• Journal of Korean Society of Coastal and Ocean Engineers
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• v.9 no.3
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• pp.115-124
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• 1997

We measured the variance of eddy diffusion and associated ‘diffusion coefficients’ in coastal regions of Korea by observing the separation distances among multiple drifters deployed simultaneously at the same initial position. The variance of eddy diffusion was found to be proportional to $t^m$, where t is the time and m is a non-integer scaling exponent between 1.5 and 3.5. The observed scaling exponent of eddy diffusion cannot be reproduced by diffusion models employing constant eddy diffusivity. In this study, we applied fractal theory in simulating exponential increase of variance of eddy diffusion. We employed the fGn(fractional Gaussian noise) as a ‘modified’ random walks corresponding to the oceanic eddy diffusion. The variance of eddy diffusion, which corresponds to the fBm(fractional Brown motion) of our diffusion model, is proportional to $t^{2H}$, where H is Hurst scaling exponent. The temporal increase of the variance. with scaling exponent between 1 and 2, was successfully reproduced by our fractal diffusion model. However, our model cannot reproduce scaling exponent greater than 2. The scaling exponents greater than 2 are associated with the velocity shear of the mean flow.

• Korea-Australia Rheology Journal
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• v.17 no.1
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• pp.15-20
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• 2005

In this study, the relationship between morphology and viscosity of the main culture broth of Cephalosporium acremonium M25 was investigated in a 2.5 L bioreactor. The differentiation of C. acremonium M25 showed a complex pattern during the main culture. The morphological changes of C. acremonium M25 were related to the rheological properties of the culture broth and it was well agreed with the power law model. As a result of rheology study, it was found that rheological properties of the main culture broths of C. acremonium M25 in bioreactor were closely related to morphological changes. Also, fractal dimension fairly predicted morphological and rheological changes in the main culture broth.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.372-375
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• 2003

The incidence of blindness resulting from diabetic retinopathy has significantly increased despite the intervention of insulin to control diabetes mellitus. Early signs are microaneurysms, exudates, intraretinal hemorrhages, cotton wool patches, microvascular abnormalities, and venous beading. Advanced stages include neovascularization, fibrous formations, preretinal and vitreous microhemorrhages, and retinal detachment. Microaneurysm count is important because it is an indicator of retinopathy progression. The purpose of this paper is to apply data mining to detect diabetic retinopathy patterns in routine fundus fluorescein angiography. Early symptoms are of principal interest and therefore the emphasis is on detecting microaneurysms rather than vessel tortuosity. The analysis does not involve image-recognition algorithms. Instead, mathematical filtering isolates microaneurysms, microhemorrhages, and exudates as objects of disconnected sets. A neural network is trained on their distribution to return fractal dimension. Hausdorff and box counting dimensions grade progression of the disease. The field is acquired on fluorescein angiography with resolution superior to color ophthalmoscopy, or on patterns produced by physical or mathematical simulations that model viscous fingering of water with additives percolated through porous media. A mathematical filter and neural network perform the screening process thereby eliminating the time consuming operation of determining fractal set dimension in every case.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1997.04a
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• pp.817-821
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• 1997

Ever since the nonlinearity of machine tool dynamics was established, researchers attempted to make use of this fact to devise better monitoring, diagnostics and system, which were hitherto based on linear models. Theory of chaos, which explains many nonlinear phenomena comes handy for furthering the analysis using nonlinear model. In this study, measuring system will be constructed using multi-sensor (Tool Dynamometer, Acoustic Emission) in end millingprocess. Then, it will be verified that cutting force is low-dimensional deterministic chaos calculating Lyapunov exponents, Fractal dimension, Embedding dimension. Aen it will be investigated that the relations between characteristic parameter caculated form sensor signal and tool wear.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 1996.10a
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• pp.295-300
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• 1996

In this study, the dynamic instabilities of a nonlinear elastic system subjected to follower force are investigated. The two-degree-of-freedom double pendulum model with nonlinear geometry, cubic spring, and linear viscous damping is used for the study. The constant and periodic follower forces are considered. The chaotic nature of the system is identified using the standard methods, such as time histories, phase portraits, and Poincare maps, etc.. The responses are chaotic and unpredictable due to the sensitivity to initial conditions. The sensitivities to parameters, such as geometric initial imperfections, magnitude of follower force, and viscous damping, etc. is analysed. The strange attractors in Poincare map have the self-similar fractal geometry. Dynamic buckling loads are computed for various parameters, where the loads are changed drastically for the small change of parameters.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2011.06a
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• pp.469-470
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• 2011

• Geomechanics and Engineering
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• v.11 no.5
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• pp.639-655
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• 2016

The effect of particle breakage and intermediate principal stress ratio on the behaviour of crushable granular assemblies under true triaxial stress conditions is studied using the discrete element method. Numerical results show that the increase of intermediate principal stress ratio $b(b=({\sigma}_2-{\sigma}_3)/({\sigma}_1-{\sigma}_3))$ results in the increase of dilatancy at low confining pressures but the decrease of dilatancy at high confining pressures, which stems from the distinct increasing compaction caused by breakage with b. The influence of b on the evolution of the peak apparent friction angle is also weakened by particle breakage. For low relative breakage, the relationship between the peak apparent friction angle and b is close to the Lade-Duncan failure model, whereas it conforms to the Matsuoka-Nakai failure model for high relative breakage. In addition, the increasing tendency of relative breakage, calculated based on a fractal particle size distribution with the fractal dimension being 2.5, declines with the increasing confining pressure and axial strain, which implies the existence of an ultimate graduation. Finally, the relationship between particle breakage and plastic work is found to conform to a unique hyperbolic correlation regardless of the test conditions.

• Tribology and Lubricants
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• v.30 no.6
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• pp.378-383
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• 2014

This study predicts the of the hysteretic friction of a rubber block sliding on an SMA asphalt road. The friction of filled rubber on a rough surface is primarily determined by two elements:the viscoelasticity of the rubber and the multi-scale perspective asperities of the road. The surface asperities of the substrate exert osillating forces on the rubber surface leading to energy dissipation via the internal friction of the rubber when rubber slides on a hard and rough substrate. This study defines the power spectra at different length scales by using a high-resolution surface profilometer, and uses rubber and road surface samples to conduct friction tests. I consider in detail the case when the substrate surface has a self affine fractal structure. The theory developed by Persson is applied to describe these tests through comparison with the hysteretic friction coefficient relevant to the energy dissipation of the viscoelastic rubber attributable to cyclic deformation. The results showed differences in the absolute values of predicted and measured friction, but with high correlation between these values. Hence, the friction prediction model is an appropriate tool for separating the effects of each factor. Therefore, this model will contribute to clearer understanding of the fundamental principles of rubber friction.

• Smart Structures and Systems
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• v.33 no.3
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• pp.227-241
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• 2024

Safety and structural integrity of civil structures, like bridges and buildings, can be substantially enhanced by employing appropriate structural health monitoring (SHM) techniques for timely diagnosis of incipient damages. The information gathered from health monitoring of important infrastructure helps in making informed decisions on their maintenance. This ensures smooth, uninterrupted operation of the civil infrastructure and also cuts down the overall maintenance cost. With an early warning system, SHM can protect human life during major structural failures. A real-time online damage localization technique is proposed using only the vibration measurements in this paper. The concept of the 'Degree of Scatter' (DoS) of the vibration measurements is used to generate a spatial profile, and fractal dimension theory is used for damage detection and localization in the proposed two-phase algorithm. Further, it ensures robustness against environmental and operational variability (EoV). The proposed method works only with output-only responses and does not require correlated finite element models. Investigations are carried out to test the presented algorithm, using the synthetic data generated from a simply supported beam, a 25-storey shear building model, and also experimental data obtained from the lab-level experiments on a steel I-beam and a ten-storey framed structure. The investigations suggest that the proposed damage localization algorithm is capable of isolating the influence of the confounding factors associated with EoV while detecting and localizing damage even with noisy measurements.

• Economic and Environmental Geology
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• v.30 no.5
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• pp.433-442
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• 1997

A dual-permeability fractal model of fluid flow is proposed. The model simulates groundwater flow in fissured dual aquifer system composed of Aquifer 1 and Aquifer 2. For this model. groundwater flow originates only from Aquifer 1 on the pumping well. The model considers wellbore storage and skin effects at the pumping well and then shows exact drawdown at the early time of pumping. Type curves for different flow dimensions and for two cases are presented and analyzed. The case 1 represents the aquifer system which consists of Aquifer 1 with low permeability and high specific storage and Aquifer 2 with high permeability and low specific storage. The case 2 is inverse to the case 1. Dimensionless drawdown curves in Aquifer 1 and Aquifer 2 shows characteristic trend each other. Consequently, the model will be useful to analyze pumping test data of different draw down patterns on the pumping well and observation wells.