Search results for: finite difference modelling

Authors: Ali K. M. Al-Nasrawi, Uday A. Al-Hamdany, Sarah M. Hamylton, Brian G. Jones, Yasir M. Alyazichi

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Surface elevation dynamics have always responded to disturbance regimes. Creating Digital Elevation Models (DEMs) to detect surface dynamics has led to the development of several methods, devices and data clouds. DEMs can provide accurate and quick results with cost efficiency, in comparison to the inherited geomatics survey techniques. Nowadays, remote sensing datasets have become a primary source to create DEMs, including LiDAR point clouds with GIS analytic tools. However, these data need to be tested for error detection and correction. This paper evaluates various DEMs from different data sources over time for Apple Orchard Island, a coastal site in southeastern Australia, in order to detect surface dynamics. Subsequently, 30 chosen locations were examined in the field to test the error of the DEMs surface detection using high resolution global positioning systems (GPSs). Results show significant surface elevation changes on Apple Orchard Island. Accretion occurred on most of the island while surface elevation loss due to erosion is limited to the northern and southern parts. Concurrently, the projected differential correction and validation method aimed to identify errors in the dataset. The resultant DEMs demonstrated a small error ratio (≤ 3%) from the gathered datasets when compared with the fieldwork survey using RTK-GPS. As modern modelling approaches need to become more effective and accurate, applying several tools to create different DEMs on a multi-temporal scale would allow easy predictions in time-cost-frames with more comprehensive coverage and greater accuracy. With a DEM technique for the eco-geomorphic context, such insights about the ecosystem dynamic detection, at such a coastal intertidal system, would be valuable to assess the accuracy of the predicted eco-geomorphic risk for the conservation management sustainability. Demonstrating this framework to evaluate the historical and current anthropogenic and environmental stressors on coastal surface elevation dynamism could be profitably applied worldwide.

Keywords: DEMs, eco-geomorphic-dynamic processes, geospatial information science. Remote sensing, surface elevation changes.

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Authors: Mustafa M. Donma, Orkide Donma

Abstract:

Alterations in lipid parameters as well as in the fat distribution of the body are noteworthy during the evaluation of obesity stages. Total cholesterol (TC), triglycerides (TRG), low density lipoprotein-cholesterol (LDL-C), high density lipoprotein-cholesterol (HDL-C) are basic lipid fractions. Fat deposited in trunk and extremities may give considerable amount of information. Ratios such as trunk-to-leg fat ratio (TLFR) and trunk-to-appendicular fat ratio (TAFR) are derived from distinct fat distribution in these areas. In this study, lipid fractions and TLFR as well as TAFR were evaluated and the distinctions among healthy, obese (OB) and morbid obese (MO) groups were investigated. Three groups [normal body mass index (N-BMI), OB, MO] were constituted. Ages and sexes of the groups were matched. The study protocol was approved by the Non-interventional Ethics Committee of Tekirdag Namik Kemal University. Written informed consent forms were obtained from the parents of the participants. Anthropometric measurements (height, weight, waist circumference, hip circumference, head circumference, neck circumference) were recorded during the physical examination. BMI values were calculated. Total, trunk, leg and arm fat mass values were obtained by TANITA Bioelectrical Impedance Analysis. These values were used to calculate TLFR and TAFR. Systolic (SBP) and diastolic blood pressures (DBP) were measured. Routine biochemical tests including lipid fractions were performed. Data were evaluated using SPSS software. p value smaller than 0.05 was accepted as significant. There was no difference among the age values and gender ratios of the groups. Any statistically significant difference was not observed in terms of DBP, TLFR as well as serum lipid fractions. Higher SBP values were measured both in OB and MO children than those with N-BMI. TAFR showed a significant difference between N-BMI and OB groups. Statistically significant increases were detected between insulin values of N-BMI group and OB as well as MO groups. There were bivariate correlations between LDL and TLFR as well as TAFR values in MO group. When adjusted for SBP and DBP, partial correlations were calculated for LDL-TLFR as well as LDL-TAFR. Much stronger partial correlations were obtained for the same couples upon controlling for TRG and HDL-C. Much stronger partial correlations observed in MO children emphasize the potential transition from morbid obesity to metabolic syndrome. These findings have concluded that LDL-C may be suggested as a discriminating parameter between OB and MO children.

