دانلود کتاب Monte Carlo Method for Solving Inverse Problems of Radiation Transfer

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Chapter 1. Monte Carlo modifications for solving problems of radiation transfer\n1.1. Elements of using the Monte Carlo method in radiation transfer computation\n1.2. The “conjugate” computation scheme\n1.3. Use of the importance function\n1.4. Method of mathematical expectation for plane slab model\n1.5. Improvement of the method of mathematical expectation\n1.6. Modification of the distribution of particle path length\n1.7. Modification of the trajectory angular distribution\n1.8. Modification of radiation transfer modelling in spherical atmosphere\n1.8.1. Statement of the problem\n1.8.2. Computational algorithm\nChapter 2. Generalized transport equation with highly peaked phase function\n2.1. Generalized transport equation\n2.2. Approximation for highly peaked phase function\n2.3. Transformation of standard transport equation\n2.4. Optimizing procedures for modelling and calculation\n2.4.1. Modification of the local estimate\n2.4.2. Modification of trajectory modelling\n2.4.3. Modifications of the calculation of the radiation flux\n2.5. Radiation transfer in broken clouds\n2.5.1. Free path density in the layer of broken clouds\n2.5.2. Results of numerical experiments\n2.6. Conclusion\nChapter 3. Calculation of the correlation characteristics of radiation field in the stochastic medium by the Monte Carlo method\n3.1. Problem statement\n3.2. Computation of derivatives of a field of brightness by the Monte Carlo method\n3.3. Dispersions of the derivatives DjI estimator\nChapter 4. Identification of the phase function\n4.1. Statement of the problem\n4.2. Method of successive approximations\n4.2.1. “Additive” method\n4.2.2. “Multiplicative” method\n4.3. Estimating the intensity of scattered radiation\n4.3.1. On the use of the plane atmosphere model\n4.3.2. “Local” estimate of intensity\n4.4. Numerical results\n4.5. Study of convergence\nChapter 5. Regularization in solving inverse problems of atmosphere optics\n5.1. Recovery of altitudinal variations of the scattering coefficient\n5.2. Analytical regularization\n5.3. Regularization in estimating the phase function\n5.4. Statistical regularization\n5.5. Application of statistically orthogonal expansions\nChapter 6. Direct and inverse problems of radiation transfer in a plant canopy\n6.1. Plant canopy model\n6.2. Transport equation for a plant canopy\n6.3. Markov chain modelling\n6.4. Taking into account the hot spot effect\n6.5. Statement of the inverse problem and an algorithm of its solution\n6.6. Evaluation of derivatives by the Monte Carlo method\n6.7. On estimating the leaf-normal distribution for a plant canopy\n6.7.1. Iterative method\n6.7.2. On calculating the integrals A, B and C\n6.8. Numerical results\n6.9. Synopsis\nChapter 7. X-ray tomography in scattering media\n7.1. Mathematical background\n7.2. The general scheme of the method\n7.2.1. Design and arrangement of the detectors\n7.2.2. Step 1: Reconstruction of the extinction coefficient distribution\n7.2.3. Step 2: Reconstruction of the scattering coefficients\n7.2.4. Step 3: Reconstruction of the absorption coefficient distribution\n7.3. Numerical results\n7.3.1. Computing the jumps of the first and the second kind\n7.3.2. Scattering effect on body image reconstruction\n7.4. Conclusions\nAppendix A. Integral equation of the second kind with stochastic kernel\nA.1. Introduction\nA.2. Decomposition of the solution\nA.3. Numerical method for solving the equation\nA.4. Numerical examples\nAppendix B. Computation of radiation field in optically thick medium by the Monte Carlo method\nB.1. Introduction\nB.2. Transformation of the transport equation\nB.3. Illustrative study of the method\nB.4. Estimation of accuracy\nB.5. Limitation on the use of the method\nB.6. Numerical experiment\nAppendix C. A new method for identification of the phase function\nC.1. Remarks concerning notation\nC.2. Problem statement\nC.3. Iterative method\nC.4. Calculation of the matrix coefficients\nC.5. Convergence of the iterations\nC.6. Results of numerical experiment\nBibliography