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Comments on the article"M.O. Katanaev, Complete separation of variables in the geodesic Hamilton–Jacobi equation in four dimensions, Physica Scripta (2023), 98, 104001"

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arXiv 2023年

作者： Obukhov, V.V. Osetrin, K.E. Shapovalov, A.V. Institute of research and development Tomsk State Pedagogical University Kievskaya str. 60 Tomsk634061 Russia Center for Mathematical and Computer Physics Tomsk State Pedagogical University Kievskaya str. 60 Tomsk634061 Russia Department of Theoretical Physics National Research Tomsk State University Lenina pr. 36 Tomsk634050 Russia International laboratory of theoretical cosmology Tomsk State University of Control Systems and Radioelectronics Lenina pr. 40 Tomsk634050 Russia

The present note is a feedback on the article by M.O. Katanaev in Physica Scripta (2023, 98, 104001), where, in our opinion, a distorted view of the classical theory of separation of variables in the Hamilton-Jacobi equation is given. We show that the metrics given in this paper, addmiting separation of variables, are special cases of V.N. Shapovalov metrics (Siberian mathematical Journal, 1979, 20, 790), finally obtained in the 70s of the last century. The results of the article in question, unlike the original ones, do not have scientific novelty and contain omissions and incorrect *** Codes 35Q75 © 2023, CC BY-NC-ND.

关键词： Equations of motion

Janus faces of dipolar sources in directional near-field coupling with an oriented misalignment

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Physical Review A 2024年第3期109卷 033505-033505页

作者： Chenxu Bian Yuhan Zhong Xuhuinan Chen Tony Low Hongsheng Chen Baile Zhang Xiao Lin State Key Laboratory of Extreme Photonics and Instrumentation ZJU-Hangzhou Global Scientific and Technological Innovation Center College of Information Science and Electronic Engineering Zhejiang University Hangzhou 310027 China and International Joint Innovation Center The Electromagnetics Academy at Zhejiang University Zhejiang University Haining 314400 China Department of Electrical and Computer Engineering University of Minnesota Minneapolis Minnesota 55455 USA Key Lab of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang Jinhua Institute of Zhejiang University Zhejiang University Jinhua 321099 China and Shaoxing Institute of Zhejiang University Zhejiang University Shaoxing 312000 China Division of Physics and Applied Physics School of Physical and Mathematical Sciences and Centre for Disruptive Photonic Technologies Nanyang Technological University Singapore 637371 Singapore

Directional near-field coupling can enable many applications, such as directional routing, on-chip information processing, and chiral quantum optics. This directional near-field coupling is generally face dependent, since the induced near-field radiation pattern is dependent on which face (e.g., the upper or lower face) of the dipolar source is facing toward the outcoupler. In other words, the dipolar sources in the directional near-field coupling intrinsically have two faces (e.g., Janus faces), whose corresponding near-field coupling strength and coupling directionality might be distinct. Here, we outline a general physical framework to control these Janus faces in the directional near-field coupling and find that they can have the feature of an oriented misalignment. To be specific, the upper and lower radiation patterns of excited surface waves can have the same shape but are misaligned with a twist angle. For example, the twist angle can be any acute angle if the source is composed of a Huygens dipole and an electric dipole, and it can be any obtuse angle if the source is constructed by a circular electric dipole and a magnetic dipole.

关键词： Classical optics Light-matter interaction Metamaterials Near-field optics Photonics Plasmonics

Fast Multi-grid Methods for Minimizing Curvature Energies

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arXiv 2022年

作者： Zhang, Zhenwei Chen, Ke Tang, Ke Duan, Yuping Center for Applied Mathematics Tianjin University Tianjin300072 China Liverpool Centre of Mathematics for Healthcare Centre for Mathematical Imaging Techniques Department of Mathematical Sciences University of Liverpool LiverpoolL69 7ZL United Kingdom The Guangdong Key Laboratory of Brain-Inspired Intelligent Computation Department of Computer Science and Engineering Southern University of Science and Technology Shenzhen518055 China The Research Institute of Trustworthy Autonomous Systems Southern University of Science and Technology Shenzhen518055 China

