Search results for: developed stream power equation

Authors: Meng-Jie Hsiao, Cam Nguyen

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Wide-band devices in Ku band (12-18 GHz) and K band (18-27 GHz) have received significant attention for high-data-rate communications and high-resolution sensing. Especially, devices operating around 24 GHz is attractive due to the 24-GHz unlicensed applications. One of the most important components in RF systems is power amplifier (PA). Various PAs have been developed in the Ku and K bands on GaAs, InP, and silicon (Si) processes. Although the PAs using GaAs or InP process could have better power handling and efficiency than those realized on Si, it is very hard to integrate the entire system on the same substrate for GaAs or InP. Si, on the other hand, facilitates single-chip systems. Hence, good PAs on Si substrate are desirable. Especially, Si-based PA having good linearity is necessary for next generation communication protocols implemented on Si. We report a 16.5 to 25.5 GHz Si-based PA having flat saturated power of 19.5 ± 1.5 dBm, output 1-dB power compression (OP1dB) of 16.5 ± 1.5 dBm, and 15-23 % power added efficiency (PAE). The PA consists of a drive amplifier, two main amplifiers, and lump-element Wilkinson power divider and combiner designed and fabricated in TowerJazz 0.18µm SiGe BiCMOS process having unity power gain frequency (fMAX) of more than 250 GHz. The PA is realized as a cascode amplifier implementing both heterojunction bipolar transistor (HBT) and n-channel metal–oxide–semiconductor field-effect transistor (NMOS) devices for gain, frequency response, and linearity consideration. Particularly, a body-floating technique is utilized for the NMOS devices to improve the voltage swing and eliminate parasitic capacitances. The developed PA has measured flat gain of 20 ± 1.5 dB across 16.5-25.5 GHz. At 24 GHz, the saturated power, OP1dB, and maximum PAE are 20.8 dBm, 18.1 dBm, and 23%, respectively. Its high performance makes it attractive for use in Ku/K-band, especially 24 GHz, communication and radar systems. This paper was made possible by NPRP grant # 6-241-2-102 from the Qatar National Research Fund (a member of Qatar Foundation). The statements made herein are solely the responsibility of the authors.

Keywords: power amplifiers, amplifiers, communication systems, radar systems

Procedia PDF Downloads 99

Authors: A. Bekbaev, M. Dzhamanbaev, R. Abitaeva, A. Karbozova, G. Nabyeva

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In this paper, the regression dependence of dancing intensity from wind speed and length of span was established due to the statistic data obtained from multi-year observations on line wires dancing accumulated by power systems of Kazakhstan and the Russian Federation. The lower and upper limitations of the equations parameters were estimated, as well as the adequacy of the regression model. The constructed model will be used in research of dancing phenomena for the development of methods and means of protection against dancing and for zoning plan of the territories of line wire dancing.

Keywords: power lines, line wire dancing, dancing intensity, regression equation, dancing area intensity

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Authors: Pijush Roy, Vinay Kumar Rai

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The present study highlights the estimation of soil loss and identification of critical area for implementation of best management practice is central to the success of soil conservation programme. The quantification of morphometric and Universal Soil Loss Equation (USLE) factors using remote sensing and GIS for prioritization of micro-watersheds in Asan River catchment, western Doon valley at foothills of Siwalik ranges in the Dehradun districts of Uttarakhand, India. The watershed has classified as a dendritic pattern with sixth order stream. The area is classified into very high, high, moderately high, medium and low susceptibility zones. High to very high erosion zone exists in the urban area and agricultural land. Average annual soil loss of 64 tons/ha/year has been estimated for the watershed. The optimum management practices proposed for micro-watersheds of Asan River basin are; afforestation, contour bunding suitable sites for water harvesting structure as check dam and soil conservation, agronomical measure and bench terrace.

