Article
Mathematics, Applied
Jean-Paul Berrut, Giacomo Elefante
Summary: The passage discusses the Lebesgue constant, Chebyshev points, and trigonometric interpolation in linear approximation theory. It shows the relationship between polynomial interpolation and trigonometric interpolation under a cosine change of variable, as well as the properties of a linear rational generalization of trigonometric interpolant on more general sets of nodes.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Donatella Occorsio, Woula Themistoclakis
Summary: This paper presents a special filtered approximation method that generates interpolation polynomials at Chebyshev zeros using de la Vallée Poussin filters. The study focuses on obtaining optimal approximations in spaces of locally continuous functions with weighted uniform norms and discusses the necessary conditions for achieving uniformly bounded Lebesgue constants. The theoretical results are validated through numerical experiments and comparisons with Lagrange interpolation at the same nodes.
APPLIED NUMERICAL MATHEMATICS
(2021)
Article
Mathematics, Applied
S. De Marchi, F. Marchetti, E. Perracchione, D. Poggiali
Summary: The main goal of the paper is to extend interpolation using mapped bases to any basis and dimension without the need for resampling. The proposed method, called Fake Nodes Approach (FNA), provides an effective way of interpolating in the multivariate setting. The theoretical results are supported by numerical experiments demonstrating the robustness of the scheme.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Engineering, Multidisciplinary
Feng Li, Yichen Zhou, Tonghui Wei, Hongfeng Li
Summary: This paper presents a reliability-based design optimization method for a car body, using a dimension-reduced Chebyshev polynomial approach to approximate the performance function and predict the reliability. The results are obtained using an improved adaptive genetic algorithm, leading to high precision and efficiency.
QUALITY AND RELIABILITY ENGINEERING INTERNATIONAL
(2023)
Article
Mathematics, Applied
Bayram Ali Ibrahimoglu
Summary: By studying the properties of mock-Chebyshev nodes and proposing a subsetting method for constructing mock-Chebyshev grids, this study addresses the issue of the Runge phenomenon in polynomial interpolation, providing an exact formula for the cardinality of a satisfactory uniform grid. Numerical experiments using points obtained by the proposed method show its effectiveness, with numerical results also being presented.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Congpei An, Hao-Ning Wu
Summary: This paper introduces the application of Tikhonov regularization in least squares approximation using orthonormal polynomials to handle noisy data. By utilizing Gauss quadrature points as nodes, coefficients of the approximation polynomial are derived and error bounds are provided. Tikhonov regularization is shown to reduce the operator norm and error term related to noise level by introducing a correction factor.
Article
Mathematics, Applied
Francesco Dell'Accio, Filomena Di Tommaso, Najoua Siar
Summary: This study proposes a simple method for numerically computing Lagrange interpolation polynomials on a set of unisolvent points in the plane, utilizing a canonical polynomial basis and PA=LU decomposition to compute Taylor polynomial coefficients. The analysis demonstrates that the 1-norm condition number of the Vandermonde matrix serves as an upper bound for the Lebesgue constant of the interpolation node set, aiding in the selection of unisolvent node sets from scattered nodes. Numerical experiments confirm the efficiency and accuracy of the proposed method.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Xiaolong Zhang, John P. Boyd
Summary: When solving differential equations using a spectral method, it is advantageous to convert Chebyshev polynomials into modified basis functions that satisfy the boundary conditions. We have demonstrated that the coefficients of different basis functions decrease at different rates, with the Chebyshev difference coefficients decreasing at a rate of 1/n and the quadratic factor coefficients decreasing at a rate of O(A(n)/n(kappa-2)). In terms of error, the Chebyshev basis functions concentrate near the boundary layers, while the quadratic factor and difference basis functions exhibit uniform oscillations over the entire interval. Additionally, we have provided asymptotic coefficients and rigorous error estimates for the approximations in these three bases.
SCIENCE CHINA-MATHEMATICS
(2023)
Article
Mathematics, Applied
Zewen Wang, Xiaoying Hu, Bin Hu
Summary: This study mainly focuses on the numerical solution to the second kind of Volterra integral equation. A new collocation method is proposed using the roots of Chebyshev polynomial as collocation points. The method interpolates the product of the kernel function and the unknown solution at the roots of Chebyshev polynomial, and transforms the Volterra integral equation into a system of linear algebra equations. The numerical solution is obtained by the Chebyshev polynomial interpolation and the effectiveness is demonstrated through numerical examples.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics
Vangelis Marinakis, Athanassios S. Fokas, George A. Kastis, Nicholas E. Protonotarios
Summary: Since their introduction, Chebyshev polynomials of the first kind have been extensively studied in the field of approximation and interpolation. However, Chebyshev interpolation is not practical for medical imaging, which requires equally spaced points. To overcome this limitation, researchers have proposed a modification of the Chebyshev method that applies to almost equally spaced points. Preliminary results show that this modified method provides superior interpolation compared to the standard Chebyshev interpolation, and it also has implications for solving inverse problems in PET and SPECT image reconstruction.
