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Monte Carlo Method for Numerical Simulation of Solar Energy Radiation Transfer in Crystal Clouds 蒙特卡洛法数值模拟晶体云中的太阳能辐射传输
IF 0.3
Numerical Analysis and Applications Pub Date : 2024-05-28 DOI: 10.1134/s1995423924020046
B. A. Kargin, E. G. Kablukova, Q. Mu, S. M. Prigarin
{"title":"Monte Carlo Method for Numerical Simulation of Solar Energy Radiation Transfer in Crystal Clouds","authors":"B. A. Kargin, E. G. Kablukova, Q. Mu, S. M. Prigarin","doi":"10.1134/s1995423924020046","DOIUrl":"https://doi.org/10.1134/s1995423924020046","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper deals with numerical simulations related to radiation transfer in ice clouds. A mathematical model of crystal particles of irregular shape and an algorithm for modeling such particles based on constructing a convex hull of a set of random points are considered. Two approaches to simulating radiation transfer in optically anisotropic clouds are studied. One approach uses pre-calculated scattering phase functions for crystals of various shapes and orientations. In the other approach, no knowledge of phase functions is required; the radiation scattering angle is simulated directly at interaction of a photon with faces of crystal. This approach enables simple adjustment of the input parameters of the problem to changing microphysical characteristics of the environment, including the shape, orientation, and transparency of particles and roughness of their boundaries, and does not require time-consuming pre-calculations. The impact of flutter on the radiation transfer by the cloud layer and angular distributions of the reflected and transmitted radiation are studied.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"39 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Monte Carlo Simulation of Wide-Angle Lidar Signals 宽角度激光雷达信号的蒙特卡罗模拟
IF 0.3
Numerical Analysis and Applications Pub Date : 2024-05-28 DOI: 10.1134/s1995423924020083
S. M. Prigarin, D. E. Mironova
{"title":"Monte Carlo Simulation of Wide-Angle Lidar Signals","authors":"S. M. Prigarin, D. E. Mironova","doi":"10.1134/s1995423924020083","DOIUrl":"https://doi.org/10.1134/s1995423924020083","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper deals with Monte Carlo modeling of spatiotemporal signals of wide-angle lidars for probing atmospheric clouds. Using computational experiments, we study the features of lidar signals for monostatic and bistatic sensing schemes which make it possible to analyze the optical and microphysical properties of the cloud environment. When probing thin cloud layers, the lidar signal looks like an expanding and attenuating light ring. It is shown that for a bistatic scheme a second ring, which appears for a short time inside the main one, is characteristic of the lidar signal.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"69 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171555","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Influence of Random Environmental Factors on Heat Transfer Processes in Aircraft 随机环境因素对飞机传热过程的影响
IF 0.3
Numerical Analysis and Applications Pub Date : 2024-05-28 DOI: 10.1134/s1995423924020034
S. A. Gusev, V. N. Nikolaev
{"title":"On the Influence of Random Environmental Factors on Heat Transfer Processes in Aircraft","authors":"S. A. Gusev, V. N. Nikolaev","doi":"10.1134/s1995423924020034","DOIUrl":"https://doi.org/10.1134/s1995423924020034","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The main goal of the work is to simulate heat transfer in structural elements of an aircraft under random temperature changes of its outer surface due to rapid changes in environmental parameters. In this case, to model the heat transfer a one-dimensional boundary value problem of the third kind is taken for the heat conduction equation. Random disturbances are specified at the boundary corresponding to the outer surface. The numerical solution is based on an application of a Galerkin method. Modeling the random disturbances of the external environment is carried out using a Wiener integral in a system of differential equations written in integral form. Calculations for a problem with a known exact solution show that when moving away from the boundary with random disturbances, the numerical solution of the boundary value problem with disturbances converges to the known exact solution of the undisturbed boundary value problem. Based on an expansion of the solution to the boundary value problem in trigonometric functions, theoretical estimates are obtained for the influence of a disturbance on the outer surface as a function of the wall thickness and the disturbance magnitude.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"31 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Efficiently Realized Approximate Models of Random Functions in Stochastic Problems of the Theory of Particle Transfer 粒子转移理论随机问题中高效实现的随机函数近似模型
