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.
Abstract:
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In order to understand the effect of (length of pile / diameter of pile) ratio on the load carrying capacity and settlement reduction behavior of piled raft resting on loose sand, laboratory model tests were conducted on small-scale models. The parameters studied were the effect of pile length and the number of piles. The load settlement behavior obtained from the tests has been validated by using 3-D finite element in ABAQUS program, was adopted to understand the load carrying response of piled raft and settlement reduction. The results of experimental work show that the increase in (Lp/dp) ratio led to increase in load carrying capacity by piled raft from (19.75 to 29.35%), (14.18 to 28.87%) and (0 to 16.49%) , the maximum load carried
... Show MoreMost studies on deep beams have been made with reinforced concrete deep beams, only a few studies investigate the response of prestressed deep beams, while, to the best of our knowledge, there is not a study that investigates the response of full scale (T-section) prestressed deep beams with large web openings. An experimental and numerical study was conducted in order to investigate the shear strength of ordinary reinforced and partially prestressed full scale (T-section) deep beams that contain large web openings in order to investigate the prestressing existence effects on the deep beam responses and to better understand the effects of prestressing locations and opening depth to beam depth ratio on the deep beam performance and b
... Show MoreIn order to understand the effect of (length of pile / diameter of pile) ratio on the load carrying capacity and settlement reduction behavior of piled raft resting on loose sand, laboratory model tests were conducted on small-scale models. The parameters studied were the effect of pile length and the number of piles. The load settlement behavior obtained from the tests has been validated by using 3-D finite element in ABAQUS program, was adopted to understand the load carrying response of piled raft and settlement reduction. The results of experimental work show that the increase in (Lp/dp) ratio led to increase in load carrying capacity by piled raft from (19.75 to 29.35%), (14.18 to 28.87%) and (0 to 16.49%) , the maximum load carr
... Show MoreThe research aims to find out the effect of Cognitive Acceleration strategy and random excitement strategy in achievement of geography material and developing the reflective thinking for students of literary fifth class .
the researcher depended a partial control experimental design with the three groups(the competence groups of the pre & post tests), The sample is deliberately selected from first AL-Rusafah Directorate General of Education in Baghdad. AL.fardoos Interme
... Show MoreIn this work, two different laser dye solutions were used to host highly-pure silicon nitride nanoparticles as scattering centers to fabricate random gain media. The laser dye was dissolved in three different solvents (ethanol, methanol and acetone) and the final results were obtained for methanol only. The silicon nitride nanoparticles were synthesized by dc reactive magnetron sputtering technique with average particle size of 35 nm. The random gain medium was made as a solid rod with high spectral efficiency and low production cost. Optical emission with narrow linewidth was detected at 532-534 nm as 9 mg of silicon nitride nanoparticles were added to the 10 -5 M dye solution. The FWHM of 0.3 and 3.52 nm was determined for Rhodamine B and
... Show MoreRecovery of time-dependent thermal conductivity has been numerically investigated. The problem of identification in one-dimensional heat equation from Cauchy boundary data and mass/energy specification has been considered. The inverse problem recasted as a nonlinear optimization problem. The regularized least-squares functional is minimised through lsqnonlin routine from MATLAB to retrieve the unknown coefficient. We investigate the stability and accuracy for numerical solution for two examples with various noise level and regularization parameter.
Thin films of CuPc of various thicknesses (150,300 and 450) nm have been deposited using pulsed laser deposition technique at room temperature. The study showed that the spectra of the optical absorption of the thin films of the CuPc are two bands of absorption one in the visible region at about 635 nm, referred to as Q-band, and the second in ultra-violet region where B-band is located at 330 nm. CuPc thin films were found to have direct band gap with values around (1.81 and 3.14 (eV respectively. The vibrational studies were carried out using Fourier transform infrared spectroscopy (FT-IR). Finally, From open and closed aperture Z-scan data non-linear absorption coefficient and non-linear refractive index have been calculated res
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