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Essentially Commuting with a Unitary

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arXiv 2025年

作者： Chung, Jui-Hui Shapiro, Jacob Program in Applied and Computational Mathematics Princeton University United States Department of Mathematics Princeton University United States

Let R be a unitary operator whose spectrum is the circle. We show that the set of unitaries U which essentially commute with R (i.e., [U, R] ≡ UR − RU is compact) is path-connected. Moreover, we also calculate the set of path-connected components of the orthogonal projections which essentially commute with R and obey a non-triviality condition, and prove it is bijective with Z. Copyright © 2025, The Authors. All rights reserved.

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Radiative Vlasov-Maxwell Equations

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arXiv 2025年

作者： Constantin, Peter Grayer, Hezekiah Department of Mathematics Princeton University PrincetonNJ08544 United States Program in Applied an Computational Mathematics Princeton University PrincetonNJ08544 United States

In the radiative Vlasov-Maxwell equations, the Lorentz force is modified by the addition of radiation reaction forces. The radiation forces produce damping of particle energy but the forces are no longer divergence-free in momentum space, which has an effect of concentration to zero momentum. We prove unconditional global regularity of solutions for a class of radiative Vlasov-Maxwell equations with large initial *** Codes 35Q70, 35Q83 © 2025, CC BY.

关键词： Maxwell equations

Thermal disorder and phonon softening in the ferroelectric phase transition of lead titanate

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Physical Review B 2025年第9期111卷 094113-094113页

作者： Pinchen Xie Yixiao Chen Weinan E Roberto Car Program in Applied and Computational Mathematics Princeton University Princeton New Jersey 08544 USA AI for Science Institute Beijing China and Center for Machine Learning Research and School of Mathematical Sciences Peking University Beijing China

We report a molecular dynamics study of ab initio quality of the ferroelectric phase transition in crystalline PbTiO3. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained on density functional theory data with modern machine learning techniques. Our simulations demonstrate that the transition has a strong order-disorder character, in agreement with diffraction experiments, and provide fresh insight into the approach to equilibrium across the phase transition. We find that the emergence and disappearance of the macroscopic polarization is driven by dipolar switching at the nanometer scale. We also computed the infrared optical absorption spectra in both the ferroelectric and the paraelectric phases, finding good agreement with the experimental Raman frequencies. Often, the almost ideal displacive character of the soft mode detected by Raman scattering in the paraelectric phase has been contrasted with the order-disorder character of the transition suggested by diffraction experiments. We settle this issue by showing that the soft mode coexists with a strong Debye relaxation associated with thermal disordering of the dipoles. The Debye relaxation feature is centered at zero frequency and appears near the transition temperature in both the ferroelectric and the paraelectric phases.

关键词： Ferroelectricity

Fast alignment of heterogeneous images in sliced Wasserstein distance

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arXiv 2025年

作者： Shi, Yunpeng Singer, Amit Verbeke, Eric J. Department of Mathematics University of California at Davis DavisCA United States Department of Mathematics Princeton University PrincetonNJ United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ United States

Many applications of computer vision rely on the alignment of similar but non-identical images. We present a fast algorithm for aligning heterogeneous images based on optimal transport. Our approach combines the speed of fast Fourier methods with the robustness of sliced probability metrics and allows us to efficiently compute the alignment between two L × L images using the sliced 2-Wasserstein distance in O(L2 log L) operations. We show that our method is robust to translations, rotations and deformations in the images. Copyright © 2025, The Authors. All rights reserved.

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GPU-Accelerated Modified Bessel Function of the Second Kind for Gaussian Processes

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GPU-Accelerated Modified Bessel Function of the Second Kind ...

ISC High Performance 2025 Research Paper Proceedings (40th International Conference)

作者： Zipei Geng Sameh Abdulah Ying Sun Hatem Ltaief David E. Keyes Marc G. Genton Statistics Program King Abdullah University of Science and Technology Thuwal Saudi Arabia Applied Mathematics and Computational Sciences (AMCS) Program King Abdullah University of Science and Technology Thuwal Saudi Arabia

ISBN: (数字)9783982633619

Modified Bessel functions of the second kind are widely used in physics, engineering, spatial statistics, and machine learning. Since contemporary scientific applications, including machine learning, rely on GPUs for acceleration, providing robust GPU-hosted implementations of special functions, such as the modified Bessel function, is crucial for performance. Existing implementations of the modified Bessel function of the second kind rely on CPUs and have limited coverage of the full range of values needed in some applications. In this work, we present a robust implementation of the modified Bessel function of the second kind on GPUs, eliminating the dependence on the CPU host. We cover a range of values commonly used in real applications, providing high accuracy compared to common libraries like the GNU Scientific Library (GSL) when referenced to Mathematica as the authority. Our GPU-accelerated approach also demonstrates a 2.68X performance improvement using a single A100 GPU compared to the GSL on 40-core Intel Cascade Lake CPUs. Our implementation is integrated into ExaGeoStat, the HPC framework for Gaussian process modeling, where the modified Bessel function of the second kind is required by the Matérn covariance function in generating covariance matrices. We accelerate the matrix generation process in ExaGeoStat by up to 12.62X with four A100 GPUs while maintaining almost the same accuracy for modeling and prediction operations using synthetic and real datasets.

