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Enhancing the Swanepoel method: precise envelope detection of thin-film transmission spectra

Optics Express 2025年第6期33卷 13376-13400页

作者： Ballester, Manuel Marquez, Almudena P. Lopez-Tapia, Santiago Fernandez, Susana Bass, John Minkov, Dorian Wuersch, Christoph Willomitzer, Florian Marquez, Emilio Katsaggelos, Aggelos K. Computer Science Department Northwestern University EvanstonIL60208 United States Department of Mathematics Faculty of Science University of Cadiz Puerto Real11510 Spain Department of Electrical and Computer Engineering Northwestern University EvanstonIL60208 United States CIEMAT Avenida Complutense 40 Madrid28040 Spain Wyant College of Optical Sciences University of Arizona TucsonAZ85721 United States Sofia1000 Bulgaria Institute for Computational Engineering ICE OST Eastern Switzerland University of Applied Sciences Switzerland Department of Condensed-matter Physics Faculty of Science University of Cadiz Puerto Real11510 Spain

The Swanepoel method is a widely used optical technique for characterizing thin films through normal-incidence transmission measurements. A critical step in this approach involves extracting the upper and lower envelopes of the measured oscillatory spectrum. By analyzing the transmission spectrum and its corresponding envelopes, the Swanepoel procedure enables precise determination of the film refractive index and extinction coefficient. However, even minor inaccuracies in envelope construction can propagate significant errors into the final characterization results. To address this challenge, we present what we believe to be a novel physics-informed optimization algorithm for envelope detection. Our mathematical model reformulates the envelope detection problem as a global optimization task that enforces the physical properties of the Swanepoel envelopes. Extensive validation on fifty randomly generated transmission spectra demonstrates unprecedented accuracy: the method achieves root-mean-square errors (RMSE) below 0.10% for the upper envelope and 0.06% for the lower envelope (more than doubling the accuracy of current state-of-the-art approaches). Furthermore, the proposed model has been assessed with two experimental transmission spectra, demonstrating its robustness and accuracy with real noisy data. We have developed an open-source Python software package (see text below). This software includes not only our innovative envelope construction algorithm but also additional envelope drawing algorithms for comparison and an efficient implementation of the Swanepoel method, enabling complete optical characterization of thin films. © 2025 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement.

关键词： Mean square error

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Unified Gas-Kinetic Wave-Particle Methods VI:Disperse Dilute Gas-Particle Multiphase Flow

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Communications in computational physics 2022年第3期31卷 669-706页

作者： Xiaojian Yang Chang Liu Xing Ji Wei Shyy Kun Xu Department of Mechanical and Aerospace Engineering Hong Kong University of Science and TechnologyClear Water BayKowloonHong KongChina Institute of Applied Physics and Computational Mathematics BeijingChina Department of Mathematics Hong Kong University of Science and TechnologyClear Water BayKowloonHong KongChina Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications Hong Kong University of Science and TechnologyHong KongChina Shenzhen Research Institute Hong Kong University of Science and TechnologyShenzhenChina

A coupled gas-kinetic scheme(GKS)and unified gas-kinetic wave-particle(UGKWP)method for the disperse dilute gas-particle multiphaseflow is *** the two-phaseflow,the gas phase is always in the hydrodynamic regime and is fol-lowed by GKS for the Navier-Stokes *** particle phase is solved by UGKWP in all regimes from particle trajectory crossing to the hydrodynamic wave interac-tion with the variation of particle’s Knudsen *** the intensive particle colli-sion regime,the UGKWP gives a hydrodynamic wave representation for the particle phase and the GKS-UGKWP for the two-phaseflow reduces to the two-fluid Eulerian-Eulerian(EE)*** the rarefied regime,the UGKWP tracks individual particle and the GKS-UGKWP goes back to the Eulerian-Lagrangian(EL)*** the tran-sition regime for the solid particle,the GKS-UGKWP takes an optimal choice for the wave and particle decomposition for the solid particle phase and connects the EE and EL methods *** GKS-UGKWP method will be tested in allflow regimes with a large variation of Knudsen number for the solid particle transport and Stokes number for the two-phase *** is confirmed that GKS-UGKWP is an efficient and accurate multiscale method for the gas-particle two-phaseflow.

