Search results for: nonlinear radiation

Authors: Sonia Sonia

Abstract:

This paper presents a family of iterative scheme for solving nonlinear systems of equations which have wide application in sciences and engineering. The proposed iterative family is based upon some parameters which generates many different iterative schemes. This family is completely derivative free and uses first of divided difference operator. Moreover some numerical experiments are performed and compared with existing methods. Analysis of convergence shows that the presented family has fourth-order of convergence. The dynamical behaviour of proposed family and local convergence have also been discussed. The numerical performance and convergence region comparison demonstrates that proposed family is efficient.

Keywords: convergence, divided difference operator, nonlinear system, Newton's method

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Authors: Kamel Al-Khaled

Abstract:

In this paper, numerical solutions for the nonlinear coupled Korteweg-de Vries, (abbreviated as KdV) equations are calculated by Sinc-collocation method. This approach is based on a global collocation method using Sinc basis functions. First, discretizing time derivative of the KdV equations by a classic finite difference formula, while the space derivatives are approximated by a $\theta-$weighted scheme. Sinc functions are used to solve these two equations. Soliton solutions are constructed to show the nature of the solution. The numerical results are shown to demonstrate the efficiency of the newly proposed method.

Keywords: Nonlinear coupled KdV equations, Soliton solutions, Sinc-collocation method, Sinc functions

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Authors: R. Loukil, M. Chtourou, T. Damak

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In this work, we use the Fault detection and isolation and the Fault tolerant control based on sliding mode observer in order to introduce the well diagnosis of a nonlinear system. The robustness of the proposed observer for the two techniques is tested through a physical example. The results in this paper show the interaction between the Fault tolerant control and the Diagnosis procedure.

Keywords: fault detection and isolation FDI, fault tolerant control FTC, sliding mode observer, nonlinear system, robustness, stability

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Authors: Kholood A. Baron

Abstract:

While radiologist numbers specialized in spine interventional procedures are limited in Kuwait, the number of patients demanding these procedures is increasing rapidly. Due to this high demand, the workload of radiologists is increasing, which might represent a radiation exposure concern. During these procedures, the doctor’s hands are in very close proximity to the main radiation beam/ if not within it. The aim of this study is to measure the radiation dose for radiologists during several interventional procedures for the spine. Methods: Two doctors carrying different workloads were included. (DR1) was performing procedures in the morning and afternoon shifts, while (DR2) was performing procedures in the morning shift only. Comparing the radiation exposures that the hand of each doctor is receiving will assess radiation safety and help to set up workload regulations for radiologists carrying a heavy schedule of such procedures. Entrance Skin Dose (ESD) was measured via TLD (ThermoLuminescent Dosimetry) placed at the right wrist of the radiologists. DR1 was covering the morning shift in one hospital (Mubarak Al-Kabeer Hospital) and the afternoon shift in another hospital (Dar Alshifa Hospital). The TLD chip was placed in his gloves during the 2 shifts for a whole week. Since DR2 was covering the morning shift only in Al Razi Hospital, he wore the TLD during the morning shift for a week. It is worth mentioning that DR1 was performing 4-5 spine procedures/day in the morning and the same number in the afternoon and DR2 was performing 5-7 procedures/day. This procedure was repeated for 4 consecutive weeks in order to calculate the ESD value that a hand receives in a month. Results: In general, radiation doses that the hand received in a week ranged from 0.12 to 1.12 mSv. The ESD values for DR1 for the four consecutive weeks were 1.12, 0.32, 0.83, 0.22 mSv, thus for a month (4 weeks), this equals 2.49 mSv and calculated to be 27.39 per year (11 months-since each radiologist have 45 days of leave in each year). For DR2, the weekly ESD values are 0.43, 0.74, 0.12, 0.61 mSv, and thus, for a month, this equals 1.9 mSv, and for a year, this equals 20.9 mSv /year. These values are below the standard level and way below the maximum limit of 500 mSv per year (set by ICRP = International Council of Radiation Protection). However, it is worth mentioning that DR1 was a senior consultant and hence needed less fluoro-time during each procedure. This is evident from the low ESD values of the second week (0.32) and the fourth week (0.22), even though he was performing nearly 10-12 procedures in a day /5 days a week. These values were lower or in the same range as those for DR2 (who was a junior consultant). This highlighted the importance of increasing the radiologist's skills and awareness of fluoroscopy time effect. In conclusion, the radiation dose that radiologists received during spine interventional radiology in our setting was below standard dose limits.

