• Structural Engineering and Mechanics
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• 제55권6호
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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.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제19권2호
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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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• 제21권2호
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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.

• 한국컴퓨터정보학회:학술대회논문집
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• 한국컴퓨터정보학회 2022년도 제65차 동계학술대회논문집 30권1호
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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.

• 수산해양기술연구
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• 제26권1호
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• pp.1-7
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• 1990

유리 원형 평판에서 힘의 세기가 1 dyne이고 면에 수직하게 작용하는 Heaviside계단 함수의 시간 의존성을 갖는 점 하중에 의한 진앙점에서 수직 변위를 이론적으로 계산하였다. 연필심 파괴시 방출되는 음향방출신호를 안정화회로가 부착된 Michelson 간섭계로 측정하여, 음향방출 발생원함수를 deconvolution방법을 이용하여 해석하였다. 연필심 파괴시 방출되는 음향방출 발생원을 파 전면에 약 0.7$\mu$sec의 지속시간이 갖는 dip부분과 약 0.5$\mu$sec인 계단 상승시간과 약 4.5N의 힘의 크기를 갖는 계단함수의 형태였다.

• Journal of Theoretical and Applied Mechanics
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• 제1권1호
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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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• 제9권6호
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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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• 제15권2호
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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.

• 한국수자원학회논문집
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• 제41권8호
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• pp.807-823
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• 2008

수위-유량 관계 곡선을 나타내는 곡선식에 포함되어 있는 매개변수의 추정을 위해 많이 사용되는 로그선형 회귀분석은 잔차의 비등분산성(heteroscedasticity)을 고려하지 못하므로 본 연구에서는 의사우도추정법(pseudolikelihood estimation, P-LE)에 의해 분산함수를 추정하고 이와 함께 회귀계수를 추정할 수 있는 방법을 제시하였다. 이 과정에서 제시된 회귀잔차를 최소화하기 위하여 SA(simulated annealing)이라는 전역 최적화 알고리즘을 적용하였다. 또한 수위-유량 관계 곡선은 단면 등의 영향으로 인해 구간에 따라 각각 다르게 구축되어져야 하므로 이를 보다 객관적으로 판단하고 분리 위치를 추정하기 위하여 Heaviside 함수를 의사우도함수에 포함시켜 결과를 추정하도록 하였으며, 2개의 구간을 가지는 유량자료를 이용하여 제시된 방법의 합리성을 통계적으로 실험하였다. 이와 같이 통계적 실험을 통해 제시된 방법들이 기존 방법과 비교하여 가질 수 있는 장점을 파악하였으며, 제시된 방법들을 금강유역 5개 지점에서 대해 수행하여 효율성을 검증하였다.

• Structural Engineering and Mechanics
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• 제47권4호
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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.