Search results for: linear Fresnel reflectors

Authors: M. Javadzadeh, H. Khoshsima

Abstract:

In this article, we present a layout printing way for producing Fresnel zone on 1294-1b doped liquid crystal with Methyl-Red azo dye. We made a Fresnel zone mask with 25 zones and radius of 5 mm using lithography technique. With layout printing way, we recorded mask’s pattern on cell with λ=532 nm solid-state diode pump laser. By recording Fresnel zone pattern on cell and making Fresnel pattern on the surface of cell, odd and even zones, will form. The printed pattern, because of Azo dye’s photoisomerization, was permanent. Experimentally, we saw focal length tunability from 32 cm to 43 cm.

Keywords: liquid crystal, lens, Fresnel zone, diffraction, Fresnel lens

Procedia PDF Downloads 172

Authors: Ahmed Aljudaya, Derek Ingham, Lin Ma, Kevin Hughes, Mohammed Pourkashanian

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Researchers, power companies, and state politicians have given concentrated solar power (CSP) much attention due to its capacity to generate large amounts of electricity whereas overcoming the intermittent nature of solar resources. The Linear Fresnel Reflector (LFR) is a well-known CSP technology type for being inexpensive, having a low land use factor, and suffering from low optical efficiency. The LFR was considered a cost-effective alternative option to the Parabolic Trough Collector (PTC) because of its simplistic design, and this often outweighs its lower efficiency. The LFR has been found to be a promising option for directly producing steam to a thermal cycle in order to generate low-cost electricity, but also it has been shown to be promising for indirect steam generation. The purpose of this important analysis is to compare the annual performance of the Direct Steam Generation (DSG) and Indirect Steam Generation (ISG) of LFR power plants using molten salt and other different Heat Transfer Fluids (HTF) to investigate their technical and economic effects. A 50 MWe solar-only system is examined as a case study for both steam production methods in extreme weather conditions. In addition, a parametric analysis is carried out to determine the optimal solar field size that provides the lowest Levelized Cost of Electricity (LCOE) while achieving the highest technical performance. As a result of optimizing the optimum solar field size, the solar multiple (SM) is found to be between 1.2 – 1.5 in order to achieve as low as 9 Cent/KWh for the direct steam generation of the linear Fresnel reflector. In addition, the power plant is capable of producing around 141 GWh annually and up to 36% of the capacity factor, whereas the ISG produces less energy at a higher cost. The optimization results show that the DSG’s performance overcomes the ISG in producing around 3% more annual energy, 2% lower LCOE, and 28% less capital cost.

Keywords: concentrated solar power, levelized cost of electricity, linear Fresnel reflectors, steam generation

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Authors: Vinita Choudhary

Abstract:

The solidly mounted resonator (SMR) is a bulk acoustic wave-based device consisting of a piezoelectric layer sandwiched between two electrodes upon Bragg reflectors, which then are attached to a substrate. To transform the effective acoustic impedance of the substrate to a near zero value, the Bragg reflectors are composed of alternating high and low acoustic impedance layers of quarter-wavelength thickness. In this work presents the design and investigation of acoustic Bragg reflectors (ABRs) for solidly mounted bulk acoustic wave resonators through analysis and simulation. This performance of the resonator is analyzed using 1D Mason modeling. The performance parameters are the effect of Bragg pairs number on transmissivity, reflectivity, insertion loss, the electromechanical and quality factor of the 5GHz operating resonator.

Keywords: bragg reflectors, SMR, insertion loss, quality factor

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Authors: Daniel Tarrazó-Serrano, Sergio Pérez-López, Sergio Castiñeira-Ibáñez, Pilar Candelas, Constanza Rubio

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Zone Plates (ZPs) are used in many areas of physics where planar fabrication is advantageous in comparison with conventional curved lenses. There are several types of ZPs, such as the well-known Fresnel ZPs or the more recent Fractal ZPs and Fibonacci ZPs. The material selection of the lens plays a very important role in the beam modulation control. This work presents a comparison between two Fresnel ZP made from different materials in the ultrasound domain: Polylactic Acid (PLA) and brass. PLA is the most common material used in commercial 3D-printers due to its high design flexibility and low cost. Numerical simulations based on Finite Element Method (FEM) and experimental results are shown, and they prove that the focusing capabilities of brass ZPs and PLA ZPs are similar. For this reason, PLA is proposed as a Magnetic Resonance Imaging (MRI) compatible material with great potential for therapeutic ultrasound focusing applications.