Keywords: radiation protection, interventional radiology dosimetry, ESD measurements, radiologist radiation exposure

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Authors: Sunghyun Kim, Hong-Gun Park

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In the performance-based design (PBD), by using the nonlinear dynamic analysis (NDA), the actual performance of the structure is evaluated. Unlike frame structures, in the wall structures, base shear force which is resulted from the NDA, is greatly amplified than that from the elastic analysis. This shear amplifying effect causes repeated designs which make designer difficult to apply the PBD. Therefore, in this paper, factors which affect shear amplification were studied. For the 20-story wall model, the NDA was performed. From the analysis results, the base shear amplification factor was proposed.

Keywords: performance based design, shear amplification factor, nonlinear dynamic analysis, RC shear wall

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Authors: Nasim Abuali Galehdari, Thomas J. Ryan, Ajit D. Kelkar

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In recent years, nanotechnology has played an important role in the design of an efficient radiation shielding polymeric composites. It is well known that, high loading of nanomaterials with radiation absorption properties can enhance the radiation attenuation efficiency of shielding structures. However, due to difficulties in dispersion of nanomaterials into polymer matrices, there has been a limitation in higher loading percentages of nanoparticles in the polymer matrix. Therefore, the objective of the present work is to provide a methodology to fabricate and then to characterize the functionally graded radiation shielding structures, which can provide an efficient radiation absorption property along with good structural integrity. Sandwich structures composed of Ultra High Molecular Weight Polyethylene (UHMWPE) fabric as face sheets and functionally graded epoxy nanocomposite as core material were fabricated. A method to fabricate a functionally graded core panel with controllable gradient dispersion of nanoparticles is discussed. In order to optimize the design of functionally graded sandwich composites and to analyze the stress distribution throughout the sandwich composite thickness, a finite element method was used. The sandwich panels were discretized using 3-Dimensional 8 nodded brick elements. Classical laminate analysis in conjunction with simplified micromechanics equations were used to obtain the properties of the face sheets. The presented finite element model would provide insight into deformation and damage mechanics of the functionally graded sandwich composites from the structural point of view.

Keywords: nanotechnology, functionally graded material, radiation shielding, sandwich composites, finite element method

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Authors: Mohamed M. El Gendy, Ibrahim A. El Arabi, Rafeek W. Abdel-Missih, Omar A. Kandil

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Nonlinear analysis is one of the most important design and safety tools in structural engineering. Based on the finite-element method, a geometrical and material nonlinear analysis of large span reinforced concrete arches is carried out considering soil-structure interaction. The concrete section details and reinforcement distribution are taken into account. The behavior of soil is considered via Winkler's and continuum models. A computer program (NARC II) is specially developed in order to follow the structural behavior of large span reinforced concrete arches up to failure. The results obtained by the proposed model are compared with available literature for verification. This work confirmed that the geometrical and material nonlinearities, as well as soil structure interaction, have considerable influence on the structural response of reinforced concrete arches.