Keywords: Children, lipid parameters, obesity, trunk-to-leg fat ratio, trunk-to-appendicular fat ratio.

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Authors: Panagiotis Kyratsis, Dr. Ing. Nikolaos Bilalis, Dr. Ing. Aristomenis Antoniadis

Abstract:

Twist drills are geometrical complex tools and thus various researchers have adopted different mathematical and experimental approaches for their simulation. The present paper acknowledges the increasing use of modern CAD systems and using the API (Application Programming Interface) of a CAD system, drilling simulations are carried out. The developed DRILL3D software routine, creates parametrically controlled tool geometries and using different cutting conditions, achieves the generation of solid models for all the relevant data involved (drilling tool, cut workpiece, undeformed chip). The final data derived, consist a platform for further direct simulations regarding the determination of cutting forces, tool wear, drilling optimizations etc.

Keywords: Drilling, CAD based simulation, 3D-modelling.

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Authors: M. Almeshal, M. O. Tokhi, K. M. Goher

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A novel design of two-wheeled robotic vehicle with moving payload is presented in this paper. A mathematical model describing the vehicle dynamics is derived and simulated in Matlab Simulink environment. Two control strategies were developed to stabilise the vehicle in the upright position. A robust Proportional- Integral-Derivative (PID) control strategy has been implemented and initially tested to measure the system performance, while the second control strategy is to use a hybrid fuzzy logic controller (FLC). The results are given on a comparative basis for the system performance in terms of disturbance rejection, control algorithms robustness as well as the control effort in terms of input torque.

Keywords: double inverted pendulum, modelling, robust control, simulation,

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Authors: U. Chattaraj, K. Dhusiya, M. Raviteja

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Perception reaction time of drivers is an outcome of human thought process, which is vague and approximate in nature and also varies from driver to driver. So, in this study a fuzzy logic based model for prediction of the same has been presented, which seems suitable. The control factors, like, age, experience, intensity of driving of the driver, speed of the vehicle and distance of stimulus have been considered as premise variables in the model, in which the perception reaction time is the consequence variable. Results show that the model is able to explain the impacts of the control factors on perception reaction time properly.

Keywords: Driver, fuzzy logic, perception reaction time, premise variable.

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Authors: Adel Smeda, Adel Alti, Mourad Oussalah, Abdallah Boukerram

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A key aspect of the design of any software system is its architecture. An architecture description provides a formal model of the architecture in terms of components and connectors and how they are composed together. COSA (Component-Object based Software Structures), is based on object-oriented modeling and component-based modeling. The model improves the reusability by increasing extensibility, evolvability, and compositionality of the software systems. This paper presents the COSA modelling tool which help architects the possibility to verify the structural coherence of a given system and to validate its semantics with COSA approach.

Keywords: Software Architecture, Architecture Description Languages, UML, Components, Connectors.

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Authors: Essam A. Al-Bahkali

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The design of a landing gear is one of the fundamental aspects of aircraft design. The need for a light weight, high strength, and stiffness characteristics coupled with techno economic feasibility are a key to the acceptability of any landing gear construction. In this paper, an approach for analyzing two different designed landing gears for an unmanned aircraft vehicle (UAV) using advanced CAE techniques will be applied. Different landing conditions have been considered for both models. The maximum principle stresses for each model along with the factor of safety are calculated for every loading condition. A conclusion is drawing about better geometry.

Keywords: Landing Gear, Model, Finite Element Analysis, Aircraft.

