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Fluid Dynamics & Materials Processing 2024年第3期20卷 525-536页

作者： Aaqib Majeed Ahmad Zeeshan Department of Mathematics The University of FaisalabadFaisalabad38000Pakistan Department of Mathematics and Statistics FBASInternational Islamic University IslamabadIslamabad44000Pakistan

The influence of brownian motion and thermophoresis on a fluid containing nanoparticles flowing over a stretchable cylinder is examined.The classical Navier-Stokes equations are considered in a porous frame.In addition,the Lorentz force is taken into account.The controlling coupled nonlinear partial differential equations are transformed into a system of first order ordinary differential equations by means of a similarity transformation.The resulting system of equations is solved by employing a shooting approach properly implemented in MATLAB.The evolution of the boundary layer and the growing velocity is shown graphically together with the related profiles of concentration and temperature.The magnetic field has a different influence(in terms of trends)on velocity and concentration.

关键词： Mixed convection brownian motion heat transfer porous surface velocity slip

First Passage Density of brownian motion with Two-sided Piecewise Linear Boundaries

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Acta Mathematica Sinica,English Series 2024年第6期40卷 1505-1520页

作者： Zhen YU Mao Zai TIAN Center for Applied Statistics School of StatisticsRenmin University of ChinaBeijing 100872P.R.China School of Mathematics and Data Science Changji UniversityChangji 831100P.R.China

The first passage time has many applications in fields like finance,econometrics,statistics,and biology.However,explicit formulas for the first passage density have only been obtained for a few cases.This paper derives an explicit formula for the first passage density of brownian motion with twosided piecewise continuous boundaries which may have some points of discontinuity.Approximations are used to obtain a simplified formula for estimating the first passage density.Moreover,the results are also generalized to the case of two-sided general nonlinear boundaries.Simulations can be easily carried out with Monte Carlo method and it is demonstrated for several typical two-sided boundaries that the proposed approximation method offers a highly accurate approximation of first passage density.

关键词： Boundary non-crossing probability first density passage density two-sided piecewise continuous boundaries brownian motion

On a Compound Poisson Risk Model Perturbed by brownian motion with Variable Premium and Tail Dependence between Claims Amounts and Inter-Claim Time

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Open Journal of Statistics 2024年第1期14卷 1-37页

作者： Delwendé Abdoul-Kabir Kafando Kiswendsida Mahamoudou Ouedraogo Pierre Clovis Nitiema Department of Mathematics University Joseph Ki-Zerbo Ouagadougou Burkina Faso Department of Mathematics University Ouaga 3s Ouagadougou Burkina Faso Department of Mathematics University Thomas-Sankara Ouagadougou Burkina Faso

This paper considers the compound Poisson risk model perturbed by brownian motion with variable premium and dependence between claims amounts and inter-claim times via Spearman copula. It is assumed that the insurance company’s portfolio is governed by two classes of policyholders. On the one hand, the first class where the amount of claims is high, and on the other hand, the second class where the amount of claims is low, this difference in claim amounts has significant implications for the insurance company’s pricing and risk management strategies. When policyholders are in the first class, they pay an insurance premium of a constant amount c1 and when they are in the second class, the premium paid is a constant amount c2 such that c1 > c2. The nature of claims (low or high) is measured via random thresholds . The study in this work will focus on the determination of the integro-differential equations satisfied by Gerber-Shiu functions and their Laplace transforms in the risk model perturbed by brownian motion with variable premium and dependence between claims amounts and inter-claim times via Spearman copula. .

关键词： Gerber-Shiu Function Copula Integro-Differential Equation Laplace Trans-form brownian motion

Solution of Smoluchowski coagulation equation for brownian motion with TEMOM

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Particuology 2022年第11期70卷 64-71页

作者： Mingliang Xie Qing He State Key Laboratory of Coal Combustion Huazhong University of Science and TechnologyWuhan 430074China Guangdong Provincial Key Laboratory of Distributed Energy Systems School of Chemical Engineering and Energy TechnologyDongguan University of TechnologyDongguan 523808China

The particle number density in the Smoluchowski coagulation equation usually cannot be solved as a whole,and it can be decomposed into the following two functions by similarity transformation:one is a function of time(the particle k-th moments),and the other is a function of dimensionless volume(self-preserving size distribution).In this paper,a simple iterative direct numerical simulation(iDNS)is proposed to obtain the similarity solution of the Smoluchowski coagulation equation for brownian motion from the asymptotic solution of the k-th order moment,which has been solved with the Taylor-series expansion method of moment(TEMOM)in our previous work.The convergence and accuracy of the numerical method are first verified by comparison with previous results about brownian coagulation in the literature,and then the method is extended to the field of brownian agglomeration over the entire size range.The results show that the difference between the lognormal function and the self-preserving size distribution is significant.Moreover,the thermodynamic constraint of the algebraic mean volume is also investigated.In short,the asymptotic solution of the TEMOM and the self-preserving size distribution form a one-to-one mapping relationship;thus,a complete method to solve the Smoluchowski coagulation equation asymptotically is established.

