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Air pollution modelling of accidents involving hazardous substances 16

Air pollution modelling of accidents involving hazardous sub...

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16th Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2024

作者： Ostromsky, Tzvetan Alexiev, Kiril Parvanov, Stefan Department of Parallel Algorithms and Machine Learning Neurotechnology Laboratory Institute of Information and Communication Technologies Bulgarian Academy of Sciences Sofia Bulgaria Faculty of Fire Safety and Civil Protection Academy of the Ministry of Interior Sofia Bulgaria

Air pollution modeling for accidents involving hazardous substances is a critical aspect of emergency response and environmental protection. This modeling aims to predict the dispersion and impact of toxic substances released into the atmosphere during accidents, such as industrial spills, transport accidents, chemical plant incidents or acts of terrorism. Such dangers are among the challenges which the modern society is facing and has to overcome. In this study we propose a systematic approach for organizing monitoring, collecting data from mobile sensors, creating situation development scenarios, modelling the spread of potential toxic-element pollution in dependence with the current meteorological conditions. The UNI-DEM model for simulation of the pollutants' dispersion and transport in the air, as well as models for spread of leaking gas and liquid vapors are involved in this study. Finally, depending on the comprehensive analysis of the modeling results, an adequate response to such severe situations can be proposed. Assessment of safety, healthcare and environmental impacts should be the final result and the most socially important application of our work. The calculated pollutant concentrations can be compared with regulatory standards or health-based guidelines to assess potential health risks to exposed populations and environmental impacts on ecosystems. The importance of this information for emergency response planning, public health interventions, and environmental management strategies is beyond dispute. © 2024 Institute of Physics Publishing. All rights reserved.

关键词： Emergency services

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Advanced Stochastic Approaches for Fredholm Integral Equations 15

Advanced Stochastic Approaches for Fredholm Integral Equatio...

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15th Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2023

作者： Todorov, Venelin Georgiev, Slavi Department of Information Modeling Institute of Mathematics and Informatics Bulgarian Academy of Sciences 8 Acad. Georgi Bonchev Str. Sofia1113 Bulgaria Department of Parallel Algorithms and Machine Learning with A Laboratory in Neurotechnologies Institute of Information and Communication Technologies Bulgarian Academy of Sciences 25A Acad. Georgi Bonchev Str. Sofia1113 Bulgaria Department of Applied Mathematics and Statistics University of Ruse 8 Studentska Str. Ruse7004 Bulgaria

Integral equations are of high applicability in different areas of applied mathematics, physics, engineering, geophysics, electricity and magnetism, kinetic theory of gases, quantum mechanics, mathematical economics, and queuing theory. That is why it is reasonable to develop and study efficient and reliable approaches to solve integral equations. For multidimensional problems the existing biased stochastic algorithms based on evaluation of finite number of integrals will suer more from the effect of high dimensionality, because they are based on quadrature points. So we need advanced unbiased algorithms for solving the multidimensional problem which is developed in this paper. A new unbiased stochastic method for solving multidimensional Fredholm integral equations of second kind is proposed and analysed. We compared the newly proposed unbiased algorithm with the old unbiased stochastic algorithm for the one dimensional problem and multidimensional problem. © Published under licence by IOP Publishing Ltd.

关键词： Stochastic systems

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Air Pollution Modeling of UNI-DEM Model by using Innovative Stochastic Approaches 15

Air Pollution Modeling of UNI-DEM Model by using Innovative ...

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15th Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2023

作者： Todorov, Venelin Georgiev, Slavi Dimov, Ivan Department of Information Modeling Institute of Mathematics and Informatics Bulgarian Academy of Sciences 8 Acad. Georgi Bonchev Str. Sofia1113 Bulgaria Department of Parallel Algorithms and Machine Learning with A Laboratory in Neurotechnologies Institute of Information and Communication Technologies Bulgarian Academy of Sciences 25A Acad. Georgi Bonchev Str. Sofia1113 Bulgaria Department of Applied Mathematics and Statistics University of Ruse 8 Studentska Str. Ruse7004 Bulgaria

