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GLOBAL EXISTENCE OF SOLUTIONS FOR A MULTI-PHASE FLOW: A BUBBLE IN A LIQUID TUBE AND RELATED CASES

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Acta Mathematica Scientia 2015年第4期35卷 832-854页

作者： Debora AMADORI Paolo BAITI Andrea CORLI Edda DAL SANTO department of Engineering and computer Science and mathematics University of L'Aquila department of mathematics and computer Science University of Udine department of mathematics and computer Science University of Ferrara

In this paper we study the problem of the global existence （in time） of weak entropic solutions to a system of three hyperbolic conservation laws, in one space dimension, for large initial data. The system models the dynamics of phase transitions in an isothermal fluid; in Lagrangian coordinates, the phase interfaces are represented as stationary contact discontinuities. We focus on the persistence of solutions consisting in three bulk phases separated by two interfaces. Under some stability conditions on the phase configuration and by a suitable front tracking algorithm we show that, if the BV-norm of the initial data is less than an explicit （large） threshold, then the Cauchy problem has global solutions.

关键词： hyperbolic systems of conservation laws phase transitions wave-front trackingalgorithm

New prediction of chaotic time series based on local Lyapunov exponent

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Chinese Physics B 2013年第5期22卷 191-197页

作者：张勇 department of mathematics and computer Wuhan Polytechnic University

A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in state space. After recon- structing state space from one-dimensional chaotic time series, neighboring multiple-state vectors of the predicting point are selected to deduce the prediction formula by using the definition of the locaI Lyapunov exponent. Numerical simulations are carded out to test its effectiveness and verify its higher precision over two older methods. The effects of the number of referential state vectors and added noise on forecasting accuracy are also studied numerically.

关键词： chaotic time series prediction of chaotic time series local Lyapunov exponent least squaresmethod

ILES for mechanism of ramp-type MVG reducing shock induced flow separation

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Science China(Physics,Mechanics & Astronomy) 2016年第12期59卷 60-71页

作者： Yong Yang YongHua Yan ChaoQun Liu department of mathematics University of Texas at Arlington department of mathematics and computer Science Alcorn State University

A high order implicit large eddy simulation (ILES) is carried out to study the mechanism of shock induced flow separation reduction under ramp-type MVG control. The mechanism was originally considered as that MVG can generate streamwise vortices which strongly mix boundary layer and the boundary layer becomes more capable to resist strong adverse pressure gradient caused by shock and to keep the boundary layer attached. However, according to our ILES, a chain of ring-like vortices is generated behind the ramp-type MVG and goes further to interact with the shock. When the ring-like vortices pass through the shock, the shock wave is weakened and altered while the vortex structures are quite stable. The instantaneous simulation shows that the spanwise ring-like vortex, not the streamwise vortex, plays a key role to weaken the shock and reduce the shock-induced separation. Detailed investigation on ring-like vortices and shock interaction will be given in this paper.

关键词： large eddy simulation MVG ring-like vortex shock

Tailoring Light–Matter Interactions in Overcoupled Resonator for Biomolecule Recognition and Detection

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Nano-Micro Letters 2025年第1期17卷 262-280页

作者： Dongxiao Li Hong Zhou Zhihao Ren Cheng Xu Chengkuo Lee department of Electrical and computer Engineering National University of SingaporeSingapore 117583Singapore Center for Intelligent Sensors and MEMS(CISM) National University of SingaporeSingapore 117608Singapore

Plasmonic nanoantennas provide unique opportunities for precise control of light–matter coupling in surface-enhanced infrared absorption(SEIRA)spectroscopy,but most of the resonant systems realized so far suffer from the obstacles of low sensitivity,narrow bandwidth,and asymmetric Fano resonance ***,we demonstrated an overcoupled resonator with a high plasmon-molecule coupling coefficient(μ)(OC-Hμresonator)by precisely controlling the radiation loss channel,the resonator-oscillator coupling channel,and the frequency detuning *** observed a strong dependence of the sensing performance on the coupling state,and demonstrated that OC-Hμresonator has excellent sensing properties of ultra-sensitive(7.25%nm^(−1)),ultra-broadband(3–10μm),and immune asymmetric Fano *** characteristics represent a breakthrough in SEIRA technology and lay the foundation for specific recognition of biomolecules,trace detection,and protein secondary structure analysis using a single array(array size is 100×100μm^(2)).In addition,with the assistance of machine learning,mixture classification,concentration prediction and spectral reconstruction were achieved with the highest accuracy of 100%.Finally,we demonstrated the potential of OC-Hμresonator for SARS-CoV-2 *** findings will promote the wider application of SEIRA technology,while providing new ideas for other enhanced spectroscopy technologies,quantum photonics and studying light–matter interactions.

