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fractal dimension of Random Attractors for Non-autonomous Fractional Stochastic Reaction-diffusion Equations

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Journal of Partial Differential Equations 2020年第4期33卷 377-394页

作者： SHU Ji BAI Qianqian HUANG Xin ZHANG Jian School of Mathematics Sciences and V.C.&V.R.Key Lab Sichuan Normal UniversityChengdu 610068China Department of Basic Courses Sichuan Vocational College of Finance and EconomicsChengdu 610101China School of Mathematical Sciences University of Electronic Science and Technology of ChinaChengdu 611731China

This paper deals with non-autonomous fractional stochastic reaction-diffusion equations driven by multiplicative noise with s∈(0,1).We first present some conditions for estimating the boundedness of fractal dimension of a random invariant *** we establish the existence and uniqueness of tempered pullback random ***,the finiteness of fractal dimension of the random attractors is proved.

关键词： Random dynamical system random attractor fractal dimension fractional reactiondiffusion equation multiplicative noise

fractal dimension OF POPULUS DAVIDIANA LEAF SURFACE ROUGH EXTENT

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Journal of Northeast Forestry University 1995年第1期6卷 39-42页

作者：韩士杰潘建平王德洪 Northeast Forestry University China

The rough extent of leaf surface may be described by protruding of waxes which like as wart and of stomatal aperture and of width of the cuticular ledge around guard cells. Because the morphology of the leaf surface has obviously similar itseIf, so one can use the theory of the fractal dimension to deal with the problems of leaf surface rough. The paper studied the rough extent and the result showed: with the leaf growing up, the waxes accumulate more and more, the leaf surface is more rough and the dimension is larger. The dimension D which indicates the rough extent of warts protruding is about 2. 10-2.20 on the above epidermis; On the beneath epidermis the dimension D of stomatal opening protruding is about 2.00-2.24, Maximum width L of cuticular ledge is about 1.0-7.4μm.

关键词： Populus davidiana fractal dimension

fractal dimension ESTIMATES FOR INVARIANT SETS OF NON-INJECTIVE MAPS

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Analysis in Theory and Applications 2003年第2期19卷 108-114页

作者： QuChengqin ZhouZuoling NavalInstituteofComputerTechnology China ZhongshanUniversity China

For a special class of non-injective maps on Riemannian manifolds an upper bound for the fractal dimension of invariant set in terms of singular values of the tangent map and degree of non-injectivity is given.

关键词： Riemannian manifold degree of non-injectivity fractal dimension

Aggregating structure in coal water slurry studied by eDLVO theory and fractal dimension

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Frontiers in Energy 2023年第2期17卷 306-316页

作者： Qiang LI Qian WANG Jian HOU Jiansheng ZHANG Yang ZHANG Key Laboratory for Thermal Science and Power Engineering of the Ministry of Education Department of Energy and Power EngineeringTsinghua UniversityBeijing 100084China Energy and Electricity Research Center Jinan UniversityZhuhai 519070China

Coal water slurry gasification is a main source of hydrogen in the developing hydrogen ***,biomass and waste can be added,making gasification process *** expand the application of coal water slurry and gasification process,it is necessary to understand the micro-structure in this large particle suspension *** this paper,the micro-structure in coal water slurry was studied by extended DLVO(eDLVO)theory and fractal dimension,which is used to explain the mechanism of stability in large particle suspension *** interaction between two coal particles was characterized from the interparticle potential and energy barrier based on the eDLVO *** rheology and stability between different types of coals are measured and explained by the aggregating structure and fractal dimension in coal water *** results indicated that there would be an aggregating structure in high rank coals,due to the interparticle potential caused by the surface properties,but probably not in low rank *** aggregating structure can be described and characterized by fractal *** aggregation of particles is the source of the stability for high rank coals,as the close-packed 3D network structure in large particle suspension can support coal particles from settling *** results have demonstrated that the combination of the eDLVO theory and rheological measurement is an effective way to investigate the stability of large particle suspension systems.

关键词： coal water slurry extended DLVO(eDLVO) fractal dimension stability

Bubble size fractal dimension,gas holdup,and mass transfer in a bubble column with dual internals

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Chinese Journal of Chemical Engineering 2020年第12期28卷 2968-2976页

作者： Xiao Xu Junjie Wang Qiang Yang Lei Wang Hao Lu Honglai Liu Hualin Wang School of Mechanical and Power Engineering East China University of Science and TechnologyShanghai 200237China National Engineering Laboratory for Industrial Wastewater Treatment East China University of Science and TechnologyShanghai 200237China State Key Laboratory of Chemical Engineering East China University of Science and TechnologyShanghai 200237China

As the scale of residual oil treatment increases and cleaner production improves in China,slurry bubble column reactors face many challenges and opportunities for residual oil hydrogenation *** internals development is critical to adapt the long-term stable *** this paper,the volumetric mass transfer coefficient,gas holdup and bubble size in a gas-liquid up-flow column are studied with two kinds of *** gas holdup and volumetric mass transfer coefficient increase by 120% and 42% when the fractal dimension of bubbles increases from 0.56 to 2.56,*** enhanced mass transfer processing may improve the coke suppression ability in the slurry reactor for residual oil *** results can be useful for the exploration of reacting conditions,scale-up strategies,and oil *** work is valuable for the design of reactor systems and technological processes.

