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 light of increasing demand for energy consumption due to life complexity and its requirements, which reflected on architecture in type and size, Environmental challenges have emerged in the need to reduce emissions and power consumption within the construction sector. Which urged designers to improve the environmental performance of buildings by adopting new design approaches, Invest digital technology to facilitate design decision-making, in short time, effort and cost. Which doesn’t stop at the limits of acceptable efficiency, but extends to the level of (the highest performance), which doesn’t provide by traditional approaches that adopted by researchers and local institutions in their studies and architectural practices, limit
... Show MoreIn practical engineering problems, uncertainty exists not only in external excitations but also in structural parameters. This study investigates the influence of structural geometry, elastic modulus, mass density, and section dimension uncertainty on the stochastic earthquake response of portal frames subjected to random ground motions. The North-South component of the El Centro earthquake in 1940 in California is selected as the ground excitation. Using the power spectral density function, the two-dimensional finite element model of the portal frame’s base motion is modified to account for random ground motions. A probabilistic study of the portal frame structure using stochastic finite elements utilizing Monte Carlo simulation
... Show MoreThe gas-lift method is crucial for maintaining oil production, particularly from an established field when the natural energy of the reservoirs is depleted. To maximize oil production, a major field's gas injection rate must be distributed as efficiently as possible across its gas-lift network system. Common gas-lift optimization techniques may lose their effectiveness and become unable to replicate the gas-lift optimum in a large network system due to problems with multi-objective, multi-constrained & restricted gas injection rate distribution. The main objective of the research is to determine the possibility of using the genetic algorithm (GA) technique to achieve the optimum distribution for the continuous gas-lift injectio
... Show MoreThe present theoretical study analyzes the legacy of the Chicago School of Urban Sociology and evaluates it in the light of the growth and development of Chicago City and the establishment of sociology in it. Sociology has become an academic discipline recognized in the United States of America in the late nineteenth century, particularly, after the establishment of the first department of sociology in the University of Chicago in 1892. That was during the period of the rapid industrialization and sustainable growth of the Chicago City. The Chicago School relied on Chicago City in particular, as one of the American cities that grew and expanded rapidly in the first two decades of the twentieth century. At the end of the nineteenth centur
... Show MoreIn an earlier paper, the basic analytical formula for particle-hole nuclear state densities was derived for non-Equidistant Spacing Model (non-ESM) approach. In this paper, an extension of the former equation was made to include pairing. Also a suggestion was made to derive the exact formula for the particle-hole state densities that depends exactly on Fermi energy and nuclear binding energies. The results indicated that the effects of pairing reduce the state density values, with similar dependence in the ESM system but with less strength. The results of the suggested exact formula indicated some modification from earlier non-ESM approximate treatment, on the cost of more calculation time
In this research a theoretical study has been carried out on the behavior and strength of simply supported composite beams strengthened by steel cover plate taking into consideration partial interaction of shear connectors and nonlinear behavior of the materials and shear connectors. Following the procedure that already has been adopted by Johnson (1975), the basic differential equations of equilibrium and compatibility were reduced to single differential equation in terms of interface slip between concrete slab and steel beam. Furthermore, in order to consider the nonlinear behavior of steel, concrete and shear connectors, the basic equation was rearranged so that all terms related to materials are isol
... Show MoreIn the present study, free convection heat and mass transfer of fluid in a square packed bed enclosure is numerically investigated. For the considered geometrical shape, the left vertical wall of enclosure was assumed to be kept at high temperature and concentration while the opposite wall was kept at low temperature and concentration with insulating both the top and bottom walls of enclosure. The Brinkman– Forchheimer extended Darcy model was used to solve the momentum equations, while the energy equations for fluid and solid phases were solved by using the local thermal non-equilibrium (LTNE) model.Computations are performed for a range of the Darcy number from 10-5 to 10-1, the porosity from 0.5 to 0.9, and buoyancy ratio from -15 t
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