Keywords: nonlinear analysis, reinforced concrete arched structure, soil-structure interaction, geotechnical engineering

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Authors: Ashok K. Satapathy, Prerana Nashine

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Radiative heat transfer in participating medium was anticipated using the finite volume method. The radiative transfer equations are formulated for absorbing and anisotropically scattering and emitting medium. The solution strategy is discussed and the conditions for computational stability are conferred. The equations have been solved for transient radiative medium and transient radiation incorporated with transient conduction. Results have been obtained for irradiation and corresponding heat fluxes for both the cases. The solutions can be used to conclude incident energy and surface heat flux. Transient solutions were obtained for a slab of heat conducting in slab by thermal radiation. The effect of heat conduction during the transient phase is to partially equalize the internal temperature distribution. The solution procedure provides accurate temperature distributions in these regions. A finite volume procedure with variable space and time increments is used to solve the transient energy equation. The medium in the enclosure absorbs, emits, and anisotropically scatters radiative energy. The incident radiations and the radiative heat fluxes are presented in graphical forms. The phase function anisotropy plays a significant role in the radiation heat transfer when the boundary condition is non-symmetric.

Keywords: participating media, finite volume method, radiation coupled with conduction, heat transfer

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Authors: Edamana Vasudevan Krishnan

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This paper studies solitons in optical materials with the help of Mapping Method. Two types of nonlinear media have been investigated, namely, the cubic nonlinearity and the quintic nonlinearity. The soliton solutions, shock wave solutions and singular solutions have been derives with certain constraint conditions.

Keywords: solitons, integrability, metamaterials, mapping method

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Authors: Felix Jr. Garde, Eric Augustus Tingatinga

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Most analysis procedures of reinforced concrete (RC) slabs are based on elastic theory. When subjected to large forces, however, slabs deform beyond elastic range and the study of their behavior and performance require nonlinear analysis. This paper presents a numerical model to simulate nonlinear behavior of RC slabs using rigid body-spring discrete element method. The proposed slab model composed of rigid plate elements and nonlinear springs is based on the yield line theory which assumes that the nonlinear behavior of the RC slab subjected to transverse loads is contained in plastic or yield-lines. In this model, the displacement of the slab is completely described by the rigid elements and the deformation energy is concentrated in the flexural springs uniformly distributed at the potential yield lines. The spring parameters are determined from comparison of transverse displacements and stresses developed in the slab obtained using FEM and the proposed model with assumed homogeneous material. Numerical models of typical RC slabs with varying geometry, reinforcement, support conditions, and loading conditions, show reasonable agreement with available experimental data. The model was also shown to be useful in investigating dynamic behavior of slabs.

Keywords: RC slab, nonlinear behavior, yield line theory, rigid body-spring discrete element method

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Authors: Xin Wang, Yuanzhong Wang

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Pipa is one of the most important Chinese traditional plucked instruments, but its directivity has never been measured systematically. In western, directivity of loudness for western instruments is deeply researched through analysis of sound pressure level, whereas the directivity of timbre is seldom studied. In this paper, a new method for directivity of timbre was proposed, and horizontal directivity patterns of loudness and timbre of Pipa were measured. Directivity of Pipa radiation was measured in an anechoic room. The sound of Pipa played by a musician was recorded simultaneously by 32 microphones with Pipa in the center. The measuring results were examined through listening test. According to the measurement of Pipa directivity radiation, we put forward the best localization of Pipa in the Chinese traditional orchestra and the optimal recording region.

