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Free Boundary Determination in Nonlinear Diffusion
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Abstract<p>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 <italic>lsqnonlin</italic> routine from the MATLAB toolbox. Accurate and stable numerical solutions are achieved. For noisy data, instability is manifest in the derivative of the moving free surface, but not in the free surface itself nor in the concentration or temperature.</p>
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Publication Date
Thu May 03 2018
Journal Name
Online Journal Of Veterinary Research
Effect of Cutibacterium acnes cell free antigen (CFAg) immunization, levofloxacin and cinnamon oil on Cutibacterium acnes infection in rabbits
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Tuaimah 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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Publication Date
Wed Sep 01 2010
Journal Name
Al-khwarizmi Engineering Journal
Free Convection in an Inclined Concentric Annular Square Cavities Filled With Porous Medium and Heated By Non-Uniform Temperature
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A numerical study of the two-dimensional steady free convection flow in an inclined annulus between two concentric square cavities filled with a porous medium is presented in this paper for the case when the side outer walls are kept with differentially heated temperature while the horizontal outer walls and the inner walls are insulated. The heated wall is assumed to have spatial sinusoidal temperature variation about a constant mean value. The Darcy model is used and the fluid is assumed to be a standard Boussinesq fluid. For the Cartesian coordinate system, the governing equations which were used in stream function form are discretized by using the finite difference method with successive under – relaxation method (SUR) and are solv

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Publication Date
Mon Dec 01 2025
Journal Name
Journal Of Engineering
Experimental Evaluation of Free-Fall Gravity Drainage in Water-Drive Reservoirs: Impact of Aquifer Strength and Reservoir Heterogeneity/Homogeneity
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This study experimentally investigated Free-Fall Gravity Drainage (FFGD) under combination-drive conditions in a two-dimensional Hele-Shaw model representing a water-drive reservoir. An initially high gravity potential from the oil column enabled early oil drainage before aquifer support became dominant. Three water-drive strengths were tested, demonstrating that a stronger aquifer (1.15 psig) accelerated oil recovery to approximately 75% of the original oil in place (OOIP) within 60 minutes, resulting in a final recovery of 79.5%. However, this was accompanied by rapid water breakthrough after 2.5 minutes and high-water cuts exceeding 90%. In contrast, a weaker aquifer (0.725 psig) stabilized the oil–water contact, delaying w

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Publication Date
Mon Jun 30 2025
Journal Name
Iraqi Journal Of Science
Numerical Simulation of Double-Sided Lid-Driven Cavity Flow Using Moment-Based Boundary Conditions for The Lattice Boltzmann Method
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The present study considers to confirming the applicability of flow with double-sided square lid driven cavity flow by using the lattice Boltzmann equation with moment-based boundary conditions for no slip boundaries.  The boundary conditions are applied over the hydrodynamic moments of the lattice Boltzmann equations locally at each node. The investigation is carried out numerically for both single and multiple relaxation time models. To simulate two-sided lid driven-cavity flow, the top and bottom walls are moving with constant velocity while other walls are stationary. Various Reynolds numbers are used in a range of 100 and up to 5000. The present method shows the effect of the moving boundaries on the two symmetrical cavities t

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Publication Date
Thu Apr 04 2024
Journal Name
Journal Of Electrical Systems
AI-Driven Prediction of Average Per Capita GDP: Exploring Linear and Nonlinear Statistical Techniques
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Average per capita GDP income is an important economic indicator. Economists use this term to determine the amount of progress or decline in the country's economy. It is also used to determine the order of countries and compare them with each other. Average per capita GDP income was first studied using the Time Series (Box Jenkins method), and the second is linear and non-linear regression; these methods are the most important and most commonly used statistical methods for forecasting because they are flexible and accurate in practice. The comparison is made to determine the best method between the two methods mentioned above using specific statistical criteria. The research found that the best approach is to build a model for predi

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Publication Date
Sun Sep 01 2019
Journal Name
Baghdad Science Journal
An Analysis of a Partial Temporary Immunity SIR Epidemic Model with Nonlinear Treatment Rate
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     A partial temporary immunity SIR epidemic model involv nonlinear treatment rate is proposed and studied. The basic reproduction number  is determined. The local and global stability of all equilibria of the model are analyzed. The conditions for occurrence of local bifurcation in the proposed epidemic model are established. Finally, numerical simulation is used to confirm our obtained analytical results and specify the control set of parameters that affect the dynamics of the model.

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Publication Date
Thu Oct 20 2016
Journal Name
Sociological Methods &amp; Research
Mean Monte Carlo Finite Difference Method for Random Sampling of a Nonlinear Epidemic System
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In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to simulate values of the variable coefficients as random sampling instead being limited as real values with respect to time. The mean of the n final solutions via this integrated technique, named in short as mean Monte Carlo finite difference (MMCFD) method, represents the final solution of the system. This method is proposed for the first time to calculate the numerical solution obtained fo

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Publication Date
Mon Jan 01 2007
Journal Name
Saudi Medical Journal
Free testosterone, luteinizing hormone/follicle stimulating hormone ratio and pelvic sonography in relation to skin manifestations in patients with polycystic ovary syndrome
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KE Sharquie, AA Al-Bayatti, AI Al-Ajeel, AJ Al-Bahar, AA Al-Nuaimy, Saudi medical journal, 2007 - Cited by 63

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Publication Date
Fri Aug 02 2024
Journal Name
Quantum Studies: Mathematics And Foundations
Implementation of a modified noise-free and noisy multistage quantum cryptography protocol using QISKIT
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Classical cryptography systems exhibit major vulnerabilities because of the rapid development of quan tum computing algorithms and devices. These vulnerabilities were mitigated utilizing quantum key distribution (QKD), which is based on a quantum no-cloning algorithm that assures the safe generation and transmission of the encryption keys. A quantum computing platform, named Qiskit, was utilized by many recent researchers to analyze the security of several QKD protocols, such as BB84 and B92. In this paper, we demonstrate the simulation and implementation of a modified multistage QKD protocol by Qiskit. The simulation and implementation studies were based on the “local_qasm” simulator and the “FakeVigo” backend, respectively. T

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Publication Date
Tue May 01 2018
Journal Name
2018 2nd Ieee Advanced Information Management,communicates,electronic And Automation Control Conference (imcec)
Hybrid Regressor and Approximation-Based Adaptive Control of Robotic Manipulators with Contact-Free Motion
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