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Authors: A. J. Mahmood, L. B. Y. Aldabbagh

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The counter flow solar air heaters, with four transverse fins and wire mesh layers are constructed and investigated experimentally for thermal efficiency at a geographic location of Cyprus in the city of Famagusta. The absorber plate is replaced by sixteen steel wire mesh layers, 0.18 x 0.18cm in cross section opening and a 0.02cm in diameter. The wire mesh layers arranged in three groups, first and second include 6 layers, while the third include 4 layers. All layers fixed in the duct parallel to the glazing and each group separated from the others by wood frame thickness of 0.5cm to reduce the pressure drop. The transverse fins arranged in a way to force the air to flow through the bed like eight letter path with flow depth 3cm. The proposed design has increased the heat transfer rate, but on other hand causes a high pressure drop. The obtained results show that, for air mass flow rate range between 0.011-0.036kg/s, the thermal efficiency increases with increasing the air mass flow. The maximum efficiency obtained is 65.6% for the mass flow rate of 0.036kg/s. Moreover, the temperature difference between the outlet flow and the ambient temperature, ΔT, reduces as the air mass flow rate increase. The maximum difference between the outlet and ambient temperature obtained was 43°C for double pass for minimum mass flow rate of 0.011kg/s. Comparison with a conventional solar air heater collector shows a significantly development in the thermal efficiency.

Keywords: Counter flow, solar air heater (SAH), Wire mesh, Fins, Thermal efficiency.

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Authors: Nguyen Viet Tan

Abstract:

The Bahnar is one of 11 indigenous groups living in the Central Highlands of Vietnam. It is one among the four most popular groups in this area, including the Mnong who speak the same language of Mon Khmer family, while both groups of the Jrai and the Rhade belong to the Malayo-Polynesian language family. These groups once captured fertile plateaus, left their cultural and artistic heritage which affected the remaining small groups. Despite the difference in ethnic origins, these groups seem to share similar beliefs, customs and related folk arts after a very long time living beside each other. However, through an in-depth study, this paper points out the fact that the decorative patterns used by the Bahnar are different from the other ethnic groups, especially in color. Based on historical materials from the local museums and some studies in 1980s when all of the ethnic groups in this area had still lived in self-sufficient condition, this paper characterizes the traditional color scheme used by the Bahnar and identifies the difference in decorative motifs of this group compared to the others by pointing out they do not use green in their usual decorative patterns. Moreover, combined with some field surveys recently, through comparative analysis, it also discovers stylistic variations of these patterns in the process of cultural exchange with the other ethnic groups, both in and out of the region, in modern living conditions. This study helps to preserve and promote the traditional values and cultural identity of the Bahnar people in the Central Highlands of Vietnam, avoiding the fusion of styles among groups during the cultural exchange.

Keywords: Bahnar ethic group, decorative patterns, the central highland of Vietnam, traditional color scheme.

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Authors: James D. Clark, Bernard H. Stark

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The paper presents a modelling methodology for small scale multi-source renewable energy systems. Using historical site-specific weather data, the relationships of cost, availability and energy form are visualised as a function of the sizing of photovoltaic arrays, wind turbines, and battery capacity. The specific dependency of each site on its own particular weather patterns show that unique solutions exist for each site. It is shown that in certain cases the capital component cost can be halved if the desired theoretical demand availability is reduced from 100% to 99%.

Keywords: Energy Analysis, Forecasting, Distributed powergeneration.

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Authors: Ivana Scidà, Francesco Alotto, Anna Osello

