Search results for: the uniqueness of solutions of PDE equations

Authors: James Skon, Irina Beshentseva, Michelle Polak

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Wifi solutions come in two major classes. Small Office/Home Office (SOHO) WiFi, characterized by inexpensive WiFi routers, with one or two service set identifiers (SSIDs), and a single shared passphrase. These access points provide no significant user management or monitoring, and no aggregation of monitoring and control for multiple routers. The other solution class is managed enterprise WiFi solutions, which involve expensive Access Points (APs), along with (also costly) local or cloud based management components. These solutions typically provide portal based login, per user virtual local area networks (VLANs), and sophisticated monitoring and control across a large group of APs. The cost for deploying and managing such managed enterprise solutions is typically about 10 fold that of inexpensive consumer APs. Low revenue organizations, such as schools, non-profits, non-government organizations (NGO's), small businesses, and even homes cannot easily afford quality enterprise WiFi solutions, though they may need to provide quality WiFi access to their population. Using available lower cost Wifi solutions can significantly reduce their ability to provide reliable, secure network access. This project explored and created a new approach for providing secured managed enterprise WiFi based on low cost hardware combined with both new and existing (but modified) open source software. The solution provides a cloud based management interface which allows organizations to aggregate the configuration and management of small, medium and large WiFi solutions. It utilizes a novel approach for user management, giving each user a unique passphrase. It provides unlimited SSID's across an unlimited number of WiFI zones, and the ability to place each user (and all their devices) on their own VLAN. With proper configuration it can even provide user local services. It also allows for users' usage and quality of service to be monitored, and for users to be added, enabled, and disabled at will. As inferred above, the ultimate goal is to free organizations with limited resources from the expense of a commercial enterprise WiFi, while providing them with most of the qualities of such a more expensive managed solution at a fraction of the cost.

Keywords: wifi, enterprise, cloud, managed

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Authors: A. Khernane, N. Khelil, L. Djerou

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The aim of this work is to study the numerical implementation of the Hilbert uniqueness method for the exact boundary controllability of Euler-Bernoulli beam equation. This study may be difficult. This will depend on the problem under consideration (geometry, control, and dimension) and the numerical method used. Knowledge of the asymptotic behaviour of the control governing the system at time T may be useful for its calculation. This idea will be developed in this study. We have characterized as a first step the solution by a minimization principle and proposed secondly a method for its resolution to approximate the control steering the considered system to rest at time T.

Keywords: boundary control, exact controllability, finite difference methods, functional optimization

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Authors: D. Pradeep Mitra, Prafulla

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Looking to the word propellant-less system it makes us to believe that it is an impossible one, but this paper demonstrates the use of microwaves to create a system which makes impossible to be possible, it means a propellant-less propulsion system using microwaves. In these thrusters, microwaves are radiated into a sealed parabolic cavity through a waveguide, which act on the surface of the cavity and follow the axis of the thrusters to produce thrust. The advantages of these thrusters are: (1) Producing thrust without propellant; without erosion, wear, and thermal stress from the hot exhaust gas; and at the same time increasing quality. (2) If the microwave output power is stable, the performance of thrusters is not affected by its working environment. This paper is demonstrated from general maxwell equations. These equations are used to create the mathematical model of the thrusters. These mathematical model helps us to calculate the Q factor and calculate the approximate thrust which would be generated in the system.

Keywords: propellant less, microwaves, parabolic wave guide, propulsion system

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Authors: Francesco Marotti de Sciarra, Raffaele Barretta

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Starting from nonlocal continuum mechanics, a thermodynamically new nonlocal model of Euler-Bernoulli nanobeams is provided. The nonlocal variational formulation is consistently provided and the governing differential equation for transverse displacement are presented. Higher-order boundary conditions are then consistently derived. An example is contributed in order to show the effectiveness of the proposed model.