Keywords: FZP, PLA, focus, ultrasound, MRI

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Authors: M. Y. Ismail, M. Inam

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This paper presents equivalent circuit modeling of active planar reflectors which can be used for the detailed analysis and characterization of reflector performance in terms of lumped components. Equivalent circuit representation has been proposed for PIN diodes and liquid crystal based active planar reflectors designed within X-band frequency range. A very close agreement has been demonstrated between equivalent circuit results, 3D EM simulated results as well as measured scattering parameter results. In the case of measured results, a maximum discrepancy of 1.05dB was observed in the reflection loss performance, which can be attributed to the losses occurred during measurement process.

Keywords: Equivalent circuit modelling, planar reflectors, reflectarray antenna, PIN diode, liquid crystal

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Authors: Sergio Pérez-López, Daniel Tarrazó-Serrano, José M. Fuster, Pilar Candelas, Constanza Rubio

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Fresnel Zone Plates (FZPs) are widely used in many areas, such as optics, microwaves or acoustics. On the design of FZPs, plane wave incidence is typically considered, but that is not usually the case in ultrasounds, especially in applications where a piston emitter is placed at a certain distance from the lens. In these cases, having control of the focal distance is very important, and with the usual Fresnel equation a focal displacement from the theoretical distance is observed due to the plane wave supposition. In this work, a comparison between FZP with plane wave incidence design and FZP with point source design in the case of piston emitter is presented. Influence of the main parameters of the piston in the final focalization profile has been studied. Numerical models and experimental results are shown, and they prove that when spherical wave incidence is considered for the piston case, it is possible to have a fine control of the focal distance in comparison with the classical design method.

Keywords: focusing, Fresnel zone plates, FZP, ultrasound

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Authors: Avadhesh Yadav, Balram Manoj Kumar

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A solar powered air heating system using parabolic trough collector was experimentally investigated. In this experimental setup, the reflected solar radiations were focused on absorber tube which was placed at focal length of the parabolic trough. In this setup, air was used as working fluid which collects the heat from absorber tube. To enhance the performance of parabolic trough, collector with different type of reflectors were used. It was observed for aluminum sheet maximum temperature is 52.3ºC, which 24.22% more than steel sheet as reflector and 8.5% more than aluminum foil as reflector, also efficiency by using Aluminum sheet as reflector compared to steel sheet as reflector is 61.18% more. Efficiency by using aluminum sheet as reflector compared to aluminum foil as reflector is 18.98% more.

Keywords: parabolic trough collector, reflectors, air flow rates, solar power, aluminum sheet

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Authors: Hassan Qandil

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Using a statistical algorithm incorporated in MATLAB, four types of non-imaging Fresnel lenses are designed; spot-flat, linear-flat, dome-shaped and semi-cylindrical-shaped. The optimization employs a statistical ray-tracing methodology of the incident light, mainly considering effects of chromatic aberration, varying focal lengths, solar inclination and azimuth angles, lens and receiver apertures, and the optimum number of prism grooves. While adopting an equal-groove-width assumption of the Poly-methyl-methacrylate (PMMA) prisms, the main target is to maximize the ray intensity on the receiver’s aperture and therefore achieving higher values of heat flux. The algorithm outputs prism angles and 2D sketches. 3D drawings are then generated via AutoCAD and linked to COMSOL Multiphysics software to simulate the lenses under solar ray conditions, which provides optical and thermal analysis at both the lens’ and the receiver’s apertures while setting conditions as per the Dallas-TX weather data. Once the lenses’ characterization is finalized, receivers are designed based on its optimized aperture size. Several cavity shapes; including triangular, arc-shaped and trapezoidal, are tested while coupled with a variety of receiver materials, working fluids, heat transfer mechanisms, and enclosure designs. A vacuum-reflective enclosure is also simulated for an enhanced thermal absorption efficiency. Each receiver type is simulated via COMSOL while coupled with the optimized lens. A lab-scale prototype for the optimum lens-receiver configuration is then fabricated for experimental evaluation. Application-based testing is also performed for the selected configuration, including that of a photovoltaic-thermal cogeneration system and solar furnace system. Finally, some future research work is pointed out, including the coupling of the collector-receiver system with an end-user power generator, and the use of a multi-layered genetic algorithm for comparative studies.