关键词： Unified gas-kinetic wave-particle method gas-kinetic scheme disperse gas-particle two-phaseflow.

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Understanding the role of confinement in the behavior of ionic liquid–organic solvent mixtures in slit carbon micropores: Insights from molecular dynamics

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Journal of Molecular Liquids 2025年 419卷

作者： Gurina, Darya Budkov, Yury Laboratory of Multiscale Modeling of Molecular Systems G.A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences 1 Akademicheskaya St. Ivanovo153045 Russia Laboratory of Computational Physics HSE University Tallinskaya St. 34 Moscow123458 Russia School of Applied Mathematics HSE University Tallinskaya st. 34 Moscow123458 Russia

In this study, we used molecular dynamics simulations to investigate the effects of diluting [EMIM][NTf2] with DMSO on the behavior of the electrolyte within negatively charged slit-like micropores. Our results demonstrate clear differences in electrolyte composition between confined and bulk phase. Increasing the DMSO content leads to higher concentrations of counterions within the pores, particularly in pores that are 0.7 and 0.9 nm wide. Oscillations in the disjoining pressure, excess charge in the center of the pore, and fluctuations in the number of hydrogen bonds occur as the pore size increases due to abrupt structural changes of the electrolyte inside the pores. Namely, the electrolyte arrangement within the pores adopts a layered structure, with a single layer in pores up to 0.9 nm wide and additional cation–anion layer forming with every 0.4 nm increase in width. This study offers insights into how confinement impacts the orientation and conformation of ions and solvent molecules within micropores. In particular, the distribution of cis- and trans-conformers of the [NTf2]− anions varies depending on the size of the pore. © 2024 Elsevier B.V.

关键词： Hydrogen bonds

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Droplet coalescence kinetics: thermodynamic non-equilibrium effects and entropy production mechanism

arXiv

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arXiv 2023年

作者： Sun, Guanglan Gan, Yanbiao Xu, Aiguo Shi, Qingfan School of Liberal Arts and Sciences Hebei Key Laboratory of Trans-Media Aerial Underwater Vehicle North China Institute of Aerospace Engineering Langfang065000 China School of Physics Beijing Institute of Technology Beijing100081 China Laboratory of Computational Physics Institute of Applied Physics and Computational Mathematics P. O. Box 8009-26 Beijing100088 China HEDPS Center for Applied Physics and Technology College of Engineering Peking University Beijing100871 China State Key Laboratory of Explosion Science and Technology Beijing Institute of Technology Beijing100081 China National Key Laboratory of Shock Wave and Detonation Physics Mianyang621999 China

The thermodynamic non-equilibrium (TNE) effects and the relationships between various TNE effects and entropy production rate, morphology, kinematics, and dynamics during two initially static droplet coalescence are studied in detail via the discrete Boltzmann method. The temporal evolutions of the total TNE strength D¯∗ and the total entropy production rate can both provide concise, effective and consistent physical criteria to distinguish the stages of droplet coalescence. Specifically, when the total TNE strength D¯∗ and the total entropy production rate reach their maxima, it corresponds to the time when the liquid-vapor interface length changes the fastest;when the total TNE strength D¯∗ and the total entropy production rate reach their valleys, it corresponds to the moment of the droplet being the longest elliptical shape. During the merging process, the force contributed by surface tension in the coalescence direction acts as the primary promoting force for droplet coalescence and reaches its maximum concurrently with coalescent acceleration. In contrast, the force contributed by non-organized momentum fluxes (NOMFs) in the coalescing direction inhibits the merging process and reaches its maximum at the same time as the total TNE strength D¯∗. For the coalescence of two unequal size droplets, contrary to the larger droplet, the smaller droplet exhibits larger values for total TNE strength D¯∗, merging velocity, driving force contributed by surface tension, and resistance contributed by the NOMFs. Moreover, these values gradually increase with the initial radius ratio of the large and small droplets due to the stronger non-equilibrium driving forces generated by larger curvature. However, non-equilibrium components and forces related to shear velocity in the small droplet, are all smaller than those in the larger droplet and gradually decrease with the radius ratio. This study offers kinetic insights into the complexity of thermodynamic non-equilibrium effects