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Due to the importance given today to innovation, the education sector is evolving thanks digital technologies. Virtual Reality (VR) can be a potential teaching tool offering many advantages in the field of training and education, as it allows to acquire theoretical knowledge and practical skills using an immersive experience in less time than the traditional educational process. These assumptions allow to lay the foundations for a new educational environment, involving and stimulating for students. Starting from the objective of strengthening the innovative teaching offer and the learning processes, the case study of the research concerns the digitalization of MastrLAB, High Quality Laboratory (HQL) belonging to the Department of Structural, Building and Geotechnical Engineering (DISEG) of the Polytechnic of Turin, a center specialized in experimental mechanical tests on traditional and innovative building materials and on the structures made with them. The MastrLAB-VR has been developed, a revolutionary innovative training tool designed with the aim of educating the class in total safety on the techniques of use of machinery, thus reducing the dangers arising from the performance of potentially dangerous activities. The virtual laboratory, dedicated to the students of the Building and Civil Engineering Courses of the Polytechnic of Turin, has been projected to simulate in an absolutely realistic way the experimental approach to the structural tests foreseen in their courses of study: from the tensile tests to the relaxation tests, from the steel qualification tests to the resilience tests on elements at environmental conditions or at characterizing temperatures. The research work proposes a methodology for the virtualization of technical laboratories through the application of Building Information Modelling (BIM), starting from the creation of a digital model. The process includes the creation of an independent application, which with Oculus Rift technology will allow the user to explore the environment and interact with objects through the use of joypads. The application has been tested in prototype way on volunteers, obtaining results related to the acquisition of the educational notions exposed in the experience through a virtual quiz with multiple answers, achieving an overall evaluation report. The results have shown that MastrLAB-VR is suitable for both beginners and experts and will be adopted experimentally for other laboratories of the University departments.

Keywords: Building Information Modelling, digital learning, education, virtual laboratory, virtual reality.

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Authors: Ardeshir Karami Mohammadi

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A Variable Structure Model Reference Adaptive Controller using state variables is proposed for a class of multi input-multi output systems. Adaptation law is of variable structure type and switching functions is designed based on stability requirements. Global exponential stability is proved based on Lyapunov criterion. Transient behavior is analyzed using sliding mode control and shows perfect model following at a finite time.

Keywords: Adaptive control, Model reference, Variablestructure, MIMO system.

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Authors: Brian H. Marsh

Abstract:

Nitrogen fertilizer is the most used and often the most mismanaged nutrient input. Nitrogen management has tremendous implications on crop productivity, quality and environmental stewardship. Sufficient nitrogen is needed to optimum yield and quality. Soil and in-season plant tissue testing for nitrogen status are a time consuming and expensive process. Real time sensing of plant nitrogen status can be a useful tool in managing nitrogen inputs. The objectives of this project were to assess the reliability of remotely sensed non-destructive plant nitrogen measurements compared to wet chemistry data from sampled plant tissue, develop in-season nitrogen recommendations based on remotely sensed data for improved nitrogen use efficiency and assess the potential for determining yield and quality from remotely sensed data. Very good correlations were observed between early-season remotely sensed crop nitrogen status and plant nitrogen concentrations and subsequent in-season fertilizer recommendations. The transmittance/absorbance type meters gave the most accurate readings. Early in-season fertilizer recommendation would be to apply 40 kg nitrogen per hectare plus 15 kg nitrogen per hectare for each unit difference measured with the SPAD meter between the crop and reference area or 25 kg plus 13 kg per hectare for each unit difference measured with the CCM 200. Once the crop was sufficiently fertilized meter readings became inconclusive and were of no benefit for determining nitrogen status, silage yield and quality and grain yield and protein.

Keywords: Wheat, nitrogen fertilization, chlorophyll meter.

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Authors: Rafat Alshorman, Walter Hussak

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Most of the concurrent transactional protocols consider serializability as a correctness criterion of the transactions execution. Usually, the proof of the serializability relies on mathematical proofs for a fixed finite number of transactions. In this paper, we introduce a protocol to deal with an infinite number of transactions which are iterated infinitely often. We specify serializability of the transactions and the protocol using a specification language based on temporal logics. It is worthwhile using temporal logics such as LTL (Lineartime Temporal Logic) to specify transactions, to gain full automatic verification by using model checkers.

Keywords: Multi-step transactions, LTL specifications, Model Checking.

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Authors: H. Bouadi, M. Bouchoucha, M. Tadjine

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In this paper; we are interested principally in dynamic modelling of quadrotor while taking into account the high-order nonholonomic constraints in order to develop a new control scheme as well as the various physical phenomena, which can influence the dynamics of a flying structure. These permit us to introduce a new state-space representation. After, the use of Backstepping approach for the synthesis of tracking errors and Lyapunov functions, a sliding mode controller is developed in order to ensure Lyapunov stability, the handling of all system nonlinearities and desired tracking trajectories. Finally simulation results are also provided in order to illustrate the performances of the proposed controller.