Keywords: COMSOL, concentrator, energy, fresnel, optics, renewable, solar

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Authors: M. Tawfik, X. Tonnellier, C. Sansom

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The Lens-Lens Beam Generator (LLBG) is a Fresnel-based optical concentrating technique which provides flexibility in selecting the solar receiver location compared to conventional techniques through generating a powerful concentrated collimated solar beam. In order to achieve that, two successive lenses are used and followed by a flat mirror. Hence the generated beam emerging from the LLBG has a high power flux which impinges on the target receiver, it is important to determine the precision of the system output. In this present work, mathematical investigation of different parameters affecting the precision of the output beam is carried out. These parameters include: Deflection in sun-facing lens and its holding arm, delay in updating the solar tracking system, and the flat mirror surface flatness. Moreover, relationships that describe the power lost due to the effect of each parameter are derived in this study.

Keywords: Fresnel lens, LLBG, solar concentrator, solar tracking

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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: Ishraq M. Anjum

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Distributed Bragg reflectors are used in vertical-cavity surface-emitting lasers (VCSELs) in order to achieve very high reflectivity. Use of metamaterial in place of distributed Bragg reflector can reduce the device size significantly. A silicon-based metamaterial near perfect reflector is designed to be used in place of distributed Bragg reflectors in VCSELs. Mie resonance in dielectric microparticles is exploited in order to design the metamaterial. A reflectivity of 98.31% is achieved using finite-difference time-domain method. An 808nm double intra-cavity contacted VCSEL structure with 1.5 λ cavity is proposed using this metamaterial near perfect reflector. The active region is designed to be composed of seven GaAs/AlGaAs quantum wells. Upon numerical investigation of the designed VCSEL structure, the threshold current is found to be 2.96 mA at an aperture of 40 square micrometers and the maximum output power is found to be 71 mW at a current of 141 mA. Miniaturization of conventional VCSELs is possible using this design.

Keywords: GaAs, LASER, metamaterial, VCSEL, vertical cavity surface emitting laser

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Authors: Denis A. Sokolov, Andrey V. Mazurkevich

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In the modern world, there is an increasing demand for highly precise measurements in various fields, such as aircraft, shipbuilding, and rocket engineering. This has resulted in the development of appropriate measuring instruments that are capable of measuring the coordinates of objects within a range of up to 100 meters, with an accuracy of up to one micron. The calibration process for such optoelectronic measuring devices (trackers and total stations) involves comparing the measurement results from these devices to a reference measurement based on a linear or spatial basis. The reference used in such measurements could be a reference base or a reference range finder with the capability to measure angle increments (EDM). The base would serve as a set of reference points for this purpose. The concept of the EDM for replicating the unit of measurement has been implemented on a mobile platform, which allows for angular changes in the direction of laser radiation in two planes. To determine the distance to an object, a high-precision interferometer with its own design is employed. The laser radiation travels to the corner reflectors, which form a spatial reference with precisely known positions. When the femtosecond pulses from the reference arm and the measuring arm coincide, an interference signal is created, repeating at the frequency of the laser pulses. The distance between reference points determined by interference signals is calculated in accordance with recommendations from the International Bureau of Weights and Measures for the indirect measurement of time of light passage according to the definition of a meter. This distance is D/2 = c/2nF, approximately 2.5 meters, where c is the speed of light in a vacuum, n is the refractive index of a medium, and F is the frequency of femtosecond pulse repetition. The achieved uncertainty of type A measurement of the distance to reflectors 64 m (N•D/2, where N is an integer) away and spaced apart relative to each other at a distance of 1 m does not exceed 5 microns. The angular uncertainty is calculated theoretically since standard high-precision ring encoders will be used and are not a focus of research in this study. The Type B uncertainty components are not taken into account either, as the components that contribute most do not depend on the selected coordinate measuring method. This technology is being explored in the context of laboratory applications under controlled environmental conditions, where it is possible to achieve an advantage in terms of accuracy. In general, the EDM tests showed high accuracy, and theoretical calculations and experimental studies on an EDM prototype have shown that the uncertainty type A of distance measurements to reflectors can be less than 1 micrometer. The results of this research will be utilized to develop a highly accurate mobile absolute range finder designed for the calibration of high-precision laser trackers and laser rangefinders, as well as other equipment, using a 64 meter laboratory comparator as a reference.

