检索结果-内蒙古大学图书馆

Partial Differential Equations in applied mathematics 2023年 8卷

作者： Aibinu, M.O. Moyo, S. Institute for Systems Science Durban University of Technology Durban 4000 South Africa Department of Applied Mathematics and School for Data Science and Computational Thinking Stellenbosch University South Africa National Institute for Theoretical and Computational Sciences (NITheCS) South Africa

The presence of delays in a mathematical model can improve its vitality and suitability in describing several phenomena. However, in the presence of delays, nonlinear fractional differential equations are more difficult to study. This paper presents the use of a blend of variational iteration method with Sumudu transform for solving delay differential equations with Caputo derivatives of fractional variable order. Moreover, the paper introduces delays into the price adjustment equations to propose new price adjustment models with more potential for vitality and suitability. The paper assigns suitable real values to the parameters for the graphical display and comparison of the obtained solutions. The paper presents the interactions that exist among the price, demand, supply and dependence of supply and demand on the price, which can be applied to estimate the equilibrium price. © 2023 The Authors

关键词： Caputo fractional derivative Market equilibrium Model Price adjustment Sumudu transform

Hematite α-Fe2O3(0001) in top and side view: Resolving long-standing controversies about its surface structure

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Redondo, Jesús Michalička, Jan Franceschi, Giada Šmid, Břetislav Kumar, Nishant Man, Ondřej Blatnik, Matthias Wrana, Dominik Kraushofer, Florian Mallada, Benjamin Švec, Martin Parkinson, Gareth S. Setvin, Martin Riva, Michele Diebold, Ulrike Čechal, Jan Charles University Faculty of Mathematics and Physics Prague Czech Republic University of the Basque Country Faculty of Chemistry Donostia-San Sebastián Spain Central European Institute of Technology Brno Czech Republic Institute for Applied Physics Technical University Wien Vienna Austria Institute of Physics Czech Academy of Science Prague Czech Republic

Hematite αFe2O3(0001) is the most-investigated iron oxide model system in photo and electrocatalytic research. The rich chemistry of Fe and O allows for many bulk and surface transformations, but their control is challenging. This has led to controversies regarding the structure of the topmost layers. This comprehensive study combines surface methods (nc-AFM, STM, LEED, and XPS) complemented by structural and chemical analysis of the near-surface bulk (HRTEM and EELS). The results show that a compact 2D layer constitutes the topmost surface of αFe2O3(0001);it is locally corrugated due to the mismatch with the bulk. Assessing the influence of naturally-occurring impurities shows that these can force the formation of surface phases that are not stable on pure samples. Impurities can also cause the formation of ill-defined inclusions in the subsurface and modify the oxidation phase diagram of hematite. The results provide a significant step forward in determining the hematite surface structure that is crucial for accurately modeling catalytic reactions. Combining surface and cross-sectional imaging provided the full view that is essential for understanding the evolution of the near-surface region of oxide surfaces under oxidative conditions. © 2023, CC BY-NC-ND.

关键词： Hematite

Fast Variational Boosting for Latent Variable Models

学校读者我要写书评

暂无评论

arXiv 2025年

作者： Gunawan, David Nott, David Kohn, Robert School of Mathematics and Applied Statistics University of Wollongong Australia School of Economics University of New South Wales Australia Australian Center of Excellence for Mathematical and Statistical Frontiers Australia Department of Statistics and Data Science National University of Singapore Singapore Institute of Operations Research and Analytics National University of Singapore Singapore

We consider the problem of estimating complex statistical latent variable models using variational Bayes methods. These methods are used when exact posterior inference is either infeasible or computationally expensive, and they approximate the posterior density with a family of tractable distributions. The parameters of the approximating distribution are estimated using optimisation methods. This article develops a flexible Gaussian mixture variational approximation, where we impose sparsity in the precision matrix of each Gaussian component to reflect the appropriate conditional independence structure in the model. By introducing sparsity in the precision matrix and parameterising it using the Cholesky factor, each Gaussian mixture component becomes parsimonious (with a reduced number of non-zero parameters), while still capturing the dependence in the posterior distribution. Fast estimation methods based on global and local variational boosting moves combined with natural gradients and variance reduction methods are developed. The local boosting moves adjust an existing mixture component, and optimisation is only carried out on a subset of the variational parameters of a new component. The subset is chosen to target improvement of the current approximation in aspects where it is poor. The local boosting moves are fast because only a small number of variational parameters need to be optimised. The efficacy of the approach is illustrated by using simulated and real datasets to estimate generalised linear mixed models and state space models. Copyright © 2025, The Authors. All rights reserved.

