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Application of genetic algorithms to texture analysis

CRYSTAL RESEARCH AND TECHNOLOGY 1999年第8期34卷 1073-1079页

作者： Salek, P Tarasiuk, J Wierzbanowski, K Akad Gorniczo Hutnicza Wydzial Fiz & Tech Jadrowej PL-30059 Krakow Poland

Application of genetic algorithms to texture analysis is presented in this paper. The genetic algorithm technique was applied to the calculation of the orientation distribution function from a set of pole figures. The results are very satisfying. The same algorithm may be also applied to other problems of texture analysis, e.g., to find an optimal texture for a given application.

关键词： genetic algorithm crystallographic texture orientation distribution function pole figure texture analysis numerical algorithm

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Surface treatment of metal by combined particle beam

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INTERNATIONAL JOURNAL OF ENGINEERING SCIENCE 2024年 205卷

作者： Parfenova, Elena S. Knyazeva, Anna G. Russian Acad Sci Siberian Branch Inst Strength Phys & Mat Sci 2-4 Pr Akad Skii Tomsk 634055 Russia

This work is related to modeling of metal surface modification process by combined particles beam. On the basis of thermodynamics of irreversible processes, including equations of state in differential form, a nonlinear model is formulated. The model takes into account the interaction of thermal, diffusion and mechanical waves and finiteness of relaxation times of thermal and diffusion processes. For the combined particle flow such model is proposed for the first time. The numerical algorithm is based on implicit difference schemes. The study of the interaction of waves of different nature is carried out on the example of a copper target treated with nickel and gold particles. It is shown that deformations take the maximal value at the left boundary, which is directly related to the presence of impurity concentration gradients. Depending on the pulse duration, the difference between the extrema on the elastic wave becomes less significant. With increasing temperature, obviously, the diffusion process accelerates. The propagation velocities of the interacting waves are different. The character of distributions of concentrations of introduced particles directly depends on the value of parameters proportional to relaxation times.

关键词： Diffusion Stress wave Heat/mass flux relaxation time Coupled model numerical algorithm Thermoelastic diffusion theory

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Monte Carlo simulation of the coffee-ring effect on porous papers

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THEORETICAL AND COMPUTATIONAL FLUID DYNAMICS 2023年第5期37卷 627-637页

作者： Hwang, Youngjin Kim, Sangkwon Lee, Chaeyoung Kwak, Soobin Lee, Gyeonggyu Kim, Junseok Korea Univ Dept Math Seoul 02841 South Korea

In this article, we present a mathematical model and numerical simulation of the coffee-ring effect on porous papers. The numerical method is based on Monte Carlo simulation. The proposed model is simple but can capture the main mechanism of coffee stain formation on porous papers. Several numerical experiments are presented to demonstrate the performance of the proposed algorithm. We can obtain the coffee-ring effect on porous papers as the computer simulation results.

关键词： Coffee-ring effect Monte Carlo simulation Computer simulation numerical algorithm

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An iterative aggregation/disaggregation procedure for modelling the long-term behaviour of continuous-time evanescent random processes

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JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 1996年第1期56卷 77-95页

作者： Stewart, DE Bebbington, MS MASSEY UNIV DEPT STATPALMERSTON NORTHNEW ZEALAND

We describe a multilevel aggregation/disaggregation method for finding the quasistationary distribution and decay parameters for continuous-time Markov chains. This complements existing techniques dealing with the discrete-time case, or for finding the stationary distribution. Finding the quasistationary distribution is equivalent to calculating the eigenvector corresponding to the smallest eigenvalue of the q-matrix restricted to the non-absorbing class. The method presented here is similar to an algebraic multigrid, with restriction operators that depend on the current approximation to the solution. The smoothers are short Arnoldi iterations or Gauss-Seidel iterations. numerical results are presented for a variety of models of differing character, including simple epidemic, bivariate SIS, predator-prey, and the cubic auto-catalator. These indicate that the number of cycles required grows only very slowly with the size of the problem.

