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Parallel Domain Decomposition-Based Solver for the Simulation of Flow over an Ahmed Reference Model

Advances in applied mathematics and Mechanics 2023年第3期15卷 769-785页

作者： Zhengzheng Yan Rongliang Chen Chao Wang Lei Xu Jingzhi Li Shenzhen Institutes of Advanced Technology Chinese Academy of SciencesShenzhen 518055China Faculty of Computational Mathematics and Cybernetics Shenzhen MSU-BIT UniversityShenzhen 518172China Department of Mathematics&National Center for Applied Mathematics Shenzhen&SUSTech International Center for Mathematics Southern University of Science and TechnologyShenzhen 518055China

The Ahmed model is a standard bluff body used to study the flow behavior around an *** important issue when investigating turbulent flow fields is the large computational load driven by accurate prediction approaches,such as the large eddy simulation *** this paper,we present a powerful domain decomposition method-based parallel solver to efficiently utilize existing supercomputer *** 3D unsteady incompressible Navier–Stokes equations with a subgridscale(SGS)fluid model are discretized on a pure unstructured tetrahedral grid by a stable P_(1-)P_(1-)finite element method in space,while an implicit second-order backward differentiation formula is employed for the time *** then solve the nonlinear algebraic system by means of the Newton–Krylov–Schwarz method by imposing a restricted additive Schwarz(RAS)right preconditioner for the parallel *** validate the proposed method toward the comparison of the flow field,including the velocity profiles and flow structures,with experimental investigations,and we show the parallel efficiency and scalability of the solver with up to 8192 processors.

关键词： Aerodynamics Ahmed model full Navier-Stokes equations Newton-Krylov-Schwarz algorithm parallel computing

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Correlations in interacting electron liquids: Many-body statistics and hyperuniformity

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Physical Review B 2024年第10期110卷 104201页

作者： Haina Wang Rhine Samajdar Salvatore Torquato Department of Chemistry Department of Physics Princeton Center for Theoretical Science Princeton Materials Institute Program in Applied and Computational Mathematics

Disordered hyperuniform many-body systems are exotic states of matter with novel optical, transport, and mechanical properties. These systems are characterized by an anomalous suppression of large-scale density fluctuations compared to ordinary liquids. The structure factor of disordered hyperuniform systems often obeys the scaling relation S(k)∼Bkα with B,α>0 in the limit k→0. Ground states of d-dimensional free fermionic gases, which are fundamental models for many metals and semiconductors, are key examples of quantum disordered hyperuniform states with important connections to random matrix theory. However, the effects of electron-electron interactions as well as the polarization of the electron liquid on hyperuniformity have not been explored thus far. In this paper, we systematically address these questions by deriving the analytical small-k behaviors (and, associated, α and B) of the total and spin-resolved structure factors of quasi-one-dimensional, two-dimensional, and three-dimensional electron liquids for varying polarizations and interaction parameters. We validate that these equilibrium disordered ground states are hyperuniform, as dictated by the fluctuation-compressibility relation. Interestingly, free fermions, partially polarized interacting fermions, and fully polarized interacting fermions are characterized by different values of the small-k scaling exponent α and coefficient B. In particular, partially polarized fermionic liquids exhibit a unique form of multihyperuniformity, in which the net configuration exhibits a stronger form of hyperuniformity (i.e., larger α) than each individual spin component. The detailed theoretical analysis of such small-k behaviors enables the construction of corresponding equilibrium classical systems under effective one- and two-body interactions that mimic the pair statistics of quantum electron liquids. Our paper thus reveals that highly unusual hyperuniform and multihyperuniform states can be achieved in simple

关键词： Electronic structure Quantum many-body systems Two-dimensional electron gas

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Dynamical behavior of a stochastic epidemiological model: stationary distribution and extinction of a SIRS model with stochastic perturbations

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SeMA Journal 2025年 1-22页

作者： Zinihi, Achraf Sidi Ammi, Moulay Rchid Ehrhardt, Matthias Department of Mathematics MAIS Laboratory AMNEA Group Faculty of Sciences and Technics Moulay Ismail University of Meknes Errachidia 52000 Morocco Chair of Applied and Computational Mathematics University of Wuppertal Gaußstrasse 20 Wuppertal 42119 Germany

