• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.827-835
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• 2005

As a tool of measuring the irregularity of curve, fractal dimensions can be used. For an irregular function, fractional calculus are more available. However, to know its fractional differentiability which is related to its complexity is complicated one. In this paper, variants of the Hausdorff dimension and the packing dimension as well as the derivative order are defined and the relations between them are investigated so that the differentiability of fractal curve can be explained through its complexity.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
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• 2000.11a
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• pp.81-84
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• 2000

Two-layer aquifer system with fractional flow dimension is composed of contiguous two layers: Layer 1 (lower layer) and Layer 2 (upper layer) with different permeability and specific storage each other. For this aquifer system, we assume that groundwater flow originates only from Layer 1 on the pumping well. The aquifer system considers wellbore storage and skin effects on the pumping well. Dimensionless drawdown curves for different flow dimensions are analyzed for different lambda (λ, crossflow coefficient) values, kappa ($textsc{k}$, permeability ratio between Layer 1 and Layer 2) values and omega ($\omega$, storativity ratio between Layer 1 and Layer 2) values. The curves for Layer 1 and Layer 2 show characteristic trend each other.

• Geomechanics and Engineering
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• v.21 no.1
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• pp.85-93
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• 2020

In this article, the generalized thermoelastic theory with fractional derivative is presented to estimate the variation of temperature, the components of stress, the components of displacement and the changes in volume fraction field in two-dimensional porous media. Easily, the exact solutions in the Laplace domain are obtained. By using Laplace and Fourier transformations with the eigenvalues method, the physical quantities are obtained analytically. The numerical results for all the physical quantities considered are implemented and presented graphically. The results display that the present model with the fractional derivative is reduced to the Lord and Shulman (LS) and the classical dynamical coupled (CT) theories when the fractional parameter is equivalent to one and the delay time is equal to zero and respectively.

• The Journal of Engineering Geology
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• v.9 no.2
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• pp.101-118
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• 1999

The pumping test analysis on 28 pumping test data in Duksan hot-spring area was performed using the fractal model, the leaky fractal model, and the steady-state dual-porosity fractal model. The fractional flow dimension 1.9 or 2.0 was determined in the central put of the hot spring and the fractional flow dimension 1.5-1.7 in the marginal area. For the flow dimension 2.0, the correlation between the transmissivity and the productivity index by the aquifer loss was much better than that between the transmissivity and the specific yield by the total drawdown. On the other hand, for the flow dimension 1.9, the correlation between the generalized transmissivity and the productivity index was very similar to that between the generalized transmissivity and the specific yield.

• Geomechanics and Engineering
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• v.23 no.3
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• pp.217-225
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• 2020

In this paper, the thermoelastic interactions in a two-dimension porous body are studied. This problem is solved by using the Green and Lindsay (GL) generalized thermoelasticity model under fractional time derivative. The derived approaches are estimated. with numeral results which are applied to the porous mediums in simplifying geometrical. The bounding plane surface of the present half-space continuum is subjected to a pulse heat flux. We use the Laplace-Fourier transforms methods with the eigenvalues approach to solve the problem. The numerical solutions for the field functions are obtained numerically using the numerical Laplace inversion technique. The effects of the fractional parameter and the thermal relaxation times on the temperature field, the displacement field, the change in volume fraction field of voids distribution and the stress fields have been calculated and displayed graphically and the obtained results are discussed.

• Journal of Electrochemical Science and Technology
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• v.5 no.2
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• pp.53-57
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• 2014

With the use of diffusion-limited aggregation modeling, we have investigated the effect of particle drift for dendritic growth. It is found that the morphology of dendritic growth is sensitive to the particle drift, i.e., the larger drift effect results in the denser growth of dendrite. From the analysis using the correlation function, we found the fractional dimension of each dendrite increases as the particles drift increases. Furthermore, we showed the height of dendrite significantly decrease for the slight change of particles drift. Finally, we discussed the strategy to reduce dendritic growth by modifying the transport properties of electrolytes.

