• Journal of Powder Materials
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• v.14 no.6
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• pp.391-398
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• 2007

The surface roughness of Al, Ag and Ni nano-powders which were prepared by pulsed wire evaporation method was quantified based upon the fractal theory. The surface fractal dimensions of metal nano-powders were determined from the linear relationship between In $V/V_{mono}$ and Inln ($P^o/P$) using multi-layer gas adsorption theory. Moreover, the fractal surface image was realized by computer simulation. The relationship between preparation condition and surface characteristics of metal nano-powders was discussed in detail.

• Journal of the Institute of Electronics Engineers of Korea TC
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• v.39 no.12
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• pp.566-574
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• 2002

In this paper, the scattered field from a perfectly conducting fractal surface by the Monte-Carlo moment method was computed. An one-dimensional fractal surface was generated by using the fractional Brownian motion model. Back scattering coefficients are calculated with different values of the spectral parameter(S$\_$0/), and fractal dimension(D) which determine characteristics of the fractal surface. The number of surface realization for the computed field, the point number, and the width of surface realization are set to be 80, 2048, and 64L, respectively. In order to verify the computed results these results are compared with those of small perturbation methods, which show good agreement between them.

• International Journal of Concrete Structures and Materials
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• v.18 no.1E
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• pp.23-28
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• 2006

In this study, the general theory of fractality is discussed to provide a fundamental understanding of fractal geometry applied to heterogeneous material surfaces like pavement surface and rock surface. It is well known that many physical phenomena and systems are chaotic, random and that the features of roughness are found at a wide spectrum of length scales from the length of the sample to the atomic scales. Studying the mechanics of these physical phenomena, it is absolutely necessary to characterize such multi scaled rough surfaces and to know the structural property of such surfaces at all length scales relevant to the phenomenon. This study emphasizes the role of fractal geometry to characterize the roughness of various surfaces. Pavement roughness and rock surface roughness were examined to correlate their roughness property to fractality.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.28 no.2A
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• pp.63-69
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• 2003

In this paper, the scattered field from a perfectly conducting fractal surface by Finite-Difference Time-Domain(FDTD) method was computed. A one-dimensional fractal surface was generated by using the fractional Brownian motion model. Back scattering coefficients are calculated with different values of the spectral parameter(S0), fractal dimension(D) which determine characteristics of the fractal surface. The number of surface realization for the computed field, the point number, and the width of surface realization are set to be 80, 1024, 16λ, respectively. In order to verify the computed results these results are compared with those of small perturbation methods, which show good agreement between them.

• Journal of Powder Materials
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• v.10 no.3
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• pp.190-194
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• 2003

Thin Ag films deposited onto $SiO_2/Si$ substrates by DC magnetron sputtering and thereafter annealed ,it temperatures 100-50$0^{\circ}C$ are investigated by scanning tunneling and atomic forte microscopy. It is shown that the film surface topography and microstructure are considerably changed as a result of annealing. To provide a quantitative estimation of the surface topography changes of Ag films the surface fractal dimension was calculated. Elasticity and hardness of the films are studied by a nanoindentation technique. The films are found to have value of elastic modulus close to that of bulk silver while their hardness and yield stress are essentially higher.

• Water Engineering Research
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• v.6 no.2
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• pp.49-61
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• 2005

This paper presents the numerical study to examine characteristics of fluid flow and solute transport in a rough fracture subject to effective normal stresses. The aperture distribution is generated by using the self-affine fractal model. In order to represent a nonlinear relationship between the supported normal stress and the fracture aperture, we combine a simple mechanical model with the local flow model. The solute transport is simulated using the random walk particle following algorithm. Results of numerical simulations show that the flow is significantly affected by the geometry of aperture distribution varying with the effective normal stress level while it is slightly affected by the fractal dimension that determines the degree of the fracture surface roughness. However, solute transport is influenced by the effective normal stress as well as the fracture surface roughness.

• Structural Engineering and Mechanics
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• v.25 no.5
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• pp.565-576
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• 2007

The article describes a technique for the measurement of the level of complexity of fracture surfaces by the method of vertical sections, and a performed statistical analysis of the effect of profile lines on the fractographic and fractal parameters of fractures, i.e. the profile line development factor, $R_L$, and the fracture surface development factor, $R_S$, (as defined by the cycloid method), as well as the fractal dimension, $D_C$, (as determined by the chord method), and the fractal dimension, $D_{BC}$, (as determined by the box method). The above-mentioned parameters were determined for fracture surfaces of basalt and gravel concretes, respectively, which had previously been subjected to fracture toughness tests. The concretes were made from mixtures of a water/cement ratio ranging from 0.41 to 0.61 and with a variable fraction of coarse aggregate to fine aggregate, $C_{agg.}/F_{agg.}$, in the range from 1.5 to 3.5. Basalt and gravel aggregate of a fraction to maximum 16 mm were used to the tests. Based on the performed analysis it has been established that the necessary number of concrete fracture profile lines, which assures the reliability of obtained testing results, should amount to 12.

