불확실성을 고려한 고고도 과학 기구의 궤적 예측 연구

학위논문 (석사)-- 서울대학교 대학원 : 기계항공공학부, 2017. 2. 이관중.Before launching a scientific balloon, one needs to precisely predict its trajectory to avoid any possible accidents, as there are no means to control the horizontal motion of the balloon once it is launched. Although earlier studies developed simulation programs that predicted the trajectory of a scientific balloon with reasonable accuracy, the simulated results were hardly the same as the actual balloon flight because there existed uncertainties in balloon trajectory prediction. To address the difference between the predicted and actual flight trajectories, the prediction should be probabilistic, which means the uncertainties involved in the calculation should be taken into account. In the present work, a numerical simulation program is developed to predict the trajectories of a balloon, while considering various uncertainties, with the use of a Monte Carlo simulation. Sensitivity studies are performed to identify the most dominant uncertainty parameter in the distribution of landing points of the balloon flight. Operational uncertainty represented by the amount of buoyant gas is shown to be the most significant source of the prediction error, although it can be overcome by controlling the amount of lifting gas during the actual flight.I. Introduction 1 II. Simulation program development and its validation 6 A. Design of the Balloon 7 B. Equations of Motion 9 C. Thermal Model 11 D. Code Validation 14 E. Balloon Specifications and Flight Simulation Information 17 III. Uncertainty Analysis Based on Monte Carlo Simulation 24 A. Operational Uncertainty: Uncertainty in Helium Injection 27 B. Uncertainty in the Prediction Model: Uncertainty in the Drag Coefficient 28 C. Environmental Uncertainty: Uncertainty in the Wind Profile Data 30 D. Manufactural Uncertainty: Uncertainty in the Volume of the Balloon 33 E. Results and Discussions 34 IV. Conclusions 46 Appendix A: Specific Procedures to Design a Natural Shape Balloon 48 Appendix B: Equations to Calculate the Heat Fluxes in the Thermal Model 52 References 55Maste