Keywords: femtosecond laser, pulse correlation, interferometer, laser absolute range finder, coordinate measurement

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Authors: Skezeer John B. Paz, Ederlina G. Nocon

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Finding an optimal binary linear code is a central problem in coding theory. A binary linear code C = [n, k, d] is called optimal if there is no linear code with higher minimum distance d given the length n and the dimension k. There are bounds giving limits for the minimum distance d of a linear code of fixed length n and dimension k. The lower bound which can be taken by construction process tells that there is a known linear code having this minimum distance. The upper bound is given by theoretic results such as Griesmer bound. One way to find an optimal binary linear code is to make the lower bound of d equal to its higher bound. That is, to construct a binary linear code which achieves the highest possible value of its minimum distance d, given n and k. Some optimal binary linear codes were presented by Andries Brouwer in his published table on bounds of the minimum distance d of binary linear codes for 1 ≤ n ≤ 256 and k ≤ n. This was further improved by Markus Grassl by giving a detailed construction process for each code exhibiting the lower bound. In this paper, we construct new optimal binary linear codes by using some construction processes on existing binary linear codes. Particularly, we developed an algorithm applied to the codes already constructed to extend the list of optimal binary linear codes up to 257 ≤ n ≤ 300 for k ≤ 7.

Keywords: bounds of linear codes, Griesmer bound, construction of linear codes, optimal binary linear codes

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Authors: Manal Azzidani

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This research consideres the extension of special functions called Positive Linear Operators. the bounded linear operator which defined from normed space to Banach space will extend to the closure of the its domain, And extend identified linear functional on a vector subspace by Hana-Banach theorem which could be generalized to the positive linear operators.

Keywords: extension, positive operator, Riesz space, sublinear function

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Authors: Myung Hwan Na, Ho- Chun Song, EunHee Hong

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We widely use normal linear mixed-effects model to analysis data in repeated measurement. In case of detecting heteroscedasticity and the non-normality of the population distribution at the same time, normal linear mixed-effects model can give improper result of analysis. To achieve more robust estimation, we use heavy tailed linear mixed-effects model which gives more exact and reliable analysis conclusion than standard normal linear mixed-effects model.

Keywords: reliability, tires, field data, linear mixed-effects model

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Authors: Fatma Susilawati Mohamad, Azizah Abdul Manaf, Fadhillah Ahmad, Zarina Mohamad, Wan Suryani Wan Awang

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A simple and robust multi-class linear classifier is proposed and implemented. For a pair of classes of the linear boundary, a collection of segments of hyper planes created as perpendicular bisectors of line segments linking centroids of the classes or part of classes. Nearest Neighbor and Linear Discriminant Analysis are compared in the experiments to see the performances of each classifier in discriminating ripeness of oil palm. This paper proposes a multi-class linear classifier using Linear Discriminant Analysis (LDA) for image identification. Result proves that LDA is well capable in separating multi-class features for ripeness identification.

Keywords: multi-class, linear classifier, nearest neighbor, linear discriminant analysis

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Authors: S. H. Nasseri, A. Ebrahimnejad

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Fuzzy set theory has been applied to many fields, such as operations research, control theory, and management sciences. In this paper, we consider two classes of fuzzy linear programming (FLP) problems: Fuzzy number linear programming and linear programming with trapezoidal fuzzy variables problems. We state our recently established results and develop fuzzy primal simplex algorithms for solving these problems. Finally, we give illustrative examples.