Article
Automation & Control Systems
Yuebang Dai, Hongkun Li, Guowei Yang, Defeng Peng
Summary: The study proposed a new predictive scheme for milling stability prediction to address the common Runge phenomenon, using Newton polynomial-Chebyshev nodes and determining the optimal approximation order through experimental validation, effectively reducing the issue of declining estimation accuracy.
INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY
(2021)
Article
Energy & Fuels
Joonho Bang, Okmin Park, Hyun-Sik Kim, Seung-Mee Hwang, Se Woong Lee, Sang Jeoung Park, Sang-il Kim
Summary: Re-based chalcogenides, such as ReSe2 and Re2Te5, have been studied for their electrical, thermal, and thermoelectric properties. The electronic band dispersions of these materials were calculated using density functional theory and compared with experimental data. The maximum power factor values for ReSe2 and Re2Te5 were 0.0066 and 0.11 mW/mK(2) at 880 K, respectively. The thermal conductivity of ReSe2 was between 1.93 and 8.73 W/mK at room temperature, while Re2Te5 had a low thermal conductivity of 0.62 to 1.23 W/mK at room temperature. The maximum zT values for ReSe2 and Re2Te5 were 0.0016 and 0.145 at 880 K, respectively.
INTERNATIONAL JOURNAL OF ENERGY RESEARCH
(2023)
Article
Engineering, Multidisciplinary
Miaomiao Yang, Wentao Ma, Yongbin Ge
Summary: In this paper, a scheme for solving the Helmholtz equation using Chebyshev interpolation nodes and barycentric Lagrange interpolation basis functions is deduced, demonstrating high calculation accuracy, good numerical stability, and less time consumption in numerical experiments.
CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES
(2021)
Article
Mathematics
Cuixia Niu, Huiqing Liao, Heping Ma, Hua Wu
Summary: This paper presents important approximation properties of Chebyshev polynomials in the Legendre norm, focusing on the Chebyshev interpolation operator at the Chebyshev-Gauss-Lobatto points. The results show that the approximation in Legendre norm plays a fundamental role in the numerical analysis of the Legendre-Chebyshev spectral method, and is also useful in Clenshaw-Curtis quadrature based on sampling at Chebyshev points.
Article
Materials Science, Composites
Feng Li, Hongfeng Li, Heng Zhao, Yichen Zhou
Summary: A prediction method for the ultimate load of composite corrugated sandwich structures (CCSS) was established using the dimension-reduction method and Chebyshev polynomial. The method showed higher fitting accuracy and calculation efficiency compared to other approximate models. The effect of the order on the fitting accuracy was studied, and an odd-order was recommended for solving uncertainty problems using UCAM.
JOURNAL OF COMPOSITE MATERIALS
(2022)
Article
Materials Science, Multidisciplinary
Sahar Ayachi, Radhika Deshpande, Prasanna Ponnusamy, Sungjin Park, Jaywan Chung, Sudong Park, Byungki Ryu, Eckhard Muller, Johannes de Boor
Summary: Optimizing interfaces between thermoelectric materials and electrodes, specifically with Ag, is crucial in thermoelectric generator development. Ag shows good adhesion and controllable interfaces, but can induce unexpected changes in Seebeck coefficient of n-type samples. Calculation results demonstrate the influence of Ag-induced defects on charge carrier concentrations, highlighting the importance of defects in selecting electrodes.
MATERIALS TODAY PHYSICS
(2021)
Correction
Materials Science, Multidisciplinary
Sahar Ayachi, Radhika Deshpande, Prasanna Ponnusamy, Sungjin Park, Jaywan Chung, SuDong Park, Byungki Ryu, Eckhard Muller, Johannes de Boor
MATERIALS TODAY PHYSICS
(2021)
Article
Nanoscience & Nanotechnology
Kyunghan Ahn, Myung-Gil Kim, Sungjin Park, Byungki Ryu
Summary: The study found that in copper-rich conditions, nearly stoichiometric phases of copper iodide with quenched copper-vacancy defects are the ground state, while in iodine-rich conditions, off-stoichiometric phases containing high-density copper vacancies are stabilized. These off-stoichiometric phases hinder hole transport and reduce hole mobility due to the presence of high-density neutral copper vacancies.
Article
Chemistry, Multidisciplinary
Hanhwi Jang, Jong Ho Park, Ho Seong Lee, Byungki Ryu, Su-Dong Park, Hyeon-Ah Ju, Sang-Hyeok Yang, Young-Min Kim, Woo Hyun Nam, Heng Wang, James Male, Gerald Jeffrey Snyder, Minjoon Kim, Yeon Sik Jung, Min-Wook Oh
Summary: Suppressing Te vacancies by Ag doping can achieve high thermoelectric performance, and the synergy between defect and carrier engineering offers a pathway for enhancing the properties of thermoelectric materials.