고차 네트워크에서의 상전이

학위논문(박사) -- 서울대학교대학원 : 자연과학대학 물리·천문학부(물리학전공), 2022. 8. 백용주.복잡계는 비균질적인 구성원들이 다양한 상호작용을 주고받는 시스템이다. 네 트워크는 이러한 시스템의 각 요소를 점, 그 사이의 상호작용을 선으로 표현함으 로써 복잡계 구조에서 나타나는 보편적인 특성과 그 동역학적 효과를 기술하는데 널리 쓰여왔다. 하지만 네트워크는 정의로부터 기인하는 내재적인 제약을 지니고 있다. 연결선은 오직 두 요소의 관계만 표현할 수 있기에 쌍으로 상호작용(pairwise interaction)하지 않는 요소들을 표현하는 것에 어려움을 갖고있다. 고차 네트워크는 정점과 고차연결선(higher-order edge)으로 이루어져 있는 네트워크의 일반화인데, 이것은 셋 이상의 고차 연결을 고려하기에 이 제약에서 자유롭다. 첫째로 우리는 본 학위논문에서 성장하는 복잡계의 데이터 및 모형을 고차 네 트워크의 관점에서 분석하여 복잡계의 단계적 구조 변화를 단체 복합체(simplicial complex) 관점으로 기술하였다. 태동의 단계를 비롯하여 연결성(connectivity)이 확 립되는 단계와 강건성(robustness)이 확립되는 단계를 위상적인 양인 베티 수(Betti number)로 구분하였다. 연결성이 확립되는 단계의 특징인 거시적인 고리 형성을 첫 째 베티 수로, 강건성이 확립되는 단계에서 계의 밀도가 높아짐에 따라 나타나는 국소적인 폐곡면(void) 형성을 둘째 베티 수로 정량화 할 수 있다는 것을 보였다. 시간에 대해 성장하는 고차 네트워크에서 베티 수들이 순차적으로 생기며 증가 한다는 것이 일반적이라는 것을 여러 고차 네트워크 모델 공부를 통해 확인하였다. 특히 성장하는 척도없는 고차 네트워크에서 정의되는 베티 수들 또한 각각 상전이를 보인다는 것을 수치적으로 확인하였다. 또한 첫째 베티수는 네트워크와 단체 복합 체 모두에서 여과 상전이와 정확히 같은 상전이 양상을 보인다는 것을 해석적으로도 보였다. 둘째로 복잡계의 고차 상호작용에서 나타나는 허브 구조가 상전이와 임계현상 에 어떤 영향을 미치는지 동기화 모형의 해석적, 수치적 분석을 통해 규명하였다. 이중 안정성, 다중 안정성을 보이는 두 가지의 전역 결합(globally coupled) 모형을 다루었는데, 공통적으로 고차 상호작용이 불연속 상전이와 임계 현상을 동시에 함 유하는 하이브리드 상전이를 유발한다는 것을 확인하였다. 비균질적 구조를 지닌 척도없는 고차 네트워크에서 정의되는 이중 안정 모형에 서연결선수분포지수의특정값(λc = 2+1/(d−1))을기준으로동기화해의 양상(임계현상) 이 급격하게 변한다는 사실을 수치적 및 해석적으로 도출했다. 도 수분포지수가임계지수보다작은경우인λ λc 일 때 폭발적인 하이브리드 동기화 상전이(hybrid synchronization transition)가 발견된다.A complex system is a system in which many elements interact one another in heterogeneous forms. Networks have been widely used to describe the universal charateristics of the structural properties and dynamical behavior of the system by representing each element as a vertex and their interactions as edges. However, network representation has an inherent limitation that stems from the definition. Since an edge can only express the relationship between two elements, it is difficult to express elements that do not show pairwise interaction. A higher-order network is a generalization of a net- work consisting of vertices and higher-order connections, which is not restricted from this limitation as it considers interactions of three or more elements. First, in this dissertation, we analyzed the empirical data and model of a growing complex system from the perspective of a higher-order network and described the evolutionary stages of the complex system in simplicial complex representation. The stages of establishing connectivity and robustness, including the stage of the birth, were separated by the topological quantity, the Betti numbers. It was shown that loop formations in the macroscopic length scale, which is a typical characteristic of the stage where connectivity is established, can be quantified by the first Betti number. Furthermore, the formation of locally closed surface which begins to appear as the density of the system increases, which can be interpreted as robustness enhancement, can be quantified by the second Betti number. It has been confirmed that the Betti numbers emerge and increase successively in growing higher-order interacting systems by studying several simplicial complexes models. In particular, it was numerically confirmed that the Betti numbers defined in the growing scale-free simplicial complexes also exhibit phase transitions, homological percolation transitions. Furthermore, we analytically show that the first Betti number exhibits the same transitional behavior as the percolation phase transition in both the graph and the simplicial complex. Second, we investigated the effect of the hub structure in higher-order interactions of complex systems on phase transitions and critical phenomena through analytical and numerical analysis of the higher-order synchronization models. Two models of globally coupled oscillators showing bistability and multistability were dealt with. It was confirmed that higher-order interactions promote a discontinuous synchronization transition with critical phenomena, a hybrid synchronization transition. It was derived numerically and analytically that the behavior of the synchronization transition changes abruptly based on a specific value of the exponent of degree distri- bution (λc = 2 + 1/(d − 1)) in the bistable model defined in a scale-free higher-order network with a heterogeneous structure. When the exponent of degree distribution is smaller than the critical value (λ λc, an explosive hybrid synchronization transition emerges.1 Introduction 1 1.1 Percolation 3 1.1.1 Overview on percolation theory 3 1.1.2 Topological viewpoint in percolation transition 4 1.1.3 Simplicial complex and simplicial homology 5 1.2 Synchronization 6 1.2.1 Kuramoto model 6 1.2.2 Synchronization transition 7 1.2.3 Hybrid synchronization transition 7 2 Homological percolations in coauthorship relations 9 2.1 Homological percolation transitions 10 2.2 Facet degree distribution 15 2.3 Minimal model 16 2.4 Kahle localization 19 2.5 Remark 20 3 Percolation of simplicial complex models 25 3.1 Percolation of static simplicial complex 25 3.1.1 Model description 25 3.1.2 Percolation threshold 28 3.1.3 Cluster size distribution 29 3.2 Percolation of growing simplicial complex 32 3.2.1 Model description 33 3.2.2 Percolation threshold 34 3.2.3 Percolation phase transition 36 3.2.4 Degree distributions 41 3.2.5 Cluster size distribution 44 3.3 Homological percolation of simplicial complex models 46 3.3.1 The first Betti number of d-GSC 46 3.3.2 The first Betti number of d-SSC 52 3.4 Remark 54 4 Higher-order interacting oscillators 55 4.1 Globally coupled higher-order interaction 55 4.1.1 Model of bistable synchronization 55 4.1.2 Model of multistable synchronization 63 4.2 Heterogeneous higher-order interaction 70 4.2.1 Heterogeneous mean-field theory 72 4.2.2 Critical behavior 77 4.2.3 Correlation size 79 4.3 Numerical simulation 81 4.4 Remark 83 5 Conclusion 85 Appendices 87 Appendix A Computation of the Betti numbers 88 Appendix B Simplifying homology via strong collapse 90 Appendix C Lagrange inversion formula 91 Bibliography 92 Abstract in Korean 98박

대장균 dnaA 프로모터와 DnaA, IciA 단백질의 상호작용

Thesis (doctoral)--서울대학교 대학원 :미생물학과,1998.Docto

La Realidad Histórica de América Latina y su Configuración Literaria: En torno a la Narrativa Contemporánea

En la historia del pensamiento de América Latina, la búsqueda de la propia identidad cultural ocupa un lugar importante. Podemos darnos cuenta de que los intelectuales se preocupan por reflexionar sobre el modo de ser propio de los pueblos latinoamericanos. La realidad histórica latinoamericana se ha caracterizado desde siempre por el enfrentamiento dualista en parejas de valores, conceptos y tendencias políticas, filosóficas y estéticas de carácter antinómico, cuando no abiertamente contradictorias. La dicotomía de la identidad cultural nos permite entender c1aramnete el problema tan polémico en la búsqueda de la identidad cultural

IciA 蛋白質에 의한 dnaA 遺傳子의 轉寫調節機作에 관한 硏究

학위논문(석사)--서울大學校 大學院 :微生物學科,1995.Maste

Case study on the changes in privatization policy applying policy window model

학위논문 (석사)-- 서울대학교 대학원 : 공기업정책학과, 2011.8. 임도빈.Maste

(A) study of the `Five Shakespeare Songs, op.23` composed by Roger Quilter

학위논문(석사) --서울대학교 대학원 :음악과(성악전공),2009.8.Maste

Method to activate the learning organization of a dental laboratory in a dental hospital

학위논문 (석사)-- 서울대학교 대학원 : 치의학과, 2011.2. 김명기.Maste