关键词： quasistationary distribution numerical algorithm V-cycle

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Development of Mathematical Modeling Methods and Solution of Present-Day Problems in Geomechanics at the Institute of Mining SB RAS

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JOURNAL OF MINING SCIENCE 2024年第4期60卷 533-555页

作者： Lavrikov, S. V. Russian Acad Sci Chinakal Inst Min Siberian Branch Novosibirsk 630091 Russia

This article commemorates a double jubilee date on February 8, 2024-the 300th anniversary of the Russian Academy of Sciences and the 80th anniversary of the Institute of Mining SB RAS. The author reviews the research and findings of the Institute's scientists over the last 10-15 years in the area of mathematical modeling and numerical solution of present-day problems in geomechanics.

关键词： rock underground opening mathematical model numerical algorithm boundary value problem software system stress pattern

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Coupling 2D thermal and 3D optical model for performance prediction of a parabolic trough solar collector

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SOLAR ENERGY 2016年 139卷 365-380页

作者： Huang, Weidong Xu, Qian Hu, Peng Univ Sci & Technol China Dept Earth & Space Sci 96 Jinzhai Rd Hefei 230026 Anhui Peoples R China Univ Sci & Technol China Dept Thermal Sci & Energy Engn 96 Jinzhai Rd Hefei 230026 Anhui Peoples R China

A 2D thermal model for tube receiver in parabolic trough solar collector is proposed, and a fast numerical algorithm is developed. Comparing to the previous models, we consider the radiation loss from the side plate of the tube receiver and direct transmission of the absorber radiation to the air to construct a physical model and mathematical equations. We also reduce the calculation by simplifying them to algebraic equations for numerical solution without needing iteration after ignoring the axial heat transfer. It is further coupled to the three-dimensional optical model to predict the performance of parabolic trough solar collector. The performances of the overall model and thermal model are tested against experimental measurements from Sandia National Laboratories. In all cases, the simulation results show a good agreement with the experimental results. The models developed in this paper can predict performance of parabolic trough solar collector with parabolic trough reflector and tube receiver accurately and quickly based on the structure and material properties of the system. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Parabolic trough Heat transfer model Thermal radiation analysis Optical model numerical algorithm

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Strong solutions of a class of hybrid diffusion processes with state-dependent regime-switching

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APPLIED numerical MATHEMATICS 2013年 72卷 72-90页

作者： Rathinasamy, A. Yin, Baojian PSG Coll Technol Dept Math Coimbatore 641004 Tamil Nadu India Huazhong Univ Sci & Technol Sch Math & Stat Wuhan 430074 Hubei Peoples R China

This work focuses on the strong solutions of a class of hybrid diffusion processes with state-dependent regime-switching. This important class of processes originates from the purpose of modeling the interest rate in finance. They have no any explicit solutions. Moreover, state-dependent regime-switching and non-Lipschitz diffusion coefficient pose a challenge to our analysis. To overcome all of these, we consider the Euler numerical schemes rather than the traditional Picard iterations in the existing results of solutions of stochastic differential equations. The weak convergence of numerical algorithms is first established by a martingale problem formulation. Using this result, we can also obtain the strong convergence of the algorithms. The existence of strong solutions is then confirmed. In addition, decreasing stepsize iterative algorithms and their weak convergence are presented. Several numerical experiments are also provided for illustration. (C) 2013 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Hybrid diffusion numerical algorithm Convergence Strong solution

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A 3-dimensional well model in the flow transport through porous media

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APPLIED MATHEMATICAL MODELLING 2014年第21-22期38卷 4949-4957页

作者： Zhang, Ting Lanzhou Univ Sch Math & Stat Lanzhou 730000 Gansu Peoples R China

In petroleum extraction and exploitation, the well is usually treated as a point or line source, due to its radius is much smaller comparing with the scale of the whole reservoir. Especially, in 3-dimensional situation, the well is regarded as a line source. In this paper, we analyze the modeling error for this treatment for steady flows through porous media and present a new algorithm for line-style well to characterize the wellbore flow potential. We also provide a numerical example to demonstrate the effectiveness of the proposed method. (C) 2014 Elsevier Inc. All rights reserved.