关键词： Plasmonic nanoantennas Light-matter interaction Surface-enhanced infrared absorption Overcoupled Biosensing

Eigenvalue Comparison Theorems on Finsler Manifolds

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Chinese Annals of mathematics,Series B 2015年第1期36卷 31-44页

作者： Songting YIN Qun HE department of mathematics Tongji University department of mathematics and computer Science Tongling University

Cheng-type inequality, Cheeger-type inequality and Faber-Krahn-type inequality are generalized to Finsler manifolds. For a compact Finsler manifold with the weighted Ricci curvature bounded from below by a negative co... 详细信息

关键词： The first eigenvalue Finsler-Laplacian Ricci curvature S-Curvature

Explicit solutions of nonlinear wave equation systems

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Chinese Physics B 2013年第1期22卷 39-45页

作者： Ahmet Bekir Burcu Ayhan M. Naci zer mathematics and computer Science department Eskisehir Osmangazi University

We apply the （G＇/G）-expansion method to solve two systems of nonlinear differential equations and construct traveling wave solutions expressed in terms of hyperbolic functions, trigonometric functions, and rational functions with arbitrary parameters. We highlight the power of the （G＇/G）-expansion method in providing generalized solitary wave solutions of different physical structures. It is shown that the （G＇/G）-expansion method is very effective and provides a powerful mathematical tool to solve nonlinear differential equation systems in mathematical physics.

关键词： (G'/G)-expansion method long-short-wave interaction system coupled integrable dispersionless system

Characterization of Essential Stability in Lower Pseudocontinuous Optimization Problems

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Journal of Systems Science & Complexity 2015年第3期28卷 638-644页

作者： ZHOU Yonghui YU Jian School of mathematics and computer Sciences Guizhou Normal University department of mathematics Guizhou University

Characterization of essential stability of minimum solutions for a class of optimization problems with boundedness and lower pseudocontinuity on a compact metric space is given. It shows that any optimization problem considered here has one essential component(resp. one essential minimum solution) if and only if its minimum solution set is connected(resp. singleton) and that those optimization problems which have a unique minimum solution form a residual set(however, which need not to be dense).

关键词： Essential component essential minimum solution pseudocontinuity unique solution.

Global Stability in a Competition Model of Plankton Allelopathy with Infinite Delay

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Journal of Systems Science & Complexity 2015年第5期28卷 1070-1079页

作者： CHEN Fengde XIE Xiangdong WANG Haina department of mathematics Ningde Teachers College College of mathematics and computer Science Fuzhou University

A competition model of plankton allelopathy with infinite delay is considered in this *** using an iterative method, the global stability of the interior equilibrium point of the system is investigated. The result shows that for this system, delay and toxic substances are harmless for the stability of the interior equilibrium point.

关键词： Equilibrium global stability infinite delay iterative method plankton allelopathy

Personalized federated few-shot node classification

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Science China(Information Sciences) 2025年第1期 204-218页

作者： Yunfeng ZHAO Xintong HE Guoxian YU Jun WANG Yongqing ZHENG Carlotta DOMENICONI School of Software Shandong University Joint SDU-NTU Centre for Artificial Intelligence Research Shandong University department of mathematics National University of Singapore department of computer Science George Mason University

Personalized federated learning(PFL) aims to train customized models for individual clients in a decentralized setting, with the account of non-independent and identically distributed data across clients. However, most PFL methods adopt uniform classification layers for diverse clients and give rise to error-prone predictions, due to the task heterogeneity notably prominent in decentralized graph data scenarios. Although some PFL solutions setup client-specific classification layers for each client and optimize them only locally, they are corrupted with limited local training data. We propose an innovative solution called federated parameter decoupling and node augmentation(Fed PANo) to address these problems and to achieve personalized federated few-shot node classification, which is a prevalent and challenging but unexplored topic. Specifically, Fed PANo first separates the local model into the GNN and classifier to handle unique client-specific task variations. The GNN is trained through federated learning to capture shared knowledge of graph nodes across clients, while the classifier is custom-designed and trained individually for each client. Additionally, a generic classifier shared among clients is adopted to encourage the GNN's grasp of shared information. Then Fed PANo further proposes the node generator along with its local and collaborative training strategies to deal with the node scarcity of clients. Extensive experimental results on benchmark datasets confirm that Fed PANo outperforms eight competitive baselines across different settings.

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