The geometric high-order regularization methods such as mean curvature and Gaussian curvature, have been intensively studied during the last decades due to their abilities in preserving geometric properties including image edges, corners, and contrast. However, the dilemma between restoration quality and computational efficiency is an essential roadblock for high-order methods. In this paper, we propose fast multi-grid algorithms for minimizing both mean curvature and Gaussian curvature energy functionals without sacrificing accuracy for efficiency. Unlike the existing approaches based on operator splitting and the Augmented Lagrangian method (ALM), no artificial parameters are introduced in our formulation, which guarantees the robustness of the proposed algorithm. Meanwhile, we adopt the domain decomposition method to promote parallel computing and use the fine-to-coarse structure to accelerate convergence. Numerical experiments are presented on image denoising, CT, and MRI reconstruction problems to demonstrate the superiority of our method in preserving geometric structures and fine details. The proposed method is also shown effective in dealing with large-scale image processing problems by recovering an image of size 1024×1024 within 40s, while the ALM method requires around 200s. Copyright © 2022, The Authors. All rights reserved.

关键词： Image reconstruction

Publisher Correction: Droplet Formation, Growth and Detachment at the Interface of a Coupled Free‑FLow–Porous Medium System: A New Model development and Comparison

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Transport in Porous Media 2023年第2期149卷 421-421页

作者： Veyskarami, Maziar Michalkowski, Cynthia Bringedal, Carina Helmig, Rainer Institute for Modelling Hydraulic and Environmental Systems University of Stuttgart Stuttgart Germany Robert Bosch GmbH Center for Research and Development Renningen Germany Department of Computer Science Electrical Engineering and Mathematical Sciences Western Norway University of Applied Sciences Bergen Norway

Novel symmetric numerical methods for solving symmetric mathematical problems

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International Journal of Circuits, systems and Signal Processing 2021年 15卷 1545-1557页

作者： Ibrahimov, V.R. Mehdiyeva, G.Y.U. Yue, Xiao-Guang Kaabar, Mohammed K.A. Noeiaghdam, Samad Juraev, Davron Aslonqulovich Institute of Control Systems named after Academician A.Huseynov BakuAZ1141 Azerbaijan Computational mathematics Baku State University BakuAZ1148 Azerbaijan Department of Computer Science and Engineering School of Sciences European University Cyprus Nicosia1516 Cyprus Institute of Mathematical Sciences Faculty of Science University of Malaya Kuala Lumpur50603 Malaysia Department of Mathematics and Statistics Washington State University PullmanWA99163 United States Industrial Mathematics Laboratory Baikal School of BRICS Irkutsk National Research Technical University Irkutsk664074 Russia Department of Applied Mathematics and Programming South Ural State University Lenin Prospect 76 Chelyabinsk454080 Russia Department of Natural Science Disciplines Higher Military Aviation School of the Republic of Uzbekistan Karshi City180100 Uzbekistan

—The mathematical model for many problems is arising in different industries of natural science, basically formulated using differential, integral and integro-differential equations. The investigation of these equations is conducted with the help of numerical integration theory. It is commonly known that a class of problems can be solved by applying numerical integration. The construction of the quadrature formula has a direct relation with the computation of definite integrals. The theory of definite integrals is used in geometry, physics, mechanics and in other related subjects of science. In this work, the existence and uniqueness of the solution of above-mentioned equations are investigated. By this way, the domain has been defined in which the solution of these problems is equivalent. All proposed four problems can be solved using one and the same methods. We define some domains in which the solution of one of these problems is also the solution of the other problems. Some stable methods with the degree p © 2021, North Atlantic University Union NAUN. All rights reserved.

