Indirect magnetic interaction in the “net fractal” systems

A localized spin system of fractal symmetry with indirect exchange between them is considered. We define a specific class of fractals as the “net fractals” which display multidimensional logarithmic periodicity. Basing on this property we model the effective indirect exchange interaction by the conventional RKKY exchange with the logarithmic coordinates playing role of the real space ones. Finally, we discuss the case of non-ideal “net fractals” in which fractional dynamics of the electrons is expected. In this case we show that RKKY exchange integrals are given by the formulas derived under assumption that a system has a fractional spectral dimension.     

Bound states and resonance states of the plasma-embedded tdμ and ddμ molecular ions

We have investigated the bound states and resonance states of plasma-embedded tdμ and ddμ molecular ions using accurate correlated basis functions. The plasma effect has been taken care of by considering the Debye shielding approach of plasma modeling which admits a variety of plasma conditions. The density of resonance states are calculated using the stabilization method. The ground and excited states energies, and the S-wave resonance energies of tdμ and ddμ molecular ions immersed in plasmas are reported for various shielding parameters, along with the 1S and 2S threshold energies of the tμ and dμ atoms.     

Complex-scaling treatment for high-lying doubly excited resonances for screened Coulomb helium atom

This work presents an investigation on the doubly excited ¹S ^e autoionizing states of screened helium atom lying below the n = 4 threshold of the He⁺ ion. The potential generated in this system is represented by a Yukawa type potential. We have employed complex-coordinate rotation method, as it is a powerful scheme to study high lying resonances. Hylleraas type wave function is used to consider the correlation effect between all the charged particles. Our resonance parameters for the resonances lying below the He⁺ (n = 2) threshold agree well with those of the existing calculations by using the stabilization method. Resonances associated with higher thresholds are new calculations. All the present results are well converged with basis length N = 444.     

Silver fractal networks for surface-enhanced Raman scattering substrates

Based on diffusion-limited aggregation process, a convenient nanotechnique is demonstrated to obtain large silver fractal networks for a surface-enhanced Raman scattering (SERS)-active substrate. The silver fractal networks are of high SERS enhancement factor, large dynamical range. The observed SERS efficiency can be explained in terms of strongly localized plasmon modes relative to the single particle plasmon resonance.     

Effect of cation doping on low-temperature specific heat of LaMnO3 manganite

We have investigated the thermodynamic properties of perovskite manganite LaMnO₃, the parent compound of colossal magnetoresistive manganites, with the Ca²⁺ doping at the A-site. As strong electron-phonon interactions are present in these compounds, the lattice part of the specific heat deserves proper attention. We have described the temperature dependence of the lattice contribution to the specific heat at constant volume (C_v(lattice)) of La_1−xCa_xMnO₃ (x=0.125, 0.175, 0.25, 0.35, 0.50, 0.67, 0.75) as a function of temperature (1 K–20 K) by means of a rigid ion model (RIM).The trends of specific heat variations with temperature are almost similar at all the composition. The Debye temperatures obtained from the lattice contributions are found to be in somewhat closer agreement with the experimental data. The specific heat values revealed by using RIM are in closer agreement with the available experimental data, particularly at low temperatures for some concentrations (x) of La_1−xCa_xMnO₃. The theoretical results at higher temperatures can be improved by including the effects of the charge ordering, van der Waals attraction and anharmonicity in the framework of RIM.     

Cluster growth poised on the edge of break-up: Size distributions with small exponent power-laws

In many naturally occurring growth processes, cluster size distributions of power-law form n(s)∝s^−τ with small exponents 0<τ<1 are observed. We suggest here that such distributions emerge naturally from cluster growth, where size dependent aggregation is counterbalanced by size dependent break-up. The model used in the study is a simple reaction kinetic model including only monomer-cluster processes. It is shown that under such conditions power-law size distributions with small exponents are obtained. Therefore, the results suggest that the ubiquity of small exponent power-law distributions is related to the growth process, where aggregation driven cluster growth is poised on the edge of cluster break-up.     