Keywords: Bernoulli-Euler beams, nanobeams, nonlocal elasticity, closed-form solutions

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Authors: Shyh Ming Chern

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Cubic equations of state (EoS), popular due to their simple mathematical form, ease of use, semi-theoretical nature and, reasonable accuracy are normally fitted to vapor-liquid equilibrium P-v-T data. As a result, They often show poor accuracy in the region near and above the critical point. In this study, the performance of the renowned Peng-Robinson (PR) and Patel-Teja (PT) EoS’s around the critical area has been examined against the P-v-T data of water. Both of them display large deviations at critical point. For instance, PR-EoS exhibits discrepancies as high as 47% for the specific volume, 28% for the enthalpy departure and 43% for the entropy departure at critical point. It is shown that incorporating P-v-T data of the supercritical region into the retuning of a cubic EoS can improve its performance above the critical point dramatically. Adopting a retuned acentric factor of 0.5491 instead of its genuine value of 0.344 for water in PR-EoS and a new F of 0.8854 instead of its original value of 0.6898 for water in PT-EoS reduces the discrepancies to about one third or less.

Keywords: equation of state, EoS, supercritical water, SCW

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Authors: Ahmad K. Samaila, Basant K. Jha

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This study is devoted to investigate the effect of transpiration on transient as well as steady-state natural convection flow of a reactive viscous fluid in a vertical channel formed by two infinite vertical parallel porous plates. The Boussinesq assumption is applied and the nonlinear governing equations of energy and momentum are developed. The problem is solved numerically using implicit finite difference method and analytically for steady-state case using perturbation method. Solutions are presented in graphical form for fluid temperature, velocity, and skin-friction and wall heat transfer rate for various parametric values. It is found that velocity, temperature, rate of heat transfer as well as skin-friction are strongly affected by mass leakage through the porous plates.

Keywords: transpiration, reactive viscous fluid, porous plates, natural convection, suction/injection

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Authors: Benedict Barnes, Anthony Y. Aidoo

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A Divergence Regularization Method (DRM) is used to regularize the ill-posed Helmholtz equation where the boundary deflection is inhomogeneous in a Hilbert space H. The DRM incorporates a positive integer scaler which homogenizes the inhomogeneous boundary deflection in Cauchy problem of the Helmholtz equation. This ensures the existence, as well as, uniqueness of solution for the equation. The DRM restores all the three conditions of well-posedness in the sense of Hadamard.

Keywords: divergence regularization method, Helmholtz equation, ill-posed inhomogeneous Cauchy boundary conditions

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Authors: Ali Heidari, Hany Saleem

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The tailwater requirements are important criteria in the design of the stilling basins as energy dissipation of the spillways. The adequate tailwater level that ensures the hydraulic jump inside the basin should be fulfilled by the river's natural water level and the apron depth downstream of the chute. The requirements of the hydraulic jump should mainly be checked for the design flood, however, the drawn jump condition should not be critical in the discharges lesser than the design flood. The tailwater requirement is not met in Almatti dam, built in 2005 in India, and the jump sweep out from the basin, resulting in significant scour in the apron and end sill of the basin. This paper discusses different hydraulic solutions as sustainable solutions for the rehabilitation program. The deep apron alternative is proposed for the fewer bays of the spillway as the most cost-effective, sustainable solution. The apron level of 15 gates out of 26 gates should decrease by 5.4 m compared to the existing design to ensure a safe hydraulic jump up to the discharge of 10,000 m3/s i.e. 30% of the updated PMF.

Keywords: dam, spillway, stilling basin, Almatti

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Authors: Gaurav Kumar Sinha

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As the world grapples with climate challenges, this study highlights the instrumental role of AWS services in amplifying the impact of LCVs. Their ability to harness the cloud, data analytics, and scalable infrastructure offered by AWS empowers LCVs to innovate, scale, and drive meaningful change in the quest for a sustainable future. This study serves as a rallying cry, urging stakeholders to recognize, embrace, and maximize the potential of AWS-powered solutions in advancing sustainable and resilient global initiatives.