关键词： Stochastic systems

Multimodal Foundation Models for Material Property Prediction and Discovery

学校读者我要写书评

暂无评论

arXiv 2023年

作者： Moro, Viggo Loh, Charlotte Dangovski, Rumen Ghorashi, Ali Ma, Andrew Chen, Zhuo Kim, Samuel Lu, Peter Y. Christensen, Thomas Soljačić, Marin Department of Physics Massachusetts Institute of Technology United States Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology United States Research and Exploratory Development John Hopkins University Applied Physics Laboratory United States Data Science Institute University of Chicago United States Department of Electrical and Photonics Engineering Technical University of Denmark Denmark

Artificial intelligence is transforming computational materials science, improving the prediction of material properties, and accelerating the discovery of novel materials. Recently, publicly available material data repositories have grown rapidly. This growth encompasses not only more materials but also a greater variety and quantity of their associated properties. Existing machine learning efforts in materials science focus primarily on single-modality tasks, i.e., relationships between materials and a single physical property, thus not taking advantage of the rich and multimodal set of material properties. Here, we introduce Multimodal Learning for Materials (MultiMat), which enables self-supervised multi-modality training of foundation models for materials. We demonstrate our framework’s potential using data from the Materials Project database on multiple axes: (i) MultiMat achieves state-of-the-art performance for challenging material property prediction tasks;(ii) MultiMat enables novel and accurate material discovery via latent space similarity, enabling screening for stable materials with desired properties;and (iii) MultiMat encodes interpretable emergent features that may provide novel scientific insights. Copyright © 2023, The Authors. All rights reserved.

关键词： Materials properties

Control of photoelectron interference dynamics with two-color laser fields

学校读者我要写书评

暂无评论

Physical Review Research 2022年第1期4卷 013140-013140页

作者： Facheng Jin Weifeng Yang Xiwang Liu Hongdan Zhang Wenhui Dong Xiaohong Song Jing Chen Research Center for Advanced Optics and Photoelectronics Department of Physics College of Science Shantou University Shantou Guangdong 515063 China Faculty of Science Xi'an Aeronautical Institute Xi'an 710077 China Department of Physics School of Science Hainan University Haikou 570288 China Institute of Applied Physics and Computational Mathematics P.O. Box 8009 Beijing 100088 China HEDPS Center for Applied Physics and Technology Peking University Beijing 100084 China

We study the multiple interference structures in photoelectron momentum distributions (PMDs) of xenon atoms, whose dynamics can be manipulated effectively by a fundamental and weaker third-harmonic two-color laser fields, especially for an oblique interference pattern. It is found that this structure is only attributed to the contributions from the forward-scattered electrons as a Coulomb effect in strong-field physics. Further, the gross structure of the oblique interference arises from the forward-scattered electron ionized within a quarter-cycle of the fundamental field, and the fine structure is identified to originate from the intercycle interference of the trajectories. Moreover, we demonstrate that the multiple interference structure can be enhanced or suppressed by adjusting the relative phase of two colors. Our investigation shows that the two-color laser fields can be tailored with the purpose of manipulating specific dynamics process, which will be helpful to resolve ultrafast spatio-temporal information from the complex interference in strong-field ionization.