• The Journal of Engineering Geology
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• v.12 no.4
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• pp.421-437
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• 2002

In order to quantify the anisotropic properties of rock included joints and shear behavior in joint surface, the mold is Produced for rock joint surface using gypsum Plaster and Peformed for replicated joint models made of cement mortar. Rock sample is measured using mechanical profilometer before testing and their result is expressed quantitatively. The statistical parameters and the fractal dimension by fractal theory for roughness is investigated its coordinate value for numerical process. The shear strength to the shear displacement in low level normal stress ismaintained or increased in most joint models. Their results present that this relationship is depended several roughness properties in joint model for natural rock joint. The relationship between the shear strength and the Properties for profiles estimated by some statistical parameter in roughness has the low correlation and is not constant. The result between the data for direct shear test and using Barton's equation, Barton's equation has not the effectiveness for the effect of anisotropy and has not suitable to recognizing the properties for joint surface. It means that JRC has not the properties of anisotropic rock surface. The fractal dimension is well correlated with the data of direct shear test than those of JRC. New experimental formulae using fractal dimension is comported with the anisotropic properties for direct shear test.

• Journal of Korea Technical Association of The Pulp and Paper Industry
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• v.47 no.4
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• pp.177-186
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• 2015

Until Mandelbrot introduced the concept of fractal geometry and fractal dimension in early 1970s, it has been generally considered that the geometry of nature should be too complex and irregular to describe analytically or mathematically. Here fractal dimension indicates a non-integer number such as 0.5, 1.5, or 2.5 instead of only integers used in the traditional Euclidean geometry, i.e., 0 for point, 1 for line, 2 for area, and 3 for volume. Since his pioneering work on fractal geometry, the geometry of nature has been found fractal. Mandelbrot introduced the concept of fractal geometry. For example, fractal geometry has been found in mountains, coastlines, clouds, lightning, earthquakes, turbulence, trees and plants. Even human organs are found to be fractal. This suggests that the fractal geometry should be the law for Nature rather than the exception. Fractal geometry has a hierarchical structure consisting of the elements having the same shape, but the different sizes from the largest to the smallest. Thus, fractal geometry can be characterized by the similarity and hierarchical structure. A process requires driving energy to proceed. Otherwise, the process would stop. A hierarchical structure is considered ideal to generate such driving force. This explains why natural process or phenomena such as lightning, thunderstorm, earth quakes, and turbulence has fractal geometry. It would not be surprising to find that even the human organs such as the brain, the lung, and the circulatory system have fractal geometry. Until now, a normal frequency distribution (or Gaussian frequency distribution) has been commonly used to describe frequencies of an object. However, a log-normal frequency distribution has been most frequently found in natural phenomena and chemical processes such as corrosion and coagulation. It can be mathematically shown that if an object has a log-normal frequency distribution, it has fractal geometry. In other words, these two go hand in hand. Lastly, applying fractal principles is discussed, focusing on pulp and paper industry. The principles should be applicable to characterizing surface roughness, particle size distributions, and formation. They should be also applicable to wet-end chemistry for ideal mixing, felt and fabric design for papermaking process, dewatering, drying, creping, and post-converting such as laminating, embossing, and printing.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.16 no.10
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• pp.6551-6557
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• 2015

This paper discusses the surface roughness of corroded reinforcement rebar-in-coil focusing on the quantitative measurement technique using 3D scanner. Reinforcement rebar-in-coil was stacked in site for 0 day, 3 days, 7 days, 14 days and 21 days. And rebar-in-coil was corroded 0.04%, 0.3367%, 0.6157%, 0.7898%, and 1.1965% respectively. Using 3-dimensional scanner, each surface profile of reinforcement rebar-in-coil was established, and surface roughness was measured. Through the tests and analyses of corroded rebar-in-coil, the increase of fractal dimension for each rebar-in-coil was measured as 0.0216, 0.0235, 0.028, 0.0319, and 0.0455 for different stacked periods. Therefore, surface assessment technique using fractal dimension showed similar results with the actual corrosion rate.