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.
This study illustrates the impact of non-thermal plasma (Cold Atmospheric Plasma CAP) on the lipids blood, the study in vivo. The lipids are (cholesterol, HDL-Cholesterol, LDL-Cholesterol and triglyceride) are tested. (FE-DBD) scheme of probe diameter 4cm is used for this purpose, and the output voltage ranged from (0-20) kV with variable frequency (0-30) kHz. The effect of non-thermal atmospheric plasma on lipids were studied with different exposure durations (20,30) sec. As a result, the longer plasma exposure duration decreases more lipids in blood.
Double-layer micro-perforated panels (MPPs) have been studied extensively as sound absorption systems to increase the absorption performance of single-layer MPPs. However, existing proposed models indicate that there is still room for improvement regarding the frequency bands of absorption for the double-layer MPP. This study presents a double-layer MPP formed with two single MPPs with inhomogeneous perforation backed by multiple cavities of varying depths. The theoretical formulation is developed using the electrical equivalent circuit method to calculate the absorption coefficient under a normal incident sound. The simulation results show that the proposed model can produce absorption coefficient with wider absorption bandwidth compared w
... Show MoreIn this work, an explicit formula for a class of Bi-Bazilevic univalent functions involving differential operator is given, as well as the determination of upper bounds for the general Taylor-Maclaurin coefficient of a functions belong to this class, are established Faber polynomials are used as a coordinated system to study the geometry of the manifold of coefficients for these functions. Also determining bounds for the first two coefficients of such functions.
In certain cases, our initial estimates improve some of the coefficient bounds and link them to earlier thoughtful results that are published earlier.
In this article, the nonlinear problem of Jeffery-Hamel flow has been solved analytically and numerically by using reliable iterative and numerical methods. The approximate solutions obtained by using the Daftardar-Jafari method namely (DJM), Temimi-Ansari method namely (TAM) and Banach contraction method namely (BCM). The obtained solutions are discussed numerically, in comparison with other numerical solutions obtained from the fourth order Runge-Kutta (RK4), Euler and previous analytic methods available in literature. In addition, the convergence of the proposed methods is given based on the Banach fixed point theorem. The results reveal that the presented methods are reliable, effective and applicable to solve other nonlinear problems.
... Show MoreIn this paper, a computational method for solving optimal problem is presented, using indirect method (spectral methodtechnique) which is based on Boubaker polynomial. By this method the state and the adjoint variables are approximated by Boubaker polynomial with unknown coefficients, thus an optimal control problem is transformed to algebraic equations which can be solved easily, and then the numerical value of the performance index is obtained. Also the operational matrices of differentiation and integration have been deduced for the same polynomial to help solving the problems easier. A numerical example was given to show the applicability and efficiency of the method. Some characteristics of this polynomial which can be used for solvin
... Show MoreIn this paper we will investigate some Heuristic methods to solve travelling salesman problem. The discussed methods are Minimizing Distance Method (MDM), Branch and Bound Method (BABM), Tree Type Heuristic Method (TTHM) and Greedy Method (GRM).
The weak points of MDM are manipulated in this paper. The Improved MDM (IMDM) gives better results than classical MDM, and other discussed methods, while the GRM gives best time for 5≤ n ≤500, where n is the number of visited cities.
Given the importance of increasing economic openness transport companies’ face various issues arising at present time, this required importing different types of goods with different means of transport. Therefore, these companies pay great attention to reducing total costs of transporting commodities by using numbers means of transport methods from their sources to the destinations. The majority of private companies do not acquire the knowledge of using operations research methods, especially transport models, through which the total costs can be reduced, resulting in the importance and need to solve such a problem. This research presents a proposed method for the sum of Total Costs (Tc) of rows and columns, in order to arrive at the init
... Show MoreTransport is a problem and one of the most important mathematical methods that help in making the right decision for the transfer of goods from sources of supply to demand centers and the lowest possible costs, In this research, the mathematical model of the three-dimensional transport problem in which the transport of goods is not homogeneous was constructed. The simplex programming method was used to solve the problem of transporting the three food products (rice, oil, paste) from warehouses to the student areas in Baghdad, This model proved its efficiency in reducing the total transport costs of the three products. After the model was solved in (Winqsb) program, the results showed that the total cost of transportation is (269,
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