Search results for: Rayleigh fading channels

Authors: B. K. Yadav, A. Gandhi, A. K. Verma, T. S. Rao, A. Saraswat, E. R. Kumar, M. Sarkar, K. N. Vyas

Abstract:

This paper deals with the conceptual design of Experimental Helium Cooling Loop (EHCL) for Indian Test Blanket Module (TBM) and its related thermal hydraulic experiments. Indian TBM team is developing Lead Lithium cooled Ceramic Breeder (IN-LLCB) TBM to be tested in ITER. The TBM box structure is cooled by high pressure (8 MPa) and high temperature (300-500C) helium gas.

The first wall of TBM made of complex channel geometry having several parallel channels carrying helium gas for efficient heat extraction. Several mock-ups of these channels need to be tested before finalizing the TBM first wall design and fabrication. Besides the individual testing of such mock-ups of breeding blanket, the testing of Pb-Li to helium heat exchanger, the operational experience of helium loop and understanding of the behavior of high pressure and high temperature system components are very essential for final development of Helium Cooling System for LLCB TBM in ITER. The main requirements and characteristics of the EHCL and its conceptual design are presented in this paper.

Keywords: DEMO, EHCL, ITER, LLCB TBM.

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Authors: Sinee Sankrusme

Abstract:

The study was a case study analysis about Thai Asia Pacific Brewery Company. The purpose was to analyze the company’s marketing objective, marketing strategy at company level, and marketing mix before liquor liberalization in 2000. Methods used in this study were qualitative and descriptive research approach which demonstrated the following results of the study demonstrated as follows: (1) Marketing objective was to increase market share of Heineken and Amtel, (2) the company’s marketing strategies were brand building strategy and distribution strategy. Additionally, the company also conducted marketing mix strategy as follows. Product strategy: The company added more beer brands namely Amstel and Tiger to provide additional choice to consumers, product and marketing research, and product development. Price strategy: the company had taken the following into consideration: cost, competitor, market, economic situation and tax. Promotion strategy: the company conducted sales promotion and advertising. Distribution strategy: the company extended channels its channels of distribution into food shops, pubs and various entertainment places. This strategy benefited interested persons and people who were engaged in the beer business.

Keywords: Marketing Strategy, Beer, Thai Asia Pacific Brewery Company.

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Authors: Ehab F. Badran, Guoxiang Gu

Abstract:

We consider optimal channel equalization for MIMO (multi-input/multi-output) time-varying channels in the sense of MMSE (minimum mean-squared-error), where the observation noise can be non-stationary. We show that all ZF (zero-forcing) receivers can be parameterized in an affine form which eliminates completely the ISI (inter-symbol-interference), and optimal channel equalizers can be designed through minimization of the MSE (mean-squarederror) between the detected signals and the transmitted signals, among all ZF receivers. We demonstrate that the optimal channel equalizer is a modified Kalman filter, and show that under the AWGN (additive white Gaussian noise) assumption, the proposed optimal channel equalizer minimizes the BER (bit error rate) among all possible ZF receivers. Our results are applicable to optimal channel equalization for DWMT (discrete wavelet multitone), multirate transmultiplexers, OFDM (orthogonal frequency division multiplexing), and DS (direct sequence) CDMA (code division multiple access) wireless data communication systems. A design algorithm for optimal channel equalization is developed, and several simulation examples are worked out to illustrate the proposed design algorithm.

Keywords: Channel equalization, Kalman filtering, Time-varying systems.

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Authors: Fadil Elmenfi

Abstract:

Edward Said in his book Culture and Imperialism devotes the introduction to the Arabic translation. He claims that the fading echo of Orientalism in the Arab world is unlike the positive reflections of its counterpart elsewhere in the world. The probable reason behind his inquiry would be that the methodology Abu Deeb applied in translating Said's book contributed to the book having the limited impact which Said is referring to. The paper adds new insights to the body of theory and the effectiveness of the performance of translation from culture to culture. It presents a survey that can provide the reader with an overview of Said's Orientalism and the two Arabic translations of the book. It investigates some of the problems of translating cultural texts, more specifically translating features of Said's style.

Keywords: Orientalism, Retranslation, Arabic Language, Muhammad Enani, Kamal Abu Deeb, Edward Said.

