process. It is possible to arrange 90 × 90 unit circuits on a chip which has an area of 1 × 1cm². The aperture ratio is expected to be about 21%, which is twice as large as that of the previously proposed circuit. An integrated circuit for image processing in real time can thus be realized by applying the two-dimensional network constructed with the proposed circuits.     

Ionic conduction and effect of cation doping in Tl<Subscript>4</Subscript>HgI<Subscript>6</Subscript>

The ionic conduction properties of undoped and doped Tl₄HgI₆ were investigated using electrical conductivity, dielectrics, differential scanning calorimetry, and X-ray diffraction techniques. The heavy Tl⁺-ions diffusion was activated at high temperature, whereas low conductivity at the lower temperature suggested electronic contribution in undoped Tl₄HgI₆. The partial replacement of heavy Tl⁺ ion by suitable cations (Ag⁺ and Cu⁺) enhanced the conductivity by several orders of magnitude, whereas diminution in conductivity results with increasing dopants’ concentration in Tl₄HgI₆. These results can be interpreted in terms of a lattice contraction and vacancy–vacancy interaction (leading to the cluster formation), respectively. The dielectric values of undoped Tl₄HgI₆ system gradually increasing with temperature, followed by a sharp change, were observed around 385 K and can be explained on the basis of increasing number of space charge polarization and ions jump orientation effects. The activation energy of undoped and doped Tl₄HgI₆ systems were calculated, and it was found that ionic conductivity activation energy for 5 mol% of cation dopants is much lower than that of undoped one, and also 10 mol% doped Tl₄HgI₆ systems.     

Ultra fine carbon nitride nanocrystals synthesized by laser ablation in liquid solution

Crystalline carbon nitride nanopowders and nanorods have been successfully synthesized at room temperature and pressure using the novel technique of pulsed laser ablation of a graphite target in liquid ammonia solution. High-resolution transmission electron microscopy (HRTEM), selected area electron diffraction (SAED), and Fourier transform infrared spectroscopy (FTIR) were used to systematically study the morphology, nanostructure and chemical bonding. The experimental composition and structure of the nanoparticles are consistent with the theoretical calculations for α-C₃N₄. After 2 h ablation the particles had a size distribution ∼8–12 nm, whereas after 5 h ablation the particles had grown into nanorod-like structures with a crystalline C₃N₄ tip. A formation mechanism for these nanorods is proposed whereby nanoparticles are first synthesized via rapid formation of an embryonic particle, followed by a slow growth, eventually leading to a one-dimensional nanorod structure.