Keywords: erosion susceptibility zones, morphometric characteristics, prioritization, remote sensing and GIS, universal soil loss equation

Procedia PDF Downloads 295

Authors: Itissam Abuiziah

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In several hydraulic systems, it is necessary to calculate the head losses which depend on the resistance flow friction factor in Darcy equation. Computing the resistance friction is based on implicit Colebrook-White equation which is considered as the standard for the friction calculation, but it needs high computational cost, therefore; several explicit approximation methods are used for solving an implicit equation to overcome this issue. It follows that the relative error is used to determine the most accurate method among the approximated used ones. Steel, cast iron and polyethylene pipe materials investigated with practical diameters ranged from 0.1m to 2.5m and velocities between 0.6m/s to 3m/s. In short, the results obtained show that the suitable method for some cases may not be accurate for other cases. For example, when using steel pipe materials, Zigrang and Silvester's method has revealed as the most precise in terms of low velocities 0.6 m/s to 1.3m/s. Comparatively, Halland method showed a less relative error with the gradual increase in velocity. Accordingly, the simulation results of this study might be employed by the hydraulic engineers, so they can take advantage to decide which is the most applicable method according to their practical pipe system expectations.

Keywords: Colebrook–White, explicit equation, friction factor, hydraulic resistance, implicit equation, Reynolds numbers

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Authors: Manisha Kankarej

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The purpose of this paper is to show a relation between CR structure and F-structure satisfying polynomial equation. In this paper, we have checked the significance of CR structure and F-structure on Integrability conditions and Nijenhuis tensor. It was proved that all the properties of Integrability conditions and Nijenhuis tensor are satisfied by CR structures and F-structure satisfying polynomial equation.

Keywords: CR-submainfolds, CR-structure, integrability condition, Nijenhuis tensor

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Authors: Matheus Fernando Pereira, Varese Salvador Timoteo

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In this work, we have solved the two-dimensional advection-diffusion equation numerically for a spatially dependent solute dispersion along non-uniform flow with a pulse type source in order to make a systematic study on the influence of medium heterogeneity, initial flow velocity, and initial dispersion coefficient parameters on the solutions of the equation. The behavior of the solutions is then investigated as we change the three parameters independently. Our results show that even though the parameters represent different physical features of the system, the effect on their variation is very similar. We also observe that the effects caused by the parameters on the concentration depend on the distance from the source. Finally, our numerical results are in good agreement with the exact solutions for all values of the parameters we used in our analysis.

Keywords: advection-diffusion equation, dispersion, numerical methods, pulse-type source

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Authors: Mohammad Mahmoud Mandurah

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The existence of InfoMiracles in scripture is evidence that the scripture has a divine origin. It is also evidence to the existence of God. An InfoMiracle is an information-based miracle. The basic component of an InfoMiracle is a piece of information that could not be obtained by a human except through a divine channel. The existence of a sufficient number of convincing InfoMiracles in a scripture necessitates the existence of the divine source to these InfoMiracles. A mathematical equation is developed to prove that the Qur’an has a divine origin, and hence, prove the existence of God. The equation depends on a single variable only, which is the number of InfoMiracles in the Qur’an. The Qur’an is rich with InfoMiracles. It is shown that the existence of less than 30 InfoMiracles in the Qur’an is sufficient proof to the existence of God and that the Qur’an is a revelation from God.

Keywords: InfoMiracle, God, mathematical proof, miracle, probability

Procedia PDF Downloads 206

Authors: Ch. Ashok Babu, J. V. R. Ravindra, K. Lalkishore

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Power has became a burning issue in modern VLSI design. As the technology advances especially below 45nm, technology of leakage power became a big problem apart of the dynamic power. This paper presents a full adder with novel PMOS and NMOS which consume less power compare to conventional full adder, DTMOS full adder. This paper shows different types of adders and their power consumption, area, and delay. All the experiments have been carried out using Cadence® Virtuoso® design lay out editor which shows power consumption of different types of adders.

Keywords: average power, leakage power, delay, DTMOS, PDP

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Authors: Ted Silva

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Dietrich de Velsa's Équation à un inconnu / Equation to an Unknown hybridizes art cinema style with the sexually explicit aesthetics of pornography to envision a uniquely queer world unmoored by heteronormative influence. This stylization evokes the memory of a queer history that once approximated such a prospect. With this historical and political context in mind, this paper utilizes formal analysis to assess how the film frames queer sexual encounters as tender acts of care, sometimes literally mending physical wounds. However, Equation to Unknown also highlights the transience of these sexual exchanges. By emphasizing the homogeneity of the protagonist’s sexual conquests, the film reveals that these practices have a darker meaning when the men reject the individualized connection to pursue purely visceral gratification. Given the lack of diversity or even recognizable identifying factors, the men become more anonymous to each other the more they pair up. Ultimately, Equation to an Unknown both celebrates and problematizes its vision of a queer utopia, highlighting areas in the community wherein intimacy and care flourish and locating those spots in which they are neglected.