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Authors: Kornchanok Chidchaisuwan

Abstract:

This project is a study of learning activities of creating experience from actual work performance to enhance career skills and technological usage abilities for uses in advertising career work performance for undergraduate students who enroll in the Creative Strategies for Advertising Course. The instructional model consisted of two learning approaches: (1) simulation-based learning, which is the learning with the use of simulations of working in various sections of creative advertisement work with their own work process and steps as well as the virtual technology learning in advertising companies; and (2) project-based learning, which is the learning that the learners engage in actual work performance based on the process of creating and producing creative advertisement works to be present on new media channels. The results of learning management showed that the effects on the students in various aspects were as follows: (1) the students had experience in the advertising process at the higher level; and (2) the students had work performance skills from the actual work performance that enabled them to possess the abilities to create and present their own work; also, they had created more efficient work outcomes and disseminated them on new media channels at a better level.

Keywords: Technical literacy, career skill, experience, simulation-based learning.

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Authors: Babu Sena Paul, Ratnajit Bhattacharjee

Abstract:

Relay based communication has gained considerable importance in the recent years. In this paper we find the end-toend statistics of a two hop non-regenerative relay branch, each hop being Nakagami-m faded. Closed form expressions for the probability density functions of the signal envelope at the output of a selection combiner and a maximal ratio combiner at the destination node are also derived and analytical formulations are verified through computer simulation. These density functions are useful in evaluating the system performance in terms of bit error rate and outage probability.

Keywords: co-operative diversity, diversity combining, maximal ratio combining, selection combining.

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Authors: Abd El Hady N. Ebraheim

Abstract:

This paper introduces a new generalization of the two parameter Weibull distribution. To this end, the quadratic rank transmutation map has been used. This new distribution is named exponentiated transmuted Weibull (ETW) distribution. The ETW distribution has the advantage of being capable of modeling various shapes of aging and failure criteria. Furthermore, eleven lifetime distributions such as the Weibull, exponentiated Weibull, Rayleigh and exponential distributions, among others follow as special cases. The properties of the new model are discussed and the maximum likelihood estimation is used to estimate the parameters. Explicit expressions are derived for the quantiles. The moments of the distribution are derived, and the order statistics are examined.

Keywords: Exponentiated, Inversion Method, Maximum Likelihood Estimation, Transmutation Map.

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Authors: Linyu Wang, Furui Huo, Jianhong Xiang

Abstract:

The Doppler shift generated by high-speed movement and multipath effects in the channel are the main reasons for the generation of a time-frequency doubly-selective (DS) channel. There is severe inter-carrier interference (ICI) in the DS channel. Channel estimation for an orthogonal frequency division multiplexing (OFDM) system over a DS channel is very difficult. The simultaneous orthogonal matching pursuit (SOMP) algorithm under distributed compressive sensing theory (DCS-SOMP) has been used in channel estimation for OFDM systems over DS channels. However, the reconstruction accuracy of the DCS-SOMP algorithm is not high enough in the low Signal-to-Noise Ratio (SNR) stage. To solve this problem, in this paper, we propose an improved DCS-SOMP algorithm based on the inner product difference comparison operation (DCS-DCSOMP). The reconstruction accuracy is improved by increasing the number of candidate indexes and designing the comparison conditions of inner product difference. We combine the DCS-DCSOMP algorithm with the basis expansion model (BEM) to reduce the complexity of channel estimation. Simulation results show the effectiveness of the proposed algorithm and its advantages over other algorithms.

Keywords: OFDM, doubly selective, channel estimation, compressed sensing

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Authors: Mark Harmon, Abdolghani Ebrahimi, Patrick Lucey, Diego Klabjan

Abstract:

In this paper, we predict the likelihood of a player making a shot in basketball from multiagent trajectories. To approach this problem, we present a convolutional neural network (CNN) approach where we initially represent the multiagent behavior as an image. To encode the adversarial nature of basketball, we use a multichannel image which we then feed into a CNN. Additionally, to capture the temporal aspect of the trajectories we use “fading.” We find that this approach is superior to a traditional FFN model. By using gradient ascent, we were able to discover what the CNN filters look for during training. Last, we find that a combined FFN+CNN is the best performing network with an error rate of 39%.

