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The Fokas method for evolution partial differential equations

Partial Differential Equations in applied mathematics 2025年 14卷

作者： Chatziafratis, A. Fokas, A.S. Kalimeris, K. Department of Mathematics and Statistics School of Pure and Applied Sciences University of Cyprus Cyprus Institute of Applied and Computational Mathematics Foundation for Research and Technology Crete Greece Department of Applied Mathematics and Theoretical Physics University of Cambridge United Kingdom Mathematics Research Center Academy of Athens Greece

In the late 1990s a novel methodology was introduced for solving boundary value problems for linear and integrable nonlinear PDEs. This new approach is known as the Unified Transform or the Fokas method. Here we discuss important developments regarding the implementation of this methodology to evolution PDEs. In particular, we analyse linear PDEs, including the heat equation, the Sobolev–Barenblatt pseudo-parabolic model, the Rubinshtein–Aifantis double-diffusion system, and the linearized Cahn–Hilliard model, as well as certain integrable nonlinear PDEs, like the nonlinear Schrödinger equation. Regarding the latter equation, emphasis is placed on the so-called linearizable boundary conditions, which remarkably, include the well-studied x-periodic initial value problem. © 2025 The Authors

关键词： Evolution PDEs Fokas method Integrable PDEs Unified transform

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Reconstructing the Magnetic Field in an Arbitrary Domain via Data-driven Bayesian Methods and Numerical Simulations

arXiv

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arXiv 2024年

作者： Pavlou, Georgios E. Pavlidou, Vasiliki Harmandaris, Vagelis Institute of Applied and Computational Mathematics Foundation for Research and Technology- Hellas HeraklionGR-71110 Greece Institute of Astrophysics Foundation for Research and Technology- Hellas Vasilika Vouton HeraklionGR-71110 Greece Department of Physics University of Crete HeraklionGR-70013 Greece Department of Mathematics and Applied Mathematics University of Crete HeraklionGR-71409 Greece Computation-Based Science and Technology Research Center The Cyprus Institute Nicosia2121 Cyprus

Inverse problems are prevalent in numerous scientific and engineering disciplines, where the objective is to determine unknown parameters within a physical system using indirect measurements or observations. The inherent challenge lies in deducing the most probable parameter values that align with the collected data. This study introduces an algorithm for reconstructing parameters by addressing an inverse problem formulated through differential equations underpinned by uncertain boundary conditions or variant parameters. We adopt a Bayesian approach for parameter inference, delineating the establishment of prior, likelihood, and posterior distributions, and the subsequent resolution of the maximum a posteriori problem via numerical optimization techniques. The proposed algorithm is applied to the task of magnetic field reconstruction within a conical domain, demonstrating precise recovery of the true parameter values. © 2024, CC BY.

关键词： Differential equations

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Dynamical properties of neuromorphic Josephson junctions

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Physical Review E 2022年第4期106卷 044206-044206页

作者： D. Chalkiadakis J. Hizanidis Department of Physics University of Crete 71003 Herakleio Greece and Institute of Applied and Computational Mathematics Foundation for Research and Technology-Hellas 70013 Herakleio Greece

Neuromorphic computing exploits the dynamical analogy between many physical systems and neuron biophysics. Superconductor systems, in particular, are excellent candidates for neuromorphic devices due to their capacity to operate at great speeds and with low energy dissipation compared to their silicon counterparts. In this paper, we revisit a prior work on Josephson Junction-based neurons to identify the exact dynamical mechanisms underlying the system's neuronlike properties and reveal complex behaviors which are relevant for neurocomputation and the design of superconducting neuromorphic devices. Our paper lies at the intersection of superconducting physics and theoretical neuroscience, both viewed under a common framework—that of nonlinear dynamics theory.

关键词： Bifurcations Chaos Neuronal dynamics Spiking neurons Josephson junctions Chaos & nonlinear dynamics

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Inferring the Parameters of Ultrafast Lasers from Images with Surface Patterns

Inferring the Parameters of Ultrafast Lasers from Images wit...

