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General Mean Reflected Backward Stochastic Differential Equations

JOURNAL OF THEORETICAL PROBABILITY 2024年第1期37卷 877-904页

作者： Hu, Ying Moreau, Remi Wang, Falei Univ Rennes CNRS IRMAR UMR 6625 F-35000 Rennes France Shandong Univ Zhongtai Secur Inst Financial Studies Jinan 250100 Peoples R China Shandong Univ Sch Math Jinan 250100 Peoples R China

The present paper is devoted to the study of backward stochastic differential equations (BSDEs) with mean reflection formulated by Briand et al. (Ann Appl Probab 28(1):482-510, 2018). We investigate the solvability of a generalized mean reflected BSDE, whose driver also depends on the distribution of solution term Y. Using a fixed-point argument, BMO martingale theory and the theta-method, we establish existence and uniqueness results for such BSDEs in several typical situations, including the case where the driver is quadratic with bounded or unbounded terminal condition.

关键词： Mean reflection fixed-point method theta-method

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Complex mathematical SIR model for spreading of COVID-19 virus with Mittag-Leffler kernel

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ADVANCES IN DIFFERENCE EQUATIONS 2021年第1期2021卷 319页

作者： Akyildiz, F. Talay Alshammari, Fehaid Salem Imam Mohammad Ibn Saud Islamic Univ IMSIU Fac Sci Dept Math & Stat Riyadh Saudi Arabia

This paper investigates a new model on coronavirus-19 disease (COVID-19), that is complex fractional SIR epidemic model with a nonstandard nonlinear incidence rate and a recovery, where derivative operator with Mittag-Leffler kernel in the Caputo sense (ABC). The model has two equilibrium points when the basic reproduction number R0>1;a disease-free equilibrium E0 and a disease endemic equilibrium E1. The disease-free equilibrium stage is locally and globally asymptotically stable when the basic reproduction number R0<1, we show that the endemic equilibrium state is locally asymptotically stable if R0>1. We also prove the existence and uniqueness of the solution for the Atangana-Baleanu SIR model by using a fixed-point method. Since the Atangana-Baleanu fractional derivative gives better precise results to the derivative with exponential kernel because of having fractional order, hence, it is a generalized form of the derivative with exponential kernel. The numerical simulations are explored for various values of the fractional order. Finally, the effect of the ABC fractional-order derivative on suspected and infected individuals carefully is examined and compared with the real data.

关键词： Coronavirus-19 disease Complex fractional SIR model Atangana-Beleanu-Caputo (ABC) derivatives fixed-point method Stability 34A08 37N30

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A Novel Modeling Technique via Coupled Magnetic Equivalent Circuit With Vector Hysteresis Characteristics of Laminated Steels

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS 2023年第2期59卷 1481-1491页

作者： Ceylan, Doga Zeinali, Reza Daniels, Bram Boynov, Konstantin O. Lomonova, Elena A. Eindhoven Univ Technol Dept Elect Engn NL-5612 AZ Eindhoven Netherlands

This paper proposes a method to include the anisotropic hysteresis characteristics of soft-magnetic laminated steels in the magnetic equivalent circuit (MEC) modeling. The loop-based MEC formulation is improved to handle the nonlinearity of the anisotropic magnetic hysteresis, including the dynamic classical eddy-current and excess fields. The developedMEC model is coupled with both the single-valued B-H curve (SVC) in magnetostatic and the dynamic vector hysteresis model (VHM) in transient analysis. Results with a single elementary MEC element show that an alternating magnetic field in a single direction with a peak value smaller than 300 A/m causes a discrepancy of more than 10% between the magnetic flux densities calculated by the VHM and SVC at 50 and 200 Hz excitation frequencies. Moreover, the proposed modeling technique is verified experimentally using the laminated transformer core of TEAMproblem 32. The induced voltage calculated by theMECmodelwith theVHMdemonstrates a good agreementwith the measurements, while the MEC model with the SVC calculates inaccurate voltage waveforms. Lastly, the total iron loss dissipated in the transformer's iron core is investigated to verify the proposed technique under different excitation levels and frequencies up to 500 Hz. It is observed that the proposed MEC model with the vector hysteresis characteristics of laminated steels is able to calculate the iron loss accurately, while the conventional single-valued curve method fails to estimate the iron loss.