Keywords: basketball, computer vision, image processing, convolutional neural network

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Authors: Sameena Tarannum, S. Pranesh

Abstract:

The effect of linear stability analysis of triple diffusive convection in a vertically oscillating viscoelastic liquid of Oldroyd-B type is studied. The correction Rayleigh number is obtained by using perturbation method which gives prospect to control the convection. The eigenvalue is obtained by using perturbation method by adopting Venezian approach. From the study, it is observed that gravity modulation advances the onset of triple diffusive convection.

Keywords: Gravity modulation, Oldroyd-B liquid, triple diffusive convection, Venezian approach.

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Authors: S. Aisyah Azizan, M. Syafiq Azmi, Yuki Harada, Yoshinobu Maeda, Takaomi Matsutani

Abstract:

We introduced an all-optical multicasting characteristics with wavelength conversion based on a novel all-optical triode using negative feedback semiconductor optical amplifier. This study was demonstrated with a transfer speed of 10 Gb/s to a non-return zero 231-1 pseudorandom bit sequence system. This multi-wavelength converter device can simultaneously provide three channels of output signal with the support of non-inverted and inverted conversion. We studied that an all-optical multicasting and wavelength conversion accomplishing cross gain modulation is effective in a semiconductor optical amplifier which is effective to provide an inverted conversion thus negative feedback. The relationship of received power of back to back signal and output signals with wavelength 1535 nm, 1540 nm, 1545 nm, 1550 nm, and 1555 nm with bit error rate was investigated. It was reported that the output signal wavelengths were successfully converted and modulated with a power penalty of less than 8.7 dB, which the highest is 8.6 dB while the lowest is 4.4 dB. It was proved that all-optical multicasting and wavelength conversion using an optical triode with a negative feedback by three channels at the same time at a speed of 10 Gb/s is a promising device for the new wavelength conversion technology.

Keywords: Cross gain modulation, multicasting, negative feedback optical amplifier, semiconductor optical amplifier.

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Authors: Samera Salimpour Abkenar

Abstract:

In this work, silk yarns were treated using ß-cyclodextrin (ß-CD) and cross-linked with citric acid (CA) via pad-dry-cure method. Elemental and FESEM analyses confirmed the presence of ß-CD on the treated silk samples even after five washing cycles. Then, the treated samples were dyed using natural dyes (carrot, orange and tomato). Results showed that the color strength (K/S) of the treated samples had been markedly enhanced compared with the control sample (after treatment with metal mordant). Finally, the color strength (K/S value) and color fastness (fading, staining and light fastness) of the treated samples with ß-CD were investigated and compared.

Keywords: ß-cyclodextrin, dyeing, natural dyes, silk yarn.

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Authors: Baha Tulu Tanju, Kamil Kahveci

Abstract:

Buoyancy driven heat transfer of nanofluids in a cylindrical enclosure used as a control unit in the subsea hydrocarbon injection wells is investigated in this study. The governing equations obtained with the Boussinesq approximation are solved using Comsol Multiphysics finite element analysis and simulation software. The base fluid is water and CuO is used as nanoparticles. Solution is obtained for nanoparticle solid volume fraction of 8% and for Rayleigh number in the range of 105-107. The results show that nanoparticle usage in the cylindrical electronic control unit has a significant effect on the flow and heat transfer.

Keywords: CuO, enclosure, nanofluid, natural convection

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Authors: N. Promsuwanna, P. Uthansakul, M. Uthansakul

Abstract:

The Carrier Frequency Offset (CFO) due to timevarying fading channel is the main cause of the loss of orthogonality among OFDM subcarriers which is linked to inter-carrier interference (ICI). Hence, it is necessary to precisely estimate and compensate the CFO. Especially for mobile broadband communications, CFO and channel gain also have to be estimated and tracked to maintain the system performance. Thus, synchronization pilots are embedded in every OFDM symbol to track the variations. In this paper, we present the pilot scheme for both channel and CFO estimation where channel estimation process can be carried out with only one OFDM symbol. Additional, the proposed pilot scheme also provides better performance in CFO estimation comparing with the conventional orthogonal pilot scheme due to the increasing of signal-tointerference ratio.

Keywords: MIMO, OFDM, carrier frequency offset, channel, estimation.

