Incompatibility networks as models of scale-free small-world graphs

We make a mapping from Sierpinski fractals to a new class of networks, the incompatibility networks, which are scale-free, small-world, disassortative, and maximal planar graphs. Some relevant characteristics of the networks such as degree distribution, clustering coefficient, average path length, and degree correlations are computed analytically and found to be peculiarly rich. The method of network representation can be applied to some real-life systems making it possible to study the complexity of real networked systems within the framework of complex network theory.     

Solid structures in a highly agitated bed of granular materials

A series of experiments are described in which bubbles and solid structures are produced in a highly agitated bed of vertically shaken granular materials. To identify the physical mechanisms behind bubbling, three-dimensional simulations of the aforementioned systems are performed on a graphics processing unit (GPU). The gas dynamics above and within shaken granular materials is solved using large-eddy simulations (LES) while the dynamics of grains is described through molecular dynamics. Here, the interaction between the grain surfaces is modeled using the generalized form of contact theory developed by Hertz. In addition, the coefficient of kinetic friction is assumed to depend on the relative velocity of slipping. The results show both a qualitative and a quantitative agreement between simulations and experiments. They imply that the instantaneous formation and failure of granular aggregates could play an important role in the nucleation, growth, departure and collapse of bubbles in shaken granular materials. This promising effort in GPU computing may position the GPU as a compelling future alternative to traditional simulation techniques.     

Influence of pressure on the relative population of the two lowest vibrational levels of the C <Superscript>3</Superscript> Π<Subscript>u</Subscript> state of nitrogen for electron beam excitation

Continuous and pulsed 12 keV electron beams were used to excite nitrogen within a gas cell at pressures ranging from 10 to 1400 hPa. The pressure dependence of the ratio of photon fluxes for emission from vibrational levels v'=0 and 1 of the C ³Π _u state has been studied. The results confirm the presence of a collisional excitation mechanism populating v'=0, 1 in addition to electron impact excitation. Rate constants of (1.27 ±0.04)×10^-11 cm³s^-1 [ v'=0] and (2.68 ±0.08)×10^-11 cm³s^-1 [ v'=1] were measured for C ³Π _u quenching by ground state nitrogen. For electron beam conditions relative excitation efficiencies of 1:0.59:0.22 for vibrational levels 0, 1 and 2 were calculated. The recorded flux ratios are compared with the predictions given by a vibrational relaxation model.     

Thermal conductivity of nanofluids and size distribution of nanoparticles by Monte Carlo simulations

Nanofluids, a class of solid–liquid suspensions, have received an increasing attention and studied intensively because of their anomalously high thermal conductivites at low nanoparticle concentration. Based on the fractal character of nanoparticles in nanofluids, the probability model for nanoparticle’s sizes and the effective thermal conductivity model are derived, in which the effect of the microconvection due to the Brownian motion of nanoparticles in the fluids is taken into account. The proposed model is expressed as a function of the thermal conductivities of the base fluid and the nanoparticles, the volume fraction, fractal dimension for particles, the size of nanoparticles, and the temperature, as well as random number. This model has the characters of both analytical and numerical solutions. The Monte Carlo simulations combined with the fractal geometry theory are performed. The predictions by the present Monte Carlo simulations are shown in good accord with the existing experimental data.     

Momentum transfer theory of ion transport under the influence of resonant charge transfer collisions: the case of argon and neon ions in parent gases

Transport properties of ion swarms in presence of Resonant Charge Transfer (RCT) collisions are studied using Momentum Transfer Theory (MTT). It was shown that, not surprisingly, RCT collisions may be represented as a special case of elastic scattering. Using the developed MTT we tested a previously available anisotropic set of cross-sections for Ar+Ar ⁺ collisions by making the comparisons with the available data for the transverse diffusion coefficient. We also developed an anisotropic set of Ne+Ne ⁺ integral cross-sections based on the available data for mobility, longitudinal and transverse diffusion. Anisotropic sets of cross-sections are needed for Monte Carlo simulations of ion transport and plasma models. Received 16 June 2002 / Received in final form 2nd August 2002 Published online 24 September 2002 RID="a" ID="a"e-mail: vrhovac@phy.bg.ac.yu RID="b" ID="b"e-mail: zoran@phy.bg.ac.yu     

Haar wavelets of higher order on fractals and regularity of functions

Wavelets of Haar type of higher order m on self-similar fractals were introduced by the author in J. Fourier Anal. Appl. 4 (1998) 329-340. These are piecewise polynomials of degree m instead of piecewise constants. It was shown that for certain totally disconnected fractals, spaces of functions defined on the fractal may be characterized by means of the magnitude of the wavelet coefficients of the functions. In this paper, the study of these wavelets is continued. It is shown that also in the case when the fractals are not totally disconnected, the wavelets can be used to study regularity properties of functions. In particular, the self-similar sets considered can be, e.g., an interval in or a cube in . It turns out that it is natural to use Haar wavelets of higher order also in these classical cases, and many of the results in the paper are new also for these sets.     

