Remote sensing of earth terrain

A systematic approach for the identification of terrain media such as vegetation canopy, forest, and snow covered fields is developed using the optimum polarimetric classifier. The covariance matrices for the various terrain cover are computed from theoretical models of random medium by evaluating the full polarimetric scattering matrix elements. The optimal classification scheme makes use of a quadratic distance measure and is applied to classify a vegetation canopy consisting of both trees and grass. Experimentally measured data are used to validate the classification scheme. Theoretical probability of classification error using the full polarimetric matrix are compared with classification based on single features including the phase difference between the VV and HH polarization returns. It is shown that the full polarimetric results are optimal and provide better classification performance than single feature measurements

Dielectric mixtures -- electrical properties and modeling

In this paper, a review on dielectric mixtures and the importance of the numerical simulations of dielectric mixtures are presented. It stresses on the interfacial polarization observed in mixtures. It is shown that this polarization can yield different dielectric responses depending on the properties of the constituents and their concentrations. Open question on the subject are also introduced.Comment: 40 pages 12 figures, to be appear in IEEE Trans. on Dielectric

Nonlinear Evolutionary Problem of Filtration Consolidation With the Non-Classical Conjugation Condition

Finite-element solutions of the initial-boundary value problem for a nonlinear parabolic equation in an inhomogeneous domain with the conjugation condition of a non-ideal contact were found. The initial boundary value problem is a mathematical model of an important technical problem of filtration consolidation of inhomogeneous soils. Inhomogeneity is considered in terms of the presence of thin inclusions, physicochemical characteristics of which differ from those of the main soil. The problem of longterm consolidation is especially pronounced in soils with low filtration coefficient. Low permeability of the porous medium causes deviation from the linear relationship between the pressure gradient and the filtration rate.Weak formulation of the problem is suggested, and the accuracy of the approximate finite element solution, its existence and uniqueness are substantiated for the case of Darcy’s nonlinear law. A test example and the effect of the nonlinear filtration law for thin inclusion on the dynamics of scattering of excess pressures in the entire area of the problem are considered

Unconditional convergence and optimal error estimates of a Galerkin-mixed FEM for incompressible miscible flow in porous media

In this paper, we study the unconditional convergence and error estimates of a Galerkin-mixed FEM with the linearized semi-implicit Euler time-discrete scheme for the equations of incompressible miscible flow in porous media. We prove that the optimal $L^2$ error estimates hold without any time-step (convergence) condition, while all previous works require certain time-step condition. Our theoretical results provide a new understanding on commonly-used linearized schemes for nonlinear parabolic equations. The proof is based on a splitting of the error function into two parts: the error from the time discretization of the PDEs and the error from the finite element discretization of corresponding time-discrete PDEs. The approach used in this paper is applicable for more general nonlinear parabolic systems and many other linearized (semi)-implicit time discretizations

Multigrid waveform relaxation for the time-fractional heat equation

In this work, we propose an efficient and robust multigrid method for solving the time-fractional heat equation. Due to the nonlocal property of fractional differential operators, numerical methods usually generate systems of equations for which the coefficient matrix is dense. Therefore, the design of efficient solvers for the numerical simulation of these problems is a difficult task. We develop a parallel-in-time multigrid algorithm based on the waveform relaxation approach, whose application to time-fractional problems seems very natural due to the fact that the fractional derivative at each spatial point depends on the values of the function at this point at all earlier times. Exploiting the Toeplitz-like structure of the coefficient matrix, the proposed multigrid waveform relaxation method has a computational cost of $O(N M \log(M))$ operations, where $M$ is the number of time steps and $N$ is the number of spatial grid points. A semi-algebraic mode analysis is also developed to theoretically confirm the good results obtained. Several numerical experiments, including examples with non-smooth solutions and a nonlinear problem with applications in porous media, are presented

Revisiting Question of Evaporation Mathematical Modeling Process

The methods of mathematical description of evaporation processes from light soils of the arid zone of Russia are discussed. The focus is on the evaporation of moisture from the aeration zone. The analysis of theoretical work in this area and the results of their practical implementation are presented. Mathematical models of evaporation are divided into two types: physical and mathematical, taking into account the interaction of moisture with the soil frame and phenomenological, based on balance relations with the use of ordinary differential equations. The analysis of the actual material on evaporation from light soils of the Privolzhskiy sands was carried out in the light of the theory of evaporation from the capillaries surface in the pore space, taking into account the diffusion and film movements of moisture. A semi-empirical model of moisture movement in the upper soil layers in the form of analytical formulas relating the evaporation rate to the physical state of the soil water was used to estimate the water loss during evaporation. Good agreement was obtained between the theoretical provisions on the capillary movement of moisture and the data on evaporation from the sandy soils of the steppe zone of Russia. Approximation of data on the precipitation falling dynamics during the year by semi-empirical dependencies in the form of analytical formulas determines their practical use in the work of agricultural producers