In this paper we develop advanced multidimensional sensitivity analysis, based on some innovative stochastic approaches for performing air pollution modelling on a large-scale model of long-range transport of air pollutants. The Unified Danish Eulerian Model (UNI-DEM) is a very important mathematical model, and can be applied in many different studies related to damaging effects caused by high air pollution levels. We shall use it in this paper to get a reliable answer to a some very important questions regrading environmental protection. We develop some advanced Monte Carlo and quasi-Monte Carlo methods, based on special lattice and digital sequences. In this paper we will improve the digital ecosystem modeling by improving the existence stochastic approaches. The computational efficiency (in terms of relative error and computational time) of the advanced Monte Carlo algorithms for multidimensional numerical integration has been studied to analyze the sensitivity of UNI-DEM model output to variation of input emissions of the anthropogenic pollutants and of rates of several chemical reactions. The algorithms will be applied to compute global Sobol sensitivity measures corresponding to the influence of several input parameters on the concentrations of important air pollutants. The study will be done for the areas of several European cities with different geographical locations. © Published under licence by IOP Publishing Ltd.

关键词： Computational efficiency

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New "walk on Equations" Monte Carlo Algorithm for Linear Systems 15

New "walk on Equations" Monte Carlo Algorithm for Linear Sys...

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15th Conference of the Euro-American Consortium for Promoting the Application of Mathematics in Technical and Natural Sciences, AMiTaNS 2023

作者： Todorov, Venelin Georgiev, Slavi Apostolov, Stoyan Department of Information Modeling Institute of Mathematics and Informatics Bulgarian Academy of Sciences 8 Acad. Georgi Bonchev Str. Sofia1113 Bulgaria Department of Parallel Algorithms and Machine Learning with A Laboratory in Neurotechnologies Institute of Information and Communication Technologies Bulgarian Academy of Sciences 25A Acad. Georgi Bonchev Str. Sofia1113 Bulgaria Department of Applied Mathematics and Statistics University of Ruse 8 Studentska Str. Ruse7004 Bulgaria Department of Mathematical Analysis University of Sofia 8 James Bourchier Blvd. Sofia1164 Bulgaria

A novel version of Monte Carlo algorithm for solving systems of linear algebraic equations is presented and studied. The algorithm is similar to the "Walk on Equations"Monte Carlo method recently developed by Ivan Dimov, Sylvain Maire and Jean Michel Sellier. It is done a comparison with the Gauss-Seidel method for matrices up to size of 212. The algorithm could be drastically improved by choosing appropriate values for the relaxation parameters, which in turn leads to dramatic reduction in time and lower relative errors for a given number of iterations. What is more, a sequential Monte Carlo method of John Halton based on an iterative use of the control variate method has been applied. Some of the most important numerical applications are the large system, coming from a finite element approximation of problems, describing a beam structure in constructive mechanics, and the block-diagonal matrices, which come from discretization of models in a regime-switching economy. © Published under licence by IOP Publishing Ltd.

关键词： Monte Carlo methods

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Stochastic Approaches for the Multidimensional Volterra Integral Equation 11th

Stochastic Approaches for the Multidimensional Volterra In...

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11th International Conference on New Trends in the Applications of Differential Equations in Sciences, NTADES 2024

作者： Todorov, Venelin Georgiev, Slavi Apostolov, Stoyan Dimov, Ivan Department of Information Modeling Institute of Mathematics and Informatics Bulgarian Academy of Sciences Sofia Bulgaria Department of Parallel Algorithms and Machine Learning with a Laboratory in Neurotechnologies Institute of Information and Communication Technologies Bulgarian Academy of Sciences Sofia Bulgaria Department of Applied Mathematics and Statistics Faculty of Natural Sciences and Education University of Ruse Ruse Bulgaria Department of Mathematical Analysis Faculty of Mathematics and Informatics University of Sofia Sofia Bulgaria

ISBN: (纸本)9783031833977

In this study, we explore a stochastic methodology for addressing Volterra integral equations, particularly focusing on a multidimensional context. We provide a comprehensive examination of the method’s potential strengths and limitations, discussing its applicability. The stochastic approach is rigorously tested against a set of multidimensional benchmark problems, demonstrating its effectiveness and providing a framework for further investigation. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Integral equations

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Advanced Stochastic Method for Linear Algebraic Systems 11th

Advanced Stochastic Method for Linear Algebraic Systems

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11th International Conference on New Trends in the Applications of Differential Equations in Sciences, NTADES 2024