关键词： Integrodifferential equations

Unveiling the Importance of Nonshortest Paths in Quantum Networks

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arXiv 2024年

作者： Hu, Xinqi Dong, Gaogao Christensen, Kim Sun, Hanlin Fan, Jingfang Tian, Zihao Gao, Jianxi Havlin, Shlomo Lambiotte, Renaud Meng, Xiangyi School of Mathematical Sciences Jiangsu University Jiangsu Zhenjiang212013 China Blackett Laboratory Centre for Complexity Science Imperial College London LondonSW7 2AZ United Kingdom Nordita KTH Royal Institute of Technology Stockholm University Hannes Alfvéns väg 12 StockholmSE-106 91 Sweden School of Systems Science Institute of Nonequilibrium Systems Beijing Normal University Beijing100875 China School of Management and Engineering Nanjing University Nanjing210093 China Network Science and Technology Center Rensselaer Polytechnic Institute TroyNY12180 United States Department of Computer Science Rensselaer Polytechnic Institute TroyNY12180 United States Department of Physics Bar-Ilan University Ramat Gan52900 Israel Mathematical Institute University of Oxford OxfordOX2 6GG United Kingdom Turing Institute LondonNW1 2DB United Kingdom Department of Physics Applied Physics and Astronomy Rensselaer Polytechnic Institute TroyNY12180 United States

Quantum networks (QNs) exhibit stronger connectivity than predicted by classical percolation, yet the origin of this phenomenon remains unexplored. We apply a statistical physics model—concurrence percolation—to uncover the origin of stronger connectivity on hierarchical scale-free networks, the (U, V) flowers. These networks allow full analytical control over path connectivity through two adjustable path-length parameters, U ≤ V. This precise control enables us to determine critical exponents well beyond current simulation limits, revealing that classical and concurrence percolations, while both satisfying the hyperscaling relation, fall into distinct universality classes. This distinction arises from how they "superpose" parallel, nonshortest path contributions into overall connectivity. Concurrence percolation, unlike its classical counterpart, is sensitive to nonshortest paths and shows higher resilience to detours as these paths lengthen. This enhanced resilience is also observed in real-world hierarchical, scale-free Internet networks. Our findings highlight a crucial principle for QN design: when nonshortest paths are abundant, they notably enhance QN connectivity beyond what is achievable with classical percolation. © 2024, CC BY.

关键词： Percolation (computer storage)

Jason-RS, a collaboration between agents and an IoT platform

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arXiv 2019年

作者： Rafalimanana, Hantanirina Felixie Razafindramintsa, Jean Luc Cherrier, Sylvain Mahatody, Thomas George, Laurent Manantsoa, Victor Laboratory for Mathematical and Computer Applied to the Development Systems University of Fianarantsoa Madagascar Marne-la-Vallée Cedex 2 77454 France

In this article we start from the observation that REST services are the most used as tools of interoperability and orchestration in the Internet of Things (IoT). But REST does not make it possible to inject artificial intelligence into connected objects, ie it cannot allow autonomy and decision-making by the objects themselves. To define an intelligence to a connected object, one can use a Beleive Desire Intention agent (BDI an intelligent agent that adopts human behavior) such as Jason Agentspeak. But Jason AgentSpeak does not guarantee orchestration or choreography between connected objects. There are platforms for service orchestration and choreography in IoT, still the interconnection with artificial intelligence needs to be built. In this article, we propose a new approach called Jason-RS. It is a result of pairing Jason BDI agent with the web service technologies to exploit the agent capacity as a service, Jason-RS turn in Java SE and it does not need any middleware. The architecture that we propose allows to create the link between Artificial Intelligence and Services choreography to reduce human intervention in the service choreography. In order to validate the proposed approach, we have interconnected the Iot BeC3 platform and the REST agent (Jason-RS). The decision-making faculty offered by Jason-RS is derived from the information sent by the objects according to the different methods of REST (GET, POST, PUT, and DELETE) that Jason-RS offers. As a result, the objects feed the inter-agent collaborations and decision-making inside the agent. Finally, we show that Jason-RS allows the Web of Objects to power complex systems such as an artificial intelligence responsible for processing data. This performance is promising. Copyright © 2019, The Authors. All rights reserved.