Article
Materials Science, Multidisciplinary
Jae Ki Lee, Byungki Ryu, Sungjin Park, Ji Hee Son, Jongho Park, Jeongin Jang, Min-Wook Oh, SuDong Park
Summary: The study examined the effect of the AgSbTe2 microstructure on the thermoelectric conversion efficiency of an AgSbTe2 based alloy. It was found that the single-phase metastable structure with nanoscale precipitates exhibited the best thermoelectric performance, while the multiphase structure, despite having low thermal conductivity, had a balanced Seebeck coefficient due to the presence of multiple phases, resulting in a lower thermoelectric power factor.
Article
Chemistry, Multidisciplinary
Jae Myoung Oh, Mohammad Nasir, Byungki Ryu, Hyung Joong Yun, Chel-Jong Choi, Jong-Seong Bae, Hee Jung Park
Summary: This study introduces an ultrathin ruthenium film with a ruthenium oxide subsurface layer as a flexible transparent electrode, demonstrating comparable performance to conventional ITO electrodes in terms of sheet resistance and transmittance, while excelling in both high transmittance and mechanical flexibility.
ADVANCED FUNCTIONAL MATERIALS
(2022)
Article
Chemistry, Physical
Sungjin Park, Byungki Ryu, SuDong Park
Summary: This study investigates the defect properties of low-symmetry Pb interstitials in PbTe using density functional theory calculations. The results show that off-centered Pb interstitials have multi-stable structures and long-range lattice relaxation. This provides an alternative explanation for the anharmonicity behavior of PbTe at high temperatures.
Article
Chemistry, Physical
Pawel Ziolkowski, Przemyslaw Blaschkewitz, Byungki Ryu, SuDong Park, Eckhard Mueller
Summary: The status of metrology for thermoelectric generator modules (TEM) was investigated through an international round robin test. The results showed significant standard deviations and high deviations compared to reference data from manufacturers, indicating the need for improvements in the standardization of TEM metrology.
Article
Energy & Fuels
Hasbuna Kamila, Byungki Ryu, Sahar Ayachi, Aryan Sankhla, Eckhard Mueller, Johannes de Boor
Summary: This study systematically investigates Li-doped Mg2Si1-xSnx materials and finds that the carrier concentration increases with Li content, but the dopant efficiency decreases. Additionally, an increase in the maximum achievable carrier concentration and dopant efficiency is observed with increasing Sn content.
JOURNAL OF PHYSICS-ENERGY
(2022)
Article
Energy & Fuels
Wabi Demeke, Yongtae Kim, Jiyoung Jung, Jaywan Chung, Byungki Ryu, Seunghwa Ryu
Summary: In this study, a systematic approach leveraging deep learning is proposed to efficiently explore and optimize the design of segmented thermoelectric legs. By combining finite element analysis and neural network modeling with a genetic optimization algorithm, high-performance design candidates are identified and the model is updated using validation results to achieve optimization of thermoelectric legs.
Article
Chemistry, Physical
Kyunghan Ahn, Ga Hye Kim, Se-Jun Kim, Jihyun Kim, Gi-Seong Ryu, Paul Lee, Byungki Ryu, Jung Young Cho, Yong-Hoon Kim, Joohoon Kang, Hyungjun Kim, Yong-Young Noh, Myung-Gil Kim
Summary: This study reports the synthesis of highly conductive transparent p-type sulfur-doped CuI (CuI:S) thin film using a liquid-iodination method with a thiol additive. The CuI:S film exhibits a remarkably high electrical conductivity and optical transmittance, achieving a record-high figure of merit (FOM) value. The CuI:S electrode is successfully utilized in transparent electronic devices.
CHEMISTRY OF MATERIALS
(2022)
Article
Mathematics, Applied
Jaywan Chung, Byungki Ryu, Hyowon Seo
Summary: A thermoelectric generator's energy conversion efficiency is determined by the steady-state temperature distribution, which can be solved by a second-order integro-differential equation with a unique solution. The efficiency can be calculated using the temperature-dependent thermal conductivity and electrical resistivity of the thermoelectric material.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2022)
Article
Multidisciplinary Sciences
Byungki Ryu, Jaywan Chung, Masaya Kumagai, Tomoya Mato, Yuki Ando, Sakiko Gunji, Atsumi Tanaka, Dewi Yana, Masayuki Fujimoto, Yoji Imai, Yukari Katsura, SuDong Park
Summary: A thermoelectric device that directly converts heat into electricity has been studied in this research. Through calculations using 12,645 published materials, the highest thermoelectric efficiency has been reported. It was found that for infinite-cascade devices, a thermoelectric efficiency larger than 33% is achievable when the heat-source temperature exceeds 1400K. Leg segmentation can further enhance the efficiency, delivering a very high efficiency of 24% when the heat-source temperature is 1100K.
