The present study has mainly focused on the modification of the HYPERBOLIC MODEL formulation so that the shortcomings of the said MODEL can be corrected and more conformity with the experimental results can also be provided. This MODEL, also known as Duncan-Chang MODEL, is a two parameter MODEL for obtaining the stress-strain curve of the triaxial test. The HYPERBOLIC MODEL which is indicative of the ideal characteristics of the soil is particularly advantageous in that it does not require the presence of extensive test programs and can easily be implemented through computer programs. As the results show, although numerous studies have already been carried out to address the MODEL shortcomings, this MODEL fails to predict the plastic behavior of the subsaturated soils. Among the shortcomings of the said MODEL are the insufficiency of the HYPERBOLIC MODEL relations for the analysis of the stage related to the soil instability, uselessness of the relations in case of soil volume variation, experimental nature of the used coefficients in the relation. HYPERBOLIC relations are useful in solving different problems of engineering and geotechnics since numerical values of HYPERBOLIC MODEL parameters can be extracted from the experimental results and all the relations that are used for the drained soils can also be applied to non-drained and unstable soils. Furthermore, numerous values of parameters have been tested and utilized for different kinds of soil over the past thirty years. Therefore, a rich source is available for comparison and interpretation of the obtained results from different projects.

This paper presents a numerical study using TWO-FLUID MODEL in order to compare the effect of hydrodynamic and hydrostatic MODELs for pressure correction term in TWO-FLUID MODEL in MODELing gasliquid two-phase flows to provide a more accurate MODEL. TWO-FLUID MODEL is solved by Godunov Approximate Riemann Solver. The TWO-FLUID MODEL is applied using both hydrodynamic pressure correction term and hydrostatic pressure correction term for four sample examples including Water Faucet Case, Water-Air Separation Case, Toumi’s Shock Tube Case, and Large Relative Velocity Shock Tube Case. Hydrostatic pressure correction term is neglected for vertical geometry, therefore, in this geometry; TWO-FLUID MODEL cannot be HYPERBOLIC. Thus, hydrostatic pressure correction term is not a stabilizing term. Also, in horizontal pipe and for atmospheric conditions, hydrostatic pressure correction term presents better results than hydrodynamic pressure correction term. But, in non-atmospheric conditions, hydrodynamic pressure correction term presents better results. Therefore, in order to select a suitable pressure correction term for TWO-FLUID MODEL, we consider geometry (vertical or horizontal) and flow conditions (atmospheric or under-pressure). Also, hydrodynamic pressure correction term in twofluid equations system is HYPERBOLIC in a broader range than hydrostatic pressure correction term.

Due to widespread application of reinforced soil media and the crucial need to understand and anticipate its actual behavior, in addition to the fact that direct numerical analysis of reinforced masses is a difficult and time-consuming procedure, homogenization methods have been introduced. In this study, multiphase approach which is considered as a new framework in homogenization methods is developed. This development is done using the Duncan-Chang HYPERBOLIC MODEL for simulating the behavior of soil in a reinforced medium. In this study, efforts have been made to propose a new multiphase MODEL for analyzing reinforced soil media, based on assigning the Duncan-Chang constitutive MODEL to soil and elastic-perfectly plastic behavior to reinforcements. A developed multiphase MODEL is used to simulate a full-scale reinforced soil wall. The wall has been analyzed by means of both direct and homogenization approaches, using Duncan-Chang constitutive MODEL and the developed multiphase MODEL, respectively. After comparing the results of the analyses, sufficient accuracy of homogenization approach using proposed multiphase MODEL has been approved. It is also observed that in contrast to its simplicity, the Duncan-Chang HYPERBOLIC MODEL presents a suitable estimation of behavior of the reinforced soil wall in case of implementing direct analysis method.

In this paper, we consider the HYPERBOLIC Ricci-Bourguignon ow on a compact man-ifold M and show that this ow has a unique solution on short-time with imposing on initial conditions. After then, we , nd evolution equations for Riemannian cur-vature tensor, Ricci curvature tensor and scalar curvature of M under this ow. In the , nal section, we give some examples of this ow on some compact manifolds.

Whereas in electrical discharge machining (EDM) the heat flux entering the work piece is extremely high, the Fourier heat conduction MODEL may fails. This article reports on determination of temperature distribution in the work piece due to EDM using non-Fourier heat conduction MODEL. Equations are solved by deriving the numerical solution. The temperature layers and profiles of sample calculations show that it is not acceptable applying the Fourier heat conduction MODEL for estimating the temperature of work piece. Also, it can be perceived that according to the amount of Vernotte number for a specific Fourier number, it is possible that the temperature of different points of work piece become even lower than initial temperature.

In the present study, we propose an e, ective nonlinear anisotropic di, usion-based HYPERBOLIC parabolic MODEL for image denoising and edge detection. The HYPERBOLIC-parabolic MODEL employs a second-order PDEs and has a second-time derivative to time t. This approach is very e, ective to preserve sharper edges and better-denoised images of noisy images. Our MODEL is well-posed and it has a unique weak solution under certain conditions, which is obtained by using an iterative , nite di, erence explicit scheme. The results are obtained in terms of peak signal to noise ratio (PSNR) as a metric, using an explicit scheme with forward-backward di, usivities.