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STRESS CONCENTRATION FOR NONLINEAR INSULATED CONDUCTIVITY PROBLEM WITH ADJACENT INCLUSIONS

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arXiv 2023年

作者： Chen, Qionglei Zhao, Zhiwen Institute of Applied Physics and Computational Mathematics Beijing100088 China Beijing Computational Science Research Center Beijing100193 China

A high-contrast two-phase nonlinear composite material with adjacent inclusions of m-convex shapes is considered for m > 2. The mathematical formulation consists of the insulated conductivity problem with p-Laplace operator in dfor p > 1 and d ≥ 2. The stress, which is the gradient of the solution, always blows up with respect to the distance ϵ between two inclusions as ϵ goes to zero. We first establish the pointwise upper bound on the gradient possessing the singularity of order ϵ-βwith β = (1 - α)/m for some α ≥ 0, where α = 0 if d = 2 and α > 0 if d ≥ 3. In particular, we give a quantitative description for the range of horizontal length of the narrow channel in the process of establishing the gradient estimates, which provides a clear understanding for the applied techniques and methods. For d ≥ 2, we further construct a supersolution to sharpen the upper bound with any β > (d + m - 2)/(m(p - 1)) when p > d + m - 1. Finally, a subsolution is also constructed to show the almost optimality of the blow-up rate ϵ-1/ max{p-1,m}in the presence of curvilinear squares. This fact reveals a novel dichotomy phenomena that the singularity of the gradient is uniquely determined by one of the convexity parameter m and the nonlinear exponent p except for the critical case of p = m + 1 in two dimensions. Copyright © 2023, The Authors. All rights reserved.

关键词： Mathematical operators

Strong gravitational lensing by and black holes embedded in dark matter halo exhibiting string cloud and quintessential field

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The European Physical Journal C 2024年第6期84卷 1-20页

作者： Molla, Niyaz Uddin Chaudhary, Himanshu Mustafa, G. Atamurotov, Farruh Debnath, Ujjal Arora, Dhruv Department of Mathematics Indian Institute of Engineering Science and Technology Howrah India Department of Applied Mathematics Delhi Technological University Delhi India Pacif Institute of Cosmology and Selfology (PICS) Sambalpur India Department of Mathematics Shyamlal College University of Delhi Delhi India Department of Physics Zhejiang Normal University Jinhua People’s Republic of China New Uzbekistan University Tashkent Uzbekistan University of Tashkent for Applied Sciences Tashkent Uzbekistan Institute of Theoretical Physics National University of Uzbekistan Tashkent Uzbekistan

We investigate the strong gravitational lensing phenomena caused by a black hole with a dark matter halo in the presence of cloud string and quintessence. This study examines strong gravitational lensing with two significant dark matter models: the universal rotation curve model and the cold dark matter model. To do this, we first numerically estimate the strong lensing coefficients and strong deflection angles for both the universal rotation curve and cold dark matter models. It is observed that the deflection angle, denoted as $$\alpha _D$$ , increases with the parameter $$\alpha $$ while holding the value of $$2M \gamma $$ constant. Additionally, it increases with the parameter $$2M \gamma $$ while keeping the value of $$\alpha $$ constant. The strong deflection angle $$\alpha _D$$ , for the black hole with a dark matter halo, with parameters $$\alpha $$ and $$2\,M \gamma $$ , greatly enhances the gravitational bending effect and surpasses the corresponding case of the standard Schwarzschild black hole ( $$A=B=0=\alpha =2M\gamma $$ ). Furthermore, we investigate the astrophysical consequences through strong gravitational lensing observations, using examples of two supermassive black holes, namely $$M87^{*}$$ and $$Sgr A^{*}$$ , located at the center of nearby galaxies. It is observed that black holes with dark matter halos in the presence of cloud string and quintessence can be quantitatively distinguished and characterized from the standard Schwarzschild black hole ( $$A=B=0=\alpha =2M\gamma $$ ). The findings in our analysis suggest that observational tests for black holes influenced by dark matter halos, cloud string and quintessence are indeed feasible and viable.