作者： Todorov, Venelin Georgiev, Slavi Chechev, Milen Dimitrov, Yuri Department of Information Modeling Institute of Mathematics and Informatics Bulgarian Academy of Sciences Sofia Bulgaria Department of Parallel Algorithms and Machine Learning with a Laboratory in Neurotechnologies Institute of Information and Communication Technologies Bulgarian Academy of Sciences Sofia Bulgaria Department of Applied Mathematics and Statistics Faculty of Natural Sciences and Education University of Ruse Ruse Bulgaria Department of Software Technologies Faculty of Mathematics and Informatics University of Sofia Sofia Bulgaria Department of Mathematics Physics and Informatics Faculty of Forest Industry University of Forestry Sofia Bulgaria

ISBN: (纸本)9783031833977

In this study, we explore an advanced stochastic approach tailored for solving large-scale systems of linear algebraic equations. The core of our research is the application and enhancement of the Monte Carlo method, specifically designed to tackle the computational challenges posed by such extensive systems. Our method builds upon the "Walk on Equations" Monte Carlo model, a technique recently developed by Ivan Dimov, Sylvain Maire, and Jean Michel Sellier. We introduce a novel hybrid algorithm that synergizes this model with traditional methods, aiming to optimize performance and efficiency. A key innovation in our approach is the introduction of the "dominancy number", a critical parameter that significantly influences the algorithm’s convergence and accuracy. Through rigorous analysis and experimentation, we demonstrate the potential of this hybrid method in improving the computational feasibility of solving large-scale linear algebraic systems. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Linear algebra

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Advanced Unbiased Monte Carlo for Multidimensional Fredholm Integral Equations 11th

Advanced Unbiased Monte Carlo for Multidimensional Fredholm ...

引用

11th International Conference on New Trends in the Applications of Differential Equations in Sciences, NTADES 2024

作者： Todorov, Venelin Georgiev, Slavi Apostolov, Stoyan Dimitrov, Yuri Department of Information Modeling Institute of Mathematics and Informatics Bulgarian Academy of Sciences Sofia Bulgaria Department of Parallel Algorithms and Machine Learning with a Laboratory in Neurotechnologies Institute of Information and Communication Technologies Bulgarian Academy of Sciences Sofia Bulgaria Department of Applied Mathematics and Statistics Faculty of Natural Sciences and Education University of Ruse Ruse Bulgaria Department of Mathematical Analysis Faculty of Mathematics and Informatics University of Sofia Sofia Bulgaria Department of Mathematics Physics and Informatics Faculty of Forest Industry University of Forestry Sofia Bulgaria

ISBN: (纸本)9783031833977

Integral equations play a crucial role in various domains of applied mathematics, physics, and engineering. They are extensively utilized in fields such as mechanics, geophysics, kinetic theory of gases, quantum mechanics, mathematical economics, and queuing theory, among others. The broad applicability of these equations necessitates the development and study of efficient, reliable, and versatile methods for their solution. In this paper, we focus on an unbiased stochastic approach to solve multidimensional Fredholm integral equations of the second kind. The proposed method is designed to maintain high accuracy while minimizing computational complexity, making it suitable for handling complex problems involving irregular kernels and solutions. Through rigorous analysis and extensive numerical experiments, we demonstrate the robustness and effectiveness of this approach, highlighting its potential advantages over traditional deterministic methods, particularly in higher-dimensional spaces where conventional techniques often struggle with the curse of dimensionality. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Fredholm integral equations

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Novel Stochastic Sequences for Multidimensional Air Pollution Modelling 11th

Novel Stochastic Sequences for Multidimensional Air Polluti...

引用

11th International Conference on New Trends in the Applications of Differential Equations in Sciences, NTADES 2024

ISBN: (纸本)9783031833977

This paper introduces a sophisticated approach to multidimensional sensitivity analysis by utilizing novel stochastic techniques for air pollution modeling within the large-scale, long-range transport framework of the Unified Danish Eulerian Model (UNI-DEM). This model plays a crucial role in assessing the detrimental impacts of elevated air pollution levels, and our research leverages it to tackle essential environmental protection issues. We develop and implement advanced Monte Carlo and quasi-Monte Carlo methods, incorporating specialized lattice sequences, to enhance the computational efficiency of multidimensional numerical integration. The study centers on evaluating the sensitivity of the UNI-DEM model outputs to variations in anthropogenic pollutant emissions and the rates of key chemical reactions. Our algorithms are applied to calculate global Sobol sensitivity indices, assessing the influence of several input parameters on significant air pollutant concentrations across diverse European cities with varying geographical characteristics. The goal of this research is to deepen the understanding of factors influencing air pollution and to support the development of effective strategies for reducing its harmful environmental impacts. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： Air quality

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