Initial Hypotheses for Modeling and Numerical Analysis of Rockfill and Earth Dams and Their Effects on the Results of the Analysis

© 2018 Mohammad Rashidi and Habib Rasouli. Since the behavior of earth dams is unreliable in different stages of construction, impounding, and exploitation, this matter is an unavoidable and essential issue with regard to the serious dangers caused by the failure of these important structures. It is crucial to evaluate the behavior of dams and examine the consistency between the carried out analyses and the behavioral parameters under different conditions in the lifespan of dams due to the uncertainty of the principles and hypotheses which have been adopted to analyze these structures. This objective will be accomplished through the help of correct numerical analyses. A series of hypotheses are adopted to simplify the parametric analyses before starting these analyses. The aim of this research is to develop and discuss these hypotheses. And so, the number of elements and their effects on the results of analyses were examined through the consolidation of unsaturated soil method, the compressible fluid method, correlated analysis, and uncorrelated analysis. It became clear after the numerical analyses that correlated analysis is a more precise method in comparison with the uncorrelated analysis method. However, this method is not economical when it comes to high dams and the replacement method is the uncorrelated analysis. Furthermore, the displacements are not that sensitive to the bulk modulus of water while the maximum settlement of the dam transfers from the middle of the dam's core to a location higher than that the core as the bulk modulus of water increases. However, pore water pressure is very sensitive to the bulk modulus of water

Gravitational Collapse of a Homogeneous Scalar Field in Deformed Phase Space

We study the gravitational collapse of a homogeneous scalar field, minimally coupled to gravity, in the presence of a particular type of dynamical deformation between the canonical momenta of the scale factor and of the scalar field. In the absence of such a deformation, a class of solutions can be found in the literature [R. Goswami and P. S. Joshi, arXiv:gr-qc/0410144], %\cite{JG04}, whereby a curvature singularity occurs at the collapse end state, which can be either hidden behind a horizon or be visible to external observers. However, when the phase-space is deformed, as implemented herein this paper, we find that the singularity may be either removed or instead, attained faster. More precisely, for negative values of the deformation parameter, we identify the emergence of a negative pressure term, which slows down the collapse so that the singularity is replaced with a bounce. In this respect, the formation of a dynamical horizon can be avoided depending on the suitable choice of the boundary surface of the star. Whereas for positive values, the pressure that originates from the deformation effects assists the collapse toward the singularity formation. In this case, since the collapse speed is unbounded, the condition on the horizon formation is always satisfied and furthermore the dynamical horizon develops earlier than when the phase-space deformations are absent. These results are obtained by means of a thoroughly numerical discussion.Comment: 17 pages, 17 figure

On Positive Solutions for Some Nonlinear Semipositone Elliptic Boundary Value

This study concerns the existence of positive solutions to classes of boundary value problems of the form−∆u = g(x,u), x ∈ Ω,u(x) = 0, x ∈ ∂Ω,where ∆ denote the Laplacian operator, Ω is a smooth bounded domain in RN (N ≥ 2) with ∂Ω of class C2, and connected, and g(x, 0) < 0 for some x ∈ Ω (semipositone problems). By using the method of sub-super solutions we prove the existence of positive solution to special types of g(x,u)

On a Nonlinear System of Reaction-Diffusion Equations

The aim of this article is to study the existence of positive weak solution for a quasilinear reaction-diffusion system with Dirichlet boundary conditions,− div(|∇u1|p1−2∇u1) = λu1α11u2α12... unα1n,   x ∈ Ω,− div(|∇u2|p2−2∇u2) = λu1α21u2α22... unα2n,   x ∈ Ω, ... , − div(|∇un|pn−2∇un) = λu1αn1u2αn2... unαnn,   x ∈ Ω,ui = 0,   x ∈ ∂Ω,   i = 1, 2, ..., n,  where λ is a positive parameter, Ω is a bounded domain in RN (N > 1) with smooth boundary ∂Ω. In addition, we assume that 1 < pi < N for i = 1, 2, ..., n. For λ large by applying the method of sub-super solutions the existence of a large positive weak solution is established for the above nonlinear elliptic system

On the existence and multiplicity of positive solutions to classes of steady state reaction diffusion systems with multiple parameters

