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Derivatives of local times for some Gaussian fields

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arXiv 2019年

作者： Hong, Minhao Xu, Fangjun School of Statistics East China Normal University Shanghai200262 China Key Laboratory of Advanced Theory and Application in Statistics and Data Science - MOE School of Statistics East China Normal University Shanghai200062 China NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai 3663 Zhongshan Road North Shanghai200062 China

In this article, we consider derivatives of local time for a (2, d)-Gaussian field Z = {Z(t, s) = XtH1 − XeH2 , s, t ≥ 0}, s where XH1 and XeH2 are two independent processes from a class of d-dimensional centered Gaussian processes satisfying certain local nondeterminism property. We first give a condition for existence of derivatives of the local time. Then, under this condition, we show that derivatives of the local time are Hölder continuous in both time and space variables. Moreover, under some additional assumptions, we show that this condition is also necessary for existence of derivatives of the local time at the origin. Copyright © 2019, The Authors. All rights reserved.

关键词： Gaussian distribution

Derivatives of local times for some Gaussian fields II

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arXiv 2020年

Given a (2, d)-Gaussian field (formula presented), s where XH1 and XeH2 are independent d-dimensional centered Gaussian processes satisfying certain properties, we will give the necessary condition for existence of de... 详细信息

关键词： Gaussian distribution

Bifurcation analysis and control of quorum sensing network model 5

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Bifurcation analysis and control of quorum sensing network m...

5th International Workshop on advanced Computational Intelligence and Intelligent Informatics, IWACIII 2017

作者： Mei, Qicheng Liu, Feng Ren, Jie Sun, Fenglan Wang, Hua School of Automation China University of Geosciences Wuhan430074 China Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems Wuhan430074 China Research Center of System Theory and Application Chongqing University of Posts and Telecommunications Chongqing400065 China Department of Mechanical Engineering Boston University BostonMA02215 United States

In this paper, a model is constructed to investigate the mechanism induced quorum sensing (QS) by coexisting of small RNA and signal molecule. The QS network model regulated by small RNAs is studied. The condition of the stability of the QS network is considered by using Routh-Hurwitz stability criterion. The conditions for the existence of Hopf bifurcation are obtained. Then, a linear feedback control is designed to make the system asymptotically stable. The numerical simulation is used to verify the results of theoretical analysis.

关键词： Hopf bifurcation

Effect of High Temperature Salt Immersion Environment on the Mechanical Properties Degradation and Long-Term Creep Failure of Carbon Fiber Reinforced Polymer

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SSRN

SSRN 2022年

作者： Li, Xueliang Zhang, Xiaoyu Chen, Jianzhong Huang, Li Lv, Yong School of Science Wuhan University of Technology Wuhan430070 China Hubei Key Laboratory of Theory and Application of Advanced Materials Mechanics Wuhan University of Technology Wuhan430070 China

In this study, the degradation of mechanical properties and long-term creep behavior of carbon fiber reinforced polymer (CFRP) materials under marine environment are investigated using molecular simulation by establishing molecular models in dry, water salt environments. The results show that the mechanical properties of CFRP will degrade under high temperature salt immersion environment, and the degradation extent increases with the increase of temperature. The degradation extent of tensile strength and Young’s modulus in the vertical fiber direction is about 39.07% and 23.17% at 354K, while the influence of the mechanical properties along the fiber direction is small, with a 4.25% decrease in Young’s modulus. In the process of creep evolution, the temperature factor has greater influence on the creep evolution at low stress level than the other factors. With the increase of stress level, the material is more likely to fail at 334K than that at the same temperature. While at high stress level, the temperature and the soaking medium have great influence on the creep of the final material, which together affect the final failure of the material. Importantly, the influence of salt environment on the mechanical properties and long-term performance of CFRP is mainly caused by water molecules in solution, but less influenced by salt ions. On the micro-scale, the mechanism of CFRP during creep failure is analyzed from energy and structure. The findings from this paper provide theoretical basis for further application of CFRP in marine engineering structures. © 2022, The Authors. All rights reserved.

关键词： Molecules

Mean-variance portfolio selection with dynamic attention behavior in a hidden Markov model

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arXiv 2022年

作者： Zhang, Yu Jin, Zhuo Wei, Jiaqin Yin, George Key Laboratory of Advanced Theory and Application in Statistics and Data Science-MOE School of Statistics East China Normal University Shanghai200062 China Department of Actuarial Studies and Business Analytics Macquarie University NSW2109 Australia Department of Mathematics University of Connecticut StorrsCT06269-1009 United States

In this paper, we study closed-loop equilibrium strategies for mean-variance portfolio selection problem in a hidden Markov model with dynamic attention behavior. In addition to the investment strategy, the investor’s attention to news is introduced as a control of the accuracy of the news signal process. The objective is to find equilibrium strategies by numerically solving an extended HJB equation by using Markov chain approximation method. An iterative algorithm is constructed and its convergence is established. Numerical examples are also provided to illustrate the results. Copyright © 2022, The Authors. All rights reserved.

关键词： Hidden Markov models

A hybrid deep learning method for finite-horizon mean-field game problems

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arXiv 2023年

This paper develops a new deep learning algorithm to solve a class of finite-horizon mean-field games. The proposed hybrid algorithm uses Markov chain approximation method combined with a stochastic approximation-based iterative deep learning algorithm. Under the framework of finite-horizon mean-field games, the induced measure and Monte-Carlo algorithm are adopted to establish the iterative mean-field interaction in Markov chain approximation method and deep learning, respectively. The Markov chain approximation method plays a key role in constructing the iterative algorithm and estimating an initial value of a neural network, whereas stochastic approximation is used to find accurate parameters in a bounded region. The convergence of the hybrid algorithm is proved;two numerical examples are provided to illustrate the results. Copyright © 2023, The Authors. All rights reserved.