Keywords: Dynamic modeling, nonholonomic constraints, Backstepping, sliding mode.

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Authors: Tomoya Okubo, Kuninori Nakamura, Shin-ichi Mayekawa

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In this research, a latent class vector model for pairwise data is formulated. As compared to the basic vector model, this model yields consistent estimates of the parameters since the number of parameters to be estimated does not increase with the number of subjects. The result of the analysis reveals that the model was stable and could classify each subject to the latent classes representing the typical scales used by these subjects.

Keywords: finite mixture models, latent class analysis, Thrustone's paired comparison method, vector model

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Authors: Long Kim Vu, Ban Dang Nguyen

Abstract:

In this paper, the finite element method (FEM) is utilized to simulate the comprehensive process including tightening, releasing and self-loosening of a bolt joint under transverse vibration. Following to the accurate geometry of helical threads, an absolutely hexahedral meshing is implemented. The accuracy of simulation process is verified and validated by comparison with the experimental results on clamping force-vibration relationship, which shows the sufficient correlation. Further analysis with different amplitude and frequency of transverse vibration is done to determine the dominant factor inducing the failure.

Keywords: Bolt self-loosening, contact state, FEM, transverse vibration.

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Authors: Habibis Saleh, Ishak Hashim

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Conjugate natural convection in a differentially heated square enclosure containing a polygon shaped object is studied numerically in this article. The effect of various polygon types on the fluid flow and thermal performance of the enclosure is addressed for different thermal conductivities. The governing equations are modeled and solved numerically using the built-in finite element method of COMSOL software. It is found that the heat transfer rate remains stable by varying the polygon types.

Keywords: Natural convection, Polygon object, COMSOL

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Authors: M. Ghorbany

Abstract:

A square matrix over the complex field with non- negative integral trace is called a quasi-permutation matrix. For a finite group G the minimal degree of a faithful representation of G by quasi-permutation matrices over the rationals and the complex numbers are denoted by q(G) and c(G) respectively. Finally r (G) denotes the minimal degree of a faithful rational valued complex character of C. The purpose of this paper is to calculate q(G), c(G) and r(G) for the group S L(2, q) when extended by a certain group of order two.

Keywords: General linear group, Quasi-permutation

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Authors: Ahmet Tekcan

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Let F(x, y) = ax2 + bxy + cy2 be a positive definite binary quadratic form with discriminant Δ whose base points lie on the line x = -1/m for an integer m ≥ 2, let p be a prime number and let Fp be a finite field. Let EF : y2 = ax3 + bx2 + cx be an elliptic curve over Fp and let CF : ax3 + bx2 + cx ≡ 0(mod p) be the cubic congruence corresponding to F. In this work we consider some properties of positive definite quadratic forms, elliptic curves and cubic congruences.

Keywords: Binary quadratic form, elliptic curves, cubic congruence.

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Authors: James A Foster, Guglielmo S Aglietti

Abstract:

Multifunctional structures are a potentially disruptive technology that allows for significant mass savings on spacecraft. The specific concept addressed herein is that of a multifunctional power structure. In this paper, a parametric optimisation of the design of such a structure that uses commercially available battery cells is presented. Using numerical modelling, it was found that there exists several trade-offs aboutthe conflict between the capacity of the panel and its mechanical properties. It was found that there is no universal optimal location for the cells. Placing them close to the mechanical interfaces increases loading in the mechanically weak cells whereas placing them at the centre of the panel increases the stress inthe panel and reduces the stiffness of the structure.

Keywords: Design Optimization, Multifunctional Structures, Power Storage.