Keywords: low carbon ventures, sustainability solutions, AWS services, data analytics

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Authors: Abdulatif Abdusalam, Mohamed Shaban

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In this paper, we consider the nonlinear pulse propagation through a nonuniform birefringent fiber Bragg grating (FBG) whose index modulation depth varies along the propagation direction. Here, the pulse propagation is governed by the nonlinear birefringent coupled mode (NLBCM) equations. To form the Bragg soliton outside the photonic bandgap (PBG), the NLBCM equations are reduced to the well known NLS type equation by multiple scale analysis. As we consider the pulse propagation in a nonuniform FBG, the pulse propagation outside the PBG is governed by inhomogeneous NLS (INLS) rather than NLS. We, then, discuss the formation of soliton in the FBG known as Bragg soliton whose central frequency lies outside but close to the PBG of the grating structure. Further, we discuss Bragg soliton compression due to a delicate balance between the SPM and the varying grating induced dispersion. In addition, Bragg soliton collision, Bragg soliton switching and possible logic gates have also been discussed.

Keywords: Bragg grating, non uniform fiber, non linear pulse

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Authors: M. O. Olayiwola

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Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

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Authors: S. S. P. M. Isa, N. M. Arifin, R. Nazar, N. Bachok, F. M. Ali, I. Pop

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A theoretical study has been presented to describe the boundary layer flow and heat transfer on an exponentially shrinking sheet with a variable wall temperature and suction, in the presence of magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically using the shooting method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented through graphs and tables for several sets of values of the parameters. The effects of the governing parameters on the flow and heat transfer characteristics are thoroughly examined.

Keywords: exponentially shrinking sheet, magnetic field, mixed convection, suction

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Authors: Kanita Beširević

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Open-source software development activities highly rely on Internet gathering communities volunteering in software development projects. Additionally, the libraries and cultural institutions share their metadata in the form of linked metadata to enable dissemination and enrichment. The open-source software provides free alternatives to traditional software solutions. The article aims to investigate the ever-increasing options for the digital library open source software adoption. The software available is presented and compared to other software solutions as well as to their previous versions. The top three open-source digital library software solutions are presented and compared. The comparison criteria are adopted from the UNESCO study by Bankier, J., & Gleason, K. Institutional Repository Software Comparison comprising of twelve criteria to appraise software, namely: infrastructure, front-end design, content discovery, publication tools, interoperability, and preservation. This article adopts a descriptive methodology based on data and information collected through selected software websites and the literature review.

Keywords: open source software, digital library, DSpace, Fedora, Greenstone

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Authors: Godwin Makaudze

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The majority of women in contemporary Zimbabwe continue to hold marginalised and insignificant positions in society and to be accorded negative and stereotyped images in literature. In light of this, government and civic organisations and even writers channel many resources, time, and efforts towards the emancipation of the female gender. Using the Africana womanist and socio-historical literary theories and focussing on two post-colonial novels, this paper re-engages the dis-empowerment of women in contemporary Zimbabwe, examining the believed causes and suggested solutions. The paper observes that the writers whip the already whipped by blaming patriarchy, African men and cultural practices as the underlying causes of such a sorry state of affairs while at the same time celebrating war against all these, as well as education, unity among women, Christianity and single motherhood as panaceas to the problem. The paper concludes that the writers’ anger is misdirected as they have fallen trap to the very popular yet mythical victim-blame motif espoused by many writers who focus on Shona people’s problems.

Keywords: cultural practices, female dis-empowerment, patriarchy, Shona novel, solutions, Zimbabwe

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Authors: A. Belay, B. Kebede

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The concentration- and temperature-dependent refractive indices of solutions extracted from defective and non-defective coffee beans have been investigated using a He–Ne laser. The refractive index has a linear relationship with the presumed concentration of the coffee solutions in the range of 0.5–3%. Higher and lower values of refractive index were obtained for immature and non-defective coffee beans, respectively. The Refractive index of bean extracts can be successfully used to separate defective from non-defective beans.