关键词： Surface tension

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Extracting the Speed of Light from Matrix Product States

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Physical Review Letters 2023年第22期131卷 226502-226502页

作者： Alexander A. Eberharter Laurens Vanderstraeten Frank Verstraete Andreas M. Läuchli Institut für Theoretische Physik Universität Innsbruck A-6020 Innsbruck Austria Department of Physics and Astronomy University of Ghent Ghent Belgium Center for Nonlinear Phenomena and Complex Systems Université Libre de Bruxelles Brussels Belgium Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge United Kingdom Laboratory for Theoretical and Computational Physics Paul Scherrer Institute 5232 Villigen Switzerland Institute of Physics École Polytechnique Fédérale de Lausanne (EPFL) 1015 Lausanne Switzerland

We provide evidence that the spectrum of the local effective Hamiltonian and the transfer operator in infinite-system matrix product state simulations are identical up to a global rescaling factor, i.e., the speed of light of the system, when the underlying system is described by a 1+1 dimensional CFT. We provide arguments for this correspondence based on a path integral point of view. This observation turns out to yield very precise estimates for the speed of light in practice, confirming exact results to high precision where available, but also allowing us to finally determine the speed of light of the non-integrable, critical SU(2) Heisenberg chains with half-integer spin S>1/2 with unprecedented accuracy. We also show that the same technology applied to doped Hubbard ladders provides highly accurate velocities for a range of dopings. Combined with measurements of compressibilities we present new results for the Luttinger liquid parameter in the Luther-Emery regime of doped Hubbard ladders, outperforming earlier approaches based on the fitting of real-space correlation functions.

关键词： Conformal field theory Luttinger liquid model Matrix product states

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GLOBAL-IN-TIME BOUNDEDNESS OF SOLUTION FOR CAUCHY PROBLEM TO THE PARABOLIC-PARABOLIC KELLER-SEGEL SYSTEM WITH LOGISTIC GROWTH

arXiv

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arXiv 2022年

作者： Nie, Yao Zheng, Xiaoxin Institute of Applied Physics and Computational Mathematics Beijing100191 China School of Mathematical Sciences Beihang University Beijing100191 China

We study global-in-time well-posedness and the behaviour and of the solution to Cauchy problem in the classical Keller-Segel system with logistic term ∂tn − ∆n = − χ∇ · (n∇c) + λn − µn2) in Rd × R+, τ∂tc − ∆c = − c + n where d ≥ 1, τ, χ, µ > 0 and λ ≥ 0. It’s inspired by a previous result [25, M. Winkler, Commun. Part. Diff. Eq., 35 (2010), 1516-1537], where the global-in-time boundedness of the above Keller-Segel system in smooth bounded convex domains is established for large µ. However, his approach in bounded domain ceases to directly apply in the entire space Rd, and then they raised an interesting question whether a similar global-in-time boundedness statement remains true of Cauchy problem. In this paper, we answer this open problem by developing local-in-space estimates. More precisely, we prove that the above Keller-Segel system possesses a uniquely global-in-time bounded solution for any τ > 0 under the assumption that µ is large. The key point of our proof heavily relies on localization in space of solution caused by "local effect" of L∞(Rd)-norm. © 2022, CC BY.

关键词： Partial differential equations

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First-principles theory of the Casimir screening effect

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Physical Review E 2025年第4期111卷 044130-044130页

作者： Yury A. Budkov Petr E. Brandyshev Laboratory of Computational Physics HSE University Tallinskaya st. 34 123458 Moscow Russia School of Applied Mathematics HSE University Tallinskaya st. 34 123458 Moscow Russia Laboratory of Multiscale Modeling of Molecular Systems G.A. Krestov Institute of Solution Chemistry of the Russian Academy of Sciences Akademicheskaya st. 1 153045 Ivanovo Russia

In this paper, we use the formalism of finite-temperature quantum field theory to investigate the Casimir force between flat, ideally conductive surfaces containing confined, but mobile ions. We demonstrate that, in the Gaussian approximation, the ionic fluctuations contribute separately from the electromagnetic fluctuations that are responsible for the standard Casimir effect. This is in line with the “separation hypothesis,” which has been previously applied on a purely intuitive basis. Our analysis demonstrates the significance of calculating the zero Matsubara frequency component in the electromagnetic contribution, using the formula developed by Schwinger et al., as opposed to the approach based on Lifshitz theory used by other researchers.