关键词： Magnetic hysteresis Static VAr compensators Integrated circuit modeling Magnetostatics Saturation magnetization Perpendicular magnetic anisotropy Finite element analysis Ferromagnetic laminations fixed-point method iron loss estimation magnetic equivalent circuit magnetic vector hysteresis

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IFOSMONDI: A Generic Co-simulation Approach Combining Iterative methods for Coupling Constraints and Polynomial Interpolation for Interfaces Smoothness 9

IFOSMONDI: A Generic Co-simulation Approach Combining Iterat...

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9th International Conference on Simulation and Modeling methodologies, Technologies and Applications (SIMULTECH)

作者： Eguillon, Yohan Lacabanne, Bruno Tromeur-Dervout, Damien Univ Lyon ULyon1 UMR5208 Inst Camille JordanCNRS Villeurbanne France Siemens Ind Software Roanne France

ISBN: (纸本)9789897583810

This paper introduces IFOSMONDI co-simulation algorithm that combines iterative coupling methods and a smooth representation of interface variables. In explicit (i.e. non-iterative) coupling methods, representing smooth interface variables requires the introduction of a delay (Busch, 2016) because the values of the interface variables at the end of a given macro-step are not known when the co-simulation only reached the beginning of this very macro-step. One of the advantages of implicit co-simulation (i.e. iterative coupling methods) is that the values of the interface variables can be known at the end of a macro-step with the possibility to replay the integration on this very macro-step. Combining this with a polynomial representation of the interface variables enables to use interpolation instead of extrapolation across the macro-steps (Kubler and Schiehlen, 2000). Taking into account time-derivatives of interface variables makes it possible to ensure C-1 smoothness even with no history of the past exchanged data: then, no delay is introduced. A new possibility then arises: the solvers of each subsystem may take into account this smoothness and be less restrictive on their restarts due to the communication times. The results obtained on the test case of the two mass oscillators (Busch, 2016) show the advantage of IFOSMONDI coupling in terms of trade-off between elapsed time and accuracy.

关键词： Solver Coupling Iterative Co-simulation Rollback Polynomial Interpolation fixed-point method

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A coupled convection-diffusion level set model for tracking epithelial cells in colonic crypts

A coupled convection-diffusion level set model for tracking ...

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International Conference on Computational Science (ICCS)

作者： Figueiredo, Isabel N. Leal, Carlos Leonori, Tommaso Romanazzi, Giuseppe Figueiredo, Pedro N. Donato, Maria M. Univ Coimbra Dept Math CMUC P-3000 Coimbra Portugal Univ Granada Dept Math Anal E-18071 Granada Spain Univ Coimbra Fac Med P-3000 Coimbra Portugal Univ Hosp Coimbra Dept Gastroenterol Coimbra Portugal

Colorectal cancer is initiated in colonic crypts as a consequence of alterations leading to the disruption of the normal colonic cellular process. We propose a model, which couples a convection-diffusion type equation with a level set equation, for tracking the time evolution of an epithelial cell set, inside a colonic crypt, until it reaches the top of the crypt. The convection-diffusion equation describes the evolution of the density of the cells in the epithelial cell set. The parameters of this equation regulate the geometric and temporal cellular mechanism, and different parameter choices lead to distinct cell behavior. The level set equation tracks the location and shape of the epithelial cell set, inside the crypt, as well as its interface, separating the cell set from the others cells, which reside within the crypt. The interfacial velocity of the epithelial cell set is obtained from the convection-diffusion type equation. Some in silico experiments are described. They are performed in a relative small time, with respect to the real biological evolution. (C) 2010 Published by Elsevier Ltd.

关键词： convection-diffusion equation level set method fixed-point method colonic crypt

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Continuation method for total variation denoising problems

Continuation method for total variation denoising problems

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Conference on Advanced Signal Processing Algorithms

作者： CHAN, TF ZHOU, HM CHAN, RH UNIV CALIF LOS ANGELES DEPT MATHLOS ANGELESCA 90024

ISBN: (纸本)0819419222

The denoising problem can be solved by posing it as a constrained minimization problem. The objective function is the TV norm of the denoised image whereas the constraint is the requirement that the denoised image does not deviate too much from the observed image. The Euler-Lagrangian equation corresponding to the minimization problem is a nonlinear equation. The Newton method for such equation is known to have a very small domain of convergence. In this paper, we propose to couple the Newton method with the continuation method. Using the Newton-Kantorovich theorem, we give a bound on the domain of convergence. Numerical results are given to illustrate the convergence.

关键词： DENOISING TOTAL-VARIATION NEWTON method fixed-point method

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Spectral stochastic finite element method for solving 3D stochastic eddy current problems

Spectral stochastic finite element method for solving 3D sto...