Keywords: fuzzy linear programming, fuzzy numbers, duality, sensitivity analysis

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Authors: Husham Mahmood Ahmed

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For so many reasons, fresh water scarcity is one of major problems facing the world and in particularly in the third world in the Northern Africa, the Middle East, the Southwest of Asia, and many other desert areas. Solar distillation offers one of the most promising solutions of renewable energy to this aggravated situation. The main obstacle hindering the spread of the use of solar technology for fresh water production is its low efficiency. Therefore, enhancing the solar stills performances by studying the parameters affecting their productivity and implementing new ideas and a different design are the main goals of the investigators in recent years. The present research is experimental work that tests a new design of solar still with a hemispherical top cover for water desalination with and without external reflectors under the climate of the Kingdom of Bahrain during the autumn season. The hemispherical cover has a base diameter of 1m and a depth of 0.4m, die cast from a 6 mm thick Lexan plastic sheet. The net effective area was 0.785 m2. It has been found that the average daily production rate obtained from the hemispherical top cover solar still is 3.610 liter/day. This yield is 11.1% higher than the yield of a conventional simple type single slope solar still having 20ᴼ slope glass cover and a larger effective area of 1 m2 obtained in previous research under similar climatic conditions. It has also been found that adding 1.2m long by 0.15 curved reflectors increased the yield of the hemispherical solar still by 5.5 %, while the 1.2 long by 0.3m curved reflector increased the yield by about 8%.

Keywords: hemispherical solar still, solar desalination, solar energy, the Northern Africa

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Authors: R. B. Ogunrinde, C. C. Jibunoh

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In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.

Keywords: spectral decomposition, linear RHS, homogeneous linear systems, eigenvalues of the Jacobian

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Authors: Marco Jan Rafael C. Sicam, Maria Daniella C. Yambao

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The Philippines is a tectonically active archipelagic country situated near the Circum-Pacific Belt. Hence, seismic hazard assessments are important in the nation-building. In 2014, the Philippines Institute of Volcanology and Seismology (PHIVOLCS) mapped a 12-km NW-trending unnamed active fault near Boso-Boso River, Rizal. Given the limited nature of their technical report, they would like to further consolidate relevant data about this fault. As such, this study aims to characterize the surface and subsurface expression of the fault along Boso-Boso River using rangefront morphology, structural criteria, and ground penetrating radar. This fault is subdivided into two segments: the first segment located in the city of Antipolo is mainly manifested in the upper Kinabuan Formation and terminating near Mt. Qutago, and the second segment in Baras, Pinugay, Rizal cuts through recent fluvial deposits and to the Guadalupe Formation. IfSAR-derived DTM data reveals the morphological expression of the fault defined by offset streams and ridges, linear sidehill valleys, and linear valleys. Fault gouges, fault breccia, transtentional flower structures, slickensides, and other shear sense markers observed in the units of the upper Cretaceous Kinabuan Formation indicate a sinistral sense of displacement. GPR radargram profiles revealed the presence of displacement in reflectors at 3-5 meters below the surface which may be suggestive of the fault within the area. Finally, the fault in Boso-Boso river may be a segment of the larger sinistral Montalban Fault in the north or largely affected by the movement from the Marikina Valley Fault System.

Keywords: NW unnamed fault, range-front morphology, shear sense markers, ground penetrating radar, boso-boso river, antipolo

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Authors: B. Güney, Ç. Teke

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In recent years, rapid and correct decision making is crucial for both people and enterprises. However, uncertainty makes decision-making difficult. Fuzzy logic is used for coping with this situation. Thus, fuzzy linear programming models are developed in order to handle uncertainty in objective function and the constraints. In this study, a problem of a factory in food industry is investigated, required data is obtained and the problem is figured out as a fuzzy linear programming model. The model is solved using Zimmerman approach which is one of the approaches for fuzzy linear programming. As a result, the solution gives the amount of production for each product type in order to gain maximum profit.

Keywords: food industry, fuzzy linear programming, fuzzy logic, linear programming

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Authors: Hazem Al-Mofleh, John Daniels, Joseph McKean

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Within geostatistics research, effective estimation of the variogram points has been examined, particularly in developing robust alternatives. The parametric fit of these variogram points which eventually defines the kriging weights, however, has not received the same attention from a robust perspective. This paper proposes the use of the non-linear Wilcoxon norm over weighted non-linear least squares as a robust variogram fitting alternative. First, we introduce the concept of variogram estimation and fitting. Then, as an alternative to non-linear weighted least squares, we discuss the non-linear Wilcoxon estimator. Next, the robustness properties of the non-linear Wilcoxon are demonstrated using a contaminated spatial data set. Finally, under simulated conditions, increasing levels of contaminated spatial processes have their variograms points estimated and fit. In the fitting of these variogram points, both non-linear Weighted Least Squares and non-linear Wilcoxon fits are examined for efficiency. At all levels of contamination (including 0%), using a robust estimation and robust fitting procedure, the non-weighted Wilcoxon outperforms weighted Least Squares.