关键词： Stresses

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Visible spectra of W8+ in an electron-beam ion trap

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Physical Review A 2021年第2期103卷 022808-022808页

作者： Q. Lu (陆祺峰) C. L. Yan (严成龙) J. Meng (孟举) G. Q. Xu (许帼芹) Y. Yang (杨洋) C. Y. Chen (陈重阳) J. Xiao (肖君) J. G. Li (李冀光) J. G. Wang (王建国) Y. Zou (邹亚明) Shanghai EBIT Laboratory Key Laboratory of Nuclear Physics and Ion-Beam Application (MOE) Institute of Modern Physics Fudan University Shanghai 200433 China Institute of Applied Physics and Computational Mathematics Beijing 100088 China

To provide spectroscopic data for lowly charged tungsten ions relevant to fusion research, this work focuses on the W8+ ion. Six visible spectra lines from W8+ in the range of 420–660 nm are observed with a compact electron-beam ion trap in Shanghai. Furthermore, transition energies are calculated for the 30 lowest levels of the 4f145s25p4, 4f135s25p5, and 4f125s25p6 configurations of W8+ by using the flexible atomic code (fac) and grasp package. Reasonably good agreement is found between our two independent atomic-structure calculations. The resulting atomic parameters are adopted to simulate the spectra based on the collisional-radiative model implemented in the fac code. This assists us with identification of six strong magnetic-dipole transitions in the 4f135s25p5 and 4f125s25p6 configurations from our experiments.

关键词： Atomic spectra

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ASYMPTOTIC-PRESERVING NEURAL NETWORKS BASED ON EVEN-ODD DECOMPOSITION FOR MULTISCALE GRAY RADIATIVE TRANSFER EQUATIONS

arXiv

引用

arXiv 2025年

作者： Wu, Keke Xie, Xizhe Chen, Wengu Wang, Han Ma, Zheng School of Mathematical Sciences Suzhou Institute for Advanced Research University of Science and Technology of China Jiangsu215217 China Institute of Applied Physics and Computational Mathematics Beijing100088 China School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China

We present a novel Asymptotic-Preserving Neural Network (APNN) approach utilizing even-odd decomposition to tackle the nonlinear gray radiative transfer equations (GRTEs). Our AP loss demonstrates consistent stability concerning the small Knudsen number, ensuring the neural network solution uniformly converges to the macro solution. This APNN method alleviates the rigorous conservation requirements while simultaneously incorporating an auxiliary deep neural network, distinguishing it from the APNN method based on micro-macro decomposition for GRTE. Several numerical problems are examined to demonstrate the effectiveness of our proposed APNN technique. Copyright © 2025, The Authors. All rights reserved.

关键词： Radiative transfer

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Remarks on Sharp Interface Limit for an Incompressible Navier-Stokes and Allen-Cahn Coupled System

arXiv

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arXiv 2022年

作者： Jiang, Song Su, Xiangxiang Xie, Feng Institute of Applied Physics and Computational Mathematics China School of Mathematical Sciences Shanghai Jiao Tong University Shanghai200240 China

We are concerned with the sharp interface limit for an incompressible Navier-Stokes and Allen-Cahn coupled system in this paper. When the thickness of the diffuse interfacial zone, which is parameterized by Ε, goes to zero, we prove that a solution of the incompressible Navier-Stokes and Allen-Cahn coupled system converges to a solution of a sharp interface model in the L∞(L2) ∩ L2(H1) sense on a uniform time interval independent of the small parameter Ε. The proof consists of two parts: one is the construction of a suitable approximate solution and another is the estimate of the error functions in Sobolev spaces. Besides the careful energy estimates, a spectral estimate of the linearized operator for the incompressible Navier-Stokes and Allen-Cahn coupled system around the approximate solution is essentially used to derive the uniform estimates of the error functions. The convergence of the velocity is well expected due to the fact that the layer of the velocity across the diffuse interfacial zone is relatively weak. Copyright © 2022, The Authors. All rights reserved.

关键词： Sobolev spaces

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