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International Symposium on Image and Signal Processing and Analysis

作者： Anastasis Litsas Fotis Fraggelakis George D. Tsibidis Emmanuel Stratakis Yannis Pantazis Computer Science Department University of Crete Heraklion Greece Institute of Electronic Structure and Laser Foundation for Research and Technology - Hellas Heraklion Greece Institute of Applied and Computational Mathematics Foundation for Research and Technology - Hellas Heraklion Greece

In this paper, we explore the potential of deep learning techniques in the field of ultra-fast laser processing. More specifically, we trained convolutional neural networks on an in-house dataset with the aim of predicting the laser parameters from images which capture the morphological characteristics of the material surface after being laser fabricated. There are several challenges related with the collected dataset stemming from stochastic variations of the material and the laser, the sampling scheme and the overall low sample size. Therefore, to further test our models we additionally construct a synthetic dataset. The results on the synthetic dataset are almost perfect showing that the proposed predictive models have the capacity to learn the assigned tasks. As expected, the predictive performance decreases when the real dataset is utilized. Nevertheless, we show that both the accuracy in the classification task and the mean square error in the majority of the regression tasks are satisfactory (e.g., classification accuracy drops from 99.9% to 94.8%).

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Day-Ahead Forecasting of Solar Irradiance & PV Power Output Through Statistical Machine Learning Methods

Day-Ahead Forecasting of Solar Irradiance & PV Power Output ...

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2022 Saudi Arabia Smart Grid Conference, SASG 2022

作者： Kamarianakis, Yiannis Pantazis, Yannis Kalligiannaki, Evangelia Katsaounis, Theodoros D. Kotsovos, Konstantinos Gereige, Issam Abdullah, Marwan Jamal, Aqil Tzavaras, Athanasios Foundation for Research and Technology-Hellas Institute of Applied and Computational Mathematics Data Science Group Greece University of Crete Dept. of Mathematics and Applied Mathematics Greece Saudi Aramco RandD Center Carbon Management Division Dhahran Saudi Arabia Computer Electrical and Mathematical Sciences and Engineering Division Thuwal Saudi Arabia

ISBN: (纸本)9781665475891

Energy production from solar photovoltaic (PV) plants is unpredictable, mainly due to the stochastic formation and movement of clouds or aerosol - dust particles which scatter or disperse solar radiation. Accurate forecasts of PV output are essential to Distribution and Transportation System Operators as they assist efficient solar energy trading and management of electricity grids. This work evaluates an autoregressive, computationally-light KNN-regression scheme (TSFKNN) for hourly, day-ahead forecasts of solar irradiance and energy yield of various PV technologies. The model is being tested and validated using data measured in Thuwal, Saudi Arabia. The available measured records span a 60-month period. The developed forecasting models are designed for online systems and provide increased levels of accuracy and low computational cost. Several parametric and nonparametric specifications, coupled with conventional versus outlier-robust estimation procedures are tested, in order to derive an optimal month-specific daily profile (MDP). Current results demonstrate that including intraday variability to the monthly-based irradiance models achieve improved predictive accuracy between 10% and 25% on average. © 2022 IEEE.

关键词： Forecasting

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Optimal control, viscosity approximation and Arrhenius Law for the shallow lake problem

arXiv

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arXiv 2024年

作者： Koutsimpela, Angeliki Loulakis, Michail Department of Mathematics University of Augsburg Augsburg86159 Germany School of Applied Mathematical and Physical Sciences National Technical University of Athens Athens15780 Greece Institute of Applied and Computational Mathematics Foundation for Research and Technology Hellas Crete Heraklion70013 Greece

We prove existence of optimal control for the deterministic and stochastic shallow lake problem without any restrictions on the parameter space and we establish a generalization of the Arrhenius Law in the case of noise-dependent potentials, which naturally arise in control theory problems. We also prove a result about convergence of the derivatives in the viscosity approximation of the value function and use this result to derive the Arrhenius Law for the shallow lake *** Codes 93E20, 60H30, 49L25 Copyright © 2024, The Authors. All rights reserved.