关键词： Internet of things

On PID control for synchronization of complex dynamical network with delayed nodes

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Science China(Technological Sciences) 2019年第8期62卷 1412-1422页

作者： GU HaiBo Lv JinHu LIN ZongLi Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing 100049 China School of Automation Science and Electrical Engineering State Key Laboratory of Software Development Environment and Beijing Advanced Innovation Center for Big Data and Brain Machine Intelligence Beihang University Beijing 100083 China Charles L. Brown Department of Electrical and Computer Engineering University of Virginia Charlottesville VA 22904-4743 USA

Over the past two decades, synchronization, as an interesting collective behavior of complex dynamical networks, has been attracting much attention. To reveal and analyze the inherent mechanism of synchronization in complex dynamical networks with time delays in nodes, this paper attempts to use PD and PI control protocols to achieve synchronization. Based on a classical network model, we investigate the PD and PI control for synchronization of complex dynamical networks with delayed nodes and obtain some sufficient conditions. By using Lyapunov functions and appropriate state transformations, we prove that global synchronization can be achieved via the above control protocols. Finally, some simulation examples are illustrated to validate the effectiveness of the proposed theoretical results.

关键词： synchronization PID control complex dynamical network networked control system delayed node

Low-Velocity-Favored Transition Radiation

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Physical Review Letters 2023年第11期131卷 113002-113002页

作者： Jialin Chen Ruoxi Chen Fuyang Tay Zheng Gong Hao Hu Yi Yang Xinyan Zhang Chan Wang Ido Kaminer Hongsheng Chen Baile Zhang Xiao Lin Interdisciplinary Center for Quantum Information State Key Laboratory of Extreme Photonics and Instrumentation ZJU-Hangzhou Global Scientific and Technological Innovation Center College of Information Science & Electronic Engineering Zhejiang University Hangzhou 310027 China International Joint Innovation Center the Electromagnetics Academy at Zhejiang University Zhejiang University Haining 314400 China Department of Electrical and Computer Engineering Technion-Israel Institute of Technology Haifa 32000 Israel Department of Electrical and Computer Engineering Rice University Houston Texas 77005 USA Applied Physics Graduate Program Smalley-Curl Institute Rice University Houston Texas 77005 USA School of Electrical and Electronic Engineering Nanyang Technological University Singapore 639798 Singapore Department of Physics University of Hong Kong Hong Kong 999077 China Key Lab of Advanced Micro/Nano Electronic Devices & Smart Systems of Zhejiang Jinhua Institute of Zhejiang University Zhejiang University Jinhua 321099 China Shaoxing Institute of Zhejiang University Zhejiang University Shaoxing 312000 China Division of Physics and Applied Physics School of Physical and Mathematical Sciences Nanyang Technological University Singapore 637371 Singapore Centre for Disruptive Photonic Technologies Nanyang Technological University Singapore 637371 Singapore

When a charged particle penetrates through an optical interface, photon emissions emerge—a phenomenon known as transition radiation. Being paramount to fundamental physics, transition radiation has enabled many applications from high-energy particle identification to novel light sources. A rule of thumb in transition radiation is that the radiation intensity generally decreases with the decrease of particle velocity v; as a result, low-energy particles are not favored in practice. Here, we find that there exist situations where transition radiation from particles with extremely low velocities (e.g., v/c<10−3) exhibits comparable intensity as that from high-energy particles (e.g., v/c=0.999), where c is the light speed in free space. The comparable radiation intensity implies an extremely high photon extraction efficiency from low-energy particles, up to 8 orders of magnitude larger than that from high-energy particles. This exotic phenomenon of low-velocity-favored transition radiation originates from the interference of the excited Ferrell-Berreman modes in an ultrathin epsilon-near-zero slab. Our findings may provide a promising route toward the design of integrated light sources based on low-energy electrons and specialized detectors for beyond-standard-model particles.

关键词： Atom or molecule scattering from surfaces Atomic & molecular collisions Cherenkov radiation Crystal optics Electron beams & optics Light-matter interaction Optical sources & detectors Optical transient phenomena Plasmonics