We study positive solutions to the steady state reaction diffusion systems of the form: \begin{equation} \left\{\begin{array}{ll} -\Delta u = \lambda f(v)+\mu h(u), & \Omega,\\ -\Delta v = \lambda g(u)+\mu q(v),& \Omega,\\ \frac{\partial u}{\partial \eta}+\sqrt[]{\lambda +\mu}\, u=0,& \partial\Omega,\\ \frac{\partial v}{\partial \eta}+\sqrt[]{\lambda +\mu}\, v=0, & \partial\Omega,\\ \end{array}\right. \end{equation} where ${\lambda,\mu>0}$ are positive parameters, ${\Omega}$ is a bounded in $\mathbb{R}^{N}$$(N>1)$ with smooth boundary ${\partial \Omega}$, or ${\Omega=(0,1)}$, ${ \frac{\partial z}{\partial \eta} }$ is the outward normal derivative of $z$. Here $f, g, h, q\in C^{2} [0,r)\cap C[0,\infty)$ for some $r>0$. Further, we assume that $f, g, h$ and $q$ are increasing functions such that $f(0) = g(0) = h(0) = {q}(0) = 0$, $f^\prime(0), g^\prime(0), h^\prime(0), q^\prime(0) > 0$, and $\lim\limits_{s\to \infty}\frac{f(M g(s))}{s}=0$ for all $M>0$. Under certain additional assumptions on $f, g, h$ and $q$ we prove our existence and multiplicity results. Our existence and multiplicity results are proved using sub-super solution methods

Fracture detection from water saturation log data using a Fourier-wavelet approach

Fracture detection as applied to reservoir characterization is a key step towards modeling of fracturedreservoirs. While different methods have been proposed for detection and characterization of fractures and fractured zones, each is associated with certain shortcomings that prevent from their full use in different related engineering application environments. In this paper a new method is proposed for detection of fractured zones and fracture density in which water saturation log data is utilized. For detection of fractures, we have used wavelet transform and properties of wavelets that are highly suitable for detection of changes and local features of data. To choose the optimum mother wavelet, we have used energy matching strategy in which a wavelet with the highest energy match between spectral energy of the signal at the dominant frequency band and the coefficient energy at the same band of wavelet decomposition of the signal is selected. We have used wavelet packet for a more narrow frequency band selection and enhanced results. Decomposing the water saturation data using wavelets showed that the majority of information of theoriginal log is hidden at low frequency bands. As a result, approximated section of wavelet transform of data was used for fracture detection, while shale volume (or gamma ray) log data was used to filter part of the errors in prediction and identification of the uncertain zones. This increased the accuracy of the results by 70%. Finally, a linear relation was derived between energy of approximated section of water saturation log and fracture density, allowing us to estimate the number of fractures in each fractured zone. The method was applied to four wells belonging to one of the Iranian oilfields located in the southwest region of the country and the results are promising. The use of large volume of data and the subsequent analysis increased the generalization ability of the proposed method

Liquid loading in wellbores and its effect on cleanup period and well productivity in tight gas sand reservoirs

Tight gas reservoirs normally have production problems due to very low matrix permeability and significant damage during well drilling, completion, stimulation and production. Therefore they might not flow gas to surface at optimum rates without advanced production improvement techniques. After well stimulation and fracturing operations, invaded liquids such as filtrate will flow from the reservoir into the wellbore, as gas is produced during well cleanup. In addition, there might be production of condensate with gas. The produced liquids when loaded and re-circulated downhole in wellbores, can significantly reduce the gas pro-duction rate and well productivity in tight gas formations.This paper presents assessments of tight gas reservoir productivity issues related to liquid loading in wellbores using numerical simulation of multiphase flow in deviated and horizontal wells. A field example of production logging in a horizontal well is used to verify reliability of the numerical simulation model outputs. Well production performance modelling is also performed to quantitatively evaluate water loading in a typical tight gas well, and test the water unloading techniques that can improve the well productivity. The results indicate the effect of downhole liquid loading on well productivity in tight gas reservoirs. It also shows how well cleanup is sped up with the improved well productivity when downhole circulating liquids are lifted using the proposed methods

Runaway electron energy measurement using hard x-ray spectroscopy in "Damavand" tokamak

Set of experiments has been developed to study existing runaway electrons in "Damavand" tokamak plasma upon characteristics of hard x-ray emissions produced by collision of the runaway electrons with the plasma particles and limiters. As a first step, spatial distribution of hard x-ray emissions on the equatorial plane of the torus was considered. Obtained spectra of hard x-ray emissions for different alignments of shielded detector indicate isotropic emissivity in the equatorial plane. This is in agreement with wide angle cone of bremsstrahlung radiations, deduced from the mean value of energy of the runaway electrons. The mean energy was calculated from the slope of the energy spectrum of hard x-ray photons. In the second stage in order to investigate time evolution of energy of the runaway electrons, similar technique were applied to obtain hard x-ray energy in every 3 ms intervals, from the beginning to the end of plasma. The mean energy of the runaway electrons increases during the ramp up phase and reaches its maximum between 3 and 9 ms after plasma formation. Also considering the time dependence of the counted photons in each energy range shows that energetic photons are emitted during the ramp up phase of the plasma current in Damavand tokamak