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15th International Symposium on Applied Electromagnetics and Mechanics (ISEM)

作者： Beddek, K. Clenet, S. Moreau, O. Le Menach, Y. L2EP Univ Lille 1 F-59655 Villeneuve Dascq France L2EP Arts & Metiers ParisTech Lille France Electricite France Dept THEMIS Clamart France

In this paper, a spectral stochastic finite element method (SSFEM) is described and applied to quantify uncertainties in an industrial eddy current non destructive testing (NDT) problem. A new iterative solver based on the fixed-point method is proposed to solve the large scale linear system. The efficiency of the suggested iterative solver to tackle the SSFEM computational complexity is demonstrated. The SSFEM results and the computation times obtained with 2 and 4 random variables are compared to those given by the anisotropic adaptive sparse grid non intrusive spectral projection (NISP). On this application, the SSFEM dedicated solver is competitive with the adaptive sparse grids strategy.

关键词： Spectral stochastic finite element method fixed-point method eddy current problem polynomial chaos expansion intrusive solver

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A Novel Modeling Technique via Coupled Magnetic Equivalent Circuit With Vector Hysteresis Characteristics of Laminated Steels

A Novel Modeling Technique via Coupled Magnetic Equivalent C...

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13th IEEE Energy Conversion Congress and Exposition (IEEE ECCE)

作者： Ceylan, Doga Zeinali, Reza Daniels, Bram Boynov, Konstantin O. Lomonova, Elena A. Eindhoven Univ Technol Dept Elect Engn NL-5612 AZ Eindhoven Netherlands

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A fast edge detection model combining mixed L₁ and L₂ fidelity terms 17

A fast edge detection model combining mixed <i>L</i><sub>1</...

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Joint 17th World Congress of International-Fuzzy-Systems-Association / 9th International Conference on Soft Computing and Intelligent Systems (IFSA-SCIS)

作者： Li, Yilin Zhang, Xiaole Shi, Yuying Zhao, Zhenbing Xin, Junfeng North China Elect Power Univ Dept Math & Phys Beijing Peoples R China North China Elect Power Univ Dept Elect & Commun Engn Baoding Peoples R China Qingdao Univ Sci & Technol Coll Electromech Engn Qingdao Peoples R China

ISBN: (纸本)9781509049172

Edge detection plays an immensely important role in image processing. In this paper, we propose a new model with the combination of the L-1 and L-2 fidelity terms on the basis of the well-known Mumford-Shah (MS) model. To solve this minimum model, we design an efficient algorithm based on a fixed-point iterative method and the Split-Bregman (SB) method. Experimental results show that the proposed model and algorithm can get better detected edges and have more advantages in efficiency and accuracy for different pure noisy images, even for mixed noisy images.

关键词： edge detection fixed-point method Split-Bregman (SB) method mixed noisy images

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Vector Hysteresis Modeling Coupled with a Loop-based Magnetic Equivalent Circuit 16

Vector Hysteresis Modeling Coupled with a Loop-based Magneti...

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16th International Conference on Ecological Vehicles and Renewable Energies (EVER)

作者： Ceylan, Doga Zeinali, Reza Daniels, Bram Boynov, Konstantin O. Lomonova, Elena A. Eindhoven Univ Technol Dept Elect Engn NL-5612 AZ Eindhoven Netherlands

ISBN: (纸本)9781665449021

This paper proposes a method to include the anisotropic magnetic hysteresis property of the soft-magnetic material in the magnetic equivalent circuit (MEC) modeling. The loop-based MEC formulation is improved to handle the non-linearity of the anisotropic magnetic hysteresis. Single MEC element of NO27 electrical steel is modeled in 2-D under both rotating and alternating magnetic fields to achieve an accurate iron loss estimation for different excitation frequencies. The developed model is coupled with both the single-valued BH curve (SVC) and the hysteresis BH loop (HL) of the non-linear magnetic material. The magnetic flux density is calculated as the output of the model and used for the comparison of both magnetic saturation calculations. The results show that an alternating magnetic field in a single direction with a peak value smaller than 300 A/m causes a discrepancy of more than 10% between HL and SVC, where the knee point of the SVC is located at 200 A/m. Although the SVC approximation gives realistic results under the deep magnetic saturation, it is not capable of estimating the iron loss accurately. The proposed model with the HL calculates the core loss density as 4 and 28 W/kg for 1000 A/m peak value with 50 and 200 Hz alternating magnetic field excitation, respectively.

关键词： Magnetic vector hysteresis magnetic equivalent circuit fixed-point method iron loss estimation

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