关键词： Stochastic systems

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A simple analytical model of laser direct-drive thin shell target implosion

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Chinese Physics B 2022年第4期31卷 481-485页

作者： Bo Yu Tianxuan Huang Li Yao Chuankui Sun Wanli Shang Peng Wang Xiaoshi Peng Qi Tang Zifeng Song Wei Jiang Zhongjing Chen Yudong Pu Ji Yan Yunsong Dong Jiamin Yang Yongkun Ding Jian Zheng School of Nuclear Science and Technology University of Science and Technology of ChinaHefei 230026China Research Center of Laser Fusion China Academy of Engineering PhysicsMianyang 621900China Institute of Applied Physics and Computational Mathematics Beijing 100088China IFSA Collaborative Innovation Center Shanghai Jiao Tong UniversityShanghai 200240China

A high-neutron yield platform imploded by a thin shell target is generally built to probe nuclear science problems,and it has the advantages of high neutron yield,ultrashort fusion time,micro fusion zone,isotropic and monoenergetic *** analytical models have been proposed to interpret exploding-pusher target implosion driven by a long wavelength laser,whereas they are imperfect for a 0.35 μm laser implosion *** using the 0.35 μm laser,the shell is ablated and accelerated to high implosion velocity governed by Newton’s law,ablation acceleration and quasi-adiabatic compression models are suitable to explain the implosion of a laser direct-drive thin shell *** new analytical model scales bang time,ion temperature and neutron yield for large variations in laser power,target radius,shell thickness,and fuel *** predicted results of the analytical model are in agreement with experimental data on the ShenguangIII prototype laser facility,100 kJ laser facility,Omega,and NIF,it demonstrates that the analytical model benefits the understanding of experiment performance and optimizing the target design of high neutron yield implosion.

关键词： direct drive analytical model thin shell target neutron yield

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A Neutrosophic Logic Ruled Based Machine Learning Approaches for Chronic Kidney Disease Risk Prediction

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Neutrosophic Sets and Systems 2025年 79卷 76-95页

作者： Mohanty, Bhabani S. Krishna Priya, R. Alias, Liya Vijaya Kumar Reddy, R. Raut, Prasanta Kumar Isaac, Samson Manibharathi, D. Saravanakumar, C. Panda, Nihar Ranjan Broumi, Said Department of Statistics and Applied Mathematics Central University of Tamil Nadu India Research and Consultancy Department University of Technology and Applied Sciences P.O. Box: 12 Khasab Governorate of Musandam Musandam811 Oman College of Engineering and Technology University of Technology and Applied Science Shinas Oman Department of CSE Koneru Lakshmaiah Education Foundation Vaddeswaram Guntur AP India Department of Mathematics Trident Academy of Technology Odisha Bhubaneswar India Division of Biomedical Engineering Karunya Institute of Technology and Sciences Coimbatore India Department of Electronics and Communication Engineering Government College of Engineering Tamilnadu Salem India Department of Electronics and Communication Engineering SRM Valliammai Engineering College Kattankulathur Tamilnadu Chengalpattu India Department of Medical Research IMS & SUM Hospital SOA Deemed to be university India Laboratory of Information Processing Faculty of Science Ben M’Sik University Hassan II Casablanca Morocco

Chronic kidney disease (CKD) represents a significant global health challenge in society, and early detection of risk is essential for on-time treatment and intervention. This research suggests a novel machine-learning technique to create a reliable and accurate CKD risk prediction model by combining neutrosophic logic with various classification algorithms. We use neutrosophic logic to address the inherent imprecision and uncertainty in medical data, resulting in a more realistic portrayal of real-world scenarios. We measure the effectiveness of the proposed neutrosophic logic-based models using various metrics, including precision, specificity, and sensitivity. The results show that the neutrosophic logic method is better than traditional machine learning methods at finding people who are likely to develop CKD because it is more accurate and stable. This study illustrates the potential for incorporating neutrosophic logic into machine learning frameworks to improve risk prediction in medical fields. © 2025, University of New Mexico. All rights reserved.