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Authors: Hossein Abbasi

Abstract:

The stability is an important topic to plan and manage the energy in the microgrids as the same as the conventional power systems. The voltage and frequency stability is one of the most important issues recently studied in microgrids. The objectives of this paper are the modelling and designing of the components and optimal controllers for the voltage and frequency control of the AC/DC hybrid microgrid under the different disturbances. Since the PI controllers have the advantages of simple structure and easy implementation, so they are designed and modeled in this paper. The harmony search (HS) algorithm is used to optimize the controllers’ parameters. According to the achieved results, the PI controllers have a good performance in voltage and frequency control of the microgrid.

Keywords: Frequency control, HS algorithm, microgrid, PI controller, voltage control.

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Authors: C. Kozkurt, A. Fenercioglu, M. Soyaslan

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In this study rack systems that are structural storage units of warehouses have been analyzed as structural with Finite Element Method (FEA). Each cell of discussed rack system storages pallets which have from 800 kg to 1000 kg weights and 0.80x1.15x1.50 m dimensions. Under this load, total deformations and equivalent stresses of structural elements and principal stresses, tensile stresses and shear stresses of connection elements have been analyzed. The results of analyses have been evaluated according to resistance limits of structural and connection elements. Obtained results have been presented as visual and magnitude.

Keywords: warehouse, structural analysis, AS/RS, FEM, FEA

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Authors: Almas Tayebi, Tayeb Saki Nejad, Alireza Shoukofar

Abstract:

The trial in the city, located 170 kilometers from the Iranian city of Ahvaz was Omidiyeh. The main factor in this project includes 4 levels in control (without hormones), use of hormones in the seed, vegetative and flowering stage respectively. And sub-plots included 3 varieties of vetch in three levels, with local names, was the jewel in the study of light and Auxin in the vegetative and reproductive different times in different varieties of vetch was investigated. This test has been taken in the plots in a randomized complete block with four replications. In order to study the effects of the hormone Auxin in the growth stages (seed, vegetative and flowering) to control (no hormone Auxin) on three local varieties of vetch, the essence of light and plant height, number of pods per plant, seed number The pods, seeds per plant, grain weight, grain yield, plant dry weight and protein content were measured. Among the vetch varieties for plant height, number of pods per plant, a seed per plant, grain weight, grain yield, and plant dry weight and protein levels of 1 percent of plant and seed number per pod per plant at 5% level of There was no significant difference. Interactions for grain yield per plant, grain yield and protein levels of 1 percent and the number of seeds per pod and seed weight are significant differences in levels 5 and plant height and plant dry weight of the interaction were INFLUENCE There was no significant difference in them.

Keywords: Auxin hormones, various periods of growth, production components, vetch

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Authors: Abhijit Mitra

Abstract:

The paper provides an in-depth tutorial of mathematical construction of maximal length sequences (m-sequences) via primitive polynomials and how to map the same when implemented in shift registers. It is equally important to check whether a polynomial is primitive or not so as to get proper m-sequences. A fast method to identify primitive polynomials over binary fields is proposed where the complexity is considerably less in comparison with the standard procedures for the same purpose.

Keywords: Finite field, irreducible polynomial, primitive polynomial, maximal length sequence, additive shift register, multiplicative shift register.

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Authors: Gilberto Gonzalez-A, Noe Barrera-G

Abstract:

An analysis of a synchronous generator in a bond graph approach is proposed. This bond graph allows to determine the simplified models of the system by using singular perturbations. Firstly, the nonlinear bond graph of the generator is linearized. Then, the slow and fast state equations by applying singular perturbations are obtained. Also, a bond graph to get the quasi-steady state of the slow dynamic is proposed. In order to verify the effectiveness of the singularly perturbed models, simulation results of the complete system and reduced models are shown.