Keywords: directivity, Pipa, roughness, listening test

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Authors: Walid Tawfik

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The interaction of intense short nano- and picosecond laser pulses with plasma leads to reach variety of important applications, including time-resolved laser induced breakdown spectroscopy (LIBS), soft x-ray lasers, and laser-driven accelerators. The progress in generating of femtosecond down to sub-10 fs optical pulses has opened a door for scientists with an essential tool in many ultrafast phenomena, such as femto-chemistry, high field physics, and high harmonic generation (HHG). The advent of high-energy laser pulses with durations of few optical cycles provided scientists with very high electric fields, and produce coherent intense UV to NIR radiation with high energy which allows for the investigation of ultrafast molecular dynamics with femtosecond resolution. In this work, we could experimentally achieve the generation of a two-octave-wide supercontinuum ultrafast pulses extending from ultraviolet at 3.5 eV to the near-infrared at 1.3 eV in neon-filled capillary fiber. These pulses are created due to nonlinear self-phase modulation (SPM) in neon as a nonlinear medium. The measurements of the generated pulses were performed using spectral phase interferometry for direct electric-field reconstruction. A full characterization of the output pulses was studied. The output pulse characterization includes the pulse width, the beam profile, and the spectral bandwidth. Under optimization conditions, the reconstructed pulse intensity autocorrelation function was exposed for the shorts possible pulse duration to achieve transform-limited pulses with energies up to 600µJ. Furthermore, the effect of variation of neon pressure on the pulse-width was studied. The nonlinear SPM found to be increased with the neon pressure. The obtained results may give an opportunity to monitor and control ultrafast transit interaction in femtosecond chemistry.

Keywords: femtosecond laser, ultrafast, supercontinuum, ultra-broadband

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Authors: Avram Irina, Coiciu Eugenia-Mihaela, Popovici Mara-Georgiana, Mitu Iani Octavian

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ELI-NP stands as a cutting-edge facility globally, hosting unique radiological setups. It conducts experiments leveraging high-power lasers capable of producing extremely brief 10 PW pulses on two fronts. Moreover, it houses an exceptional gamma beam system with distinctive spectral characteristics. The facility hosts various experiments across designated experimental areas, encompassing ultra-short high-power laser tests, high-intensity gamma beam trials, and combined experiments utilizing both setups. The facility hosts a dosimetry laboratory, which recently obtained accreditation, where the radiation safety group employs a host of different types of detectors for monitoring the personnel, environment, and public exposure to ionizing radiation generated in experiments performed. ELI-NP's design was shaped by radiological protection assessments conducted through Monte Carlo simulations. The poster exemplifies an assessment conducted using the FLUKA code in an experimental area where a high-power laser system is implemented, and the future diagnostic system for variable energy gamma beams will soon be operational.

Keywords: radiation protection, Monte Carlo simulation, FLUKA, dosimetry

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Authors: Nagwa E. Abd Elazim, Maha S. El-naggar, Rania H. Mohamed, Sara M. Awad

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Background: Radiodermatitis is a common side effect of radiation therapy for breast cancer. However, there is no current consensus about effective standard therapy for the prevention and management of radiation dermatitis. Topical ectoine has demonstrated efficacy in the treatment of atopic dermatitis owing to its anti-inflammatory activity. Objective: To evaluate the efficacy of topical ectoine in comparison to traditional topical dexpanthenol treatment in the management of acute radiodermatitis in breast cancer patients undergoing adjuvant radiotherapy. Methods: Fifty patients were randomized to use either dexpanthenol 0.5% cream (25 patients), or ectoin 7% cream (25 patients), applied twice daily to the irradiated area during the radiation period and continued for 2 weeks after cessation of radiotherapy. Assessment of radiation skin toxicity using Common Terminology Criteria of Adverse Events (CTCAE) v4.0, radiation-associated symptoms, and adverse events were undertaken weekly during radiotherapy and 2 weeks after the end of radiotherapy. Results: Topical ectoine showed some clinical benefit over dexpanthenol, as shown by delayed time to onset (at week 3 versus week 2, respectively) and larger number of patients who reached grade 0 at the end of treatment (64% vs. 48%, respectively). The clinical symptoms of pain (p = 0.003) and itching (p = 0.001) attributable to radiation were less pronounced with ectoine than with dexpanthenol. Burning and hyperpigmentation were the most common side effects with ectoine. However, no significant difference between dexpanthenol and ectoine treatments was found in any of the side effects (p = 0.1). Conclusion: Ectoin was overall more effective in improving radiation dermatitis than topical dexpanthenol in breast cancer patients. Ectoin could be proposed as a preventive or curative treatment for patients undergoing postoperative irradiation for breast cancer. Further clinical studies with a larger number of patients are recommended for the confirmation of these preliminary results.