关键词： Prediction models

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The effects of incident light wavelength difference on the collective stimulated Brillouin scattering in plasmas

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Matter and Radiation at Extremes 2023年第5期8卷 42-49页

作者： Qiang Wang Zhichao Li Zhanjun Liu Tao Gong Wenshuai Zhang Tao Xu Bin Li Ping Li Xin Li Chunyang Zheng Lihua Cao Xincheng Liu Kaiqiang Pan Hang Zhao Yonggang Liu Bo Deng Lifei Hou Yingjie Li Xiangming Liu Yulong Li Xiaoshi Peng Zanyang Guan Qiangqiang Wang Xingsen Che Sanwei Li Qiang Yin Wei Zhang Liqiong Xia Peng Wang Xiaohua Jiang Liang Guo Qi Li Minqing He Liang Hao Hongbo Cai Wudi Zheng Shiyang Zou Dong Yang Feng Wang Jiamin Yang Baohan Zhang Yongkun Ding Xiantu He Institute of Applied Physics and Computational Mathematics Beijing 100094China Laser Fusion Research Center China Academy of Engineering PhysicsMianyangSichuan 621900China HEDPS Center for Applied Physics and Technologyand College of EngineeringPeking UniversityBeijing 100871China

The first laser–plasma interaction experiment using lasers of eight beams grouped into one octad has been conducted on the Shenguang Octopus *** each beam intensity is below its individual threshold for stimulated Brillouin backscattering(SBS),collective behaviors are excited to enhance the octad *** particular,when two-color/cone lasers with wavelength separation 0.3 nm are used,the backward SBS reflectivities show novel behavior in which beams of longer wavelength achieve higher SBS *** property of SBS can be attributed to the rotation of the wave vectors of common ion acoustic waves due to the competition of detunings between geometrical angle and wavelength *** mechanism is confirmed using massively parallel supercomputer simulations with the three-dimensional laser–plasma interaction code LAP3D.

关键词： scattering tuning collective

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Emerging single-atom nanozymes for catalytic biomedical uses

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Nano research 2023年第12期16卷 13056-13076页

作者： Shuangfei Cai Wei Zhang Rong Yang CAS Key Laboratory for Biomedical Effects of Nanomaterials and Nanosafety Center of Materials Science and Optoelectronics EngineeringCAS Center for Excellence in NanoscienceNational Center for Nanoscience and TechnologyUniversity of Chinese Academy of SciencesBeijing 100190China Sino-Danish College Sino-Danish Center for Education and ResearchUniversity of Chinese Academy of SciencesBeijing 100049China Institute of Applied Physics and Computational Mathematics Beijing 100088China

The past four years have witnessed booming progress in single-atom nanozymes(SANs),one of the newest generations of nanozymes with atomically dispersed metal sites for catalytic biomedical *** show distinct advantages over their nanoparticle-based counterparts,such as well-defined electronic/geometric structures and complete atomic utilization efficiency,thus offering opportunities to develop advanced nanozymes for practical *** atomically dispersed active centers in SANs could also facilitate the precise regulation of catalytic performance,while probing structure–activity relationship for in-depth understanding of *** this review,we first introduce the synthetic approaches,surface engineering,and characterization techniques of ***,we discuss the enzyme-like properties of SANs,including some strategies for boosting their catalytic ***,we present their biomedical applications,ranging from biosensors,antibacterial uses,antioxidants,to ***,the challenges and opportunities of SANs are prospected.

关键词： single atom metal nanozyme enzyme-like catalysis biomedical

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