关键词： Population balance equation Particle size distribution Moment method Similarity solution brownian motion

Individual dynamics and local heterogeneity provide a microscopic view of the epidemic spreading

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Chinese Physics B 2024年第5期33卷 656-663页

作者：朱友源沈瑞哲董昊王炜 Kuang Yaming Honors School Nanjing UniversityNanjing 210023China Collaborative Innovation Center of Advanced Microstructures National Laboratory of Solid State MicrostructureSchool of PhysicsNanjing UniversityNanjing 210093China Institute for Brain Sciences Nanjing UniversityNanjing 210023China State Key Laboratory of Analytical Chemistry for Life Science Nanjing UniversityNanjing 210023China

The COVID-19 pandemic has caused severe global disasters,highlighting the importance of understanding the details and trends of epidemic transmission in order to introduce efficient intervention measures.While the widely used deterministic compartmental models have qualitatively presented continuous “analytical” insight and captured some transmission features,their treatment usually lacks spatiotemporal variation.Here,we propose a stochastic individual dynamical(SID)model to mimic the random and heterogeneous nature of epidemic propagation.The SID model provides a unifying framework for representing the spatiotemporal variations of epidemic development by tracking the movements of each individual.Using this model,we reproduce the infection curves for COVID-19 cases in different areas globally and find the local dynamics and heterogeneity at the individual level that affect the disease outbreak.The macroscopic trend of virus spreading is clearly illustrated from the microscopic perspective,enabling a quantitative assessment of different interventions.Seemingly,this model is also applicable to studying stochastic processes at the “meter scale”,e.g.,human society’s collective dynamics.

关键词： brownian motion epidemic spreading heterogeneity

Millisecond dynamics of colloidal suspension studied by X-ray photon correlation spectroscopy at the Shanghai Synchrotron Radiation Facility

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Nuclear Science and Techniques 2024年第1期35卷 1-9页

作者： Chen-Hui Cui Zi-Mu Zhou Lin-Feng Wei Song-Lin Li Feng Tian Xiu-Hong Li Zhi Guo Yi-Hui Xu Huai-Dong Jiang Ren-Zhong Tai Shanghai Synchrotron Radiation Facility Shanghai Advanced Research InstituteChinese Academy of SciencesShanghai 201204China School of Physical Science and Technology ShanghaiTech UniversityShanghai 201210China Shanghai Institute of Applied Physics Chinese Academy of SciencesShanghai 201800China University of Chinese Academy of Sciences Chinese Academy of SciencesBeijing 100049China Center for Transformative Science ShanghaiTech UniversityShanghai 201210China

X-ray photon correlation spectroscopy(XPCS)has emerged as a powerful tool for probing the nanoscale dynamics of soft condensed matter and strongly correlated materials owing to its high spatial resolution and penetration capabilities.This technique requires high brilliance and beam coherence,which are not directly available at modern synchrotron beamlines in China.To facilitate future XPCS experiments,we modified the optical setup of the newly commissioned BL10U1 USAXS beamline at the Shanghai Synchrotron Radiation Facility(SSRF).Subsequently,we performed XPCS measurements on silica suspensions in glycerol,which were opaque owing to their high concentrations.Images were collected using a high frame rate area detector.A comprehensive analysis was performed,yielding correlation functions and several key dynamic parameters.All the results were consistent with the theory of brownian motion and demonstrated the feasibility of XPCS at SSRF.Finally,by carefully optimizing the setup and analyzing the algorithms,we achieved a time resolution of 2 ms,which enabled the characterization of millisecond dynamics in opaque systems.

关键词： XPCS SSRF Silica suspension Glycerol brownian motion Millisecond dynamics

On the Strong Approximation for a Simple Reentrant Line in Light Traffic Under First-buffer First-served Service Discipline

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Acta Mathematicae Applicatae Sinica 2024年第3期40卷 823-839页

作者： Kai-ming YANG Yong-jiang GUO School of Science Beijing University of Posts and TelecommunicationsBeijing 100876China

For a 2-station and 3-class reentrant line under first-buffer first-served(FBFS)service discipline in light traffic,we firstly construct the strong approximations for performance measures including the queue length,workload,busy time and idle time processes.Based on the obtained strong approximations,we use a strong approximation method to find all the law of the iterated logarithms(LILs)for the above four performance measures,which are expressed as some functions of system parameters:means and variances of interarrival and service times,and characterize the fluctuations around their fluid approximations.