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Authors: Radouane Elbahjaoui, Hamid El Qarnia

Abstract:

The present work aims to investigate numerically the thermal and flow characteristics of a rectangular latent heat storage unit (LHSU) during the melting process of a phase change material (PCM). The LHSU consists of a number of vertical and identical plates of PCM separated by rectangular channels. The melting process is initiated when the LHSU is heated by a heat transfer fluid (HTF: water) flowing in channels in a downward or upward direction. The proposed study is motivated by the need to optimize the thermal performance of the LHSU by accelerating the charging process. A mathematical model is developed and a fixed-grid enthalpy formulation is adopted for modeling the melting process coupling with convection-conduction heat transfer. The finite volume method was used for discretization. The obtained numerical results are compared with experimental, analytical and numerical ones found in the literature and reasonable agreement is obtained. Thereafter, the numerical investigations were carried out to highlight the effects of the HTF flow direction and the aspect ratio of the PCM slabs on the heat transfer characteristics and thermal performance enhancement of the LHSU.

Keywords: Phase change material, thermal energy storage, latent heat storage unit, melting.

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Authors: S. Etaig, R. Hasan, N. Perera

Abstract:

This paper analyses the heat transfer performance and fluid flow using different nanofluids in a square enclosure. The energy equation and Navier-Stokes equation are solved numerically using finite volume scheme. The effect of volume fraction concentration on the enhancement of heat transfer has been studied icorporating the Brownian motion; the influence of effective thermal conductivity on the enhancement was also investigated for a range of volume fraction concentration. The velocity profile for different Rayleigh number. Water-Cu, water AL2O3 and water-TiO2 were tested.

Keywords: Computational fluid Dynamics, Natural convection, Nanofluid and Thermal conductivity.

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Authors: Rahil Garnavi, Mohammad Aldeen, M. Emre Celebi, Alauddin Bhuiyan, Constantinos Dolianitis, George Varigos

Abstract:

Automatic segmentation of skin lesions is the first step towards development of a computer-aided diagnosis of melanoma. Although numerous segmentation methods have been developed, few studies have focused on determining the most discriminative and effective color space for melanoma application. This paper proposes a novel automatic segmentation algorithm using color space analysis and clustering-based histogram thresholding, which is able to determine the optimal color channel for segmentation of skin lesions. To demonstrate the validity of the algorithm, it is tested on a set of 30 high resolution dermoscopy images and a comprehensive evaluation of the results is provided, where borders manually drawn by four dermatologists, are compared to automated borders detected by the proposed algorithm. The evaluation is carried out by applying three previously used metrics of accuracy, sensitivity, and specificity and a new metric of similarity. Through ROC analysis and ranking the metrics, it is shown that the best results are obtained with the X and XoYoR color channels which results in an accuracy of approximately 97%. The proposed method is also compared with two state-ofthe- art skin lesion segmentation methods, which demonstrates the effectiveness and superiority of the proposed segmentation method.

Keywords: Border detection, Color space analysis, Dermoscopy, Histogram thresholding, Melanoma, Segmentation.

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Authors: M. Tridi, N. Nacereddine, N. Oucief

Abstract:

This paper describes a novel method for automatic estimation of the contours of weld defect in radiography images. Generally, the contour detection is the first operation which we apply in the visual recognition system. Our approach can be described as a region based maximum likelihood formulation of parametric deformable contours. This formulation provides robustness against the poor image quality, and allows simultaneous estimation of the contour parameters together with other parameters of the model. Implementation is performed by a deterministic iterative algorithm with minimal user intervention. Results testify for the very good performance of the approach especially in synthetic weld defect images.

Keywords: Contour, gaussian, likelihood, rayleigh.

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Authors: Tanveer Ahmed Bhuiyan, Samiul Hayder Choudhury, Asif Al - Rasheed, S.P. Majumder

Abstract:

In this paper, the effect of atmospheric turbulence on bit error probability in free-space optical CDMA scheme with Sequence Inverse Keyed (SIK) optical correlator receiver is analyzed. Here Intensity Modulation scheme is considered for transmission. The turbulence induced fading is described by the newly introduced gamma-gamma pdf[1] as a tractable mathematical model for atmospheric turbulence. Results are evaluated with Gold and Kasami code & it is shown that Gold sequence can be used for more efficient transmission than Kasami sequence in an atmospheric turbulence channel.

Keywords: CDMA, gamma-gamma pdf, atmospheric turbulence, Kasami, Gold, SIK, BER, Power Penalty, FSO.

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Authors: Sebastian B. Mendes

Abstract:

The presence of a vertical edge-crack within a web plate subjected to pure bending induces local compressive stresses about the crack which may cause tension buckling. Approximate theoretical expressions were derived for the critical far-field tensile stress and bending moment capacity of an edge-cracked web plate associated with tension buckling. These expressions were validated with finite element analyses and used to investigate the possibility of tension buckling in web-cracked trial girders. It was found that tension buckling is an unlikely occurrence unless the web is relatively thin or the crack is very long.

Keywords: Fatigue crack, tension buckling, Rayleigh-Ritz, structural stability.

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Authors: B. Kubrak J. Wissink H. Herlina

Abstract:

Two-dimensional Direct Numerical Simulation (DNS) of high Schmidt number mass transfer in a convective flow environment (Rayleigh-B'enard) is carried out and results are compared to experimental data. A fourth-order accurate WENO-scheme has been used for scalar transport in order to aim for a high accuracy in areas of high concentration gradients. It was found that the typical spatial distance between downward plumes of cold high concentration water and the eddy size are in good agreement with experiments using a combined PIV-LIF technique for simultaneous and spatially synoptic measurements of 2D velocity and concentration fields.

Keywords: Air-Water Interface, DNS, Gas Transfer, LIF.

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Authors: Anurag Saxena, Alkesh Agrawal, Dinesh Kumar

Abstract:

The next generation mobile communication systems i.e. fourth generation (4G) was developed to accommodate the quality of service and required data rate. This project focuses on multiple access technique proposed in 4G communication systems. It is attempted to demonstrate the IDMA (Interleave Division Multiple Access) technology. The basic principle of IDMA is that interleaver is different for each user whereas CDMA employs different signatures. IDMA inherits many advantages of CDMA such as robust against fading, easy cell planning; dynamic channel sharing and IDMA increase the spectral efficiency and reduce the receiver complexity. In this, performance of IDMA is analyzed using QC-LDPC coding scheme further it is compared with LDPC coding and at last BER is calculated and plotted in MATLAB.

Keywords: 4G, QC-LDPC, CDMA, IDMA.

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Authors: Muhammad R. Alrabeiah, Ibrahim S. Alnomay

Abstract:

The need in cognitive radio system for a simple, fast, and independent technique to sense the spectrum occupancy has led to the energy detection approach. Energy detector is known by its dependency on noise variation in the system which is one of its major drawbacks. In this paper, we are aiming to improve its performance by utilizing a weighted collaborative spectrum sensing, it is similar to the collaborative spectrum sensing methods introduced previously in the literature. These weighting methods give more improvement for collaborative spectrum sensing as compared to no weighting case. There is two method proposed in this paper: the first one depends on the channel status between each sensor and the primary user while the second depends on the value of the energy measured in each sensor.

Keywords: Cognitive radio, Spectrum sensing, Collaborative sensors, Weighted Decisions.

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Authors: T. V. S. Sekhar, B. Hema Sundar Raju

Abstract:

Laminar natural-convective heat transfer from a horizontal cylinder is studied by solving the Navier-Stokes and energy equations using higher order compact scheme in cylindrical polar coordinates. Results are obtained for Rayleigh numbers of 1, 10, 100 and 1000 for a Prandtl number of 0.7. The local Nusselt number and mean Nusselt number are calculated and compared with available experimental and theoretical results. Streamlines, vorticity - lines and isotherms are plotted.

Keywords: Higher order compact scheme, Navier-Stokes equations, Energy equation, Natural convection, Boussinesq's approximation and Mean Nusselt number.

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Authors: Sahila Chopra, Hemdeep, Arshdeep Kaur, Raj K. Gupta

Abstract:

In recent times, we noticed an interesting and important role of non-coplanar degree-of-freedom (Φ = 00) in heavy ion reactions. Using the dynamical cluster-decay model (DCM) with Φ degree-of-freedom included, we have studied three compound systems 246Bk∗, 164Yb∗ and 105Ag∗. Here, within the DCM with pocket formula for nuclear proximity potential, we look for the effects of including compact, non-coplanar configurations (Φc = 00) on the non-compound nucleus (nCN) contribution in total fusion cross section σfus. For 246Bk∗, formed in 11B+235U and 14N+232Th reaction channels, the DCM with coplanar nuclei (Φc = 00) shows an nCN contribution for 11B+235U channel, but none for 14N+232Th channel, which on including Φ gives both reaction channels as pure compound nucleus decays. In the case of 164Yb∗, formed in 64Ni+100Mo, the small nCN effects for Φ=00 are reduced to almost zero for Φ = 00. Interestingly, however, 105Ag∗ for Φ = 00 shows a small nCN contribution, which gets strongly enhanced for Φ = 00, such that the characteristic property of PCN presents a change of behaviour, like that of a strongly fissioning superheavy element to a weakly fissioning nucleus; note that 105Ag∗ is a weakly fissioning nucleus and Psurv behaves like one for a weakly fissioning nucleus for both Φ = 00 and Φ = 00. Apparently, Φ is presenting itself like a good degree-of-freedom in the DCM.

Keywords: Dynamical cluster-decay model, fusion cross sections, non-compound nucleus effects, non-coplanarity.

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Authors: Dongheon Shin, Kyungnam Ko, Jongchul Huh

Abstract:

The investigation on wind turbine degradation was carried out using the nacelle wind data. The three Vestas V80-2MW wind turbines of Sungsan wind farm in Jeju Island, South Korea were selected for this work. The SCADA data of the wind farm for five years were analyzed to draw power curve of the turbines. It is assumed that the wind distribution is the Rayleigh distribution to calculate the normalized capacity factor based on the drawn power curve of the three wind turbines for each year. The result showed that the reduction of power output from the three wind turbines occurred every year and the normalized capacity factor decreased to 0.12%/year on average.

Keywords: Wind energy, Power curve, Capacity factor, Annual energy production.

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Authors: A. Ja, J. Belabid, A. Cheddadi

Abstract:

This paper reports the numerical simulation of doublediffusive natural convection flows within a horizontal annular filled with a saturated porous medium. The analysis concerns the influence of the different parameters governing the problem, namely, the Rayleigh number Ra, the Lewis number Le and the buoyancy ratio N, on the heat and mass transfer and on the flow structure, in the case of a fixed radius ratio R = 2. The numerical model used for the discretization of the dimensionless equations governing the problem is based on the finite difference method, using the ADI scheme. The study is focused on steady-state solutions in the cooperation situation.

Keywords: Natural convection, double-diffusion, porous medium, annular geometry, finite differences.

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Authors: Salah Salmi, Karim Kemih, Malek Benslama

Abstract:

Synchronization is a difficult problem in CDMA satellite communications. Due to the influence of additive noise and fading in the mobile channel, it is not easy to keep up with the attenuation and offset. This paper considers a recently proposed approach to solve the problem of synchronization chaotic Chen system in CDMA satellite communication in the presence of constant attenuation and offset. An analytic algorithm that provides closed form channel and carrier offset estimates is presented. The principle of this approach is based on adding a compensation block before the receiver to compensate the distortion of the imperfect channel by using genetic algorithm. The resultants presented, show that the receiver is able to recover rapidly the synchronization with the transmitter.

Keywords: Chaotic Chen system, genetic algorithm, Synchronization, CDMA

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Authors: Youssef Khmou, Said Safi

Abstract:

In this paper, we investigated the effect of real valued transformation of the spectral matrix of the received data for Angles Of Arrival estimation problem.  Indeed, the unitary transformation of Partial Propagator (UPP) for narrowband sources is proposed and applied on Uniform Linear Array (ULA).

Monte Carlo simulations proved the performance of the UPP spectrum comparatively with Forward Backward Partial Propagator (FBPP) and Unitary Propagator (UP). The results demonstrates that when some of the sources are fully correlated and closer than the Rayleigh angular limit resolution of the broadside array, the UPP method outperforms the FBPP in both of spatial resolution and complexity.

Keywords: DOA, Uniform Linear Array, Narrowband, Propagator, Real valued transformation, Subspace, Unitary Operator.

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Authors: H. Rong, X. C. Yin, J. Yang, Y. N. Shen

Abstract:

Based on Rayleigh beam theory, the sub-impacts of a free-free beam struck horizontally by a round-nosed rigid mass is simulated by the finite difference method and the impact-separation conditions. In order to obtain the sub-impact force, a uniaxial compression elastic-plastic contact model is employed to analyze the local deformation field on contact zone. It is found that the horizontal impact is a complicated process including the elastic plastic sub-impacts in sequence. There are two sub-zones of sub-impact. In addition, it found that the elastic energy of the free-free beam is more suitable for the Poisson collision hypothesis to explain compression and recovery processes.

Keywords: beam, sub-impact, elastic-plastic deformation, finite difference method.

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