Linear Theory of Hydrologic Systems

Distance vector‐hop (DVHop), as a range‐independent positioning algorithm, is a significant positioning method in wireless sensor networks (WSNs). It is composed of three parts, including connectivity detection, distance estimation, and position estimation. However, this simple positioning method results in a larger positioning error. Therefore, to enhance the positioning precision, this paper investigates the characteristic of error distribution between the estimated and real distance in the DVHop algorithm and reveals that the error is subjecting to the Gaussian distribution, N∼(0,1/3CR). Furthermore, to improve positioning accuracy, we propose a Gaussian error correction multi‐objective positioning model with non‐dominated sorting (NSGA‐II), which named GGAII‐DVHop. Finally, this model is tested on three complex network topologies, and the results demonstrate that it is significantly superior to other four algorithms in both positioning precision and robustness.

A Gaussian error correction multi‐objective positioning model with NSGA‐II

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Optimal Shape Design For Elliptic Systems

The assessment of soil erosion risk, sediment yield and their controlling factors on a large scale: Example of Morocco

https://portlandpress.com/biochemsoctrans/article-pdf/7/4/813/553370/bst0070813.pdf

Enzyme-Activated Irreversible Inhibitors

We study a simplified multidimensional version of the phenomenological surface growth continuum model derived in [ 6 ]. The considered model is a partial differential equation for the surface height profile \begin{document}$ u $\end{document} which possesses the following free energy functional: \begin{document}$ E(u) = \int_{\Omega} \left[ \frac{1}{2} \ln\left(1+\left|\nabla u \right|^2\right) - \left|\nabla u \right| \arctan\left(\left|\nabla u \right|\right) + \frac{1}{2} \left|\Delta u \right|^2 \right] {\rm d}x, $\end{document} where \begin{document}$ \Omega $\end{document} is the domain of a fixed support on which the growth is carried out. The term \begin{document}$ \left|\Delta u \right|^2 $\end{document} designates the standard surface diffusion in contrast to the second order term which phenomenologically describes the growth instability. The energy above is mainly carried out in regions of higher surface slope \begin{document}$ \left( \left|\nabla u \right| \right) $\end{document} . Hence minimizing such energy corresponds to reducing surface defects during the growth process from a given initial surface configuration. Our analysis is concerned with the energetic and coarsening behaviours of the equilibrium solution. The existence of global energy minimizers and a scaling argument are used to construct a sequence of equilibrium solutions with different wavelength. We apply our minimum energy estimates to derive bounds in terms of the linear system size \begin{document}$ \left| \Omega \right| $\end{document} for the characteristic interface width and average slope. We also derive a stable numerical scheme based on the convex-concave decomposition of the energy functional and study its properties while accommodating these results with 1d and 2d numerical simulations.

https://www.aimsciences.org/article/exportPdf?id=9c3cb58c-83ca-418c-8f63-d3aa58918557

Energetics and coarsening analysis of a simplified non-linear surface growth model

The aim of this work is to study a quasilinear elliptic equation where we are particularly interested in the characterization of the critical value, which appears as the Lagrange multiplier in the functional minimization associated with the dual problem, over one close convex subset of $$L^\infty \times (W^{1,\infty })^N$$. We are going to give a generalization of Alaa (Etude d’equations elliptiques non lineaires a dependance convexe en le gradient et a donnees mesures. Ph.D. Thesis, University of Nancy I, 1989) method in the case of an upper space dimension $$(N\ge 2)$$.

Characterization of the Critical Value for a Quasilinear Elliptic Equation with Arbitrary Growth with Respect to the Gradient

As one of the most important tasks in image processing, texture analysis is related to a class of mathematical models that characterize the spatial variations of an image. In this paper, in order to extract features of interest, we propose a reaction diffusion based model which uses the variational approach. In the first place, we describe the mathematical model, then, aiming to simulate the latter accurately, we suggest an efficient numerical scheme. Thereafter, we compare our method to literature findings. Finally, we conclude our analysis by a number of experimental results showing the robustness and the performance of our algorithm.

https://jmm.guilan.ac.ir/article_4611_61d3f592963b388acd8a5af68fabf8f8.pdf

A computational model for texture analysis in images with a reaction-diffusion based filter

We establish a new method for estimating parameters in reaction-adsorption-diffusion systems modelling the greywater treatment through a horizontal subsurface flow of a constructed wetland. Two cost functions are presented to estimate the permeability coefficients, the initial concentration and the degradation of the phosphor in the considered model. A Lagrangian method is considered to compute the derivative of the cost functions with respect to the state variable. An iterative algorithm is illustrated with the reaction-adsorption-diffusion systems using optimisation techniques and the adjoint state model. We were able to estimate our parameters and our initial data. In addition, the performance of our algorithm is evaluated by perturbing the data with various levels of additive noise.

An efficient and robust algorithm for estimating parameters in a horizontal subsurface flow of a constructed wetland treating greywater

This work presents a new approach for the mathematical analysis and numerical simulation of a class of periodic parabolic equations with discontinuous coefficients. Our technique is based on the minimization of a least squares cost function. By the means of variational calculus, we prove that the considered optimization problem admits an optimal solution. Using the Lagrangian method, we compute the gradient of the cost function associated with our problem. Finally, we give several numerical simulations that show the efficiency and robustness of our method.

/pdf/periodic-parabolic-problem-with-discontinuous-coefficients-28934l8w.pdf

Nour Eddine Alaa

Papers

Energetics and coarsening analysis of a simplified non-linear surface growth model

Characterization of the Critical Value for a Quasilinear Elliptic Equation with Arbitrary Growth with Respect to the Gradient

A computational model for texture analysis in images with a reaction-diffusion based filter

An efficient and robust algorithm for estimating parameters in a horizontal subsurface flow of a constructed wetland treating greywater

Periodic parabolic problem with discontinuous coefficients: Mathematical analysis and numerical simulation