This paper is concerned with finding solutions to free-boundary inverse coefficient problems. Mathematically, we handle a one-dimensional non-homogeneous heat equation subject to initial and boundary conditions as well as non-localized integral observations of zeroth and first-order heat momentum. The direct problem is solved for the temperature distribution and the non-localized integral measurements using the Crank–Nicolson finite difference method. The inverse problem is solved by simultaneously finding the temperature distribution, the time-dependent free-boundary function indicating the location of the moving interface, and the time-wise thermal diffusivity or advection velocities. We reformulate the inverse problem as a non-linear optimization problem and use the lsqnonlin non-linear least-square solver from the MATLAB optimization toolbox. Through examples and discussions, we determine the optimal values of the regulation parameters to ensure accurate, convergent, and stable reconstructions. The direct problem is well-posed, and the Crank–Nicolson method provides accurate solutions with relative errors below 0.006% when the discretization elements are M=N=80. The accuracy of the forward solutions helps to obtain sensible solutions for the inverse problem. Although the inverse problem is ill-posed, we determine the optimal regularization parameter values to obtain satisfactory solutions. We also investigate the existence of inverse solutions to the considered problems and verify their uniqueness based on established definitions and theorems.
The physical, the thermal and the mechanical properties of Nano-composites, that consisted of Polyprime EP epoxy that reinforced by multi-walled carbon nanotubes (MWCNTs), have been studied. Various loading ratios, 0.1, 0.5, and 1 wt. %of MWCNT shave been infused into epoxy by a magnetic stirrer and then the hardener mixed with the mthat supplied with the epoxy. All sample shave been cutting using CNC machine. Tensile test, three-point bending, hardness tests, lee's disk, differential scanning calorimetry, water absorption and dielectric and electrical conductivity test were utilized on unfilled, MWCNT-filled epoxy to identify the loading effect on the properties of materials. Scanning electron microscopy (SEM) was used to determine the
... Show MoreThe Assignment model is a mathematical model that aims to express a real problem facing factories and companies which is characterized by the guarantee of its activity in order to make the appropriate decision to get the best allocation of machines or jobs or workers on machines in order to increase efficiency or profits to the highest possible level or reduce costs or time To the extent possible, and in this research has been using the method of labeling to solve the problem of the fuzzy assignment of real data has been approved by the tire factory Diwaniya, where the data included two factors are the factors of efficiency and cost, and was solved manually by a number of iterations until reaching the optimization solution,
... Show MoreThis article proposes a new strategy based on a hybrid method that combines the gravitational search algorithm (GSA) with the bat algorithm (BAT) to solve a single-objective optimization problem. It first runs GSA, followed by BAT as the second step. The proposed approach relies on a parameter between 0 and 1 to address the problem of falling into local research because the lack of a local search mechanism increases intensity search, whereas diversity remains high and easily falls into the local optimum. The improvement is equivalent to the speed of the original BAT. Access speed is increased for the best solution. All solutions in the population are updated before the end of the operation of the proposed algorithm. The diversification f
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Photorefractive keratectomy (PRK) is the refractive technique that began with a physical scraping of the epithelial layer of cornea subsequent by laser treatment. Post this procedure to about 48 hours the removed epithelial layer regenerated to protect the eye again. The regeneration process (called re-epithelization) started from the limbus of the cornea toward the central part of it. The re-epithelization mechanism consists of a change in cell density (mitosis) and cell concentration (migration) with a velocity in two directions: radial and tangential. In the present study, an estimation for both radial (responsible for the overlapped layers toward the outward direction of the cornea) and tangential comp
... Show MoreDegenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied mathematical models arising in porous media, population dynamics, financial mathematics, etc. With this new challenge in mind, this paper considers investigating newly formulated direct and inverse problems associated with non-uniform parabolic PDEs where the leading space- and time-dependent coefficient is allowed to vanish on a non-empty, but zero measure, kernel set. In the context of inverse analysis, we consider the linear but ill-pose
In this study, silver nanoparticles (AgNPs) were synthesized using a cold plasma technique and a plasma jet. They were then used to explore how photothermal treatment may be used to treat lung cancer (A549) and normal cells (REF) <i>in vitro</i>. The anti-proliferative activity of these nanoparticles was studied after A549 cells were treated with (AgNPs) at various concentrations (100%, 50%, or 25%) and exposure times (6 or 8 min) of laser after 1 h or 24 h from exposed AgNPs. The highest growth inhibition for cancer cells is (75%) at (AgNPs) concentration (100%) and the period of exposure to the laser is (8 min). Particle size for the prepared samples varied according to the diameter o
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