关键词： Markov chains

Investigation of shock–shock interaction in hypersonic rarefied flow using direct simulation Monte Carlo method

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arXiv 2024年

作者： Jiang, Yazhong Ma, Tianju Hubei Key Laboratory of Theory and Application of Advanced Materials Mechanics School of Science Wuhan University of Technology Wuhan430070 China Academy of Aerospace Propulsion Technology Xi’an710100 China

The majority of studies on shock–shock interactions assume the high-Reynolds-number or inviscid condition for the fluid flows. However, the rarefied flows encountered by the hypersonic vehicles in their high-altitude flights call for investigations coupling the shock–shock interaction and the rarefied-gas effect. An in-house direct simulation Monte Carlo (DSMC) solver is employed to simulate a series of hypersonic air flows over a wedge–cylinder configuration at the freestream Mach number of 10. The DSMC simulations cover 15 different Knudsen numbers Kn∞, spanning from 6.688×10−3 to 6.688×10−1. At the lowest Knudsen number, the numerical results are validated by the corresponding wind-tunnel experiment, and demonstrate the features of an Edney type IV shock–shock interaction, including the type IV wave pattern, the supersonic jet impingement, the augmentations of surface shear stress, pressure and heat flux, as well as the shifts in the angular positions of the peak shear stress, pressure and heat flux over the cylinder surface. In ascending order of Kn∞, the overviews and details of the flow fields with and without shock–shock interaction, as well as the distributions of the shear stress, pressure and heat flux over the cylinder surface are displayed and analyzed. The increase of flow rarefaction continuously alters the flow pattern of the shock–shock interaction, in which the wave system gradually losses the abilities to deflect the streamlines or to concentrate the energy in the flow. As the flow becomes more rarefied, the shock–shock interaction will result in smaller augmentation factors and less angular shifts of the peak aerodynamic/aerothermal loads. At the highest Kn∞ in this study, the augmentation factors for skin friction and heat flux are found to be less than unity. The existence/vanishment of the supersonic jet and its position relative to the cylinder account for the distribution characteristics of aerodynamic/aerothermal loads over the cylinder surf

关键词： Shear stress

Enhanced High-Temperature Energy Storage Density in P-Type Niox Quantum Dots and P(Vdf-Hfp) Composite Dielectrics

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SSRN

SSRN 2024年

作者： Fang, Cheng Zhang, Ziyi Wang, Jian Ye, Zhanwen Li, Kaiyuan Wu, Luoqi Feng, Xiaobin Duan, Bo Dong, Lijie Zhou, Ling Shen, Zhonghui Hubei Key Laboratory of Theory and Application of Advanced Materials Mechanics School of Physics and Mechanics Wuhan University of Technology Wuhan430070 China Center for Smart Materials and Devices State Key Laboratory of Advanced Technology for Materials Synthesis and Processing Wuhan University of Technology Hubei Wuhan430070 China

The harsh application environment imposes higher requirements on the operating temperature of dielectric energy storage capacitors. Suppressing carrier transmission at high temperatures is a critical way to enhance the breakdown field strength (Eb) and the operating temperature of the dielectrics. In this paper, low-concentration nickel oxide quantum dots (NiOx QDs) with P-type defects are introduced into the polymer matrix, and hot carriers are captured by constructing hole traps, thus improving the high-temperature Eb and energy storage density (Udis) of the polymer. The NiOx QDs were synthesized by the chemical precipitation method and were modified with polydopamine (PDA) to prepare P(VDF-HFP)-based composite films. The results show that the NiOx@PDA QDs can effectively enhance the Eb and Udis of the films. What's more, at 90°C, the Eb of the composite film reaches 2242.78 kV/cm, representing a 42.41% increase compared to pure P(VDF-HFP) film (1574.83 kV/cm), and the Udis reaches 2.94 J/cm3, demonstrating an impressive improvement of 164.86% when compared with pure P(VDF-HFP) (1.11 J/cm3). The results confirmed that the P-type NiOx QDs restricted the Poole-Frenkel emission within the dielectrics. Together with the enhanced compatibility of the organic-inorganic composite interface, the macro defects of the composites were suppressed, and higher Eb and Udis were obtained. This work offers a straightforward and efficient approach for manufacturing high-temperature energy storage dielectrics. © 2024, The Authors. All rights reserved.

关键词： Nanocrystals

An improved point-to-surface contact algorithm with penalty method for peridynamics

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arXiv 2024年

作者： Zhang, Haoran Liu, Lisheng Lai, Xin Li, Jun Department of Engineering Structure and Mechanics Wuhan University of Technology Wuhan430070 China Hubei Key Laboratory of Theory and Application of Advanced Materials Mechanics Wuhan University of Technology Wuhan430070 China

It is significantly challenging to obtain accurate contact forces in peridynamics (PD) simulations due to the difficulty of surface particles identification, particularly for complex geometries. Here, an improved point-to-surface contact model is proposed for PD with high accuracy. First, the outer surface is identified using the eigenvalue method and then we construct a Verlet list to identify potential contact particle pairs efficiently. Subsequently, a point-to-surface contact search algorithm is utilized to determine precise contact locations with the penalty function method calculating the contact force. Finally, the accuracy of this point-to-surface contact model is validated through several representative contact examples. The results demonstrate that the point-to-surface contact model model can predict contact forces and deformations with high accuracy, aligning well with the classical Hertz contact theory solutions. This work presents a contact model for PD that automatically recognizes external surface particles and accurately calculates the contact force, which provides guidance for the study of multi-body contact as well as complex contact situations. Copyright © 2024, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions