Numerical simulation of magnetic-field-enhanced plasma immersion ion implantation in cylindrical geometry

Recent studies have demonstrated that the sheath dynamics in plasma immersion ion implantation (PIII) is significantly affected by an external magnetic field. In this paper, a two-dimensional computer simulation of a magnetic-field-enhanced PHI system is described. Negative bias voltage is applied to a cylindrical target located on the axis of a grounded vacuum chamber filled with uniform molecular nitrogen plasma. A static magnetic field is created by a small coil installed inside the target holder. The vacuum chamber is filled with background nitrogen gas to form a plasma in which collisions of electrons and neutrals are simulated by the Monte Carlo algorithm. It is found that a high-density plasma is formed around the target due to the intense background gas ionization by the magnetized electrons drifting in the crossed E x B fields. The effect of the magnetic field intensity, the target bias, and the gas pressure on the sheath dynamics and implantation current of the PHI system is investigated.

Structural characteristics of gels prepared from sonohydrolysis and conventional hydrolysis of TEOS: an emphasis on the mass fractal as determined from the pore size distribution

Silica gels were preparated from fixed proportion mixtures of tetraethoxysilane, water and hydrocloric acid, using either ultrasound stimulation (US) or conventional method (CO) in the hydrolysis step of the process. Wet gets were obtained with the same silica volume concentration and density. According to small-angle X-ray scattering, the structure of the wet gels can be described as mass fractal structures with mass fractal dimension D = 2.20 in a length scale xi = 7.9 nm, in the case of wet gels US, and D = 2.26 in a length scale 6.9 nm, in the case of wet gels CO. The mass fractal characteristics of the wet gels US and CO account for the different structures evolved in the drying of the gels US and CO in the obtaining of xerogels and aerogels. The pore structure of the dried gels was studied by nitrogen adsorption as a function of the temperature. Aerogels (US and CO) present high porosity with pore size distribution (PSD) curves in the mesopore region while xerogels (US and CO) present minor porosity with PSD curves mainly in the micropore region. The dried gels US (aerogels and xerogels) generally present pore volume and specific surface area greater than the dried gels CO. The mass fractal structure of the aerogels has been studied from an approach based on the PSD curves exclusively. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Effect of tillage on fractal indices describing soil surface microrelief of a Brazilian Alfisol

Soil surface roughness is known to influence water infiltration, runoff and erosion. Soil surface roughness changes with management and weather and its mathematical description still remains an important issue. The main objective of this study was to investigate the effect of tillage on the two fractal indices, fractal dimension, D, and crossover length, 1, currently used in characterizing soil surface microrelief. The statistical index random roughness, RR, was also assessed. Field experiments were done on an Alfisol located at Rio Grande do Sul State (Brazil). Two tillage treatments (conventional versus direct drilling) were tested. The soil surface microrelief was assessed by point elevation measurements in 16 plots for each treatment. The sampling scheme was a square grid with 20 x 20 mm between point spacing and the plot size was 280 x 280 mm, so that each data set consisted of 225 individual elevation points. All indices were calculated after trend removal, both by slope correction, i.e., oriented microrelief, and by slope plus tillage marks correction, i.e., random microrelief. The implemented algorithm for estimating D and 1 consisted in evaluating the roughness around the local root mean square deviation (RMS) of the point elevation values. Irrespective of tillage treatment and detrending procedure, fractal behavior extended only over a bounded range of scales, from 40 to 100 mm, due to the experimental setup. In these conditions, assessing fractal indices was not always straightforward. The statistical index RR and the fractal index I were significantly different between tillage treatments for oriented and random surface conditions. D values of random soil surfaces were not affected by tillage treatment, whereas D values of oriented microrelief were significantly lower in the direct drilled plots. Removal of tillage marks trend resulted in a significant increase in D values. Within each tillage treatment, 1 and D were significantly correlated. (c) 2006 Elsevier B.V. All rights reserved.

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

Wet silica gels with similar to 1.4 x 10(-3) mol SiO2/cm(3) and similar to 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 xi decreasing from similar to 9.4 nm to similar 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 similar to 2.6 and surface fractal dimension D-s similar to 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. (c) 2006 Elsevier B.V. All rights reserved.

Fluctuating commutative geometry

We use the framework of noncommutative geometry to define a discrete model for fluctuating geometry. Instead of considering ordinary geometry and its metric fluctuations, we consider generalized geometries where topology and dimension can also fluctuate. The model describes the geometry of spaces with a countable number n of points. The spectral principle of Connes and Chamseddine is used to define dynamics. We show that this simple model has two phases. The expectation value , the average number of points in the universe, is finite in one phase and diverges in the other. Moreover, the dimension delta is a dynamical observable in our model, and plays the role of an order parameter. The computation of is discussed and an upper bound is found, < 2. We also address another discrete model defined on a fixed d = 1 dimension, where topology fluctuates. We comment on a possible spontaneous localization of topology.