Keywords: pornography studies, queer cinema, French cinema, history

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Authors: Amani Amamou, Sabra Habli, Nejla Mahjoub Saïd, Philippe Bournot, Georges Le Palec

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A counterflowing jet is a particular configuration of turbulent jets issuing into a moving ambient which has not carried much attention in literature compared with jet in a coflow or in a crossflow. This is due to the marked instability of the jet in a counterflow coupled with experimental and theoretical difficulties related to the flow inversion phenomenon. Nevertheless, jets in a counterflow are encountered in many engineering applications which required enhanced mixing as combustion, process and environmental engineering. In this work, we propose to investigate a round turbulent jet flowing into a uniform counterflow stream through a numerical approach. A hydrodynamic and thermal study of a slightly oblique round jets issuing into a uniform counterflow stream is carried out for different jet-to-counterflow velocity ratios ranging between 3.1 and 15. It is found that even a slight inclination of the jet in the vertical direction of the flow affects the structure and the velocity field of the counterflowing jet. In addition, the evolution of passive scalar temperature and pertinent length scales are presented at various velocity ratios, confirming that the flow is sensitive to directional perturbations.

Keywords: jet, counterflow, velocity, temperature, jet inclination

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Authors: So-Ra Jeon, Chan Byon

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This study investigates the heat transfer characteristics of aluminum foam heat sink and pin fin heat sink subjected to an impinging air jet under a fixed pumping power condition as well as fixed flow rate condition. The effects of dimensionless pumping power or the Reynolds number and the impinging distance ratio on the Nusselt number are considered. The result shows that the effect of the impinging distance on the Nusselt number is negligible under a fixed pumping power condition, while the Nusselt number increases with decreasing the impinging distance under a fixed pumping power condition. A correlation for the pressure drop is obtained as a function of the flow rate and the impinging distance ratio. And correlations for the stagnation Nusselt number of the impinging jet are developed as a function of the pumping power. The aluminum foam heat sinks did not show higher thermal performance compared to a conventional pin fin heat sink under a fixed pumping power condition.

Keywords: aluminum foam, heat sinks, impinging jet, pumping power

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Authors: Tomoaki Hashimoto

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Recent technological advance has prompted significant interest in developing the control theory of quantum systems. Following the increasing interest in the control of quantum dynamics, this paper examines the control problem of Schrödinger equation because quantum dynamics is basically governed by Schrödinger equation. From the practical point of view, stochastic disturbances cannot be avoided in the implementation of control method for quantum systems. Thus, we consider here the robust stabilization problem of Schrödinger equation against stochastic disturbances. In this paper, we adopt model predictive control method in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. The objective of this study is to derive the stability criterion for model predictive control of Schrödinger equation under stochastic disturbances.

Keywords: optimal control, stochastic systems, quantum systems, stabilization

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Authors: S. Nagheli, N. Samani, D. A. Barry

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In this paper, the velocity potential and stream function of capture zone for a well field in an aquifer bounded by two parallel streams with or without a uniform regional flow of any directions are presented. The well field includes any number of extraction or injection wells or a combination of both types with any pumping rates. To delineate the capture envelope, the potential and streamlines equations are derived by conformal mapping method. This method can help us to release constrains of other methods. The equations can be applied as useful tools to design in-situ groundwater remediation systems, to evaluate the surface–subsurface water interaction and to manage the water resources.

Keywords: complex potential, conformal mapping, image well theory, Laplace’s equation, superposition principle

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Authors: Vishal V. Choudhari, Gaurao A. Dongre, S. P. Diwan

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A number of reference current generation have been developed for analysis of shunt active power filter to mitigate the load compensation. Depending upon the type of load the technique has to be chosen. In this paper, six reference current generation techniques viz. instantaneous reactive power theory(IRP), Synchronous reference frame theory(SRF), Perfect harmonic cancellation(PHC), Unity power factor method(UPF), Self-tuning filter method(STF), Predictive filtering method(PFM) are compared for different operating conditions. The harmonics are introduced because of non-linear loads in the system. These harmonics are eliminated using above techniques. The results and performance of system simulated on MATLAB/Simulink platform. The system is experimentally implemented using DS1104 card of dSPACE system.

