Browsing by Issue Date, starting with "2019-01-15"

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最小曲面的黃金年代：柯丁/米尼庫齊理論
(國立交通大學丘成桐中心, 2019-01-15)
裴瑞茲
;
王夏聲
;
Joaquín Pérez
作者裴瑞茲是西班牙格蘭納達大學的數學與拓樸學教授與數學研究所（IEMath-GR）的主任。該研究所是屬於西班牙國家研究委員會所設的四個數學研究所其中之一。他也是西班牙皇家數學學會的國際關係委員會的一員。歷史上許多偉大的數學家都曾面對過最小曲面問題的挑戰，其中有一些數學家在相對確定的時期內獲得了驚人的進展，而促成了最小曲面的黃金年代。
大型線性方程組解法
(國立交通大學丘成桐中心, 2019-01-15)
許進超
．如何找線性代數方程組的解？這在數學與應用中是一個非常基本的問題，作者在本文討論求解的數值方法。．從最古老的高斯消去法到現代的多層網格法，作者在文中演示如何以數學技術研發大規模線性方程組的有效方法。．作者也有對於電腦硬體的開發與數學演算法的開發之間作出比較與探討。
解決物理難題的數學大師：我熟識的丘成桐先生
(國立交通大學丘成桐中心, 2019-01-15)
薛其坤
著者簡介:薛其坤是國際著名的實驗物理學家，現在是北京清華大學副校長，物理學教授，中國科學院院士。他的主要研究方向為量子物理。2013年他所帶領的團隊與合作者首次從實驗上發現量子反常霍爾效應，被2016年諾貝爾物理獎評獎委員會列入該領域過去三十年最重要的實驗發現。丘成桐先生是馳名中外的數學家，哈佛大學終身教授，國際數學最高獎「費爾茲獎」得主。我們都知道丘先生少年成名，標準的「學霸」一枚。22歲博士畢業，25 歲任副教授，27 歲攻克世界數學難題「卡拉比猜想」，34 歲獲得費爾茲獎。他幾乎拿遍了世界級的數學大獎，並已成為受人尊重的華人數學家領袖。
Growth of foreign-catalyst-free vertical InAs/InSb heterostructure nanowires on Si (111) substrate by MOCVD
(2019-01-15)
Anandan, Deepak
;
Kakkerla, Ramesh Kumar
;
Yu, Hung Wei
;
Ko, Hua Lun
;
Nagarajan, Venkatesan
In this study, growth of Au-free InAs/InSb vertical heterostructure (HS) nanowires (NWs) on highly lattice mismatched Si (1 1 1) substrate by metal organic chemical vapor deposition (MOCVD) is demonstrated. Careful selections of InSb growth parameters lead to In-rich growth regime such that direct impingement of growth precursors on top of grown InAs NW (self-assembled) stems result in axial InSb HSs nucleation on InAs stems. The observed indium (In) droplet on InSb HS NW tip shows that InSb HS growth followed a self-catalyzed growth mechanism. InSb HS axial growth rate and morphology are controlled by growth temperature and growth time. A small change in the growth parameters significantly affects In particle accumulation, particle size and its chemical composition, and thus affects the InSb nucleation on the stem. Especially, it is found that (i) growth time of less 10 min yields vertical InSb HS NW on the top of the InAs stem, (ii) as the growth time increases above 10 min, the growth turned to be InSb wrapped InAs/InSb core-shell HS due to coaxial lateral growth. High resolution transmission electron microscopy (HRTEM) study reveals that all the InSb HSs exhibit pure zinc-blende (ZB) crystal structure. The results presented here provide significant guidelines for external catalyst-free InAs/InSb HS NW growth using MOCVD on silicon (Si) substrate for various optoelectronics and electronics applications.
Relaxation high-temperature ratchets
(2019-01-15)
Shapochkina, I. V.
;
Rozenbaum, V. M.
;
Sheu, S. -Y.
;
Yang, D. -Y.
;
Lin, S. H.
We consider the overdamped motion of a Brownian particle in an asymmetric spatially periodic potential which fluctuates periodically in time, under assumption of finite duration of the relaxation response of the system on deterministic dichotomous fluctuations. It is assumed that the period of these fluctuations is much larger than the characteristic diffusion time and the potential barrier height is small as compared to the thermal energy (an adiabatic high-temperature flashing ratchet). We derive an analytical expression for the average particle velocity, which is concretized for a saw-tooth potential profile. It is revealed the different, linear and quadratic, asymptotic behavior of the average velocity as a function of the relaxation time for extremely and not extremely asymmetric potential profiles, respectively. The result is interpreted in terms of the self-similar representation. (C) 2018 Elsevier B.V. All rights reserved.
將物理應用於數學
(國立交通大學丘成桐中心, 2019-01-15)
時枝正
;
江孟蓉
;
Tadashi Tokieda
作者時枝正在日本長大，最初是一位畫家，後來在法國成為古典語文學者。然後轉行從事數學研究，再換到物理領域。他現在是史丹福大學的數學教授，之前曾以英國劍橋大學為根據地工作多年。他積極參與在開發中國家的教育推廣，尤其是透過非洲數學科學研究院（African Institute for Mathematical Sciences，AIMS）。有時候數學定理是這樣湧現的：設定一個物理情境，從物理學的經驗來看會發生什麼現象，把它翻成數學語言，就成為一個定理。本文展示四個初階的例子：三角形的餘弦定律、正弦定律、柯西 / 史瓦茲不等式、算數幾何平均不等式。
無用研究的有效性：大栗博司Kavli IPMU 主任就職演說
(國立交通大學丘成桐中心, 2019-01-15)
大栗博司
;
陳明鈺
;
Hirosi Ooguri
作者大栗博司是加州理工大學的理論物理與數學的卡弗里講座教授與柏克（Walter Burke）理論物理研究所所長，卡弗里數物連攜宇宙研究機構（Kavli Institute for the Physics and Mathematics of the Universe，Kavli IPMU）與東京大學國際高等研究所（The University of Tokyo Institute for Advanced Study，UTIAS）主任。他的研究領域是基本粒子物理，弦論和相關的數學理論。本文出自大栗博司的2018 年 10 月 8 日Kavli IPMU 主任就職演說。
編輯曲線
(國立交通大學丘成桐中心, 2019-01-15)
編輯室
本期內容:畢氏法則
只有詠唱才能學會詠唱（下）：悼威廉‧瑟斯頓(1946～2012)
(國立交通大學丘成桐中心, 2019-01-15)
噶拜
;
科寇夫
;
翁秉仁
;
David Gabai
;
Steve Kerckhoff
作者噶拜現為普林斯頓大學教授。科寇夫現為史丹福大學教授。本文出自“William P. Thurston 1946-2012” Notices of the AMS (63) 2016 No. 1。這裡是下篇（上篇請見數理人文 14 期）。
Electro-autotrophs induced the growth of exoelectrogens on the anode in a microbial fuel cell
(2019-01-15)
Chen, Kuo-Ti
;
Bai, Min-Der
;
Wu, Shao-I
;
Chen, Chang-Chieh
;
Lu, Wen-Jang
In microbial fuel cells (MFCs), exoelectrogens act as a catalyst and produce electricity directly. Exoelectrogens such as Geobacter in the heterotrophic condition acts as electron donors but when they transferred to the autotrophic condition, they act as electron acceptors and undergo continuous growth. However, most of the nonelectrochemical bacteria will collapse and disperse in the liquid phase with environmental change. In this study, we used electro-autotroph and acetate enrichment alternately rather than only an acetate-fed control system in the batch operation. After the five-batch operation, the microorganism diversity shifted from complex to simple, and Geobacter was the most abundant microorganism in the experimental system. The coulombic efficiency (CE) and the highest current density were 20%--45%, and 657 mA/m(2), respectively, for the experimental group and 8%-20%, and 511 mA/m(2), respectively, for the control group. The monosodium glutamate wastewater was treated in this study. The control group was acclimated in a shorter time, but the experimental group had higher current density and CE. The results indicate that the electro-autotroph process reduced the number of non-bioelectrochemical bacteria but induced the growth of exoelectrogens on the electrode, resulting in the MFCs achieving a higher efficiency.