Keywords: non-linear wilcoxon, robust estimation, variogram estimation, wilcoxon norm

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Authors: Sadeg M. Ghnia, Mahmud Alghattawi

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The NC-210 study area is located in Atshan Saddle between both Ghadamis and Murzuq basins, west Libya. The preserved Palaeozoic successions are predominantly clastics reaching thickness of more than 20,000 ft in northern Ghadamis Basin depocenter. The Carboniferous series consist of interbedded sandstone, siltstone, shale, claystone and minor limestone deposited in a fluctuating shallow marine to brackish lacustrine/fluviatile environment which attain maximum thickness of over 5,000ft in the area of Atshan Saddle and recorded 3,500 ft. in outcrops of Murzuq Basin flanks. The Carboniferous strata was uplifted and eroded during Late Paleozoic and early Mesozoic time in northern Ghadamis Basin and Atshan Saddle. The M'rar Formation age is Tournaisian to Late Serpukhovian based on palynological markers and contains about 12 cycles of sandstone and shale deposited in shallow to outer neritic deltaic settings. The hydrocarbons in the M'rar reservoirs possibly sourced from the Lower Silurian and possibly Frasinian radioactive hot shales. The M'rar Formation lateral, vertical and thickness distribution is possibly influenced by the reactivation of Tumarline Strik-Slip fault and its conjugate faults. A pronounced structural paleohighs and paleolows, trending SE & NW through the Gargaf Saddle, is possibly indicative of the present of two sub-basins in the area of Atshan Saddle. A number of identified seismic reflectors from existing 2D seismic covering Atshan Saddle reflect M’rar deltaic 12 sandstone cycles. M’rar7, M’rar9, M’rar10 and M’rar12 are characterized by high amplitude reflectors, while M’rar2 and M’rar6 are characterized by medium amplitude reflectors. These horizons are productive reservoirs in the study area. Available seismic data in the study area contributed significantly to the identification of M’rar potential traps, which are prominently 3- way dip closure against fault zone. Also seismic data indicates the presence of a significant strikeslip component with the development of flower-structure. The M'rar Formation hydrocarbon discoveries are concentrated mainly in the Atshan Saddle located in southern Ghadamis Basin, Libya and Illizi Basin in southeast of Algeria. Significant additional hydrocarbons may be present in areas adjacent to the Gargaf Uplift, along structural highs and fringing the Hoggar Uplift, providing suitable migration pathways.

Keywords: hydrocarbon potential, stratigraphy, Ghadamis basin, seismic, well data integration

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Authors: Mehdi Jafari Matehkolaee

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In this paper, we have obtained the adjoint of an arbitrary operator (linear and nonlinear) in Hilbert space by introducing an n-dimensional Riemannian manifold. This general formalism covers every linear operator (non – differential) in Hilbert space. In fact, our approach shows that instead of using the adjoint definition of an operator directly, it can be obtained directly by relying on a suitable generalized space according to the action of the operator in question. For the case of nonlinear operators, we have to change the definition of the linear operator adjoint. But here, we have obtained an adjoint of these operators with respect to the definition of the derivative of the operator. As a matter of fact, we have shown one of the straight applications of the ''Frechet derivative'' in the algebra of the operators.

Keywords: adjoint operator, non-linear operator, differentiable operator, manifold

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Authors: Mishu Gupta, Rama Gupta

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It has been elucidated here that non- autonomous discrete non-linear Schrödinger equation is associated with saturable non-linearity through photo-refractive media. We have investigated the localized solution of non-autonomous saturable discrete non-linear Schrödinger equations. The similarity transformation has been involved in converting non-autonomous saturable discrete non-linear Schrödinger equation to constant-coefficient saturable discrete non-linear Schrödinger equation (SDNLSE), whose exact solution is already known. By back substitution, the solution of the non-autonomous version has been obtained. We have analysed our solution for the hyperbolic and periodic form of gain/loss term, and interesting results have been obtained. The most important characteristic role is that it helps us to analyse the propagation of electromagnetic waves in glass fibres and other optical wave mediums. Also, the usage of SDNLSE has been seen in tight binding for Bose-Einstein condensates in optical mediums. Even the solutions are interrelated, and its properties are prominently used in various physical aspects like optical waveguides, Bose-Einstein (B-E) condensates in optical mediums, Non-linear optics in photonic crystals, and non-linear kerr–type non-linearity effect and photo refracting medium.

