Free boundary problems with nonlinear diffusion occur in various applications, such as solidification over a mould with dissimilar nonlinear thermal properties and saturated or unsaturated absorption in the soil beneath a pond. In this article, we consider a novel inverse problem where a free boundary is determined from the mass/energy specification in a well-posed one-dimensional nonlinear diffusion problem, and a stability estimate is established. The problem is recast as a nonlinear least-squares minimisation problem, which is solved numerically using the
In this paper, the methods of weighted residuals: Collocation Method (CM), Least Squares Method (LSM) and Galerkin Method (GM) are used to solve the thin film flow (TFF) equation. The weighted residual methods were implemented to get an approximate solution to the TFF equation. The accuracy of the obtained results is checked by calculating the maximum error remainder functions (MER). Moreover, the outcomes were examined in comparison with the 4th-order Runge-Kutta method (RK4) and good agreements have been achieved. All the evaluations have been successfully implemented by using the computer system Mathematica®10.
Abstract
In this paper, the solutions to class of robust non-linear semi-explicit descriptor control systems with matching condition via optimal control strategy are obtained. The optimal control strategy has been introduced and developed in the sense that, the optimal control solution is robust solution to the given non-linear uncertain semi-explicit descriptor control system. The necessary mathematical proofs and remarks as well as discussions are also proposed. The present approach is step-by-step illustrated by application example to show its effectiveness a and efficiency to compensate the structure uncertainty in the given semi-explicit (descriptor) control
... Show MoreSome nonlinear differential equations with fractional order are evaluated using a novel approach, the Sumudu and Adomian Decomposition Technique (STADM). To get the results of the given model, the Sumudu transformation and iterative technique are employed. The suggested method has an advantage over alternative strategies in that it does not require additional resources or calculations. This approach works well, is easy to use, and yields good results. Besides, the solution graphs are plotted using MATLAB software. Also, the true solution of the fractional Newell-Whitehead equation is shown together with the approximate solutions of STADM. The results showed our approach is a great, reliable, and easy method to deal with specific problems in
... Show MoreColloidal crystals (opals) made of close-packed polymethylmethacrylate (PMMA) were fabricated and grown by Template-Directed methods to obtain porous materials with well-ordered periodicity and interconnected pore systems to manufacture photonic crystals. Opals were made from aqueous suspensions of monodisperse PMMA spheres with diameters between 280 and 415 nm. SEM confirmed the PMMA spheres crystallized uniformly in a face-centered cubic (FCC) array. Optical properties of synthesized pores PMMA were characterized by UV–Visible spectroscopy. It shows that the colloidal crystals possess pseudo photonic band gaps in the visible region. A combination of Bragg’s law of diffraction and Snell’s law of refraction were used to calculate t
... Show MoreThe objective of this study is to determination the content of some heavy metals (lead, cadmium, chromium) in colored tattoo stickers. twelve kinds of colored tattoo stikcers were collected from Baghdad markets, it was estimated heavy metals using atomic absorption spectrophotometer (Shimadzu A5000). The results indicated the concentrations of lead in all samples (1.61_1.00 mg / kg) and chromium in the three samples (0.85_0.97 mg / kg) while other samples are free of chromium , and cadmium. These elements are the components of printing inks and dyes in tattoo stickers, and this does not conform to the health and safety conditions for the packaging of food according to the organizations of the health and safety of
... Show MoreTuaimah GS, AQ Al-Awadi, Ahmed ME., Effect of Cutibacterium acnes cell free antigen (CFAg) immunization, levofloxacin and cinnamon oil on Cutibacterium acnes infection in rabbits, Onl J Vet Res., 22 (9):811-822, 2018. C. acnes causes acne vulgaris most commonly in 12-24 year olds. Five albino rabbits were immunized at day 1 and 14 with Cutibacterium acnes cell free antigen (CFAg) and then infected intradermally with 0.1 ml C. acnes suspension (2×108 cfu/ml) at day 30. Two groups of five infected rabbits were then treated at Day 30 with 0.5% levofloxacin or 0.2% cinnamon oil twice daily for 12 days. Five control rabbits were infected intradermally with 0.1 ml 2×108 cfu/ml Cutibacterium acnes n (2×108 cfu/ml). At day 42, skin test (mm), se
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