关键词： Well model Error estimate numerical algorithm

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Kinematics of a planar slider-crank linkage in screw form

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PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF MECHANICAL ENGINEERING SCIENCE 2022年第3期236卷 1588-1597页

作者： Zhao, Jing-Shan Wei, Songtao Ji, Junjie Tsinghua Univ Dept Mech Engn State Key Lab Tribol Beijing Peoples R China

This paper investigates the forward and inverse kinematics in screw coordinates for a planar slider-crank linkage. According to the definition of a screw, both the angular velocity of a rigid body and the linear velocity of a point on it are expressed in screw components. Through numerical integration on the velocity solution, we get the displacement. Through numerical differential interpolation of velocity, we gain the acceleration of any joint. Traditionally, position and angular parameters are usually the only variables for establishing the displacement equations of a mechanism. For a series mechanism, the forward kinematics can be expressed explicitly in the variable of position parameters while the inverse kinematics will have to resort to numerical algorithms because of the multiplicity of solution. For a parallel mechanism, the inverse kinematics can be expressed explicitly in the variable of position parameters of the end effector while the forward kinematics will have to resort to numerical algorithms because of the nonlinearity of system. Therefore this will surely lead to second order numerical differential interpolation for the calculation of accelerations. The most prominent merit of this kinematic algorithm is that we only need the first order numerical differential interpolation for computing the acceleration. To calculate the displacement, we also only need the first order numerical integral of the velocity. This benefit stems from the screw the coordinates of which are velocity components. The example of planar four-bar and five-bar slider-crank linkages validate this algorithm. It is especially suited to developing numerical algorithms for forward and inverse velocity, displacement and acceleration of a linkage.

关键词： Screw kinematics open kinematic chain closed kinematic chain numerical algorithm

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Mathematical simulation of nonlinear oscillations of viscoelastic pipelines conveying fluid

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APPLIED MATHEMATICAL MODELLING 2019年 66卷 662-679页

作者： Khudayarov, B. A. Turaev, F. Zh Tashkent Inst Irrigat & Agr Mechanizat Engineers Dept Higher Math Str Kari Niyazova 39 Tashkent 100000 Uzbekistan

A mathematical model of the problem of nonlinear oscillations of a viscoelastic pipeline conveying fluid is developed in the paper. The Boltzmann-Volterra integral model with weakly singular kernels of heredity is used to describe the processes of pipeline strain. Using the Bubnov-Galerkin method, the mathematical model of the problem is reduced to the study of a system of ordinary integro-differential equations, where time is an independent variable. The solution of integro-differential equations is determined by a numerical method based on the elimination of the singularity in the relaxation kernel of the integral operator. Using the numerical method for unknowns, a system of algebraic equations is obtained. To solve a system of algebraic equations, the Gauss method is used. A computational algorithm is developed to solve the problems of the dynamics of viscoelastic pipelines with a flowing fluid. The algorithm of the proposed method makes it possible to investigate in detail the effect of rheological parameters on the character of vibrational strength of viscoelastic pipelines with a fluid flow, in particular, in the study of free oscillations of pipelines based on the theory of ideally elastic shells. On the basis of the computational algorithm developed, a set of applied computer programs has been created, which makes it possible to carry out numerical studies of pipeline oscillations. The influence of singularity in the heredity kernels and the geometric parameters of the pipeline on the vibrations of structures possessing viscoelastic properties is numerically investigated. It is shown that an account of viscoelastic properties of pipeline material leads decrease in the amplitude and frequency of oscillation. It is established that to reveal the influence of viscoelastic properties of structure material on the pipeline oscillations, it is necessary to use the Abel-type weakly singular kernels of heredity. The obtained results of numerical simulation can be us

关键词： Mathematical model Simulation Viscous-elasticity lntegro-differential equations numerical algorithm Pipeline Fluid Cylindrical shell Oscillatory process Relaxation kernel

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