Keywords: Bond graph modelling, synchronous generator, singular perturbations

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Authors: J. Schmidt, O. Kornadt

Abstract:

The major part of light weight timber constructions consists of insulation. Mineral wool is the most commonly used insulation due to its cost efficiency and easy handling. The fiber orientation and porosity of this insulation material enables flowthrough. The air flow resistance is low. If leakage occurs in the insulated bay section, the convective flow may cause energy losses and infiltration of the exterior wall with moisture and particles. In particular the infiltrated moisture may lead to thermal bridges and growth of health endangering mould and mildew. In order to prevent this problem, different numerical calculation models have been developed. All models developed so far have a potential for completion. The implementation of the flow-through properties of mineral wool insulation may help to improve the existing models. Assuming that the real pressure difference between interior and exterior surface is larger than the prescribed pressure difference in the standard test procedure for mineral wool ISO 9053 / EN 29053, measurements were performed using the measurement setup for research on convective moisture transfer “MSRCMT". These measurements show, that structural inhomogeneities of mineral wool effect the permeability only at higher pressure differences, as applied in MSRCMT. Additional microscopic investigations show, that the location of a leak within the construction has a crucial influence on the air flow-through and the infiltration rate. The results clearly indicate that the empirical values for the acoustic resistance of mineral wool should not be used for the calculation of convective transfer mechanisms.

Keywords: convection, convective transfer, infiltration, mineralwool, permeability, resistance, leakage

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Authors: M. Sedighizadeh, A. Rezazadeh

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A method has been developed for preparing load models for power flow and stability. The load modeling (LOADMOD) computer software transforms data on load class mix, composition, and characteristics into the from required for commonly–used power flow and transient stability simulation programs. Typical default data have been developed for load composition and characteristics. This paper defines LOADMOD software and describes the dynamic and static load modeling techniques used in this software and results of initial testing for BAKHTAR power system.

Keywords: Load Modelling, Static, Power Flow.

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Authors: M. H. M. Rashid

Abstract:

A Banach space operator T obeys property (gm) if the isolated points of the spectrum σ(T) of T which are eigenvalues are exactly those points λ of the spectrum for which T − λI is a left Drazin invertible. In this article, we study the stability of property (gm), for a bounded operator acting on a Banach space, under perturbation by finite rank operators, by nilpotent operators, by quasi-nilpotent operators, or more generally by algebraic operators commuting with T.

Keywords: Weyl’s theorem, Weyl spectrum, polaroid operators, property (gm), property (m).

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Authors: Neil Bar, Andrew Heweston

Abstract:

Probability of failure (PF) often appears alongside factor of safety (FS) in design acceptance criteria for rock slope, underground excavation and open pit mine designs. However, the design acceptance criteria generally provide no guidance relating to how PF should be calculated for homogeneous and heterogeneous rock masses, or what qualifies a ‘reasonable’ PF assessment for a given slope design. Observational and kinematic methods were widely used in the 1990s until advances in computing permitted the routine use of numerical modelling. In the 2000s and early 2010s, PF in numerical models was generally calculated using the point estimate method. More recently, some limit equilibrium analysis software offer statistical parameter inputs along with Monte-Carlo or Latin-Hypercube sampling methods to automatically calculate PF. Factors including rock type and density, weathering and alteration, intact rock strength, rock mass quality and shear strength, the location and orientation of geologic structure, shear strength of geologic structure and groundwater pore pressure influence the stability of rock slopes. Significant engineering and geological judgment, interpretation and data interpolation is usually applied in determining these factors and amalgamating them into a geotechnical model which can then be analysed. Most factors are estimated ‘approximately’ or with allowances for some variability rather than ‘exactly’. When it comes to numerical modelling, some of these factors are then treated deterministically (i.e. as exact values), while others have probabilistic inputs based on the user’s discretion and understanding of the problem being analysed. This paper discusses the importance of understanding the key aspects of slope design for homogeneous and heterogeneous rock masses and how they can be translated into reasonable PF assessments where the data permits. A case study from a large open pit gold mine in a complex geological setting in Western Australia is presented to illustrate how PF can be calculated using different methods and obtain markedly different results. Ultimately sound engineering judgement and logic is often required to decipher the true meaning and significance (if any) of some PF results.

Keywords: Probability of failure, point estimate method, Monte-Carlo simulations, sensitivity analysis, slope stability.

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