This paper introduces a non-conventional approach with multi-dimensional random sampling to solve a cocaine abuse model with statistical probability. The mean Latin hypercube finite difference (MLHFD) method is proposed for the first time via hybrid integration of the classical numerical finite difference (FD) formula with Latin hypercube sampling (LHS) technique to create a random distribution for the model parameters which are dependent on time [Formula: see text]. The LHS technique gives advantage to MLHFD method to produce fast variation of the parameters’ values via number of multidimensional simulations (100, 1000 and 5000). The generated Latin hypercube sample which is random or non-deterministic in nature is further integrated with the FD method to complete one cycle of LHS-FD simulation iteration. This process is repeated until [Formula: see text] final iterations of LHS-FD are obtained. The means of these [Formula: see text] final solutions (MLHFD solutions) are tabulated, graphed and analyzed. The numerical simulation results of MLHFD for the SEIR model are presented side-by-side with deterministic solutions obtained from the classical FD scheme and homotopy analysis method with Pade approximation (HAM-Pade). The present MLHFD results are also compared with the previous non-deterministic statistical estimations from 1995 to 2015. Good agreement between the two is perceived with small errors. MLHFD method can be used to predict future behavior, range and prediction interval for the epidemic model solutions. The expected profiles of the cocaine abuse subpopulations are projected until the year 2045. Both the statistical estimations and the deterministic results of FD and HAM-Pade are found to be within the MLHFD prediction intervals for all the years and for all the subpopulations considered.
In this study the most stable isobar for some isobaric families (light and intermediate ) nuclei with mass number (A) equals to (15-30) & (101- 115) have been determined. This determination of stable nuclide can help to determine the suitable nuclide, which can be used in different fields.
Most stable isobar can be determined by two means. First: plot mass parabolas (plotting the binding energy (B.E) as a function of the atomic number (Z)) for these isobaric families, in this method most stable isobars represent the lowest point in mass parabola (the nuclide with the highest value of binding energy).
Second: calculated the atomic number for most stable isobar (ZA) value.
Our results show that
... Show MoreA numerical study has been carried out to investigate heat transfer by natural convection and radiation under the effect of magnetohydrodynamic (MHD) for steady state axisymmetric twodimensional laminar flow in a vertical cylindrical channel filled with saturated porous media. Heat is generated uniformly along the center of the channel with its vertical surface remain with cooled constant wall temperature and insulated horizontal top and bottom surfaces. The governing equations which used are continuity, momentum and energy equations which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using the MATLAB-7 programming. The parameters affected on the system are Rayl
... Show MoreUnder-reamed piles defined by having one or more bulbs have the potential for sizeable major sides over conventional straight-sided piles, most of the studies on under-reamed piles have been conducted on the experimental side, while theoretical studies, such as the finite element method, have been mainly confined to conventional straight-sided piles. On the other hand, although several laboratory and experimental studies have been conducted to study the behavior of under-reamed piles, few numerical studies have been carried out to simulate the piles' performance. In addition, there is no research to compare and evaluate the behavior of these piles under dynamic loading. Therefore, this study aimed to numerically investigate bearing capaci
... Show MoreUnder-reamed piles are piles with enlarged bases, which may be single bulb or multi bulbs. Such piles are suitable for resisting considerable soil movement of filed up ground, soft clay, and loose sand and have the advantages of increasing the soil strength and decreasing the displacement. In the present study, the finite element method was used to analyse the performance of a single pile with under-reamed bulbs of different shapes, that is, single cone, double cone, and half and full sphere, embedded in homogeneous, poorly graded sandy soil. The model of under-reamed pile was made of reinforced concrete and the bulb located at the middle of the embedded length of the pile. The dynami
In this work, a joint quadrature for numerical solution of the double integral is presented. This method is based on combining two rules of the same precision level to form a higher level of precision. Numerical results of the present method with a lower level of precision are presented and compared with those performed by the existing high-precision Gauss-Legendre five-point rule in two variables, which has the same functional evaluation. The efficiency of the proposed method is justified with numerical examples. From an application point of view, the determination of the center of gravity is a special consideration for the present scheme. Convergence analysis is demonstrated to validate the current method.
One of the unique properties of laser heating applications is its powerful ability for precise pouring of energy on the needed regions in heat treatment applications. The rapid rise in temperature at the irradiated region produces a high temperature gradient, which contributes in phase metallurgical changes, inside the volume of the irradiated material. This article presents a comprehensive numerical work for a model based on experimentally laser heated AISI 1110 steel samples. The numerical investigation is based on the finite element method (FEM) taking in consideration the temperature dependent material properties to predict the temperature distribution within the irradiated material volume. The finite element analysis (FEA) was carried
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