Meson-baryon s-wave resonances with strangeness -3

Starting from a consistent SU(6) extension of the Weinberg-Tomozawa (WT) meson-baryon chiral Lagrangian ( Phys. Rev. D 74, 034025 (2006)), we study the s-wave meson-baryon resonances in the strangeness S = - 3 and negative-parity sectors. Those resonances are generated by solving the Bethe-Salpeter equation with the WT interaction used as kernel. The considered mesons are those of the 35-SU(6)-plet, which includes the pseudoscalar (PS) octet of pions and the vector (V) nonet of the rho-meson. For baryons we consider the 56-SU(6)-plet, made of the 1/2⁺ octet of the nucleon and the 3/2⁺ decuplet of the Delta. Quantum numbers I(J ^P) = 0(3/2^-) are suggested for the experimental resonances Ω ^*(2250)^- and Ω ^*(2380)^-. Among other, resonances with I = 1 are found, which minimal quark content is sssˉl', being s the strange quark and l, l' any of the the light up or down quarks. A clear signal for such a pentaquark would be a baryonic resonance with strangeness -3 and electric charge -2 or 0, in proton charge units. We suggest looking for K ^- Ξ ^- resonances with masses around 2100 and 2240MeV in the sector 1(1/2^-), and for π ^± Ω ^- and K ^- Ξ ^*- resonances with masses around 2260MeV in the sector 1(3/2^-).     

Design, Fabrication and Measurement of Ni/Ti Multilayer Used for Neutron Monochromator

Ni/Ti multilayers, which can be used for neutron monochromators, are designed, fabricated and measured. Firstly, their reflectivities are simulated based on the Nevot-Croce model. Reflectivities of two Ni/Ti multilayer mirrors with periods d = 10.3 nm （M1） and d = 7.8 nm （M2） are calculated. In the calculation, the reflectivity of the Ni/Ti multilayer is taken as a function of the gazing angle with different roughness factors δ =1.0 nm and = 1.5 nm. Secondly, these two multilayers are fabricated by the direct current magnetron sputtering technology. Thirdly their structures are characterized by small-angle x-ray diffraction. The roughness factors are fitted to be 0.68 nm and 1.16nm for M1 and M2, respectively. Finally their reflective performances are measured on the V14 neutron beam line at the Berlin Neutron Scattering Centre （BENSC）, Germany. The experimental data show that the grazing angle of the reflected neutron intensity peak increases, but the reflected neutron intensity decreases, with the decreasing periods of the multilayers.     

Scaling and self-similarity in Pb<Subscript>1-x</Subscript>Fe<Subscript>x</Subscript>S nanoparticle films

This paper addresses the issues of scaling and self-similarity in typical nanoparticle films. The role played by microscopic processes contributing to growth on these issues is probed. While we perform this investigation for a specific system viz., Pb_1-xFe_xS nanoparticle films for clarity of the procedures, the analysis is general and can be applied to a variety of systems obtained using different deposition techniques.     

Inevitable self-similar topology of binary trees and their diverse hierarchical density

Self-similar topology, which can be characterized as power law size distribution, has been found in diverse tree networks ranging from river networks to taxonomic trees. In this study, we find that the statistical self-similar topology is an inevitable consequence of any full binary tree organization. We show this by coding a binary tree as a unique bifurcation string. This coding scheme allows us to investigate trees over the realm from deterministic to entirely random trees. To obtain partial random trees, partial random perturbation is added to the deterministic trees by an operator similar to that used in genetic algorithms. Our analysis shows that the hierarchical density of binary trees is more diverse than has been described in earlier studies. We find that the connectivity structure of river networks is far from strict self-similar trees. On the other hand, organization of some social networks is close to deterministic supercritical trees.