This paper deals with a new epidemiological model of SIRS with stochastic perturbations. The primary objective is to establish the existence of a unique non-negative nonlocal solution. Using the basic reproduction number R0 derived from the associated deterministic model, we demonstrate the existence of a stationary distribution in the stochastic model. In addition, we study the fluctuation of the unique solution of the deterministic problem around the disease-free equilibrium under certain conditions. In particular, we reveal scenarios where random effects induce disease extinction, contrary to the persistence predicted by the deterministic model. The theoretical insights are complemented by numerical simulations, which provide further validation of our findings. © The Author(s) 2025.

关键词： Epidemiological model Itô formula Lyapunov function Numerical approximations Stochastic model

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A Partial RKDG Method for Solving the 2D Ideal MHD Equations Written in Semi-Lagrangian Formulation on Moving Meshes with Exactly Divergence-Free Magnetic Field

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Advances in applied mathematics and Mechanics 2023年第4期15卷 932-963页

作者： Shijun Zou Xijun Yu Zihuan Dai Fang Qing Xiaolong Zhao School of Mathematical Sciences Peking UniversityBeijing 100871China Institute of Applied Physics and Computational Mathematics Beijing 100088China Department of Mathematics Southern University of Science and TechnologyShenzhenGuangdong 518055China School of Mathematics and Statistics Zhengzhou UniversityZhengzhouHenan 450001China

A partial Runge-Kutta Discontinuous Galerkin(RKDG)method which preserves the exactly divergence-free property of the magnetic field is proposed in this paper to solve the two-dimensional ideal compressible magnetohydrodynamics(MHD)equations written in semi-Lagrangian formulation on moving quadrilateral *** this method,the fluid part of the ideal MHD equations along with zcomponent of the magnetic induction equation is discretized by the RKDG method as our previous paper[47].The numerical magnetic field in the remaining two directions(i.e.,x and y)are constructed by using the magnetic flux-freezing principle which is the integral form of the magnetic induction equation of the ideal *** the divergence of the magnetic field in 2D is independent of its z-direction component,an exactly divergence-free numerical magnetic field can be obtained by this *** propose a new nodal solver to improve the calculation accuracy of velocities of the moving meshes.A limiter is presented for the numerical solution of the fluid part of the MHD equations and it can avoid calculating the complex eigen-system of the MHD *** numerical examples are presented to demonstrate the accuracy,non-oscillatory property and preservation of the exactly divergence-free property of our method.

关键词： Ideal compressible MHD equations semi-Lagrangian formulation exactly divergence-free magnetic field Runge-Kutta discontinuous Galerkin method

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A study on agriculture engineering implements using machine learning

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Materials Today: Proceedings 2022年 62卷 4996-5002页

作者： Sakthipriya, Dhinakaran Chandrakumar, Thangavel Department of Applied Mathematics & Computational Science Thiagarajar College of Engineering Tamil Nadu Madurai 625015 India

India's primary source of income is agriculture. Farmers in India have differing perspectives on how to integrate technology into their farming operations. However, farmers lack the knowledge necessary to put technology into practice, even though crop yield productivity is improving. We performed a literature survey to get the suggestion of what types of agriculture engineering machinery had been employed to boost up crop production output. After some literature survey, this research work followed to implement machine learning techniques to provide better advice to farmers to use the agriculture engineering machinery to minimize manpower and boost crop productivity. According to this additional analysis, clustering is the most widely used machine learning technique to solve problems in agriculture fields. Regarding the execution time, k-means performed well for other clustering techniques for small and large datasets. In this research initiates three thousands of combined data in agri-machinery in various districts, this selective data should be assured the preferable results with the help of k-means clustering for an crops highest yield production. This research work fully engaged with k-means techniques to deeply analysis in the Agri machinery benefits for south region districts and it provides the strongly recommended machinery's knowledge to farmers to implement the farming works effectively. In this research that statistical ranges are predicted what type of machinery's gives good results for crop development in south TamilNadu farming land in the district wise. The goal of this study was to evaluate statistical ranges of agriculture types of machinery in south TamilNadu districts. This proposed effort aims to provide a better proposal for achieving a suitable level of crop output with the use of more agricultural technology. © 2022