Keywords: breast cancer, dexapanthenol, ectoin, radiation dermatitis

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Authors: Sharmi Mukherjee, Anindita Chakraborty

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Cellular irradiation incites complex responses including arrest of cell cycle progression. This article accentuates the effects of radiation on cell cycle status of radiation non-targeted cells. Human Hepatoma HepG2 cells were exposed to increasing doses of γ radiations (1, 2, 4, 6 Gy) and their cell culture media was transferred to non-targeted HepG2 cells cultured in other Petri plates. These radiation non-targeted cells cultured in the ICCM (Irradiated cell conditioned media) were the bystander cells on which cell cycle analysis was performed using flow cytometry. An apparent decrease in the distribution of bystander cells at G0/G1 phase was observed with increased radiation doses upto 4 Gy representing a linear relationship. This was accompanied by a gradual increase in cellular distribution at G2/M phase. Interestingly the number of cells in G2/M phase at 1 and 2 Gy irradiation was not significantly different from each other. However, the percentage of G2 phase cells at 4 and 6 Gy doses were significantly higher than 2 Gy dose indicating the IC50 dose to be between 2 and 4 Gy. Cell cycle arrest is an indirect indicator of genotoxic damage in cells. In this study, bystander stress signals through the cell culture media of irradiated cells disseminated the radiation induced DNA damages in the non-targeted cells which resulted in arrest of the cell cycle progression at G2/M phase checkpoint. This implies that actual radiation biological effects represent a penumbra with effects encompassing a larger area than the actual beam. This article highlights the existence of genotoxic damages as bystander effects of γ rays in human Hepatoma cells by cell cycle analysis and opens up avenues for appraisal of bystander stress communications between tumor cells. Contemplation of underlying signaling mechanisms can be manipulated to maximize damaging effects of radiation with minimum dose and thus has therapeutic applications.

Keywords: bystander effect, cell cycle, genotoxic damage, hepatoma

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Authors: Shubham Jaiswal

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During modeling of transport phenomena in porous media, many nonlinear partial differential equations (NPDEs) encountered which greatly described the convection, diffusion and reaction process. To solve such types of nonlinear problems, a reliable and efficient technique is needed. In this article, the numerical solution of NPDEs encountered in porous media is derived. Here Jacobi collocation method is used to solve the considered problems which convert the NPDEs in systems of nonlinear algebraic equations that can be solved using Newton-Raphson method. The numerical results of some illustrative examples are reported to show the efficiency and high accuracy of the proposed approach. The comparison of the numerical results with the existing analytical results already reported in the literature and the error analysis for each example exhibited through graphs and tables confirms the exponential convergence rate of the proposed method.

Keywords: nonlinear porous media equation, shifted Jacobi polynomials, operational matrix, spectral collocation method

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Authors: Du Kim, Nelson Baro

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According to a report of International Atomic Energy Agency (IAEA), there are approximately 437 nuclear power stations are in operation in the present around the world in order to meet increasing energy demands. Indeed, nearly, a third of the world’s energy demands are met through nuclear power because it is one of the most efficient and long-lasting sources of energy. However, there are also consequences when a major event takes place at a nuclear power station. Over the past years, a few major nuclear accidents have occurred around the world. According to a report of International Nuclear and Radiological Event Scale (INES), there are six nuclear accidents that are considered to be high level (risk) of the events: Fukushima Dai-chi (Level 7), Chernobyl (Level 7), Three Mile Island (Level 5), Windscale (Level 5), Kyshtym (Level 6) and Chalk River (Level 5). Today, many people still have doubt about using nuclear power. There is growing number of people who are against nuclear power after the serious accident occurred at the Fukushima Dai-chi nuclear power plant in Japan. In other words, there are public concerns about radiation impacts which emphasize Linear-No-Threshold (LNT) Issues, Radiation Health Effects, Radiation Protection and Social Impacts. This paper will address those keywords by looking back at the history of these major nuclear accidents worldwide, based on INES. This paper concludes that all major mistake from nuclear accidents are preventable due to the fact that most of them are caused by human error. In other words, the human factor has played a huge role in the malfunction and occurrence of most of those events. The correct handle of a crisis is determined, by having a good radiation protection program in place, it’s what has a big impact on society and determines how acceptable people are of nuclear.