关键词： reentrant line queueing network FBFS service discipline strong approximation LIL brownian motion

Numerical Analysis of the Magnetic Dipole Effect on a Radiative Ferromagnetic Liquid Flowing over a Porous Stretched Sheet

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Fluid Dynamics & Materials Processing 2024年第2期20卷 293-310页

作者： G.Dharmaiah F.Mebarek-Oudina K.S.Balamurugan N.Vedavathi Department of Mathematics Narasaraopeta Engineering CollegeNarasaraopetIndia Department of Physics Faculty of SciencesUniversity of 20 Août 1955-SkikdaSkikdaAlgeria Department of Mathematics RVR&JC College of EngineeringGunturIndia Department of Mathematics Koneru Lakshmaiah Education FoundationVaddeswaramIndia

The effects of a magnetic dipole on a nonlinear thermally radiative ferromagnetic liquidﬂowing over a stretched surface in the presence of brownian motion and thermophoresis are investigated.By means of a similarity transformation,ordinary differential equations are derived and solved afterwards using a numerical(the BVP4C)method.The impact of various parameters,namely the velocity,temperature,concentration,is presented graphically.It is shown that the nanoparticles properties,in conjunction with the magnetic dipole effect,can increase the thermal conductivity of the engineered nanoﬂuid and,consequently,the heat transfer.Comparison with earlier studies indicates high accuracy and effectiveness of the numerical approach.An increase in the Brow-nian motion parameter and thermophoresis parameter enhances the concentration and the related boundary layer.The skin-friction rises when the viscosity parameter is increased.A larger value of the ferromagnetic para-meter results in a higher skin-friction and,vice versa,in a smaller Nusselt number.

关键词： brownian motion thermo-phoresis radiation magnetic dipole BVP4C non-linear

Stochastic process-based degradation modeling and RUL prediction: from brownian motion to fractional brownian motion

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Science China(Information Sciences) 2021年第7期64卷 5-24页

作者： Hanwen ZHANG Maoyin CHEN Jun SHANG Chunjie YANG Youxian SUN School of Automation and Electrical Engineering University of Science and Technology Beijing State Key Laboratory of Industrial Control Technology College of Control Science and EngineeringZhejiang University Department of Automation Tsinghua University School of Automation and Electrical Engineering Linyi University Department of Electrical and Computer Engineering University of Alberta

brownian motion(BM) has been widely used for degradation modeling and remaining useful life(RUL) prediction, but it is essentially Markovian. This implies that the future state in a BM-based degradation process relies only on its current state, independent of the past states. However, some practical industrial devices such as Li-ion batteries, ball bearings, turbofans, and blast furnace walls show degradations with long-range dependence(LRD), where the future degradation states depend on both the current and past degradation states. This type of degradation naturally brings two interesting problems, that is, how to model the degradations and how to predict their RULs. Recently, in contrast to the work that uses only BM, fractional brownian motion(FBM) is introduced to model practical degradations. The most important feature of the FBM-based degradation models is the ability to characterize the non-Markovian degradations with LRD. Although FBM is an extension of BM, it is neither a Markovian process nor a semimartingale. Therefore, how to obtain the first passage time of an FBM-based degradation process has become a challenging task. In this paper, a review of the transition of RUL prediction from BM to FBM is provided. The peculiarities of FBM when addressing the LRD inherent in some practical degradations are discussed. We first review the BM-based degradation models of the past few decades and then give details regarding the evolution of FBM-based research. Interestingly, the existing BM-based models scarcely consider the effect of LRD on the prediction of RULs. Two practical cases illustrate that the newly developed FBMbased models are more generalized and suitable for predicting RULs than the BM-based models, especially for degradations with LRD. Along with the direction of FBM-based RUL prediction, we also introduce some important and interesting problems that require further study.

关键词： remaining useful life degradation model brownian motion fractional brownian motion long-range dependence

Coupling effect of brownian motion and laminar shear flow on colloid coagulation:a brownian dynamics simulation study

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Chinese Physics B 2012年第5期21卷 364-371页

作者：徐升华孙祉伟李旭 Jin Tong Wang Key Laboratory of Microgravity Institute of Mechanics Chinese Academy of SciencesBeijing 100190China National Microgravity Laboratory Institute of MechanicsChinese Academy of SciencesBeijing 100190China Department of Physics Southern University and A&M CollegeBaton RougeLA 70813USA

Simultaneous orthokinetic and perikinetic coagulations（SOPCs） are studied for small and large Peclet numbers（P e） using brownian dynamics simulation.The results demonstrate that the contributions of the brownian motion and the shear flow to the overall coagulation rate are basically not additive.At the early stages of coagulation with small Peclet numbers,the ratio of overall coagulation rate to the rate of pure perikinetic coagulation is proportional to P 1/2 e,while with high Peclet numbers,the ratio of overall coagulation rate to the rate of pure orthokinetic coagulation is proportional to P 1/2 e.Moreover,our results show that the aggregation rate generally changes with time for the SOPC,which is different from that for pure perikinetic and pure orthokinetic coagulations.By comparing the SOPC with pure perikinetic and pure orthokinetic coagulations,we show that the redistribution of particles due to brownian motion can play a very important role in the SOPC.In addition,the effects of redistribution in the directions perpendicular and parallel to the shear flow direction are different.This perspective explains the behavior of coagulation due to the joint effects of the brownian motion（perikinetic） and the fluid motion（orthokinetic）.

关键词： simultaneous orthokinetic and perikinetic coagulation brownian motion shear flow,colloidal aggregation