关键词： Crops

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A Novel Segment White Matter Hyperintensities Approach for Detecting Alzheimer

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Computer Systems Science & Engineering 2023年第3期44卷 2715-2726页

作者： Antonitta Eileen Pious U.K.Sridevi Department of Science and Humanities Sri Krishna College of Engineering and TechnologyCoimbatore641008India Department of Applied Mathematics and Computational Sciences PSG College of TechnologyCoimbatore641008India

Segmentation has been an effective step that needs to be done before the classification or detection of an anomaly like Alzheimer’s on a brain *** helps detect pixels of the same intensity or volume and group them together as one class or region,where in that particular region of interest(ROI)can be concentrated on,rather than focusing on the entire *** this paper White Matter Hyperintensities(WMH)is taken as a strong biomarker that supports and determines the presence of Alzheimer’*** thefirst step a proper segmentation of the lesions has to be carried *** pointed out in various other research papers,when the WMH area is very small or in places like the Septum Pellucidum the detection of the lesion is hard *** overcome such problem areas a very optimized and accurate Threshold would be required to have a precise segmentation to detect the area of *** would help in proper detection and classification of the *** this paper an elaborate comparison of various thresholding techniques has been done for segmentation.A novel idea for detection of Alzheimer’s has been presented in this paper,which encompasses the effectiveness of an optimized and adaptive *** Unet architecture has been taken as the baseline model with an adaptive kernel model embedded within the *** state-of-the-art technologies have been used with the dataset and a comparative study has been presented with the current architecture used in the *** lesion segmentation in narrow areas has accurately been detected compared to the other models and the number of false positives has been reduced to a great extent.

关键词： Alzheimer’s adaptive threshold deep learning segmentation

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Nearly optimal state preparation for quantum simulations of lattice gauge theories

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Physical Review A 2024年第1期110卷 012455-012455页

作者： Christopher F. Kane Niladri Gomes Michael Kreshchuk Department of Physics Applied Mathematics and Computational Research Division Physics Division

We present several improvements to the recently developed ground-state preparation algorithm based on the quantum eigenvalue transformation for unitary matrices (QETU), apply this algorithm to a lattice formulation of U(1) gauge theory in (2+1) dimensions, as well as propose an alternative application of QETU, a highly efficient preparation of Gaussian distributions. The QETU technique was originally proposed as an algorithm for nearly optimal ground-state preparation and ground-state energy estimation on early fault-tolerant devices. It uses the time-evolution input model, which can potentially overcome the large overall prefactor in the asymptotic gate cost arising in similar algorithms based on the Hamiltonian input model. We present modifications to the original QETU algorithm that significantly reduce the cost for the cases of both exact and Trotterized implementation of the time evolution circuit. We use QETU to prepare the ground state of a U(1) lattice gauge theory in two spatial dimensions, explore the dependence of computational resources on the desired precision and system parameters, and discuss the applicability of our results to general lattice gauge theories. We also demonstrate how the QETU technique can be utilized for preparing Gaussian distributions and wave packets in a way which outperforms existing algorithms for as little as nq≳2–5 qubits.

关键词： Quantum algorithms Quantum simulation Lattice gauge theory

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Taenia solium taeniasis and cysticercosis:extinction or outbreak

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Animal Diseases 2023年第2期3卷 90-103页

作者： Jacob I.Irunde Faraja B.Luhanda Department of Mathematics Physics and InformaticsMkwawa University College of EducationIringaTanzania Department of Applied Mathematics and Computational Sciences The Nelson Mandela African Institution of Science and TechnologyArushaTanzania