Keywords: SAPF, power quality, THD, IRP, SRF, dSPACE module DS1104

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Authors: Ákos Cserny

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The unequivocal increase of the area of operation of the executive power can happen with the appearance of new areas to be influenced and its integration in the power, or at the expense of the scopes of other organs with public authority. The extension of the executive can only be accepted within the framework of the rule of law if parallel with this process we get constitutional guarantees that the exercise of power is kept within constitutional framework. Failure to do so, however, may result in the lack, deficit of democracy and democratic sense, and may cause an overwhelming dominance of the executive power. Therefore, the aim of this paper is to present executive power and responsibility in the context of different dimensions.

Keywords: confidence, constitution, executive power, liabiliy, parliamentarism

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Authors: Tiao Chang, Ivan Caballero, Hong Zhou

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Streams carry water and sediment naturally by maintaining channel dimensions, pattern, and profile over time. Watershed erosion as a natural process has occurred to contribute sediment to streams over time. The formation of channel dimensions is complex. This study is to relate quantifiable and consistent channel dimensions at the bankfull stage to the corresponding watershed erosion estimation by the Revised Universal Soil Loss Equation (RUSLE). Twelve sites of which drainage areas range from 7 to 100 square miles in the Hocking River Basin of Ohio were selected for the bankfull geometry determinations including width, depth, cross-section area, bed slope, and drainage area. The twelve sub-watersheds were chosen to obtain a good overall representation of the Hocking River Basin. It is of interest to determine how these bankfull channel dimensions are related to the soil erosion of corresponding sub-watersheds. Soil erosion is a natural process that has occurred in a watershed over time. The RUSLE was applied to estimate erosions of the twelve selected sub-watersheds where the bankfull geometry measurements were conducted. These quantified erosions of sub-watersheds are used to investigate correlations with bankfull channel dimensions including discharge, channel width, channel depth, cross-sectional area, and pebble distribution. It is found that drainage area, bankfull discharge and cross-sectional area correlates strongly with watershed erosion well. Furthermore, bankfull width and depth are moderately correlated with watershed erosion while the particle size, D50, of channel bed sediment is not well correlated with watershed erosion.

Keywords: watershed, stream, sediment, channel

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Authors: Toufic Abd El-Latif Sadek

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The Asphalt object represents the asphalted areas, like roads. The best original data of thermal images occurred at a specific time during the days of the year, by preventing the gaps in times which give the close and same brightness from different objects, using seven sample objects, asphalt, concrete, metal, rock, dry soil, vegetation, and water. It has been found in this study a general timing equation for capturing satellite thermal images at different locations, depends on a fixed time the sunrise and sunset; Capture Time= Tcap =(TM*TSR) ±TS.

Keywords: asphalt, satellite, thermal images, timing equation

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Authors: Ranajay Bhowmick

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Analysis of stresses for an infinitesimal tetrahedron leads to a situation where we obtain a cubic equation consisting of three stress invariants. This cubic equation, when solved for a definite condition, gives the principal stresses directly without requiring any cumbersome and time-consuming trial and error methods or iterative numerical procedures. Since the failure criterion of different materials are generally expressed as functions of principal stresses, an attempt has been made in this study to incorporate the solutions of the cubic equation in the form of principal stresses, obtained for a definite condition, into some of the established failure theories to determine their modified descriptions. It has been observed that the failure theories can be represented using the quadratic stress invariant and the orientation of the principal plane.

Keywords: cubic equation, stress invariant, trigonometric, explicit solution, principal stress, failure criterion

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Authors: Sagardeep Talukdar, Gautam Kumar Saharia, Riki Dutta, Sudipta Nandy

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In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain bright soliton. We have obtained bright 1-soliton, 2-soliton solutions and propose the scheme for obtaining N-soliton solution. We have used an additional parameter which is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

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Authors: Aklilu Getahun Sulito

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Land Use and Land Cover change dynamics is a result of complex interactions betweenseveral bio- physical and socio-economic conditions. The impacts of the landcoverchange on stream flow and sediment yield were analyzed statistically usingthehydrological model, SWAT. Genale Dawa Dam III watershed is highly af ectedbydeforestation, over grazing, and agricultural land expansion. This study was aimedusingSWAT model for the assessment of impacts of land use land cover change on sediment yield, evaluating stream flow on wet &dry seasons and spatial distribution sediment yieldfrom sub-basins of the Genale Dawa Dam III watershed. Land use land cover maps(LULC) of 2000, 2008 and 2016 were used with same corresponding climate data. During the study period most parts of the forest, dense forest evergreen and grass landchanged to cultivated land. The cultivated land increased by 26.2%but forest land, forest evergreen lands and grass lands decreased by 21.33%, 11.59 % and 7.28 %respectively, following that the mean annual sediment yield of watershed increased by 7.37ton/haover16 years period (2000 – 2016). The analysis of stream flow for wet and dry seasonsshowed that the steam flow increased by 25.5% during wet season, but decreasedby29.6% in the dry season. The result an average annual spatial distribution of sediment yield increased by 7.73ton/ha yr -1 from (2000_2016). The calibration results for bothstream flow and sediment yield showed good agreement between observed and simulateddata with the coef icient of determination of 0.87 and 0.84, Nash-Sutclif e ef iciencyequality to 0.83 and 0.78 and percentage bias of -7.39% and -10.90%respectively. Andthe result for validation for both stream flow and sediment showed good result withCoef icient of determination equality to 0.83 and 0.80, Nash-Sutclif e ef iciency of 0.78and 0.75 and percentage bias of 7.09% and 3.95%. The result obtained fromthe model based on the above method was the mean annual sediment load at Genale DawaDamIIIwatershed increase from 2000 to 2016 for the reason that of the land uses change. Sotouse the Genale Dawa Dam III the land use management practices are neededinthefuture to prevent further increase of sediment yield of the watershed.

Keywords: Genale Dawa Dam III watershed, land use land cover change, SWAT, spatial distribution, sediment yield, stream flow

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Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

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The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups

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Authors: Rana M. Mostafa, Nouby M. Ghazaly, Ahmed S. Ali

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This article introduces a solution for increasing the wind energy extracted from turbines to overcome the more electric power required. This objective provides a new science discipline; wind turbine control. This field depends on the development in power electronics to provide new control strategies for turbines. Those strategies should deal with all turbine operating modes. Here there are two control strategies developed for variable speed horizontal axis wind turbine for rated and over rated wind speed regions. These strategies will support wind energy validation, decrease manufacturing overhead cost. Here nonlinear adaptive method was used to design speed controllers to a scheme for ‘Aeolos50 kw’ wind turbine connected to permanent magnet generator via a gear box which was built on MATLAB/Simulink. These controllers apply maximum power point tracking concept to guarantee goal achievement. Procedures were carried to test both controllers efficiency. The results had been shown that the developed controllers are acceptable and this can be easily declared from simulation results.

Keywords: adaptive method, pitch controller, wind energy, nonlinear control

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Authors: Amine Benmoussa, Mohamed Bouanini, Mebrouk Rebhi

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Stirring is one of the unifying processes which form part of the mechanical unit operations in process technology such chemical, biotechnological, pharmaceutical, petrochemical, cosmetic, and food processing. Therefore determining the level of mixing and overall behavior and performance of the mixing tanks are crucial from the product quality and process economics point of views. The most fundamental needs for the analysis of these processes from both a theoretical and industrial perspective are the knowledge of the hydrodynamic behavior and the flow structure in such tanks. Depending on the purpose of the operation carried out in mixer, the best choice for geometry of the tank and agitator type can vary widely. Initially, a local and global study namely the velocity and power number on a typical agitation system agitated by a mobile-type two-blade straight (d/D=0.5) allowed us to test the reliability of the CFD, the result were compared with those of experimental literature, a very good concordance was observed. The stream function, the velocity profile, the velocity fields and power number are analyzed. It was shown that the hydrodynamics is modified by the curvature of the mobile which plays a key role.

Keywords: agitated vessels, curved blade agitator, laminar flow, finite volume method

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Authors: Anil Kumar Pandey

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Power plane noise is the most significant source of signal integrity (SI) issues in a high-speed digital design. In this paper, power integrity (PI) analysis of multiple power planes in a power delivery system of a 12-layer high-speed FPGA board is presented. All 10 power planes of HSD board are analyzed separately by using 3D Electromagnetic based PI solver, then the transient simulation is performed on combined PI data of all planes along with voltage regulator modules (VRMs) and 70 current drawing chips to get the board level power noise coupling on different high-speed signals. De-coupling capacitors are placed between power planes and ground to reduce power noise coupling with signals.

Keywords: power integrity, power-aware signal integrity analysis, electromagnetic simulation, channel simulation

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Authors: Olusegun Solomon

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This paper describes the concept for the design and maximum power point tracking control for an interior permanent magnet synchronous generator wind turbine system. Two design concepts are compared to outline the effect of magnet design on the performance of the interior permanent magnet synchronous generator. An approximate model that includes the effect of core losses has been developed for the machine to simulate the dynamic performance of the wind energy system. An algorithm for Maximum Power Point Tracking control is included to describe the process for maximum power extraction.

Keywords: permanent magnet synchronous generator, wind power system, wind turbine

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Authors: Raj Kumar Rajak, Bharat Mishra

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Bio-battery represents an entirely new long term, reasonable, reachable and ecofriendly approach to production of sustainable energy. Types of batteries have been developed using MnO₂ in various ways. MnO₂ is suitable with physical, chemical, electrochemical, and catalytic properties, serving as an effective cathodic depolarizer and may be considered as being the life blood of the battery systems. In the present experimental work, we have studied the effect of generation of power by bio-battery using different concentrations of MnO₂. The tests show that it is possible to generate electricity using cow’s urine as an electrolyte. After ascertaining the optimum concentration of MnO₂, various battery parameters and performance indicates that cow urine solely produces power of 695 mW, while a combination with MnO₂ (40%) enhances power of bio-battery, i.e. 1377 mW. On adding more and more MnO₂ to the electrolyte, the power suppressed because inflation of internal resistance. The analysis of the data produced from experiment shows that MnO₂ is quite suitable to energize the bio-battery.

Keywords: bio-batteries, cow’s urine, manganese dioxide, non-conventional

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Authors: Surinder Singh, Gursewak Singh Lovkesh

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We have designed wavelength conversion based on four wave mixing in an optical fiber at 10 Gb/s. The power of converted signal increases with increase in signal power. The converted signal power is investigated as a function of input signal power and pump power. On comparison of converted signal power at different value of input signal power, we observe that best converted signal power is obtained at -2 dBm input signal power for both up conversion as well as for down conversion. Further, FWM efficiency, quality factor is observed for increase in input signal power and optical fiber length.

Keywords: FWM, optical fiiber, wavelngth converter, quality

Procedia PDF Downloads 571

Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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Authors: Yanpei Zhen

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The nonlinear Schrödinger (NLS) equation models wave dynamics in many physical problems related to fluids, plasmas, and optics. The standing periodic waves are known to be modulationally unstable, and rogue waves (localized perturbations in space and time) have been observed on their backgrounds in numerical experiments. The exact solutions for rogue waves arising on the periodic standing waves have been obtained analytically. It is natural to ask if the rogue waves persist on the standing periodic waves in the integrable discretizations of the integrable NLS equation. We study the standing periodic waves in the semidiscrete integrable system modeled by the high-order Ablowitz-Ladik (AL) equation. The standing periodic wave of the high-order AL equation is expressed by the Jacobi cnoidal elliptic function. The exact solutions are obtained by using the separation of variables and one-fold Darboux transformation. Since the cnoidal wave is modulationally unstable, the rogue waves are generated on the periodic background.

Keywords: Darboux transformation, periodic wave, Rogue wave, separating the variables

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Authors: Nadaniela Egidi, Pierluigi Maponi

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The approximate solution of a time-harmonic electromagnetic scattering problem for inhomogeneous media is required in several application contexts, and its two-dimensional formulation is a Fredholm integral equation of the second kind. This integral equation provides a formulation for the direct scattering problem, but it has to be solved several times also in the numerical solution of the corresponding inverse scattering problem. The discretization of this Fredholm equation produces large and dense linear systems that are usually solved by iterative methods. In order to improve the efficiency of these iterative methods, we use the Symmetric SOR preconditioning, and we propose an algorithm for the evaluation of the associated relaxation parameter. We show the efficiency of the proposed algorithm by several numerical experiments, where we use two Krylov subspace methods, i.e., Bi-CGSTAB and GMRES.

Keywords: Fredholm integral equation, iterative method, preconditioning, scattering problem

Procedia PDF Downloads 96