Numerical analysis of energy-minimizing wavelengths of equilibrium states for diblock copolymers

정다래,신재민,Yibao Li,최용호,JUNG JAE HUN(정재훈),이승규,김준석 한국물리학회 2014 Current Applied Physics Vol.14 No.9

We present a robust and accurate numerical algorithm for calculating energy-minimizing wavelengths of equilibrium states for diblock copolymers. The phase-field model for diblock copolymers is based on the nonlocal CahneHilliard equation. The model consists of local and nonlocal terms associated with shortand long-range interactions, respectively. To solve the phase-field model efficiently and accurately, we use a linearly stabilized splitting-type scheme with a semi-implicit Fourier spectral method. To find energy-minimizing wavelengths of equilibrium states, we take two approaches. One is to obtain an equilibrium state from a long time simulation of the time-dependent partial differential equation with varying periodicity and choosing the energy-minimizing wavelength. The other is to directly solve the ordinary differential equation for the steady state. The results from these two methods are identical, which confirms the accuracy of the proposed algorithm.We also propose a simple and powerful formula: h ¼ L*/m, where h is the space grid size, L* is the energy-minimizing wavelength, and m is the number of the numerical grid steps in one period of a wave. Two- and three-dimensional numerical results are presented validating the usefulness of the formula without trial and error or ad hoc processes.

COMPARISON OF NUMERICAL METHODS (BI-CGSTAB, OS, MG) FOR THE 2D BLACK-SCHOLES EQUATION

정다래,김성기,최용호,황형석,김준석 한국수학교육학회 2014 純粹 및 應用數學 Vol.21 No.2

In this paper, we present a detailed comparison of the performance ofthe numerical solvers such as the biconjugate gradient stabilized, operator splitting,and multigrid methods for solving the two-dimensional Black-Scholes equation. Theequation is discretized by the finite difference method. The computational resultsdemonstrate that the operator splitting method is fastest among these solvers withthe same level of accuracy.

도시 내 창업 활성화를 위한 메이커 스페이스 계획방향에 대한 연구

정다래,채얼,권순민,김도년 대한건축학회 2019 대한건축학회논문집 Vol.35 No.2

도시 내 산업 생태계 회복과 창조 인력 및 메이커의 창업활동을 촉진할 수 있는 메이커 스페이스 조성 방향을 제시하는 것이 목적이다. 이를 위해 미국과 국내 메이커 스페이스 사례를 비교 분석 했으며 분석 결과는 다음과 같다. 첫째, 입지와 공간에 대한 계획이 필요하다. 둘째, 장비 구축에 대한 원칙 수립이 필요하다. 셋째, 교육, 협업과 교류를 위한 다양한 프로그램을 제공해야 한다. 본 연구를 통해 도출한 메이커 스페이스 계획 및 구축 방향은 향후 국내 메이커 스페이스 조성에 활용될 수 있는 기초자료가 될 수 있을 것이라 판단된다. The purpose is to suggest directions for the creation of a manufacturing space that can promote the recovery of the industrial ecosystem inthe city and the start-up activities of creative workers and manufacturers. To do this, we compared the cases of US and domestic makerspace. The analysis results are as follows. First, we need a plan of location and space. Second, it is necessary to establish the principle ofequipment construction. Third, various programs for education, collaboration and exchange should be provided. It is thought that the makerspace plan and construction direction derived from this study can be used as a basic data to be used for the formation of domesticmakerspace in the future.

DIRECT COMPARISON STUDY OF THE CAHN–HILLIARD EQUATION WITH REAL EXPERIMENTAL DATA

정다래,SEOKJUN HAM,김준석 한국산업응용수학회 2022 Journal of the Korean Society for Industrial and A Vol.26 No.4

In this paper, we perform a direct comparison study of real experimental data for domain rearrangement and the Cahn–Hilliard (CH) equation on the dynamics of morphological evolution. To validate a mathematical model for physical phenomena, we take initial conditions from experimental images by using an image segmentation technique. The image segmentation algorithm is based on the Mumford–Shah functional and the Allen–Cahn (AC) equation. The segmented phase-field profile is similar to the solution of the CH equation, that is, it has hyper- bolic tangent profile across interfacial transition region. We use unconditionally stable schemes to solve the governing equations. As a test problem, we take domain rearrangement of lipid bilayers. Numerical results demonstrate that comparison of the evolutions with experimental data is a good benchmark test for validating a mathematical model.

도시 내 산업거점으로서 공공의 지식산업센터의 역할에 대한 연구

정다래,임재헌,이유성,이동준,김도년 사단법인 스마트도시건축학회 2021 사단법인 스마트도시건축학회 논문집 Vol.2 No.1

The knowledge industry center is a space that has undergone a major change from an 'apartment-type factory' following the revival of the manufacturing industry to a 'knowledge industry center' based on the knowledge industry. Currently, the knowledge industry center is an industrial facility in the city center and is supplied in the city center as a facility to support other production activities such as manufacturing, knowledge-based industry, information communication industry, and venture companies. However, the current knowledge industry center has lost its original purpose and is being used in the form of profit-type real estate and supply overheating due to speculative demand. It is time to diagnose the problem and examine the future direction. Therefore, through this study, the change process and present of the knowledge industry center are diagnosed, and the problems are identified, and the role of the center as an industrial base in the city is presented in the future.