Taenia solium taeniasis and cysticercosis are neglected zoonotic diseases that affect human health and economies of developing *** this work,we formulate and analyze deterministic and continuous time Markov chain(CTMC)stochastic models to determine parameters that drive Taenia solium taeniasis and cysticercosis and the likelihood of their *** basic reproduction number R0 is computed by the next generation matrix approach,sensitivity index of each parameter in R0 is derived by the normalized forward sensitivity index and the likelihood of diseases’extinction is computed by the multitype branching *** analysis shows that humans with Taenia solium taeniasis,infectious pork and Taenia solium eggs in the environment play an important role in the transmission of Taenia solium taeniasis and cysticercosis,and the model exhibits forward bifurcation at R0=*** implies that R0<1 is a sufficient condition to eliminate Taenia solium taeniasis and *** CTMC model,analysis shows that the probability of Taenia solium taeniasis and cysticercosis extinction is high if the diseases emerge from humans with Taenia solium cysticercosis and there is an outbreak if the diseases emerge from either humans with Taenia solium taeniasis or infectious pork or Taenia solium eggs in the *** control Taenia solium taeniasis and cysticercosis,the intervention strategies should focus on improving hygiene and sanitation for reducing shedding rate of Taenia solium eggs in the environment,inspection of pork for reducing the rate of acquiring Taenia solium taeniasis and spraying of insecticides for killing Taenia solium eggs in the environment.

关键词： Taeniasis Cysticercosis Basic reproduction number Sensitivity analysis Multitype branching process Stochastic model

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Strategy Arrangement of Road Cycling Individual Time Trial Based on Topology Optimization Algorithm 22

Strategy Arrangement of Road Cycling Individual Time Trial B...

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6th International Conference on Medical and Health Informatics, ICMHI 2022

作者： Xu, Yuelin Dai, Yue Zhang, Haonan Mathematics and Applied Mathematics Department of Computational Mathematics and Cybernetics Shenzhen MSU-BIT University Shenzhen China

ISBN: (纸本)9781450396301

For more efficient training, it is of great significance to know the position-power relationship of riders of different types and genders on different venues for guiding riders' training. A number of previous studies have used pacing strategies to examine the impact of different venues on rider decision-making. Firstly, according to the test data of different athletes, the OmPD model is used to establish the rider's own power profile. Through force analysis, after discretization, the relationship between power and position is numerically simulated. In addition, the limitation of anaerobic work ability to decision-making is added. In order to facilitate the calculation, the two-dimensional situation is considered first, and then the three-dimensional situation of the turning is corrected separately. For different regions and courses, after determining the local environmental parameters according to the data, the optimization goal is to take the shortest time after spline interpolation. Anaerobic working capacity and maximum power are the constraints. The optimal numerical solution is carried out by using Method of Moving Asymptotes. The 2020 Olympic Games and the 2021 UCI World Championship are simulated, and the power-position curves are obtained. © 2022 ACM.

关键词： Decision making

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Predator Prey Scavenger Model using Holling’s Functional Response of Type III and Physics-Informed Deep Neural Networks

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International Journal of applied and computational mathematics 2025年第2期11卷 1-32页

作者： Panchal, Aneesh Beniwal, Kirti Kumar, Vivek Department of Computational and Data Sciences Indian Institute of Science Karnataka Bangalore 560012 India Department of Applied Mathematics Delhi Technological University Delhi New Delhi 110042 India

Nonlinear mathematical models introduce the relation between various physical and biological interactions present in nature. One of the most famous models is the Lotka–Volterra model which defined the interaction between predator and prey species present in nature. However, predators, scavengers, and prey populations coexist in a natural system where scavengers can additionally rely on the dead bodies of predators present in the system. Keeping this in mind, the formulation and simulation of the predator–prey scavenger model is introduced in this paper. For the predation response, respective prey species are assumed to have Holling’s functional response of type III. The proposed model is tested for various simulations and is found to be showing satisfactory results in different scenarios. After simulations, the American forest dataset is taken for parameter estimation which imitates the real-world case. For parameter estimation, a physics-informed deep neural network is used with the Adam backpropagation method which prevents the avalanche effect in trainable parameters updation. For neural networks, mean square error and physics-informed informed error are considered. After the neural network, the hence-found parameters are fine-tuned using the Broyden–Fletcher–Goldfarb–Shanno algorithm. Finally, the hence-found parameters using a natural dataset are tested for stability using Jacobian stability analysis. © The Author(s), under exclusive licence to Springer Nature India Private Limited 2025.

关键词： Broyden–Fletcher–Goldfarb–Shanno optimization Physics-informed deep neural network Predator prey scavenger model Stability analysis

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