关键词： Accuracy computational modeling Graphics processing units Gaussian processes Machine learning Libraries computational efficiency Covariance matrices Optimization Synthetic data

Revealing Actual Viscoelastic Relaxation Times in Capillary Breakup

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arXiv 2025年

作者： Hu, Nan Hwang, Jonghyun Ruangkriengsin, Tachin Stone, Howard A. Department of Mechanical and Aerospace Engineering Princeton University NJ08544 United States Program in Applied and Computational Mathematics Princeton University NJ08544 United States

We use experiments and theory to elucidate the size effect in capillary breakup rheometry, where pre-stretching in the visco-capillary stage causes the apparent relaxation time to be consistently smaller than the actual value. We propose a method accounting for both the experimental size and the finite extensibility of polymers to extract the actual relaxation time. A phase diagram characterizes the expected measurement variability and delineates scaling law conditions. The results refine capillary breakup rheometry for viscoelastic fluids and advance the understanding of breakup dynamics across scales. Copyright © 2025, The Authors. All rights reserved.

关键词： Relaxation time

Learning algorithms for mean field optimal control

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arXiv 2025年

作者： Soner, H. Mete Teichmann, Josef Yan, Qinxin Department of Operations Research and Financial Engineering Princeton University PrincetonNJ08540 United States Department of Mathematics ETH Zürich Switzerland Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States

We analyze an algorithm to numerically solve the mean-field optimal control problems by approximating the optimal feedback controls using neural networks with problem specific architectures. We approximate the model by an N-particle system and leverage the exchangeability of the particles to obtain substantial computational efficiency. In addition to several numerical examples, a convergence analysis is provided. We also developed a universal approximation theorem on Wasserstein *** Codes 35Q89, 35D40, 49L25, 60G99 © 2025, CC BY-NC-ND.

关键词： Optimal control systems

Synergetic effects of multiple junction and surface hydroxyl in Cu/CuO/Cu2O/TiO2 heterostructures towards highly efficient photocatalysts for hydrogen generation

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Materials Science for Energy Technologies 2025年 8卷 131-142页

作者： Subagyo, Riki Anindika, Garcelina Rizky Aufkani, Afif Akmal Zhang, Lei Ardhyananta, Hosta Burhan, R.Y. Perry Nugraheni, Zjahra Vianita Akhlus, Syafsir Bahruji, Hasliza Prasetyoko, Didik Wellia, Diana Vanda Ivansyah, Atthar Luqman Arramel Kusumawati, Yuly Department of Chemistry Faculty of Science and Analytic Data Institut Teknologi Sepuluh Nopember Surabaya60111 Indonesia Center of Excellence Applied Physics and Chemistry Nano Center Indonesia Jl PUSPIPTEK South Tangerang Banten15314 Indonesia Department of Physics National University of Singapore Singapore117551 Singapore Department of Materials and Metallurgical Engineering Faculty of Industrial Technology and Systems Engineering Institut Teknologi Sepuluh Nopember Surabaya60111 Indonesia Centre of Advanced Material and Energy Science Universiti Brunei Darussalam Jalan Tungku Link BE 1410 Brunei Department of Chemistry Faculty of Mathematics and Natural Sciences Universitas Andalas Padang25163 Indonesia Master Program in Computational Science Faculty of Mathematics and Natural Science Institut Teknologi Bandung Jalan Ganesha No. 10 Bandung40132 Indonesia Instrumentation and Computational Physics Research Group Department of Physics Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung Jalan Ganesha No.10 West Java Bandung40132 Indonesia

The implementation of titanium dioxide (TiO2) as a photocatalyst material in hydrogen (H2) evolution reaction (HER) has embarked renewed interest in the past decade. Rapid electron-hole pairs recombination and wide band gap of a photo-sensitive material of TiO2 are detrimental toward the targeted catalytical reaction. In this study, we present the rational design, fabrication, photocatalytic performance of TiO2-Cu/CuO/Cu2O heterostructures (CuTi) using viable chemical reduction method. The Z-scheme and S-scheme are succesfully generated across the TiO2/CuO/Cu2O interfaces, while the Schottky junction arises on the Cu perimeters. This is evidenced from the blue shifted about 0.3 eV of Cu 2p core level determined by using X-ray photoemission spectroscopy (XPS), in combination with the formation of inverse V-shape of the Mott-Schottky plots. In addition, we find that Cu/CuO/Cu2O facilitates photon absorption range up to the visible region. The multiple heterojunction and the large number of OHsurface enhanced charge carrier transfer are associated to the suppression of photoluminescence (PL) intensity, high surface hydroxyl (OHsurface) density in CuTi probed by XPS, and fast electron transfer based on the electrochemical measurements. The presence of OHsurface inhibits the recombination of electron. A significant H2 photogeneration rate enhancement is achieved when an optimized 5 wt% Cu/CuO/Cu2O concentration is used on TiO2 to achieve 7,157.19 μmol·g−1 (1,789.30 μmol·g−1·h−1). Based on this finding, zero emission energy innitiative could be materialized under multiple heterojunctions in photocatalytic process is beneficial for enhancing the H2 production. © 2025 The Authors

关键词： Titanium dioxide

FLUID-STRUCTURE INTERACTION WITH POROUS MEDIA: THE BEAVER-JOSEPH CONDITION IN THE STRONG SENSE

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arXiv 2025年

作者： Binz, Tim Hieber, Matthias Roy, Arnab Princeton University Program in Applied & Computational Mathematics Fine Hall Washington Road PrincetonNJ08544 United States Technische Universität Darmstadt Schloßgartenstraße 7 Darmstadt64289 Germany

This article considers fluid structure interaction describing the motion of a fluid contained in a porous medium. The fluid is modelled by Navier-Stokes equations and the coupling between fluid and the porous medium is described by the classical Beaver-Joseph or the Beaver-Joseph-Saffman interface condition. In contrast to previous work these conditions are investigated for the first time in the strong sense and it is shown that the coupled system admits a unique, global strong solution in critical spaces provided the data are small enough. Furthermore, a Serrin-type blow-up criterium is developed and higher regularity estimates at the interface are established, which say that the solution is even analytic provided the forces are so. Copyright © 2025, The Authors. All rights reserved.

关键词： Navier Stokes equations