Keywords: coffee extract, refractive index, temperature dependence

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Authors: Paolo Russu

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This paper investigates the economic and ecological dynamics that emerge in Protected Areas (PAs) due to interactions between visitors and the animals that live there. The PAs contain two species whose interactions are determined by the Lotka-Volterra equations system. Visitors' decisions to visit PAs are influenced by the entrance cost required to enter the park and the chance of witnessing the species living there. Visitors have contradictory effects on the species and thus on the sustainability of the protected areas: on the one hand, an increase in the number of tourists damages the natural habitat of the regions and thus the species living there; on the other hand, it increases the total amount of entrance fees that the managing body of the PAs can use to perform defensive expenditures that protect the species from extinction. For a given set of parameter values, saddle-node bifurcation, Hopf bifurcation, homoclinic orbits, and a Bogdanov–Takens bifurcation of codimension two has been investigated. The system displays periodic doubling and chaotic solutions, as numerical examples demonstrate. Pontryagin's Maximum Principle was utilised to develop an optimal admission charge policy that maximised social gain and ecosystem conservation.

Keywords: chaos, bifurcation points, dynamical model, optimal control

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Authors: Tomáš Bublík, Miroslav Virius

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This paper presents general results on the Java source code snippet detection problem. We propose the tool which uses graph and sub graph isomorphism detection. A number of solutions for all of these tasks have been proposed in the literature. However, although that all these solutions are really fast, they compare just the constant static trees. Our solution offers to enter an input sample dynamically with the Scripthon language while preserving an acceptable speed. We used several optimizations to achieve very low number of comparisons during the matching algorithm.

Keywords: AST, Java, tree matching, scripthon source code recognition

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Authors: Shao-Yuan Huang

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We study the shape of the bifurcation curve of positive solutions for the semipositone problem with the Minkowski-curvature operator. The Minkowski-curvature problem plays an important role in certain fundamental issues in differential geometry and in the special theory of relativity. In addition, it is well known that studying the multiplicity of positive solutions is equivalent to studying the shape of the bifurcation curve. By the shape of the bifurcation curve, we can understand the change in the multiplicity of positive solutions with varying parameters. In this paper, our main technique is a time-map method used in Corsato's PhD Thesis. By this method, studying the shape of the bifurcation curve is equivalent to studying the shape of a certain function T with improper integral. Generally speaking, it is difficult to study the shape of T. So, in this paper, we consider two cases that the nonlinearity is convex or concave. Thus we obtain the following results: (i) If f''(u) < 0 for u > 0, then the bifurcation curve is C-shaped. (ii) If f''(u) > 0 for u > 0, then there exists η>β such that the bifurcation curve does not exist for 0 η. Furthermore, we prove that the bifurcation is C-shaped for L > η under a certain condition.

Keywords: bifurcation curve, Minkowski-curvature problem, positive solution, time-map method

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Authors: Abdulai Abubakari

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The rollercoaster relationship between farmers and herders in Sub-Saharan Africa has compelled most governments to undertake different mitigating strategies. Over the past two decades, the expulsion of migrant herdsmen, the killing of cattle and human beings, and fines have been used by the state and aggrieved individuals to resolve the conflicts. Unlike this paper, most of the research conducted on this subject matter has been largely theoretical and lacks practical solutions to the conflicts. This paper is unique because it focuses on concrete strategies and practical solutions to ending the century-old phenomenon of farmer-herder conflicts in Ghana. The paper employed power or compete (fight) theory as well as compromise and negotiation theories in the analyses. The paper employed, basically, socio-anthropological methods: interviews, focus group discussions, and observations to gather data. The paper found that compromises through negotiation with the stakeholders are the best ways of resolving these conflicts. Through this, we support the compromise and negotiation approach rather than expulsion to resolve farmer-herder conflicts.

