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Approximating Nash Equilibrium for Optimal Consumption in Stochastic Growth Model with Jumps

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Acta Mathematica Sinica,English Series 2022年第9期38卷 1621-1642页

作者： Li Jun BO tong qing LI School of Mathematical Sciences University of Science and Technology of ChinaHefei 230026P.R.China Wu Wen Tsun Key Laboratory of Mathematics Chinese Academy of ScienceHefei 230026P.R.China

In this paper,we study a class of dynamic games consisting of finite agents under a stochastic growth model with *** jump process in the dynamics of the capital stock of each agent models announcements regarding each agent in the game occur at Poisson distributed random *** aim of each agent is to maximize her objective functional with mean-field interactions by choosing an optimal consumption *** prove the existence of a fixed point related to the so-called consistence condition as the number of agents goes *** upon the fixed point,we establish an optimal feedback consumption strategy for all agents which is in fact an approximating Nash equilibrium which describes strategies for each agent such that no agent has any incentive to change her strategy.

关键词： Stochastic growth jump processes mean field interaction optimal consumption fixed point approximating Nash equilibrium

Numerical Simulations of Coastal Overwash Using A Phase-Averaged Wave−Current−Sediment Transport Model

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China Ocean Engineering 2022年第2期36卷 191-207页

作者： LI Song-zhe JI Chao ZHANG qing-he CHEN tong-qing State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin UniversityTianjin 300350China Key Laboratory of Engineering Sediment Tianjin Research Institute for Water Transport EngineeringMinistry of TransportTianjin 300456China

Coastal overwash is a natural phenomenon that commonly occurs during storm events and can cause considerable changes in nearshore morphology within a short *** this study,a complete set of empirical overwash transport algorithms is developed and introduced into a phase-averaged wave-current-sediment transport coupling model that integrates the Finite-Volume Community Ocean Model(FVCOM)and the Simulating Waves Nearshore(SWAN)*** resulting morphological evolution model can simulate coastal *** against the data obtained from multiple sets of laboratory overwash experiments demonstrates that the model performs relatively well in simulating morphological changes caused by runup overwash and inundation overwash under different hydrodynamic and beach profile *** sensitivity of each empirical coefficient in the overwash transport algorithms is comprehensively *** effects of each coefficient on the output of the model are discussed,and a recommended value range is provided for each coefficient.

关键词： wave-current coupling phase-averaged model overwash wave runup morphological evolution

Nonlinear Tripartite Entangled State Representation and Related Generalized Wigner Function

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Communications in Theoretical Physics 2005年第3X期44卷 541-546页

作者： WANG Pei-qing SONG tong-Qiang Physics Department Ningbo University Ningbo 315211 China

We construct the nonlinear tripartite entangled state representation and the related generalized Wigner operator. Then we discussed the Wigner functions of the nonlinear tripartite entangled state and the three-mode nonlinear squeezed vacuum state, and obtained the classical Weyl corresponding function of the three-mode nonlinear squeezed state.

关键词： nonlinear entangled states generalized Wigner operator IWOP technique

Squeezing Transformation of Three-Mode Entangled State

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Communications in Theoretical Physics 2005年第5X期44卷 911-916页

作者： QIAN Xiao-qing SONG tong-Qiang Department of Physics Ningbo University Ningbo 315211 China

We introduce the three-mode entangled state and set up an experiment to generate it. Then we discuss the three-mode squeezing operator squeezed ｜p, X2, X3〉→μ^-3/2｜p/μ, X2/μ, X3/μ） and the optical implement to realize such a squeezed state. We also reveal that c-number .asymmetric shrink transform in the three-mode entangled state, i.e. ｜p, X2,X3）→μ^-1/2｜p/μ, X2,X3）, maps onto a kind of one-sided three-mode squeezing operator {iλ （∑i^3=1 Pi）（∑i^3=1 Qi） -λ/2}. Using the technique of integration within an ordered product （IWOP） of operators, we derive their normally ordered forms and construct the corresponding squeezed states.

关键词： three-mode entangled state c-number asymmetric shrink transform one-sided three-mode squeezing operator

Solution of the Dirac Equation for Ring-Shaped Modified Kratzer Potential

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Communications in Theoretical Physics 2007年第3X期48卷 431-434页

作者： CHENG Yan-Fu DAI tong-qing College of Electronics and Information Engineering South-Central University for Nationalities Wuhan 430074 China

We propose a new exactly solvable potential which is Formed by modified Kratzer potential plus a new ring-shaped potential η cot^2 θ/r^2 The solutions of the Dirac equation with equal scalar and vector ring-shaped modified Kratzer potential are found by using the Nikiforov-Uvarov method. The nonrelativistic limit of the energy spectrum has been discussed.