• Bulletin of the Korean Chemical Society
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• v.26 no.11
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• pp.1723-1727
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• 2005

A generalized fractional diffusion equation (FDE) is presented, which describes the time-evolution of the spatial distribution of a particle performing continuous time random walk (CTRW) on a fractal lattice. For a case corresponding to the CTRW with waiting time distribution that behaves as $\psi(t) \sim (t) ^{-(\alpha+1)}$, the FDE is solved to give analytic expressions for the Green’s function and the mean squared displacement (MSD). In agreement with the previous work of Blumen et al. [Phys. Rev. Lett. 1984, 53, 1301], the time-dependence of MSD is found to be given as < $r^2(t)$ > ~ $t ^{2\alpha/dw}$, where $d_w$ is the walk dimension of the given fractal. A Monte-Carlo simulation is also performed to evaluate the range of applicability of the proposed FDE.

• Journal of Chest Surgery
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• v.27 no.8
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• pp.656-663
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• 1994

Evaluation of heart function is of importance in assessing the results of valvular heart surgery. Information on volume and functional change of heart chamber can be obtained by cardiac catheterization and echocardiography. We studied 41 patients with mitral stenosis[MS] and 23 patients with mitral regurgitation[MR] using M-mode echocardiography before and after mitral valve replacement[MVR] at Pusan Paik Hospital. Preoperative cardiac catheterization was available in 56 cases, and the results were obtained as follows. 1. In patients with MS, preoperative average LV end-diastolic dimension[EDD] and end-systolic dimension[ESD] were remained within normal range, but postoperative EDD and ESD were significantly decreased[P<0.01]. The preoperative and postoperative LV ejection fraction[EF] were remained within the normal range and no significant change[P>0.05]. The preoperative left atrial dimension[LAD] was enlarged considerably above normal[P<0.01], but was significantly decreased after surgery[P<0.001]. The preoperative LV posterior wall thickness[PWTh] was within normal range, and no significant change after surgery[P>0.05]. 2. In patients with MR, preoperative average end-diastolic dimension[EDD] and end-systolic dimension[ESD] were significantly greater than normal[P<005], but postoperative EDD and ESD were significantly decreased[P<0.01]. The preoperative LV ejection fraction[EF] and fractional shortening[FS] were within normal range, and no significant change after surgery[P>0.05].The preoperative left atrial dimension[LAD] was enlarged considerably above normal [P<0.01], but was significantly decreased after surgery[P<0.001].The preoperative LV posterior wall thickness[PWTh] was within normal range, and no significant change after surgery[P>0.05].

• Proceedings of the Korea Concrete Institute Conference
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• 2001.05a
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• pp.333-338
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• 2001

Fractal geometry is a non-Euclidean geometry which has been developed to quantitative analysis irregular or fractional shapes. Fractal dimension of irregular surface has fractal values ranging from 2 to 3 and of irregular line profile has fractal values ranging from 1 to 2. In this paper, quantitative analysis of crack growth patterns during the fracture processing of fiber-reinforced cement composites based on fractal geometry. The fracture behaviors of fiber reinforced mortar beams subjected to three-point loading in flexure. The beams all had a single notch depth, but varing volume fractions of polypropylene, cellulose fibers. The crack growth behaviors, as observed through the image processing system, and the box counting method was used to determine the fractal dimension, Df. The results showed that the linear correlation exists between fractal dimension and fracture energy of the fiber reinforced cement mortar.

• Proceedings of the KOSOMBE Conference
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• v.1995 no.05
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• pp.37-41
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• 1995

In this paper, we proposed the 2-stage ultrasound liver image classifier which uses the fractal dimensions obtained from the original image and its 1/2 subsampled image, and the Normalized Fourier Power Spectrum. The fractal dimension based on Fractional Brownian Motion (FBM) is calculated from the variance of the same scale pixels instead of the mean of them. Since the actual ultrasound. liver images does not fully match the FBM, to get the fractal dimension, we use the scale vectors which satisfy the FBM model. In 2-stage classifier, we first classified normal and diffuse liver and then classified the fat liver and cirrhosis from the diffuse liver. For the test liver images. 70% of normal liver and 80% of fat liver and 90% of cirrhosis is classified classified with our 2-stage classifier.