An accurate and robust numerical method for micromagnetics simulations

정다래,김준석 한국물리학회 2014 Current Applied Physics Vol.14 No.3

We propose a new robust, accurate, and fast numerical method for solving the LandaueLifshitz equation which describes the relaxation process of the magnetization distribution in ferromagnetic material. The proposed numerical method is second-order accurate in both space and time. The approach uses the nonlinear multigrid method for handling the nonlinearities at each time step. We perform numerical experiments to show the efficiency and accuracy of the new algorithm on two- and three-dimensional space. The numerical results show excellent agreements with exact analytical solutions, the secondorder accuracy in both space and time, and the energy conservation or dissipation property.

Energy-minimizing wavelengths of equilibrium states for diblock copolymers in the hex-cylinder phase

정다래,이승규,최용호,김준석 한국물리학회 2015 Current Applied Physics Vol.15 No.7

We investigate the energy-minimizing wavelengths of equilibrium states for diblock copolymers in the hex-cylinder phase. The mathematical model is the CahneHilliard equation with long-range interactions. The numerical scheme is based on a linearly gradient stable method and the resulting discrete system of equations is solved by a Fourier-spectral method.We solve the equations in non-square domains because the periodic unit is not a square. We choose the computational domains as rectangles of aspect ratio √3 (height/width). We run the computation until the system reaches a numerical equilibrium state. We repeat these calculations in domains of gradually increasing size and then find the wavelength that minimizes the domain-size-scaled total energy. We investigate the effect of the parameters on the energy-minimizing wavelength. We also propose a formula for a non-square domain that is close to a square domain and has an exact periodicity.

혁신지구의 스마트시티 계획 요소에 관한 연구 - 보스턴, 런던, 뉴욕 사례를 중심으로 -

정다래(Jung, Da-Rae),한승균(Han, Seunggyun),장은교(Jang, Eun Kyeo),김도년(Kim, Donyun) 서울연구원 2020 서울도시연구 Vol.21 No.3

속도의 관점에서 매끄러운 곡선의 의미 분석

최명숙,정다래,김준석 대한수학교육학회 2012 수학교육학연구 Vol.22 No.1

The purpose of this paper is to describe the true meaning of smooth curve and to let people understand the smooth curve by way of velocity. It is true that it is not easy for us to perceive smooth curve because when there are no cups in the curve and the shape of the curve looks smooth, we often perceive it is smooth curve. However, even when the shape of curve looks smooth, it happens that it is not smooth curve. When the particle moves on the curve, depending on the velocity, it can be smooth curve or not. That is, even though the shape looks smooth, when the velocity is discontinuous or it is 0, it is not smooth curve. Therefore, this paper shows that it is important to understand and to teach smooth curve by way of velocity. In other words, when parameter of path for the smooth curve is taught in the calculus of high school, it needs to be understood by way of velocity. Finally, this paper tries to suggest that we need to shift our paradigm in teaching of smooth curve from fixed curve to dynamic curve. 일반적으로 학생들은 종이에 곡선을 그려 뾰족한 점이 없어 눈에 보이는 모양이 부드러우면 매끄러운 곡선(smooth curve)으로 인식한다. 이것은 고등학교에서 매개변수 방정식이 움직이는 자연현상을 설명하기 위해 방향과 속도를 모델링하여 만들어진 본래의 의미에 대한 충분한 교수학습이 이루어지지 않아 매끄러운 곡선을 시각적으로 고정된 곡선으로만 이해하는 원인이 될 수 있다. 그리고 동일한 부드러운 곡선이라도 그 곡선을 표현하는 경로에 따라 속도가 불연속이 되거나 속도가 이 되어 매끄러운 곡선이 아닌 경로가 존재한다는 것을 인식하기 어렵다. 그래서 동일한 곡선을 나타내는 다양한 속도의 경로를 제시하여 속도의 연속성을 구체화 하여 매끄러운 곡선의 의미를 분석한다. 아울러 매끄러운 곡선을 바라보는 관점을 정적인 시각에서 동적인 시각으로 패러다임을 바꾼다면 미적분학의 전반적인 분야가 석화 같은 수학에서 역동하는 수학으로 발전할 수 있다.

A comparison study of explicit and implicit numerical methods for the equity-linked securities

유민현,정다래,서승석,김준석 호남수학회 2015 호남수학학술지 Vol.37 No.4

In this paper, we perform a comparison study of explicit and implicit numerical methods for the equity-linked securities (ELS). The option prices of the two-asset ELS are typically computed using an implicit finite difference method because an explicit finite difference scheme has a restriction for time steps. Nowadays, the three-asset ELS is getting popularity in the real world financial market. In practical applications of the finite difference methods in computational finance, we typically use relatively large space steps and small time steps. Therefore, we can use an accurate and efficient explicit finite difference method because the implementation is simple and the computation is fast. The computational results demonstrate that if we use a large space step, then the explicit scheme is better than the implicit one. On the other hand, if the space step size is small, then the implicit scheme is more efficient than the explicit one.