Keywords: farmer-herder, conflict, prevention, strategies, stakeholders

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Authors: Felipe Azocar Simonet, Luis Acosta Espejo

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In this article, we will try to find an efficient boundary approximation for the bi-objective location problem with coherent coverage for two levels of hierarchy (CCLP). We present the mathematical formulation of the model used. Supported efficient solutions and unsupported efficient solutions are obtained by solving the bi-objective combinatorial problem through the weights method using a Lagrangean heuristic. Subsequently, the results are validated through the DEA analysis with the GEM index (Global efficiency measurement).

Keywords: coherent covering location problem, efficient frontier, lagragian relaxation, data envelopment analysis

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Authors: Tahir Nawaz Cheema, Dumitru Baleanu, Ali Raza

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In this research work, we design intelligent computing through Bayesian Regularization artificial neural networks (BRANNs) introduced to solve the mathematical modeling of infectious diseases (Covid-19). The dynamical transmission is due to the interaction of people and its mathematical representation based on the system's nonlinear differential equations. The generation of the dataset of the Covid-19 model is exploited by the power of the explicit Runge Kutta method for different countries of the world like India, Pakistan, Italy, and many more. The generated dataset is approximately used for training, testing, and validation processes for every frequent update in Bayesian Regularization backpropagation for numerical behavior of the dynamics of the Covid-19 model. The performance and effectiveness of designed methodology BRANNs are checked through mean squared error, error histograms, numerical solutions, absolute error, and regression analysis.

Keywords: mathematical models, beysian regularization, bayesian-regularization backpropagation networks, regression analysis, numerical computing

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Authors: Mounir Adal, Baalal Azeddine, Afifi Moulay Larbi

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Numerical analysis is a branch of mathematics devoted to the development of iterative matrix calculation techniques. We are searching for operations optimization as objective to calculate and solve systems of equations of order n with time and energy saving for computers that are conducted to calculate and analyze big data by solving matrix equations. Furthermore, this scientific discipline is producing results with a margin of error of approximation called rates. Thus, the results obtained from the numerical analysis techniques that are held on computer software such as MATLAB or Simulink offers a preliminary diagnosis of the situation of the environment or space targets. By this we can offer technical procedures needed for engineering or scientific studies exploitable by engineers for water.

Keywords: numerical analysis methods, obstacles solving, engineering, simulation, numerical modeling, iteration, computer, MATLAB, water, underground, velocity

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Authors: Madhu Aneja, Sapna Sharma

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The water-based bioconvection of a nanofluid containing motile gyrotactic micro-organisms over nonlinear inclined stretching sheet has been investigated. The governing nonlinear boundary layer equations of the model are reduced to a system of ordinary differential equations via Oberbeck-Boussinesq approximation and similarity transformations. Further, the modified set of equations with associated boundary conditions are solved using Finite Element Method. The impact of various pertinent parameters on the velocity, temperature, nanoparticles concentration, density of motile micro-organisms profiles are obtained and analyzed in details. The results show that with the increase in angle of inclination δ, velocity decreases while temperature, nanoparticles concentration, a density of motile micro-organisms increases. Additionally, the skin friction coefficient, Nusselt number, Sherwood number, density number are computed for various thermophysical parameters. It is noticed that increasing Brownian motion and thermophoresis parameter leads to an increase in temperature of fluid which results in a reduction in Nusselt number. On the contrary, Sherwood number rises with an increase in Brownian motion and thermophoresis parameter. The findings have been validated by comparing the results of special cases with existing studies.