Mass fractal characteristics of sonogels prepared from sonohydrolysis of tetraethoxysilane with additions of dimethylformamide

Wet silica gels with ∼1.4 × 10⁻³ mol SiO₂/cm³ and ∼90 vol.% liquid phase were prepared from the sonohydrolysis of tetraethoxysilane (TEOS) with different additions of dimethylformamide (DMF). Aerogels were obtained by CO₂ supercritical extraction. The samples were studied mainly by small-angle X-ray scattering (SAXS) and nitrogen adsorption. Wet gels exhibit a mass fractal structure with fractal dimension D increasing from 2.23 to 2.35 and characteristic length ξ decreasing from ∼9.4 nm to ∼5.1 nm, as the DMF/TEOS molar ratio is increased from 0 to 4. The supercritical process apparently eliminates some porosity, shortening the fractality domain in the mesopore region and developing an apparent surface/mass fractal (with correlated mass fractal dimension D_m ∼ 2.6 and surface fractal dimension D_s ∼ 2.3) in the micropore region. The fundamental role of the DMF addition on the structure of the aerogels is to diminish the porosity and the pore mean size, without, however, modify substantially the specific surface area and the average size of the silica particle of the solid network.     

Structural evolution up to 1100 °C of xerogels prepared from TEOS sonohydrolysis and liquid phase exchanged by acetone

Silica xerogels were prepared from sonohydrolysis of tetraethoxysilane and exchange of the liquid phase of the wet gel by acetone. Monolithic xerogels were obtained by slow evaporation of acetone. The structural characteristics of the xerogels were studied as a function of temperature up to 1100 °C by means of bulk and skeletal density measurements, linear shrinkage measurements and thermal analyses (DTA, TG and DL). The results were correlated with the evolution in the UV-Vis absorption. Particularly, the initial pore structure of the dried acetone-exchanged xerogel was studied by small-angle X-ray scattering and nitrogen adsorption. The acetone-exchanged xerogels exhibit greater porosity in the mesopore region presenting greater mean pore size (∼4 nm) when compared to non-exchanged xerogels. The porosity of the xerogels is practically stable in the temperature range between 200 °C and 800 °C. Evolution in the structure of the solid particles (silica network) is the predominant process upon heating up to about 400 °C and pore elimination is the predominant process above 900 °C. At 1000 °C the xerogels are still monolithic and retain about 5 vol.% pores. The xerogels exhibited foaming phenomenon after hold for 10 h at 1100 °C. This temperature is even higher than that found for foaming of non-exchanged xerogels.     

Visualizing the log-periodic pattern before crashes

We present a method for visualizing the pattern which we believe to be a precursor signature of financial crashes (or ruptures). The log-periodicity of the pattern is investigated through the envelope function technique. Three periods of the Dow Jones Industrial Average (DJIA) are investigated: 1982-1987, 1992-1997 and 1993-1998. The presence of a rupture in the end of 1998 is outlined from data taken before the end of August 1998. Received 15 October 1998 and Received in final form 19 November 1998     

Energy transfer studies in krypton-xenon mixtures excited in a cooled DC discharge

The VUV spectrum of gaseous mixtures of krypton with a small amount of xenon added was investigated in the range 115-200 nm. The mixtures were excited in a capillary DC discharge where the capillary could be cooled by using liquid nitrogen. The mixed molecule band around the XeI resonance line at nm and the mixed molecule continuum to the long wavelength side from the line were analysed. The band around nm was identified as transitions between a weakly bound excited state and the weakly bound ground state of XeKr molecules. When cooling the capillary wall, the appearance of the Xe₂ continuum was observed. The effect is ascribed to energy transfer between molecular states as a consequence of radiation trapping in the band around nm. The role of the mixed molecule in the formation of the VUV spectrum of the gas mixture is discussed and underlined. Received 12 May 1999 and Received in final form 27 August 1999