关键词： Dirac equation solution ring-shaped modified Kratzer potential

Scaling limits of interacting diffusions in domains

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Frontiers of Mathematics in China 2014年第4期9卷 717-736页

作者： Zhen-qing CHEN Wai-tong (Louis) FAN Department of Mathematics University of Washington Seattle WA 98195 USA

We survey recent effort in establishing the hydrodynamic limits and the fluctuation limits for a class of interacting diffusions in domains. These systems are introduced to model the transport of positive and negative charges in solar cells. They are general microscopic models that can be used to describe macroscopic phenomena with coupled boundary conditions, such as the popula- tion dynamics of two segregated species under competition. Proving these two types of limits represents establishing the functional law of large numbers and the functional central limit theorem, respectively, for the empirical measures of the spatial positions of the particles. We show that the hydrodynamic limit is a pair of deterministic measures whose densities solve a coupled nonlinear heat equations, while the fluctuation limit can be described by a Gaussian Markov process that solves a stochastic partial differential equation.

关键词： Hydrodynamic limit fluctuation interacting diffusion reflecteddiffusion Dirichlet form non-linear boundary condition coupled partiMdifferential equation martingales stochastic partial differential equation,Guassian process

Experimental Investigation of Local Scour Around A New Pile-Group Foundation for Offshore Wind Turbines in Bi-Directional Current

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China Ocean Engineering 2018年第6期32卷 737-745页

作者： JI Chao ZHANG Jin-feng ZHANG qing-he LI Ming-xing CHEN tong-qing State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin University Fourth Harbor Engineering Investigation and Design Institute Co. Ltd. China Communications Construction Company

The local scour around a new pile-group foundation of offshore wind turbine subjected to a bi-directional current was physically modeled with a bi-directional flow flume. In a series of experiments, the flow velocity and topography of the seabed were measured based on a system composed of plane positioning equipment and an *** results indicate that the development of the scour hole was fast at the beginning, but then the scour rate decreased until reaching equilibrium. Erosion would occur around each pile of the foundation. In most cases, the scour pits were connected in pairs and the outside widths of the scour holes were larger than the inner widths. The maximum scour depth occurred at the side pile of the foundation for each test. In addition, a preliminary investigation shows that the larger the flow velocity, the larger the scour hole dimensions but the shorter equilibrium time. The field maximum scour depth around the foundation was obtained based on the physical experiments with the geometric length scales of 1:27.0, 1:42.5 and 1:68.0, and it agrees with the scour depth estimated by the HEC-18 equation.

关键词： offshore wind turbines new pile-group foundation local scour bi-directional current

Effects of organic matter and salinity on the flocculation of kaolinites in a settling column

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Journal of Hydrodynamics 2021年第1期33卷 150-156页

作者： Zhong-yue Li Jin-feng Zhang qing-he Zhang Xiao-teng Shen tong-qing Chen State Key Laboratory of Hydraulic Engineering Simulation and Safety Tianjin UniversityTianjin 300072China Key Laboratory of Earthquake Engineering Simulation and Seismic Resilience of China Earthquake Administration Tianjin UniversityTianjin 300350China Key Laboratory of Ministry of Education for Coastal Disaster and Protection Hohai UniversityNanjing 210098China State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering Nanjing 210029China

The flocculation and the settling of the cohesive sediment play an important role in the sediment transport process,and they are affected by many *** the coasts and in the estuaries,the organic matter and the salinity are two significant *** this study,experiments are carried out to evaluate the flocculation and the settling of the kaolinite in cases of various organic matter and salinity solutions in quiescent *** optical multi-channel suspended concentration monitoring system is used to measure the sediment concentration and the floc *** results show that the settling velocity decreases with the increase of the organic matter content,and the floc size increases with the increase of the organic matter *** addition,an empirical formula for the settling velocity under the influence of the organic matter and the salinity based on the experimental results is proposed.

关键词： Kaolinite humic acid salinity settling velocity floc size distribution

Large conversion of energy in dielectric elastomers by electromechanical phase transition

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Acta Mechanica Sinica 2012年第4期28卷 1106-1114页

作者： tong-qing Lu Zhi-Gang Suo State Key Lab for Strength and Vibration of Mechanical Structures International Center of Applied MechanicsSchool of Aerospace EngineeringXi'an Jiaotong University 710049 Xi' an China School of Engineering and Applied Sciences Harvard University CambridgeMA 02138 USA

When air is pumped in, a tubular balloon initially inflates slightly and homogeneously. A short section of the balloon then forms a bulge, which coexists with the unbulged section of the balloon. As more air is pumped in, the bulged section elongates at the expense of the unbulged section, until the entire balloon is bulged. The phenomenon is analogous to the liquid-to-vapor phase transition. Here we study the bulging transition in a dielectric elastomer tube as air is pumped into the balloon and a voltage is applied through the thickness of the membrane. We formulate the condition for coexistent budged and unbulged sections, and identify allowable states set by electrical breakdown and mechanical rupture. We find that the bulging transition dramatically amplifies electromechanical energy conversion. Energy converted in an electromechanical cycle consisting of unbulged and bulged states is thousands of times that in an electromechanical cycle consisting of only unbulged states.

关键词： Dielectric elastomer Bulge Electromechanical energy conversion. Tubular balloon Electromechanical transition