iSIRA: Integrated shift-invert residual Arnoldi method for graph Laplacian matrices from big data
(2019-01-15)
Huang, Wei-Qiang
;
Lin, Wen-Wei
;
Lu, Henry Horng-Shing
;
Yau, Shing-Tung
;
交大名義發表
The eigenvalue problem of a graph Laplacian matrix L arising from a simple, connected and undirected graph has been given more attention due to its extensive applications, such as spectral clustering, community detection, complex network, image processing and so on. The associated matrix L is symmetric, positive semi-definite, and is usually large and sparse. It is often of interest for finding some smallest positive eigenvalues and corresponding eigenvectors. However, the singularity of L makes the classical eigensolvers inefficient since we need to factorize L for the purpose of solving large and sparse linear systems exactly. The next difficulty is that it is usually prohibitive to factorize L generated by real network problems from big data such as social media transactional databases, and sensor systems because there is in general not only local connections. In this paper, we propose a trimming to cure the singularity of L according to its special property: zero row/column sum. This remedy technique leads us to solve a positive definite linear system reduced in one dimension and then recover the result to get a suitable solution of the original system involved in an eigensolver. Besides, we apply a deflating approach to exclude the influence of converged eigenvalues. We show how to apply the idea of trimming to the graph Laplacian eigenvalue problem together with a deflated term and a target shift. Accordingly, based on the inexact residual Arnoldi (Lee, 2007; Lee and Stewart, 2007) method, we propose an integrated eigensolver for this kind of L combining with the implicit remedy of the singularity, an effective deflation for convergent eigenvalues and the shift-invert enhancement. Numerical experiments reveal that the integrated eigensolver outperforms the classical Arnoldi/Lanczos method for computing some smallest positive eigeninformation especially when the LU factorization is not available. (C) 2018 Elsevier B.V. All rights reserved.
畢氏法則：第一個數學定理？！
(國立交通大學丘成桐中心, 2019-01-15)
大衛 ‧ 曼弗德
;
趙學信
;
David Mumford
作者曼弗德現為哈佛大學與布朗大學退休榮譽教授，研究領域是代數幾何與圖形視覺與模式理論。曾獲頒費爾茲獎（1974），麥克阿瑟獎（1987）與沃爾夫獎（2008）
中英名詞對照表
(國立交通大學丘成桐中心, 2019-01-15)
編輯室
中英名詞對照
Exploring the DBR superlattice effect on the thermal performance of a VECSEL with the finite element method
(2019-01-15)
Huo, Yongjun
;
Cho, Chun Yu
;
Huang, Kai Feng
;
Chen, Yung Fu
;
Lee, Chin C.
The design criterion of thermal conductivity for the GaAs/AlAs distributed Bragg reflector (DBR) superlattice structure was thoroughly investigated to precisely analyze the thermal behaviors of the optically pumped vertically external cavity surface-emitting laser (VECSEL). A finite element model with detailed configuration of a VECSEL gain chip was constructed to fulfill the analysis. A 1060 nm VECSEL with different pump conditions was further demonstrated to verify the finite element analysis. At the VECSEL thermal rollover point, the analysis results show that the model with the superlattice property predicts more precise temperature values than that using a bulk composite property. It reveals that the accurate determination of the thermal conductivity of the DBR superlattice is significantly important for the VECSEL thermal analysis. (C) 2019 Optical Society of America
The photovoltaic-thermal system parameter optimization design and practical verification
(2019-01-15)
Kuo, Chung-Feng Jeffrey
;
Liu, Jui-Min
;
Umar, Mega Lazuardi
;
Lan, Wei-Lun
;
Huang, Chao-Yang
This study used the Taguchi method combined with Analytic Hierarchy Process (AHP) to present optimization design of the Photovoltaic-Thermal (PV/T) system for improving the two quality characteristics namely electrical and thermal efficiency. The control parameters for PV/T design including the collector plate material, collector azimuth, number of collector tubes, mass flow rate, collector angle, and storage tank volume to area (V/A) ratio are crucial factors affecting the performance of the PV/T. First, Taguchi method coupled with main effect analysis (MEA) and analysis of variance (ANOVA) was used to obtain the best parameters combination on each single quality characteristic of electricity and thermal efficiency. In order to achieve the maximum total efficiency of the PV/T system, multi-quality analysis AHP was used to obtain the optimal control parameters combination according to the contribution degrees of quality weight. Then, the computational fluid dynamic (CFD) software used to simulate the PV/T module thermal distribution before and after optimization. The optimization control parameters combination are: collector plate material is copper, collector azimuth is due south, number of collector tubes is 12, mass flow rate is 0.01 kg/s-m(2), collector angle is 25 degrees, and V/A ratio is 123. The effectiveness of the proposed method was evaluated by the confirmation experiments. The optimization properties under these parameters are electrical efficiency 14.29% and thermal efficiency 44.96% which is improved than traditional PV/T system (electrical efficiency 12.74% and thermal efficiency 34.06%). The findings of CFD showed that the temperature of the PV/T module decreased by about 10 degrees C after optimality analysis, and the coefficient of correlation between the simulated and actual PV/T water temperatures was 0.991 (very close to 1). The CFD simulated performance testing proposed in this study has a good verification effect.