Keywords: B-E-Bose-Einstein, DNLSE-Discrete non linear schrodinger equation, NLSE-non linear schrodinger equation, SDNLSE - saturable discrete non linear Schrodinger equation

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Authors: Rabia Khan, Nargis Munir, Suriya Gharib, Syeda Roshana Ali

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In this paper linear equations are discussed in detail along with elimination method. Gaussian elimination and Gauss Jordan schemes are carried out to solve the linear system of equation. This paper comprises of matrix introduction, and the direct methods for linear equations. The goal of this research was to analyze different elimination techniques of linear equations and measure the performance of Gaussian elimination and Gauss Jordan method, in order to find their relative importance and advantage in the field of symbolic and numeric computation. The purpose of this research is to revise an introductory concept of linear equations, matrix theory and forms of Gaussian elimination through which the performance of Gauss Jordan and Gaussian elimination can be measured.

Keywords: direct, indirect, backward stage, forward stage

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Authors: Qasim M. Kriri

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Few Saudi Arabia production companies face financial profit issues until this moment. This work presents a linear integer programming model that solves a production problem of a Saudi Food Company in Saudi Arabia. An optimal solution to the above-mentioned problem is a Linear Programming solution. In this regard, the main purpose of this project is to maximize profit. Linear Programming Technique has been used to derive the maximum profit from production of natural juice at Saudi Food Co. The operations of production of the company were formulated and optimal results are found out by using Lindo Software that employed Sensitivity Analysis and Parametric linear programming in order develop Linear Programming. In addition, the parameter values are increased, then the values of the objective function will be increased.

Keywords: parameter linear programming, objective function, sensitivity analysis, optimize profit

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Authors: Suparman

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Piecewise linear regression models are very flexible models for modeling the data. If the piecewise linear regression models are matched against the data, then the parameters are generally not known. This paper studies the problem of parameter estimation of piecewise linear regression models. The method used to estimate the parameters of picewise linear regression models is Bayesian method. But the Bayes estimator can not be found analytically. To overcome these problems, the reversible jump MCMC algorithm is proposed. Reversible jump MCMC algorithm generates the Markov chain converges to the limit distribution of the posterior distribution of the parameters of picewise linear regression models. The resulting Markov chain is used to calculate the Bayes estimator for the parameters of picewise linear regression models.

Keywords: regression, piecewise, Bayesian, reversible Jump MCMC

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Authors: Sie Long Kek, Wah June Leong, Kok Lay Teo

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Linear quadratic Gaussian model is a standard mathematical model for the stochastic optimal control problem. The combination of the linear quadratic estimation and the linear quadratic regulator allows the state estimation and the optimal control policy to be designed separately. This is known as the separation principle. In this paper, an efficient computational method is proposed to solve the linear quadratic Gaussian problem. In our approach, the Hamiltonian function is defined, and the necessary conditions are derived. In addition to this, the output error is defined and the least-square optimization problem is introduced. By determining the first-order necessary condition, the gradient of the sum squares of output error is established. On this point of view, the stochastic approximation approach is employed such that the optimal control policy is updated. Within a given tolerance, the iteration procedure would be stopped and the optimal solution of the linear-quadratic Gaussian problem is obtained. For illustration, an example of the linear-quadratic Gaussian problem is studied. The result shows the efficiency of the approach proposed. In conclusion, the applicability of the approach proposed for solving the linear quadratic Gaussian problem is highly demonstrated.

Keywords: iteration procedure, least squares solution, linear quadratic Gaussian, output error, stochastic approximation

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Authors: M. Berrehail, F. Benamira

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We study the quantum motion of a particle in the presence of a time- dependent linear potential using an operator invariant that is quadratic in p and linear in q within the framework of the Lewis-Riesenfeld invariant, The special invariant operator proposed in this work is demonstrated to be an Hermitian operator which has an Airy wave packet as its Eigenfunction

Keywords: airy wave packet, ivariant, time-dependent linear potential, unitary transformation

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