IF 0.3
Numerical Analysis and Applications Pub Date : 2024-05-28 DOI: 10.1134/s1995423924020058
G. A. Mikhailov, G. Z. Lotova, I. N. Medvedev
{"title":"Efficiently Realized Approximate Models of Random Functions in Stochastic Problems of the Theory of Particle Transfer","authors":"G. A. Mikhailov, G. Z. Lotova, I. N. Medvedev","doi":"10.1134/s1995423924020058","DOIUrl":"https://doi.org/10.1134/s1995423924020058","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper presents efficiently realized approximations of random functions, which have been developed by the authors and are numerically simulated for study of stochastic processes of particle transfer, including the problems of process criticality fluctuations in random media with multiplication. Efficient correlation-randomized algorithms are constructed for approximating an ensemble of particle trajectories using a correlation function or only a correlation scale of medium. A simple grid model of an isotropic random field is formulated, which reproduces a given average correlation length. This ensures high accuracy in solving stochastic transfer problems for a small correlation scale. The algorithms are tested by solving a test problem of photon transfer and a problem of estimating the overexponential average particle flux in a random medium with multiplication.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"98 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Rosenbrock-Type Methods for Solving Stochastic Differential Equations 求解随机微分方程的罗森布洛克式方法
IF 0.3
Numerical Analysis and Applications Pub Date : 2024-05-28 DOI: 10.1134/s1995423924020010
T. A. Averina, K. A. Rybakov
{"title":"Rosenbrock-Type Methods for Solving Stochastic Differential Equations","authors":"T. A. Averina, K. A. Rybakov","doi":"10.1134/s1995423924020010","DOIUrl":"https://doi.org/10.1134/s1995423924020010","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>This paper reviews recent publications that describe mathematical models with stochastic differential equations (SDEs) and applications in various fields. The purpose of this paper is to briefly describe Rosenbrock-type methods for approximate solution of SDEs. It shows how the performance of the numerical methods can be improved and the accuracy of calculations can be increased without increasing the implementation complexity too much. The paper also proposes a new Rosenbrock-type method for SDEs with multiplicative non-commutative noise. Its testing is carried out by modeling rotational diffusion.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"72 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171643","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stochastic Simulation Algorithm for Solving the System of Lame Equations for Two- and Three-Dimensional Domains by Combining the Slobodianskii Representation, the Method of Fundamental Solutions and a Stochastic Projection Method 结合斯洛博迪安斯基表示法、基本解法和随机投影法求解二维和三维域拉姆方程组的随机模拟算法
IF 0.3
Numerical Analysis and Applications Pub Date : 2024-05-28 DOI: 10.1134/s1995423924020095
K. K. Sabelfeld, D. D. Smirnov
{"title":"Stochastic Simulation Algorithm for Solving the System of Lame Equations for Two- and Three-Dimensional Domains by Combining the Slobodianskii Representation, the Method of Fundamental Solutions and a Stochastic Projection Method","authors":"K. K. Sabelfeld, D. D. Smirnov","doi":"10.1134/s1995423924020095","DOIUrl":"https://doi.org/10.1134/s1995423924020095","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper, a new stochastic algorithm for solving the system of Lame equations based on the Slobodianskii representation is proposed, in which the recovery of boundary conditions for the harmonic functions involved is carried out implicitly using the method of fundamental solutions, while the unknown coefficients in this method are calculated using a stochastic projection method. Results of numerical experiments for several examples of two- and three-dimensional boundary value problems are presented, which demonstrate the high efficiency of the proposed method.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"66 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171494","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Analyzing the Semilocal Convergence of a Fourth-Order Newton-Type Scheme with Novel Majorant and Average Lipschitz Conditions 分析四阶牛顿式方案的半局部收敛与新的主要和平均 Lipschitz 条件
IF 0.3
Numerical Analysis and Applications Pub Date : 2024-03-13 DOI: 10.1134/s1995423924010026
J. P. Jaiswal