Keywords: linear-no-threshold (LNT) issues, radiation health effects, radiation protection, social impacts

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Authors: Ayda Nikkar, Roghayye Ahmadiasl

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In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.

Keywords: homotopy perturbation method, Whitham–Broer–Kaup (WBK) equation, Modified Boussinesq, Approximate Long Wave

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Authors: Ghania Zidani, Said Drid, Larbi Chrifi-Alaoui, Abdeslam Benmakhlouf, Souad Chaouch

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In this paper, we focus on the study for path tracking control of unicycle-type Wheeled Mobile Robots (WMR), by applying the Backstepping technic. The latter is a relatively new technic for nonlinear systems. To solve the problem of constraints nonholonomics met in the path tracking of such robots, an adaptive Backstepping based nonlinear controller is developed. The stability of the controller is guaranteed, using the Lyapunov theory. Simulation results show that the proposed controller achieves the objective and ensures good path tracking.

Keywords: Backstepping control, kinematic and dynamic controllers, Lyapunov methods, nonlinear control systems, Wheeled Mobile Robot (WMR).

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Authors: Mohammad Khosravi, Ali Kiani, Behroz Dastar, Parvin Showrang

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Review was carried out on important anti-nutritional compounds of livestock and poultry foods and the effect of radiation usage. Nowadays, with advancement in technology, different methods have been considered for the optimum usage of nutrients in livestock and poultry foods. Steaming, extruding, pelleting, and the use of chemicals are the most common and popular methods in food processing. Use of radiation in food processing researches in the livestock and poultry industry is currently highly regarded. Ionizing (electrons, gamma) and non-ionizing beams (microwave and infrared) are the most useable rays in animal food processing. In recent researches, these beams have been used to remove and reduce the anti-nutritional factors and microbial contamination and improve the digestibility of nutrients in poultry and livestock food. The evidence presented will help researchers to recognize techniques of relevance to them. Simplification of some of these techniques, especially in developing countries, must be addressed so that they can be used more widely.

Keywords: antitrypsin, gamma anti-nutritional components, phytic acid, radiation

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Authors: Guy Joseph Eyebe, Gambo Betchewe, Alidou Mohamadou, Timoleon Crepin Kofane

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In the present study, the dynamics of nanobeam resting on fractional order softening nonlinear viscoelastic pasternack foundations is studied. The Hamilton principle is used to derive the nonlinear equation of the motion. Approximate analytical solution is obtained by applying the standard averaging method. The Melnikov method is used to investigate the chaotic behaviors of device, the critical curve separating the chaotic and non-chaotic regions are found. It is shown that appearance of chaos in the system depends strongly on the fractional order parameter.

Keywords: chaos, fractional-order, Melnikov method, nanobeam

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Authors: M. Rahou, A. J. Andrews, G. Rosengarten

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One of the main challenges in high-temperature solar thermal applications transfer concentrated solar radiation to the load with minimum energy loss and maximum overall efficiency. The use of a solar concentrator in conjunction with bundled optical fibres has potential advantages in terms of transmission energy efficiency, technical feasibility and cost-effectiveness compared to a conventional heat transfer system employing heat exchangers and a heat transfer fluid. In this paper, a theoretical and computer simulation method is described to estimate the net solar radiation transmission from a solar concentrator into and through optical fibres to a thermal application at the end of the fibres over distances of up to 100 m. A key input to the simulation is the angular distribution of radiation intensity at each point across the aperture plane of the optical fibre. This distribution depends on the optical properties of the solar concentrator, in this case, a parabolic mirror with a small secondary mirror with a common focal point and a point-focus Fresnel lens to give a collimated beam that pass into the optical fibre bundle. Since solar radiation comprises a broad band of wavelengths with very limited spatial coherence over the full range of spectrum only ray tracing models absorption within the fibre and reflections at the interface between core and cladding is employed, assuming no interference between rays. The intensity of the radiation across the exit plane of the fibre is found by integrating across all directions and wavelengths. Results of applying the simulation model to a parabolic concentrator and point-focus Fresnel lens with typical optical fibre bundle will be reported, to show how the energy transmission varies with the length of fibre.

Keywords: concentrated radiation, fibre bundle, parabolic dish, fresnel lens, transmission

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Authors: Selda Uzal Seyfi, Levent Seyfi

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The technological devices are more often being used days by day. Thus, electro magnetic pollution is being more important now than last decades. Especially mobile phones and their base stations are subject to assessment in respect of all living beings health as well as of human beings. In this context, it is worth to evaluate the situation of electromagnetic radiation exposing living beings such as animals. In this study, electromagnetic radiation levels to which sheep are exposed in Konya/Turkey are presented. The electromagnetic radiation is measured at 1800 MHz for GSM base stations. 1085 sheep farms are determined in areas of Konya center region (Selçuklu, Meram, and Karatay) in which sheep and goat breeding is widely carried out. In this study, 790 sheep and goat farms, 10.8 % for total farms in Konya region (7276), having more than 100 animals are assessed. Then, the data obtained are depicted. As a conclusion, the results should be evaluated together with the future measurements to determine the exact effect on health of sheep and their productivity.

Keywords: electromagnetic pollution, sheep housing, sheep and goat farm, environmental pollution

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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Authors: Youssef Abdelli, Rachid Nasri

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The large amplitude free vibration analysis of three-layered symmetric sandwich beams is carried out using two different approaches. The governing nonlinear partial differential equations of motion in free natural vibration are derived using Hamilton's principle. The formulation leads to two nonlinear partial differential equations that are coupled both in axial and binding deformations. In the first approach, the method of multiple scales is applied directly to the governing equation that is a nonlinear partial differential equation. In the second approach, we discretize the governing equation by using Galerkin's procedure and then apply the shooting method to the obtained ordinary differential equations. In order to check the validity of the solutions obtained by the two approaches, they are compared with the solutions obtained by two approaches; they are compared with the solutions obtained numerically by the finite difference method.

Keywords: finite difference method, large amplitude vibration, multiple scales, nonlinear vibration

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Authors: Sara Mahesar, Saleem M. Chandio, Hira Soomro

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Nonlinear system of equations in two variables is a system which contains variables of degree greater or equal to two or that comprises of the transcendental functions. Mathematical modeling of numerous physical problems occurs as a system of nonlinear equations. In applied and pure mathematics it is the main dispute to solve a system of nonlinear equations. Numerical techniques mainly used for finding the solution to problems where analytical methods are failed, which leads to the inexact solutions. To find the exact roots or solutions in case of the system of non-linear equations there does not exist any analytical technique. Various methods have been proposed to solve such systems with an improved rate of convergence and accuracy. In this paper, a new scheme is developed for solving system of non-linear equation in two variables. The iterative scheme proposed here is modified form of the conventional Newton’s Method (CN) whose order of convergence is two whereas the order of convergence of the devised technique is three. Furthermore, the detailed error and convergence analysis of the proposed method is also examined. Additionally, various numerical test problems are compared with the results of its counterpart conventional Newton’s Method (CN) which confirms the theoretic consequences of the proposed method.