关键词： Gas-liquid reactor fractal dimension Mass transfer Bubble column

Heart-Rate Analysis of Healthy and Insomnia Groups with Detrended fractal dimension Feature in Edge

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Tsinghua Science and Technology 2022年第2期27卷 325-332页

作者： Xuefei Wang Yichao Zhou Chunxia Zhao the School of Computer Science and Engineering Nanjing University of Science and TechnologyNanjing 210094China

Insomnia,whether situational or chronic,affects over a third of the general population in today’s ***,given the lack of non-contact and non-inductive quantitative evaluation approaches,most insomniacs are often unrecognized and *** Polysomnographic(PSG)is considered as one of the assessment methods,it is poorly tolerated and *** this paper,with the recent development of Internet-of-Things devices and edge computing techniques,we propose a detrended fractal dimension(DFD)feature for the analysis of heart-rate signals,which can be easily acquired by many wearables,of good sleepers and *** feature was derived by calculating the fractal dimension(FD)of detrended *** the trend component removal,we improved the null space pursuit algorithm and proposed an adaptive trend extraction *** experimental results demonstrated the efficacy of the proposed DFD index through numerical statistics and significance testing for healthy and insomnia groups,which renders it a potential biomarker for insomnia assessment and management.

关键词： insomnia fractal dimension adaptive signal separation hypothesis testing

Experimental validation of a signal-based approach for structural earthquake damage detection using fractal dimension of time frequency feature

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Earthquake Engineering and Engineering Vibration 2014年第4期13卷 671-680页

作者： Tao Dongwang Mao Chenxi Zhang Dongyu Li Hui Key Laboratory of Earthquake Engineering and Engineering Vibration Institute of Engineering Mechanics China Earthquake Administration Key Lab of Structures Dynamic Behavior and Control (Harbin Institute of Technology) Ministry of Education Center of Structural Monitoring and Control School of Civil Engineeing Harbin Institute of Technology

This article extends a signal-based approach formerly proposed by the authors, which utilizes the fractal dimension of time frequency feature （FDTFF） of displacements, for earthquake damage detection of moment resist frame （MRF）, and validates the approach with shaking table tests. The time frequency feature （TFF） of the relative displacement at measured story is defined as the real part of the coefficients of the analytical wavelet transform. The fractal dimension （FD） is to quantify the TFF within the fundamental frequency band using box counting method. It is verified that the FDTFFs at all stories of the linear MRF are identical with the help of static condensation method and modal superposition principle, while the FDTFFs at the stories with localized nonlinearities due to damage will be different from those at the stories without nonlinearities using the reverse-path methodology. By comparing the FDTFFs of displacements at measured stories in a structure, the damage-induced nonlinearity of the structure under strong ground motion can be detected and localized. Finally shaking table experiments on a 1：8 scale sixteen-story three-bay steel MRF with added frictional dampers, which generate local nonlinearities, are conducted to validate the approach.

关键词： earthquake damage detection time frequency feature fractal dimension signal-based shaking table test frictional damper

Characterizing the Spheroidization Grade and Strength of 15CrMo Steel through Determining fractal dimension

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Chinese Journal of Mechanical Engineering 2012年第4期25卷 826-831页

作者： LIU Changjun DONG Leiyun JIANG Xiaodong Key Laboratory of Safety Science of Pressurized System of Ministry of Education School of Mechanical and Power Engineering East China University of Science and Technology Shanghai 20023 7 China

The fractal dimension（FD） of surfaces has been widely used to characterize the properties of ***,most of the previous researches were concentrated on the correlation between the FD of surfaces and mechanical properties of materials,such as impact energy and fracture toughness,*** aim of this paper is to characterize the spheroidization grade and strength of 15CrMo steel through determination of FD of cementite phase on the basis of two-dimension microstructural *** methods,namely slit-island method（SIM） and box-counting method（BCM）,are used to determine the value of *** is found that the FD value evaluated by using BCM is generally higher than that evaluated by *** phenomenon may be due to the difference in the principles used in different *** SIM or BCM is used,the spheroidization grade in 15CrMo steel linearly increases with decreasing the value of *** relationship between the FD value,D,and spheroidization grade,Sg,can be approximately expressed as D≌-0.11Sg＋A,where A is a constant value which is depended on the evaluation *** the ultimate strength and the yielding strength of 15CrMo steel increase with increasing FD of cementite *** may be a common relationship between the FD of cementite phase and strength of 15CrMo *** the FD of cementite phase in 15CrMo steel is determined,the strength of this steel can be *** present paper can provide a novel method to evaluate the strength and spheroidization grade of carbon steel through determination of fractal dimension（FD） of cementite phase.

关键词： spheroidization grade fractal dimension strength cementite phase

A New Method for fractal dimension Determination by STM at Nanometer Scale

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International Journal of Minerals,Metallurgy and Materials 1999年第1期13卷 64-68页

作者： Qikai Li Yue Zhang Wuyang Chu Chen Wang Chunli Bai (Applied Science School. University of Science and Technology Beijing, Beijing 100083. China)(Chemical Institute, Chinese Academy of Science, Beijing 100080. China) Applied Science School University of Science and Technology Beijing Beijing 100083 China Chemical Institute Chinese Academy of Science Beijing 100080 China

A new method for determining the fractal dimension by STM at nanomeler scale has been ***- Mandelbrot fractal curves were used to verify the accuracy and reliability. The Computer simulation showed that fractal dimen- sion obtained with this method generally outran the traditional yard method. The new method has been applied to the fractal dimension determination of the fractures of Ti3Al and Ti-24Al-11Nb alloys. The results show that the fractal dimension of Ti-24Al-11Nb alloy is higher than that of Ti3Al, and it varies with the crark extending orientation.

关键词： fractal dimension STM nanometer scale Ti-Al alloy