• Structural Engineering and Mechanics
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• v.55 no.6
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• pp.1157-1176
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• 2015

This study presents optimizing structural topology patterns using regularization of Heaviside function. The present method needs not filtering process to typical SIMP method. Using the penalty formulation of the SIMP approach, a topology optimization problem is formulated in co-operation, i.e., couple-signals, with design variable values of discrete elements and a regularized Heaviside step function. The regularization of discontinuous material distributions is a key scheme in order to improve the numerical problems of material topology optimization with 0 (void)-1 (solid) solutions. The weak forms of an equilibrium equation are expressed using a coupled regularized Heaviside function to evaluate sensitivity analysis. Numerical results show that the incorporation of the regularized Heaviside function and the SIMP leads to convergent solutions. This method is tested using several examples of a linear elastostatic structure. It demonstrates that improved optimal solutions can be obtained without the additional use of sensitivity filtering to improve the discontinuous 0-1 solutions, which have generally been used in material topology optimization problems.

• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.147-169
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• 2012

We introduce a Heaviside-function formulation of the interaction between incompressible two-phase fluid and a non-deformable solid. Fluid and solid interact in two ways : fluid satises the Dirichlet boundary condition imposed by the velocity field of solid, and solid is accelerated by the surface traction exerted by fluid. The two-way couplings are formulated by the Heaviside function to the interface between solid and fluid. The cumbersome treatment of interface is taken care of by the Heaviside function, and the interaction is discretized in a simple manner. The discretization results in a stable and accurate projection method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.21 no.2
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• pp.75-79
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• 2017

This paper approaches the subject of consciousness and unconsciousness from a mathematical point of view. It sets up a hypothesis that when unconscious state becomes conscious state, high density energy is released. We argue that the process of transformation of unconsciousness into consciousness can be expressed using the infinite recursive Heaviside step function. We claim that differentiation of the potential of unconsciousness with respect to time is the process of being conscious in a world where only time exists, since the thinking process never have any concrete space. We try to attribute our unconsciousness to a special solution of the multi-dimensional advection partial differential equation which can be represented by the finite recursive Heaviside step function. Mathematical language explains how the infinitive neural process is perceived and understood by consciousness in a definitive time.

• Proceedings of the Korean Society of Computer Information Conference
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• 2022.01a
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• pp.339-340
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• 2022

본 논문에서는 사용자의 다양한 물리적 속성 중 부드러운 헤비사이드 계단 함수와 다양한 물리적 속성(속도, 시점 등)을 활용하여 가중치 맵을 계산하고 이로부터 논플레이어 캐릭터(Non-player character, NPC)의 경로를 효율적으로 제어할 수 있는 NavMesh 제어 기법을 제시한다. 게임과 같은 가상환경에서 NPC는 일반적으로 네비게이션 메쉬(Navigation mesh, NavMesh)를 이용하여 이동한다. 하지만, NavMesh는 정적인 형태이기 때문에 사용자에 의해 디자인되어야 하고, 이러한 문제를 완화하고자 자동으로 NavMesh를 업데이트하는 기술이 연구되고 있지만, 메쉬 복원을 자동화할 뿐 실제 NPC 행동 제어라고 하기에는 힘든 접근법이다. 본 논문에서는 동적 네비게이션 프레임워크를 유지한 채, 사용자의 시점과 물리적 특성을 통해 NPC를 효율적이고 정확하게 경로 제어할 수 있는 방법을 제안하고, NavMesh의 형태에만 의존하던 NPC의 움직임을 완화하여 좀 더 사실적인 경로 제어를 보여준다.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.26 no.1
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• pp.1-7
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• 1990

Theoretical evaluations of the vertical displacement at the epicenter on the circular glass plate have been carried out in the case of the unit point loading(1 dyne force strength) with the Heaviside step-function time dependency. Acoustic emission signals generated during pencil lead($\Phi$=0.5mm, HB) fracture on the soda-lime glass($\Phi$=22cm, thickness=2.8cm) were observed by the optical Michelson interferometer with the stabilized circuit, and then the source function of the observed acoustic emission signals was analyzed by the deconvolution method. The source function of acoustic emission during pencil lead fracture had a 'dip' of~0.7$\mu$sec duration time at the front portion and a step function of~0.5$\mu$sec rise time with a force strength of~4.5N.

• Journal of Theoretical and Applied Mechanics
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• v.1 no.1
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• pp.89-96
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• 1995

An analytical method is presented for predicting the effect of a local deviation in the form of a concentrated mass along a radial line on the free bending vibration characteristics of a nearly axisymmetric circular plate. The approach is based on the Rayleigh-Ritz method and the expression of local deviation of the concentrated radial mass as the variation of heaviside unit step function. The effects of the concentrated mass on the natural frequencies and mode shapes of the plate are predicted with a proposed nondimensional mass parameter.

• Advances in aircraft and spacecraft science
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• v.9 no.6
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• pp.507-523
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• 2022

This study is aimed to accurately predict the vibration response of two types of functionally graded sandwich plates, one with FGM core and another with FGM face sheets. The gradation in FGM layer is quantified by exponential method. An efficient zig-zag theory is used and the zigzag impacts are established via a linear unit Heaviside step function. The present theory fulfills interlaminar transverse stress continuity at the interface and zero condition at the top and bottom surfaces of the plate for transverse shear stresses. Nine-noded C-0 FE having 8DOF/node is utilized throughout analysis. The present model is free from the obligation of any penalty function or post-processing technique and hence is computationally efficient. Numerical results have been presented on the free vibration behavior of sandwich FGM for different end conditions, lamination schemes and layer orientations. The applicability of present model is confirmed by comparing with published results. Several new results are also specified, which will serve as the benchmark for future studies.

• Journal of Electrochemical Science and Technology
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• v.15 no.2
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• pp.276-290
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• 2024

A study of the transition from transitory state to steady state in DSSCs based on natural dyes is presented; cochineal was used as dye and Li⁺, Na⁺, and K⁺ were the ions added to the electrolyte. The photocurrent profiles were obtained as a function of time. Several DSSCs were prepared with different cations and their role and the transitory-to-steady transition was determined. A novel hybrid charge carrier source model based on the Heaviside function H(t) and the Lambert-Beer law, was developed and applied to analysis of the transient response of the output photocurrent. Additionally, the maximum effective light absorption coefficient α and the electronic extraction rate κ for each ion were determined: ${\alpha}_{Li^+,Na^+,K^+}\,=\,(0.486,\,0.00085,\,0.1126)\,cm^{-1}$, and also the electronic extraction rate ${\kappa}^{Li^+,Na^+,K^+}_{ext.}\,=\,(1410,\,19.07,\,19.69)\,cm\,s^{-1}$. The impedance model using Fick's second law was developed for carrier recombination to characterize the photocurrent.

• Journal of Korea Water Resources Association
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• v.41 no.8
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• pp.807-823
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• 2008

This paper presents a technique for estimating discharge rating curve parameters. In typical practical applications, the original non-linear rating curve is transformed into a simple linear regression model by log-transforming the measurement without examining the effect of log transformation. The model of pseudo-likelihood estimation is developed in this study to deal with heteroscedasticity of residuals in the original non-linear model. The parameters of rating curves and variance functions of errors are simultaneously estimated by the pseudo-likelihood estimation(P-LE) method. Simulated annealing, a global optimization technique, is adapted to minimize the log likelihood of the weighted residuals. The P-LE model was then applied to a hypothetical site where stage-discharge data were generated by incorporating various errors. Results of the P-LE model show reduced error values and narrower confidence intervals than those of the common log-transform linear least squares(LT-LR) model. Also, the limit of water levels for segmentation of discharge rating curve is estimated in the process of P-LE using the Heaviside function. Finally, model performance of the conventional log-transformed linear regression and the developed model, P-LE are computed and compared. After statistical simulation, the developed method is then applied to the real data sets from 5 gauge stations in the Geum River basin. It can be suggested that this developed strategy is applied to real sites to successfully determine weights taking into account error distributions from the observed discharge data.

• Structural Engineering and Mechanics
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• v.47 no.4
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• pp.559-573
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• 2013

Geometrically non-linear axisymmetric bending of a shallow spherical shell with a clamped or a simply supported edge under axisymmetric load was investigated numerically. The partial load was introduced by the Heaviside step function, and the solution was obtained by the finite difference and the Newton-Raphson methods. The thickness of the shell was considered to be uniform and the material was assumed to be homogeneous and isotropic. Sensitivity analysis was made for three geometrical parameters. The accuracy of the algorithm was checked by comparing the central deflection, the radial membrane stress at the edge, or the transverse shear force with the solutions of plates and shells in the literature and good agreement was obtained. The main findings of the study can be outlined as follows: (i) If the shell is fully loaded the central deflection of a clamped shell is larger than that of a simply supported shell provided that the shell is not very shallow, (ii) if the shell is partially loaded the central deflection of the shell is sensitive to the parameters of thickness, depth, and partial loading but the influence of the boundary conditions is negligible.