Keywords: conventional Newton’s method, modified Newton’s method, order of convergence, system of nonlinear equations

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Authors: Juliana V. Pereira, Adriana S. M. Batista, Jefferson P. Nascimento, Clascídia A. Furtado, Luiz O. Faria

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Exposure to ionizing radiation has been found to induce changes in poly(vinylidene fluoride) (PVDF) homopolymers. The high dose gamma irradiation process induces the formation of C=C and C=O bonds in its [CH₂-CF₂]_n main chain. The irradiation also provokes crosslinking and chain scission. All these radio-induced defects lead to changes in the PVDF crystalline structure. As a consequence, it is common to observe a decrease in the melting temperature (T_M) and melting latent heat (L_M) and some changes in its ferroelectric features. We have investigated the possibility of preparing nanocomposites of PVDF with graphene oxide (GO) through the radio-induction of molecular bonds. In this work, we discuss how the gamma radiation interacts with the nanocomposite crystalline structure.

Keywords: gamma irradiation, graphene oxide, nanocomposites, PVDF

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Authors: M. Zamurad Shah, M. Kemal Ozgoren, Raza Samar

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This paper presents a 3D guidance scheme for Unmanned Aerial Vehicles (UAVs). The proposed guidance scheme is based on the sliding mode approach using nonlinear sliding manifolds. Generalized 3D kinematic equations are considered here during the design process to cater for the coupling between longitudinal and lateral motions. Sliding mode based guidance scheme is then derived for the multiple-input multiple-output (MIMO) system using the proposed nonlinear manifolds. Instead of traditional sliding surfaces, nonlinear sliding surfaces are proposed here for performance and stability in all flight conditions. In the reaching phase control inputs, the bang-bang terms with signum functions are accompanied with proportional terms in order to reduce the chattering amplitudes. The Proposed 3D guidance scheme is implemented on a 6-degrees-of-freedom (6-dof) simulation of a UAV and simulation results are presented here for different 3D trajectories with and without disturbances.

Keywords: unmanned aerial vehicles, sliding mode control, 3D guidance, nonlinear sliding manifolds

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Authors: Akın Kuyulu, Hanife Genç

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In present study, it was aimed to evaluate the gamma radiation impacts on tomato leaf miner at different biological stages. The laboratory colony of tomato leaf miner was used to set up the experiments. Different biological stages of the insects (eggs, 4^th instars and pupae) were irradiated using Cobalt-60 at doses of 0 (control), 100 Gray (Gy), 200 Gy, 300 Gy and 400 Gy in Cos-44HH-N source, at dose rate of 480 Gy/h. After irradiation, the eggs were incubated until hatching; the mature larvae were reared to complete their developments. Adult emergences from irradiated pupae were also evaluated. The results showed that there were no egg hatching at all tested irradiation doses. Although, the pupal percentages of irradiated mature larvae were 54%, 15% and 8% at doses of 100 Gy, 200 Gy and 300 Gy respectively, there were no adult emergences from irradiated mature larvae. On the other hand, the adult emergences were observed from irradiated pupae, decreased as radiation doses increased along with malformed adult appearance. Male and female individuals were out crossed with laboratory reared adults. Fecundity was correlated with radiation doses.

Keywords: irradiation, tomato, tomato leafminer, Tuta absoluta

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Authors: Jitendra Kumar Chawla, Mukesh Kumar Mishra

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The nonlinear amplitude modulation of ion-acoustic wave is studied in the presence of two-electron temperature distribution in unmagnetized electron-positron-ion plasmas. The Krylov-Bogoliubov-Mitropolosky (KBM) perturbation method is used to derive the nonlinear Schrödinger equation. The dispersive and nonlinear coefficients are obtained which depend on the temperature and concentration of the hot and cold electron species as well as the positron density and temperature. The modulationally unstable regions are studied numerically for a wide range of wave number. The effects of the temperature and concentration of the hot and cold electron on the modulational stability are investigated in detail.

Keywords: modulational instability, ion acoustic wave, KBM method

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