关键词： Atomic & molecular processes in external fields Multiphoton or tunneling ionization & excitation

Randomized Submanifold Subgradient Method for Optimization over Stiefel Manifolds

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Cheung, Andy Yat-Ming Wang, Jinxin Yue, Man-Chung So, Anthony Man-Cho Department of Applied Mathematics The Hong Kong Polytechnic University Hong Kong Department of Systems Engineering and Engineering Management The Chinese University of Hong Kong Hong Kong Department of Industrial and Manufacturing Systems Engineering Musketeers Foundation Institute of Data Science The University of Hong Kong Hong Kong

Optimization over Stiefel manifolds has found wide applications in many scientific and engineering domains. Despite considerable research effort, high-dimensional optimization problems over Stiefel manifolds remain challenging, and the situation is exacerbated by nonsmooth objective functions. The purpose of this paper is to propose and study a novel coordinate-type algorithm for weakly convex (possibly nonsmooth) optimization problems over high-dimensional Stiefel manifolds, named randomized submanifold subgradient method (RSSM). Similar to coordinate-type algorithms in the Euclidean setting, RSSM exhibits low per-iteration cost and is suitable for high-dimensional problems. We prove that RSSM converges to the set of stationary points and attains Ε-stationary points with respect to a natural stationarity measure in O(Ε−4) iterations in both expectation and the almost-sure senses. To the best of our knowledge, these are the first convergence guarantees for coordinate-type algorithms to optimize nonconvex nonsmooth functions over Stiefel manifolds. An important technical tool in our convergence analysis is a new Riemannian subgradient inequality for weakly convex functions on proximally smooth matrix manifolds, which could be of independent interest. Copyright © 2024, The Authors. All rights reserved.

关键词： Optimization algorithms

Photogeneration of Spin Quintet Triplet-Triplet Excitations in DNA-Assembled Pentacene Stacks (vol 145, pg 5431, 2023)

学校读者我要写书评

暂无评论

JOURNAL OF THE AMERICAN CHEMICAL SOCIETY 2023年第14期145卷 8271-8271页

作者： Orsborne, Sarah R. E. Gorman, Jeffrey Weiss, Leah R. . Sridhar, Akshay Panjwani, Naitik A. . Divitini, Giorgio Budden, Peter Palecek, David Ryan, Sean T. J. Rao, Akshay Collepardo-Guevara, Rosana El-Sagheer, Afaf H. Brown, Tom Behrends, Jan Friend, Richard H. Auras, Florian Cavendish Laboratory Department of Physics University of Cambridge CB3 0HE Cambridge U.K. Pritzker School of Molecular Engineering University of Chicago Chicago Illinois 60637 United States Department of Applied Physics Science for Life Laboratory KTH Royal Institute of Technology 17121 Solna Sweden Berlin Joint EPR Laboratory Fachbereich Physik Freie Universität Berlin 14195 Berlin Germany Department of Materials Science & Metallurgy University of Cambridge CB3 0FS Cambridge U.K. Yusuf Hamied Department of Chemistry University of Cambridge Cambridge CB2 1EW U.K. Department of Chemistry University of Oxford OX1 3TA Oxford U.K. Department of Science and Mathematics Faculty of Petroleum and Mining Engineering Suez University Suez 43721 Egypt

Singlet fission (SF), an exciton-doubling process observed in certain molecular semiconductors where two triplet excitons are generated from one singlet exciton, requires correctly tuned intermolecular coupling to allow separation of the two triplets to different molecular units. We explore this using DNA-encoded assembly of SF-capable pentacenes into discrete π-stacked constructs of defined size and geometry. Precise structural control is achieved via a combination of the DNA duplex formation between complementary single-stranded DNA and the local molecular geometry that directs the SF chromophores into a stable and predictable slip-stacked configuration, as confirmed by molecular dynamics (MD) modeling. Transient electron spin resonance spectroscopy revealed that within these DNA-assembled pentacene stacks, SF evolves via a bound triplet pair quintet state, which subsequently converts into free triplets. SF evolution via a long-lived quintet state sets specific requirements on intermolecular coupling, rendering the quintet spectrum and its zero-field-splitting parameters highly sensitive to intermolecular geometry. We have found that the experimental spectra and zero-field-splitting parameters are consistent with a slight systematic strain relative to the MD-optimized geometry. Thus, the transient electron spin resonance analysis is a powerful tool to test and refine the MD-derived structure models. DNA-encoded assembly of coupled semiconductor molecules allows controlled construction of electronically functional structures, but brings with it significant dynamic and polar disorders. Our findings here of efficient SF through quintet states demonstrate that these conditions still allow efficient and controlled semiconductor operation and point toward future opportunities for constructing functional optoelectronic systems.