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Atomic determination of the nuclear quadrupole moment Q(209Bi) using the multi-configuration Dirac-Hartree-Fock method

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arXiv 2025年

作者： Li, Jiguang Bieron, Jacek Godefroid, Michel Jönsson, Per Institute of Applied Physics and Computational Mathematics Beijing100088 China Instytut Fizyki Teoretycznej Uniwersytet Jagielloński Kraków Poland Université Libre de Bruxelles Brussels1050 Belgium Department of Materials Science and Applied Mathematics Malmö University MalmöS-20506 Sweden

The multiconfiguration Dirac-Hartree-Fock method implemented in the Grasp2018 package was employed to calculate the magnetic dipole hyperfine interaction constants and electric field gradients of levels in the ground configuration of the neutral bismuth atom. Combining the calculated electric field gradient of the ground state with the measured electric quadrupole hyperfine interaction constant, we extracted the nuclear quadrupole moment for the 209Bi isotope, Q(209Bi) = −422(22) mb. This value, together with other results obtained from atomic- and molecular-structure calculations, created the "world average" nuclear quadrupole moment of this isotope, Q(209Bi) = −420(17) mb. © 2025, CC BY.

关键词： Atoms

Message Verification Protocol Based on Bilinear Pairings and Elliptic Curves for Enhanced Security in Vehicular Ad Hoc Networks

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Computers, Materials & Continua 2024年第10期81卷 1029-1057页

作者： Vincent Omollo Nyangaresi Arkan A.Ghaib Hend Muslim Jasim Zaid Ameen Abduljabbar Junchao Ma Mustafa A.Al Sibahee Abdulla J.Y.Aldarwish Ali Hasan Ali Husam A.Neamah Department of Computer Science and Software Engineering Jaramogi Oginga Odinga University of Science and TechnologyBondo40601Kenya Department of Applied Electronics Saveetha School of EngineeringSIMATSChennaiTamilnadu602105India Information Technology Department Management Technical CollegeSouthern Technical UniversityBasrah61004Iraq Department of Computer Science College of Education for Pure SciencesUniversity of BasrahBasrah61004Iraq College of Big Data and Internet Shenzhen Technology UniversityShenzhen518118China Huazhong University of Science and Technology Shenzhen InstituteShenzhen518000China National Engineering Laboratory for Big Data System Computing Technology Shenzhen UniversityShenzhen518060China Computer Technology Engineering Department Iraq University CollegeBasrah61004Iraq Department of Mathematics College of Education for Pure SciencesUniversity of BasrahBasrah61004Iraq Institute of Mathematics University of DebrecenDebrecenH-4002Hungary Department of Electrical Engineering and Mechatronics Faculty of EngineeringUniversity of DebrecenDebrecen4028Hungary

Vehicular ad hoc networks(VANETs)provide intelligent navigation and efficient route management,resulting in time savings and cost reductions in the transportation ***,the exchange of beacons and messages over public channels among vehicles and roadside units renders these networks vulnerable to numerous attacks and privacy *** address these challenges,several privacy and security preservation protocols based on blockchain and public key cryptography have been proposed ***,most of these schemes are limited by a long execution time and massive communication costs,which make them inefficient for on-board units(OBUs).Additionally,some of them are still susceptible to many *** such,this study presents a novel protocol based on the fusion of elliptic curve cryptography(ECC)and bilinear pairing(BP)*** formal security analysis is accomplished using the Burrows–Abadi–Needham(BAN)logic,demonstrating that our scheme is verifiably *** proposed scheme’s informal security assessment also shows that it provides salient security features,such as non-repudiation,anonymity,and ***,the scheme is shown to be resilient against attacks,such as packet replays,forgeries,message falsifications,and *** the performance perspective,this protocol yields a 37.88%reduction in communication overheads and a 44.44%improvement in the supported security ***,the proposed scheme can be deployed in VANETs to provide robust security at low overheads.