Keywords: bioconvection, finite element method, gyrotactic micro-organisms, inclined stretching sheet, nanofluid

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Authors: Teh Raihana Nazirah Roslan, Siti Zulaiha Ibrahim, Sharmila Karim

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A warrant is a financial contract that confers the right but not the obligation, to buy or sell a security at a certain price before expiration. The standard procedure to value equity warrants using call option pricing models such as the Black–Scholes model had been proven to contain many flaws, such as the assumption of constant interest rate and constant volatility. In fact, existing alternative models were found focusing more on demonstrating techniques for pricing, rather than empirical testing. Therefore, a mathematical model for pricing and analyzing equity warrants which comprises stochastic interest rate and stochastic volatility is essential to incorporate the dynamic relationships between the identified variables and illustrate the real market. Here, the aim is to develop dynamic pricing formulations for hybrid equity warrants by incorporating stochastic interest rates from the Cox-Ingersoll-Ross (CIR) model, along with stochastic volatility from the Heston model. The development of the model involves the derivations of stochastic differential equations that govern the model dynamics. The resulting equations which involve Cauchy problem and heat equations are then solved using partial differential equation approaches. The analytical pricing formulas obtained in this study comply with the form of analytical expressions embedded in the Black-Scholes model and other existing pricing models for equity warrants. This facilitates the practicality of this proposed formula for comparison purposes and further empirical study.

Keywords: Cox-Ingersoll-Ross model, equity warrants, Heston model, hybrid models, stochastic

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Authors: Krzysztof Pomorski

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In the given work we present universal mathematical framework for modeling of cattle farm system that can set and validate various hypothesis that can be tested against experimental data. The presented work is preliminary but it is expected to be valid tool for future deeper analysis that can result in new class of prediction methods allowing early detection of cow dieseaes as well as cow performance. Therefore the presented work shall have its meaning in agriculture models and in machine learning as well. It also opens the possibilities for incorporation of certain class of biological models necessary in modeling of cow behavior and farm performance that might include the impact of environment on the farm system. Particular attention is paid to the model of coupled oscillators that it the basic building hypothesis that can construct the model showing certain periodic or quasiperiodic behavior.

Keywords: coupled ordinary differential equations, cattle farm system, numerical methods, stochastic differential equations

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Authors: Damir Latypov

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A hybrid classical-quantum algorithm to solve boundary integral equations (BIE) arising in problems of electromagnetic and acoustic scattering is proposed. The quantum speed-up is due to a Quantum Linear System Algorithm (QLSA). The original QLSA of Harrow et al. provides an exponential speed-up over the best-known classical algorithms but only in the case of sparse systems. Due to the non-local nature of integral operators, matrices arising from discretization of BIEs, are, however, dense. A QLSA for dense matrices was introduced in 2017. Its runtime as function of the system's size N is bounded by O(√Npolylog(N)). The run time of the best-known classical algorithm for an arbitrary dense matrix scales as O(N².³⁷³). Instead of exponential as in case of sparse matrices, here we have only a polynomial speed-up. Nevertheless, sufficiently high power of this polynomial, ~4.7, should make QLSA an appealing alternative. Unfortunately for the QLSA, the asymptotic separability of the Green's function leads to high compressibility of the BIEs matrices. Classical fast algorithms such as Multilevel Fast Multipole Method (MLFMM) take advantage of this fact and reduce the runtime to O(Nlog(N)), i.e., the QLSA is only quadratically faster than the MLFMM. To be truly impactful for computational electromagnetics and acoustics engineers, QLSA must provide more substantial advantage than that. We propose a computational scheme which combines elements of the classical fast algorithms with the QLSA to achieve the required performance.

Keywords: quantum linear system algorithm, boundary integral equations, dense matrices, electromagnetic scattering theory

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Authors: Sara Ramezanzadeh, Nashid Nabian

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Historically, pandemics in different periods have caused compulsory changes in human life. In the case of Covid-19, according to the limitations and established care instructions, spatial alignment with the conditions is important. Following the outbreak of Covid-19, the question raised in this study is how to do spatial design in five scales, namely object, space, architecture, city, and infrastructure, in response to the consequences created in the realms under study. From the beginning of the pandemic until now, some changes in the spatial realm have been created spontaneously or by space users. These transformations have been mostly applied in modifiable parts such as furniture arrangement, especially in work-related spaces. To implement other comprehensive requirements, flexibility and adaptation of space design to the conditions resulting from the pandemics are needed during and after the outbreak. Studying the effects of pandemics from the past to the present, this research covers eight major realms, including three categories of ramifications, solutions, and paradigm shifts, and analytical conclusions about the solutions that have been created in response to them. Finally, by the consideration of epidemiology as a modern discipline influencing the design, spatial solutions in the five scales mentioned (in response to the effects of the eight realms for spatial adaptation in the face of pandemics and their following conditions) are presented as a series of guidelines. Due to the unpredictability of possible pandemics in the future, the possibility of changing and updating the provided guidelines is considered.