关键词： DNA

Emergence and Ordering of Polygonal Breathers in Polariton Condensates

学校读者我要写书评

暂无评论

Physical Review Letters 2022年第1期129卷 015301-015301页

作者： Samuel N. Alperin Natalia G. Berloff Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge CB3 0WA United Kingdom Skolkovo Institute of Science and Technology Novaya Street 100 Skolkovo 143025 Russian Federation

We show that the simultaneous driving of a polariton condensate with both nonresonant and nth order resonant pump frequencies allows for a generic mechanism of breather formation. From this we construct for the second order resonance a family of exotic breathers with nontrivial discrete order of rotational symmetry. Finally, we demonstrate the spontaneous emergence of both crystalline and glassy orderings of lattices of polygonal breathers, depending on the degree of polygonal excitations at the lattice sites.

关键词： Cold atoms & matter waves Bose-Einstein condensates Breathers Polariton condensate

Local well-posedness of a system coupling compressible atmospheric dynamics and a micro-physics model of moisture in air

学校读者我要写书评

暂无评论

arXiv 2024年

作者： Doppler, Sabine Klein, Rupert Liu, Xin Titi, Edriss S. Fakultät für Mathematik Universität Wien Wien Austria Institut für Mathematik Freie Universität Berlin Berlin Germany Department of Mathematics Texas A&M University College StationTX77843 United States Department of Mathematics Texas A&M University College StationTX77840 United States Department of Applied Mathematics and Theoretical Physics University of Cambridge CambridgeCB3 0WA United Kingdom Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot76100 Israel

We establish here the local-in-time well-posedness of strong solutions with large initial data to a system coupling compressible atmospheric dynamics with a refined moisture model introduced in Hittmeir and Klein [10] (Theor. Comput. Fluid Dyn. 32:137–164, 2018). This micro-physics moisture model is a refinement of the one communicated by Klein and Majda [15] (Theor. Comput. Fluid Dyn. 20:525–551, 2006), which serves as a foundation of multi-scale asymptotic expansions for moist deep convection in the atmosphere. Specifically, we show, in this paper, that the system of compressible Navier–Stokes equations coupled with the moisture dynamics is well-posed. In particular, the micro-physics of moisture model incorporates the phase changes of water in moist air. © 2024, CC BY.

关键词： Navier Stokes equations

Decomposed photon anomalous dimension in QCD and the {β}-expanded representations for the Adler function

学校读者我要写书评

暂无评论

Physical Review D 2023年第9期108卷 096027-096027页

作者： A. L. Kataev V. S. Molokoedov Institute for Nuclear Research of the Russian Academy of Science 117312 Moscow Russia Research Computing Center Moscow State University 119991 Moscow Russia Moscow Center for Fundamental and Applied Mathematics 119992 Moscow Russia Moscow Institute of Physics and Technology 141700 Dolgoprudny Moscow Region Russia

This work is devoted to the study of the {β} expansion of the perturbative expressions for the e+e− annihilation Adler function D(Q2) and for the related renormalization group functions, namely, for the photon vacuum polarization function and its anomalous dimension γ(αs) in QCD at the O(αs4) order. We emphasize that γ(αs) is not a conformal-invariant contribution to D(Q2); therefore, for a consistent analysis, it is necessary to decompose its higher-order perturbation theory coefficients in powers of the β-function coefficients in the same way as for the Adler function. The arguments in favor of this statement are given. The comparison of the MS¯ and principal of maximum conformality and Brodsky-Lepage-Mackenzie scale approximants are demonstrated. We comment briefly on theoretical and phenomenologically related consequences of this comparison.

关键词： Perturbation theory Quantum chromodynamics Renormalization group