关键词： Attacks bilinear elliptic curve cryptography(ECC) privacy security vehicular ad hoc network(VANET)

Ginzburg-Landau Functionals in the Large-Graph Limit

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arXiv 2024年

作者： Zhang, Edith Scott, James Du, Qiang Porter, Mason A. Department of Applied Physics and Applied Mathematics Columbia University New YorkNY10027 United States Data Science Institute Columbia University New YorkNY10027 United States Department of Mathematics Department of Sociology University of California Los Angeles Los AngelesCA90095 United States Santa Fe Institute Santa FeNM87501 United States

Ginzburg-Landau (GL) functionals on graphs, which are relaxations of graph-cut functionals on graphs, have yielded a variety of insights in image segmentation and graph clustering. In this paper, we study large-graph limits of GL functionals by taking a functional-analytic view of graphs as nonlocal kernels. For a graph Wn with n nodes, the corresponding graph GL functional GLWn∊ is an energy for functions on Wn. We minimize GL functionals on sequences of growing graphs that converge to functions called graphons. For such sequences of graphs, we show that the graph GL functional Γ-converges to a continuous and nonlocal functional that we call the graphon GL functional. We also investigate the sharp-interface limits of the graph GL and graphon GL functionals, and we relate these limits to a nonlocal total variation. We express the limiting GL functional in terms of Young measures and thereby obtain a probabilistic interpretation of the variational problem in the large-graph limit. Finally, to develop intuition about the graphon GL functional, we compute the GL minimizer for several example families of graphons. © 2024, CC BY.

关键词： Stochastic systems

SymILO: A Symmetry-Aware Learning Framework for Integer Linear Optimization

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arXiv 2024年

作者： Chen, Qian Zhang, Tianjian Yang, Linxin Han, Qingyu Wang, Akang Sun, Ruoyu Luo, Xiaodong Chang, Tsung-Hui School of Science and Engineering The Chinese University of Hong Kong Shenzhen China Shenzhen Research Institute of Big Data China School of Data Science The Chinese University of Hong Kong Shenzhen China Shenzhen International Center For Industrial And Applied Mathematics Shenzhen Research Institute of Big Data China

Integer linear programs (ILPs) are commonly employed to model diverse practical problems such as scheduling and planning. Recently, machine learning techniques have been utilized to solve ILPs. A straightforward idea is to train a model via supervised learning, with an ILP as the input and an optimal solution as the label. An ILP is symmetric if its variables can be permuted without changing the problem structure, resulting in numerous equivalent and optimal solutions. Randomly selecting an optimal solution as the label can introduce variability in the training data, which may hinder the model from learning stable patterns. In this work, we incorporate the intrinsic symmetry of ILPs and propose a novel training framework called SymILO. Specifically, we modify the learning task by introducing solution permutation along with neural network weights as learnable parameters and then design an alternating algorithm to jointly optimize the loss function. We conduct extensive experiments on ILPs involving different symmetries and the computational results demonstrate that our symmetry-aware approach significantly outperforms three existing methods—-achieving 50.3%, 66.5%, and 45.4% average improvements, respectively. Copyright © 2024, The Authors. All rights reserved.

关键词： Integer linear programming

Modulation of Biaxial Strains on the Optical Responses of Defective Ti3c2 Tx (T = F, O, Oh) Mxenes

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SSRN

SSRN 2025年

作者： Zhang, Yulong Zhao, Zhongwei Yan, Jieyun Song, Huajie Lv, Wenting Yang, Yu Institute of Applied Physics and Computational Mathematics Beijing100088 China National Key Laboratory of Computational Physics Beijing100088 China School of Science Beijing University of Posts and Telecommunications Beijing100876 China

The influences of external strain on optical properties of defective functionalized MXenes Ti3C2Tx (T = F, O, OH) are systematically studied by first-principles calculations. We find that biaxial strains significantly change the position and width of different energy bands. For Ti3C2F2 and Ti3C2(OH)2, tensile strain makes the occupied energy bands move towards higher level, while compressive strain makes the occupied energy bands move towards lower level. The hybridization area broadens with compression while narrows with stretching for Ti3C2O2. Corresponding to such electronic influences, the absorption spectra show blueshift under compressive strain, while redshift occurs under tensile strain for both ideal and defective MXenes. © 2025, The Authors. All rights reserved.