Keywords: pandemics, Covid 19, spatial design, ramifications, solutions, paradigm shifts, guidelines

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Authors: Faruk Firat Çalim, Nurullah Karaca, Hakan Tacettin Türker

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In this study, out-of-plane free vibrations of a circular rods is investigated theoretically. The governing equations for naturally twisted and curved spatial rods are obtained using Timoshenko beam theory and rewritten for circular rods. Effects of the axial and shear deformations are considered in the formulations. Ordinary differential equations in scalar form are solved analytically by using transfer matrix method. The circular rods of the mass matrix are obtained by using straight rod of consistent mass matrix. Free vibrations frequencies obtained by solving eigenvalue problem. A computer program coded in MATHEMATICA language is prepared. Circular beams are analyzed through various examples for free vibrations analysis. Results are compared with ANSYS results based on finite element method and available in the literature.

Keywords: circular rod, out-of-plane free vibration analysis, transfer matrix method

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Authors: Ranadhir Roy

Abstract:

Inverse problems arise in medical (molecular) imaging. These problems are characterized by large in three dimensions, and by the diffusion equation which models the physical phenomena within the media. The inverse problems are posed as a nonlinear optimization where the unknown parameters are found by minimizing the difference between the predicted data and the measured data. To obtain a unique and stable solution to an ill-posed inverse problem, a priori information must be used. Mathematical conditions to obtain stable solutions are established in Tikhonov’s regularization method, where the a priori information is introduced via a stabilizing functional, which may be designed to incorporate some relevant information of an inverse problem. Effective determination of the Tikhonov regularization parameter requires knowledge of the true solution, or in the case of optical imaging, the true image. Yet, in, clinically-based imaging, true image is not known. To alleviate these difficulties we have applied the penalty/modified barrier function (PMBF) method instead of Tikhonov regularization technique to make the inverse problems well-posed. Unlike the Tikhonov regularization method, the constrained optimization technique, which is based on simple bounds of the optical parameter properties of the tissue, can easily be implemented in the PMBF method. Imposing the constraints on the optical properties of the tissue explicitly restricts solution sets and can restore uniqueness. Like the Tikhonov regularization method, the PMBF method limits the size of the condition number of the Hessian matrix of the given objective function. The accuracy and the rapid convergence of the PMBF method require a good initial guess of the Lagrange multipliers. To obtain the initial guess of the multipliers, we use a least square unconstrained minimization problem. Three-dimensional images of fluorescence absorption coefficients and lifetimes were reconstructed from contact and noncontact experimentally measured data.

Keywords: constrained minimization, ill-conditioned inverse problems, Tikhonov regularization method, penalty modified barrier function method

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Authors: Elsayed M. A. Elbashbeshy, T. G. Emam, M. S. El-Azab, K. M. Abdelgaber

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The effect of thermal radiation on flow, heat and mass transfer of an incompressible viscous nanofluid over a stretching horizontal cylinder embedded in a porous medium with suction/injection is discussed numerically. The governing boundary layer equations are reduced to a system of ordinary differential equations. Mathematica has been used to solve such system after obtaining the missed initial conditions. Comparison of obtained numerical results is made with previously published results in some special cases, and found to be in a good agreement.

Keywords: laminar flow, boundary layer, stretching horizontal cylinder, thermal radiation, suction/injection, nanofluid

Procedia PDF Downloads 365