{"title":"Analyzing the Semilocal Convergence of a Fourth-Order Newton-Type Scheme with Novel Majorant and Average Lipschitz Conditions","authors":"J. P. Jaiswal","doi":"10.1134/s1995423924010026","DOIUrl":"https://doi.org/10.1134/s1995423924010026","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The main focus of this paper is the analysis of the semilocal convergence (S.C.) of a three-step Newton-type scheme (TSNTS) used for finding the solution of nonlinear operators in Banach spaces (B.S.). A novel S.C. analysis of the TSNTS is introduced, which is based on the assumption that a generalized Lipschitz condition (G.L.C.) is satisfied by the first derivative of the operator. The findings contribute to the theoretical understanding of TSNTS in B.S. and have practical implications in various applications, such as integral equation further validating our results.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"363 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Sensitivity of Functionals to Input Data in a Variational Assimilation Problem for a Sea Thermodynamics Model 海洋热力学模型变量同化问题中函数对输入数据的敏感性
IF 0.3
Numerical Analysis and Applications Pub Date : 2024-03-13 DOI: 10.1134/s1995423924010087
V. P. Shutyaev, E. I. Parmuzin
{"title":"Sensitivity of Functionals to Input Data in a Variational Assimilation Problem for a Sea Thermodynamics Model","authors":"V. P. Shutyaev, E. I. Parmuzin","doi":"10.1134/s1995423924010087","DOIUrl":"https://doi.org/10.1134/s1995423924010087","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A problem of variational data assimilation for a sea thermodynamics model is considered, with the aim to reconstruct sea surface heat fluxes taking into account the covariance matrices of input data errors. The sensitivity of some solution functionals to input data in this problem of variational assimilation is studied, and the results of numerical experiments for a model of dynamics of the Baltic Sea are presented.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"97 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Difference Scheme for Wave Equation 波方程的差分方案
IF 0.3
Numerical Analysis and Applications Pub Date : 2024-03-13 DOI: 10.1134/s1995423924010063
A. F. Mastryukov
{"title":"A Difference Scheme for Wave Equation","authors":"A. F. Mastryukov","doi":"10.1134/s1995423924010063","DOIUrl":"https://doi.org/10.1134/s1995423924010063","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>The paper deals with a numerical solution of a wave equation. The solution algorithm uses optimal parameters which are obtained by using Laguerre transform in time for the wave equation. Additional parameters are introduced into a difference scheme of 2nd-order approximation for the equation. The optimal values of these parameters are obtained by minimizing the error of a difference approximation of the Helmholtz equation. Applying the inverse Laguerre transform in the equation for harmonics, a differential-difference wave equation with the optimal parameters is obtained. This equation is difference in the spatial variables and differential in time. An iterative algorithm for solving the differential-difference wave equation with the optimal parameters is proposed. The results of numerical calculations of the differential-difference equations for 2-dimensional and 1-dimensional versions of the equation are presented. It is shown that the difference schemes with the optimal parameters give an increase in the accuracy of solving the equations.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"8 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140125917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Fourth Order Accurate Interpolation Operator for the Difference Solution of the 3-Dimensional Laplace Equation 论三维拉普拉斯方程差分解的四阶精确插值算子
IF 0.3
Numerical Analysis and Applications Pub Date : 2024-03-13 DOI: 10.1134/s1995423924010038
A. A. Dosiyev, E. Celiker
{"title":"On the Fourth Order Accurate Interpolation Operator for the Difference Solution of the 3-Dimensional Laplace Equation","authors":"A. A. Dosiyev, E. Celiker","doi":"10.1134/s1995423924010038","DOIUrl":"https://doi.org/10.1134/s1995423924010038","url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A three-dimensional (3D) matching operator is proposed for the fourth-order accurate solution of the Dirichlet problem of Laplace’s equation in a rectangular parallelepiped. The operator is constructed based on homogeneous, orthogonal-harmonic polynomials in three variables, and employs the cubic grid difference solution of the problem for the approximate solution inbetween the grid nodes. The difference solution on the nodes used by the interpolation operator is calculated by a novel formula, developed on the basis of the discrete Fourier transform. This formula can be applied on the required nodes directly, without requiring the solution of the whole system of difference equations. The fourth-order accuracy of the constructed numerical tools are demonstrated further through a numerical example.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"135 1","pages":""},"PeriodicalIF":0.3,"publicationDate":"2024-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140126017","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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