关键词： Tensile strain

Anomalous refinement and uniformization of grains in metallic thin films

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Nano Research 2023年第12期16卷 13358-13365页

作者： Lei Wang Shu Wang Xiaofeng Wang Jianming Zhang Jianjie Dong Bin Wei Haiguang Yang Zhongchang Wang Ziyang Zhang ChuanFei Guo Qian Liu Chinese Academy of Sciences(CAS)Key Laboratory of Nanosystem and Hierarchical Fabrication CAS Center for Excellence in NanoscienceNational Center for Nanoscience and Technology&University of Chinese Academy of SciencesBeijing 100190China College of Mathematics and Physics Qingdao University of Science and TechnologyQingdao 266061China Department of Materials Science and Engineering Southern University of Science and TechnologyShenzhen 518055China School of Materials Sun Yat-Sen UniversityGuangzhou 510275China International Iberian Nanotechnology Laboratory(INL) Department of Quantum and Energy MaterialsBraga 4715-330Portugal School of Electronic and Information Engineering Qingdao UniversityQingdao 266071China The MOE Key Laboratory of Weak-Light Nonlinear Photonics and TEDA Applied Physics Institute and School of Physics Nankai UniversityTianjin 300457China

When a laser beam writes on a metallic film,it usually coarsens and deuniformizes grains because of Ostwald ripening,similar to the case of *** we show an anomalous refinement effect of metal grains:A metallic silver film with large grains melts and breaks into uniform,close-packed,and ultrafine(~10 nm)grains by laser direct writing with a nanoscale laser spot size and nanosecond pulse that causes localized heating and adaptive *** method exhibits high controllability in both grain size and uniformity,which lies in a linear relationship between the film thickness(h)and grain size(D),D∝*** linear relationship is significantly different from the classical spinodal dewetting theory obeying a nonlinear relationship(D∝h5/3)in common laser *** also demonstrate the application of such a silver film with a grain size of~10.9 nm as a surface-enhanced Raman scattering chip,exhibiting superhigh spatial-uniformity and low detection limit down to 10-15 *** anomalous refinement effect is general and can be extended to many other metallic films.

关键词： laser direct writing anomalous refinement localized heating ripening linear relationship

Climate change attribution of the 2021 Henan extreme precipitation: Impacts of convective organization

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science China Earth sciences 2022年第10期65卷 1837-1846页

作者： Han QIN Wei YUAN Jun WANG Yang CHEN Panxi DAI Adam HSOBEL Zhiyong MENG Ji NIE Laboratory for Climate and Ocean-Atmosphere Studies Department of Atmospheric and Oceanic SciencesSchool of PhysicsPeking UniversityBeijing 100871China Aviation Meteorological Center Civil Aviation Administration of ChinaBeijing 100621China Key Laboratory of Regional Climate-Environment for Temperate East Asia(RCE-TEA) Institute of Atmospheric PhysicsChinese Academy of SciencesBeijing 100029China State Key Laboratory of Severe Weather Chinese Academy of Meteorological SciencesBeijing 100081China Department of Atmospheric Science School of Earth SciencesZhejiang UniversityHangzhou 310027China Department of Applied Physics and Applied Mathematics and Lamont-Doherty Earth Observatory Columbia University

In this study, we investigate the climate attribution of the 21·7 Henan extreme precipitation event. A conditional storyline attribution method is used, based on simulations of the event with a small-domain high-resolution cloud-resolving model. Large-scale vertical motion is determined by an interactive representation of large-scale dynamics based on the quasigeostrophic omega equation, with dynamical forcing terms taken from observation-based reanalysis data. It is found that warming may lead to significant intensification of both regional-scale(10–14% K, depending on convective organization) and station-scale precipitation extremes(7–9% K^(-1)). By comparing clustered convection organized by a localized surface temperature anomaly and squall-line convection organized by vertical wind shear, we further explored how convective organization may modify precipitation extremes and their responses to warming. It is found that shear convective organization is much more sensitive to large-scale dynamic forcing and results in much higher precipitation extremes at both regional and station scales than unorganized convection is. The clustered convection increases station-scale precipitation only slightly during heavy precipitation events. For regional-scale extreme precipitation sensitivity, shear-organized convection has a larger sensitivity by 2–3% Kthan that of unorganized convection, over a wide temperature range, due to its stronger diabatic heating feedback. For the station-scale extreme precipitation sensitivity, no systemic dependence on convective organization is found in our simulations.

关键词： Extreme precipitation Global warming Climate change attribution Convective organization Hourly precipitation