我在普林斯頓高等研究所的經歷：1979幾何分析年
(國立交通大學丘成桐中心, 2019-01-15)
丘成桐
作者丘成桐為哈佛大學數學與物理教授，費爾茲獎、克拉福德獎、沃爾夫獎、格羅斯曼獎得主，中央研究院院士。科普著作有《丘成桐談空間的內在形狀》，並為《數理人文》主編。
弦論是否有暗能量的容身之處？一篇有爭議的新論文認為，像我們這種暗能量型態的宇宙，並不存在於弦論所容許的宇宙「地景」中。
(國立交通大學丘成桐中心, 2019-01-15)
渥秋華
;
戴守煌
;
Natalie Wolchover
作者渥秋華是Quanta的物理科學類資深撰稿人。她是塔夫斯大學物理學學士，曾於柏克萊大學攻讀研究所，並為多本雜誌撰稿。這篇由哈佛大學知名物理學家瓦法（Cumrun Vafa）與同僚合著的論文，根據弦論理論架構推敲出一條簡潔的方程式，決定哪些宇宙可以存在，哪些不被允許。弦論是結合重力與量子物理之「萬有理論」（Theory of Everything）的首選，它將一切物質與力定義為一縷縷微小能量的各種振動模式。
Removal of ultrafine particles by porous nanomaterials with varied morphologies
(2019-01-15)
Yin, Likun
;
Yang, Xiong
;
Xing, Yi
;
Lu, Pei
;
Tsai, Chuen-Jinn
The removal characteristics of sub-25 nm ultrafine particles (UFPs) by different porous nanomaterials with different morphologies were studied based on efficiency curves obtained with specially designed filtration system. The material morphological effects on UFPs collection were investigated. The results demonstrate a complex and synergic mechanism of material structural framework, pore size distribution, and porosity order in terms of diffusion and interception dependent on flow velocity. Both porosity and fiber-like tubular structures promoted the UFPs removal. Microporosity and disordered mesoporosity could enhance the roughness of the internal surface and intensify the interaction with UFPs. Specifically, the large and ordered mesoporosity was able to render selectivity for UFPs at certain sizes and exhibited the best particle collection performance which can be largely associated with significant pore size and volume. The dependence of the ratio of diffusion to interception on flow velocity and the comparison of different pores in terms of the matching sizes with particles derived from single sphere efficiency model fitting results were also discussed. This work is significant to deeper understanding of interactions between airborne nanoparticles and porous surfaces. (C) 2018 Published by Elsevier B.V.
假如朱子是位物理學家：朱子的物論
(國立交通大學丘成桐中心, 2019-01-15)
楊儒賓
作者楊儒賓是臺灣臺中人，臺灣大學文學博士，現為新竹清華大學哲學研究所講座教授，專長領域是身體理論、神話思想與宋明理學。
數理簡訊
(國立交通大學丘成桐中心, 2019-01-15)
編輯室
2018 年費爾茲獎