Temperature dependence of fractal dimension of grain boundary region in SnO2 based ceramics

Fractal dimensions of grain boundary region in doped SnO2 ceramics were determined based on previously derived fractal model. This model considers fractal dimension as a measure of homogeneity of distribution of charge carriers. Application of the derived fractal model enables calculation of fractal dimension using results of impedance spectroscopy. The model was verified by experimentally determined temperature dependence of the fractal dimension of SnO2 ceramics. Obtained results confirm that the non-Debye response of the grain boundary region is connected with distribution of defects and consequently with a homogeneity of a distribution of the charge carriers. Also, it was found that C-T-1 function has maximum at temperature at which the change in dominant type of defects takes place. This effect could be considered as a third-order transition.

Study of plasma immersion ion implantation into silicon substrate using magnetic mirror geometry

The effect of magnetic field enhanced plasma immersion ion implantation (PIII) in silicon substrate has been investigated at low and high pulsed bias voltages. The magnetic field in magnetic bottle configuration was generated by two magnetic coils installed outside the vacuum chamber. The presence of both, electric and magnetic field in PIII creates a system of crossed E x B fields, promoting plasma rotation around the target. The magnetized electrons drifting in crossed E x B fields provide electron-neutral collision. Consequently, the efficient background gas ionization augments the plasma density around the target where a magnetic confinement is achieved. As a result, the ion current density increases, promoting changes in the samples surface properties, especially in the surface roughness and wettability and also an increase of implantation dose and depth. (C) 2012 Elsevier B. V. All rights reserved.

The Meaningful Fractal Fuzzy Dimension Applied to the Design of Self Organizing Maps

This paper presents the principal results of a detailed study about the use of the Meaningful Fractal Fuzzy Dimension measure in the problem in determining adequately the topological dimension of output space of a Self-Organizing Map. This fractal measure is conceived by combining the Fractals Theory and Fuzzy Approximate Reasoning. In this work this measure was applied on the dataset in order to obtain a priori knowledge, which is used to support the decision making about the SOM output space design. Several maps were designed with this approach and their evaluations are discussed here.

Fractal dimension and anisotropy of soil CO2 emission in an agricultural field during fallow

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Quantum geometry of chiral bosons on a circle

We extend the geometric treatment done for the Majorana-Weyl fermions in two dimensions by Sanielevici and Semenoff to chiral bosons on a circle. For this case we obtain a generalized Floreanini-Jackiw Lagrangian density, and the corresponding gravitational (or Virasoro) anomalies are found as expected. © 1989 The American Physical Society.

On the geometry of non-classical curves

In this paper we relate the numerical invariants attached to a projective curve, called the order sequence of the curve, to the geometry of the varieties of tangent linear spaces to the curve and to the Gauss maps of the curve. © 1992 Sociedade Brasileira de Matemática.

Evolution of the fractal structure during sintering of SnO2 compacted sol-gel powder

The structural evolution during sintering of compacted SnO2 sol-gel powder was investigated using nitrogen adsorption isotherm analysis. Results show that for sintering temperatures up to 400°C the samples have a fractal pore size distribution. As the sintering temperature increases, a structural rearragement occurs, allowing an increase of the efficiency of particle packing and the reduction of fractality. Above 400°C, the pore size growth associated with grain coalescence is the main structural change observed as the sintering temperature increases. © 1995.

A abordagem fractal em Geociencias

This is a synthesis of the use of fractal approaches in geosciences. It presents references and a list of publications, taking into account sectors of many fields, including geophysics, petrology, mineralogy, sedimentology, tectonics, meteorology, climatology, geomorphology, hydrogeology, oceanography, geomechanics, geochemistry and soil studies. -English summary

Combining genetic algorithm and simulated annealing: A molecular geometry optimization study

We introduce a new hybrid approach to determine the ground state geometry of molecular systems. Firstly, we compared the ability of genetic algorithm (GA) and simulated annealing (SA) to find the lowest energy geometry of silicon clusters with six and 10 atoms. This comparison showed that GA exhibits fast initial convergence, but its performance deteriorates as it approaches the desired global extreme. Interestingly, SA showed a complementary convergence pattern, in addition to high accuracy. Our new procedure combines selected features from GA and SA to achieve weak dependence on initial parameters, parallel search strategy, fast convergence and high accuracy. This hybrid algorithm outperforms GA and SA by one order of magnitude for small silicon clusters (Si6 and Si10). Next, we applied the hybrid method to study the geometry of a 20-atom silicon cluster. It was able to find an original geometry, apparently lower in energy than those previously described in literature. In principle, our procedure can be applied successfully to any molecular system. © 1998 Elsevier Science B.V.