Search results for: formulation

Authors: Cheng-En Tsai, Chung-Chun Hsiao, Fu-Yuan Chang, Liang-Lun Lan, Jia-Ying Tu

Abstract:

New design of three dimensional (3D) flywheel system based on gimbal and gyro mechanics is proposed. The 3D flywheel device utilizes the rotational motion of three spherical shells and the conservation of angular momentum to achieve planar locomotion. Actuators mounted to the ring-shape frames are installed within the system to drive the spherical shells to rotate, for the purpose of steering and stabilization. Similar to the design of 2D flywheel system, it is expected that the spherical shells may function like a “flyball” to store and supply mechanical energy; additionally, in comparison with typical single-wheel and spherical robots, the 3D flywheel can be used for developing omnidirectional robotic systems with better mobility. The Lagrangian method is applied to derive the equation of motion of the 3D flywheel system, and simulation studies are presented to verify the proposed design.

Keywords: Gimbal, spherical robot, gyroscope, Lagrangian formulation, flyball.

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Authors: Cheng-En Tsai, Chung-Chun Hsiao, Fu-Yuan Chang, Liang-Lun Lan, Jia-Ying Tu

Abstract:

New design of three dimensional (3D) flywheel system based on gimbal and gyro mechanics is proposed. The 3D flywheel device utilizes the rotational motion of three spherical shells and the conservation of angular momentum to achieve planar locomotion. Actuators mounted to the ring-shape frames are installed within the system to drive the spherical shells to rotate, for the purpose of steering and stabilization. Similar to the design of 2D flywheel system, it is expected that the spherical shells may function like a “flyball” to store and supply mechanical energy; additionally, in comparison with typical single-wheel and spherical robots, the 3D flywheel can be used for developing omnidirectional robotic systems with better mobility. The Lagrangian method is applied to derive the equation of motion of the 3D flywheel system, and simulation studies are presented to verify the proposed design.

Keywords: Gimbal, spherical robot, gyroscope, Lagrangian formulation, flyball.

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Authors: Athanasios Theoharidis, Thomas Kamalakis, Ioannis Neokosmidis, Thomas Sphicopoulos

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In this paper, the application of the Mode Matching (MM) method in the case of photonic crystal waveguide discontinuities is presented. The structure under consideration is divided into a number of cells, which supports a number of guided and evanescent modes. These modes can be calculated numerically by an alternative formulation of the plane wave expansion method for each frequency. A matrix equation is then formed relating the modal amplitudes at the beginning and at the end of the structure. The theory is highly efficient and accurate and can be applied to study the transmission sensitivity of photonic crystal devices due to fabrication tolerances. The accuracy of the MM method is compared to the Finite Difference Frequency Domain (FDFD) and the Adjoint Variable Method (AVM) and good agreement is observed.

Keywords: Optical Communications, Integrated Optics, Photonic Crystals, Optical Waveguide Discontinuities.

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Authors: B. I. Yun

Abstract:

A dual-reciprocity boundary element method is presented for the numerical solution of a class of axisymmetric elastodynamic problems. The domain integrals that arise in the integrodifferential formulation are converted to line integrals by using the dual-reciprocity method together suitably constructed interpolating functions. The second order time derivatives of the displacement in the governing partial differential equations are suppressed by using Laplace transformation. In the Laplace transform domain, the problem under consideration is eventually reduced to solving a system of linear algebraic equations. Once the linear algebraic equations are solved, the displacement and stress fields in the physical domain can be recovered by using a numerical technique for inverting Laplace transforms.

Keywords: Axisymmetric elasticity, boundary element method, dual-reciprocity method, Laplace transform.

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Authors: Zebiri Chemseddine, Benabdelaziz Fatiha

Abstract:

The effect of a chiral bianisotropic substrate on the complex resonant frequency of a rectangular microstrip resonator has been studied on the basis of the integral equation formulation. The analysis is based on numerical resolution of the integral equation using Galerkin procedure for moment method in the spectral domain. This work aim first to study the effect of the chirality of a bianisotopic substrate upon the resonant frequency and the half power bandwidth, second the effect of a magnetic anisotropy via an asymptotic approach for very weak substrate upon the resonant frequency and the half power bandwidth has been investigated. The obtained results are compared with previously published work [11-9], they were in good agreement.

Keywords: Microstrip antenna, bianisotropic media, resonant frequency, moment method.

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Authors: Rafael Jorge Menezes Santos, Ginalber Luiz de Oliveira Serra, Carlos César Teixeira Ferreira

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This paper proposes a methodology for analysis of the dynamic behavior of a robotic manipulator in continuous time. Initially this system (nonlinear system) will be decomposed into linear submodels and analyzed in the context of the Linear and Parameter Varying (LPV) Systems. The obtained linear submodels, which represent the local dynamic behavior of the robotic manipulator in some operating points were grouped in a Takagi-Sugeno fuzzy structure. The obtained fuzzy model was analyzed and validated through analog simulation, as universal approximator of the robotic manipulator.

Keywords: modeling of nonlinear dynamic systems, Takagi- Sugeno fuzzy model, Linear and Parameter Varying (LPV) System.

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Authors: Buntara Sthenly Gan, Naohiro Kawada

Abstract:

A simple and easy algorithm is presented for a fast calculation of kernel functions which required in fluid simulations using the Smoothed Particle Hydrodynamic (SPH) method. Present proposed algorithm improves the Linked-list algorithm and adopts the Pair-Wise Interaction technique, which are widely used for evaluating kernel functions in fluid simulations using the SPH method. The algorithm is easy to be implemented without any complexities in programming. Some benchmark examples are used to show the simulation time saved by using the proposed algorithm. Parametric studies on the number of divisions for sub-domains, smoothing length and total amount of particles are conducted to show the effectiveness of the present technique. A compact formulation is proposed for practical usage.

Keywords: Technique, fluid simulation, smoothing particle hydrodynamic (SPH), particle interaction.

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Authors: E. G. Bautista, J. M. Reyes, O. Bautista, J. C. Arcos

Abstract:

In this work, we analyze the deformation of surface waves in shallow flows conditions, propagating in a channel of slowly varying cross-section. Based on a singular perturbation technique, the main purpose is to predict the motion of waves by using a dimensionless formulation of the governing equations, considering that the longitudinal variation of the transversal section obey a power-law distribution. We show that the spatial distribution of the waves in the varying cross-section is a function of a kinematic parameter,κ , and two geometrical parameters εh and w ε . The above spatial behavior of the surface elevation is modeled by an ordinary differential equation. The use of single formulas to model the varying cross sections or transitions considered in this work can be a useful approximation to natural or artificial geometrical configurations.

Keywords: Surface waves, Asymptotic solution, Power law function, Non-dispersive waves.

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Authors: Malkhaz Jokhadze, Vakhtang Mshvildadze, Levan Makaradze, Ekaterine Mosidze, Salome Barbaqadze, Mariam Murtazashvili, Dali Berashvili, Koba sivsivadze, Lasha Bakuridze, Aliosha Bakuridze

Abstract:

Essential oils are one of the most important groups of biologically active substances present in plants. Due to the chemical diversity of components, essential oils and their preparations have a wide spectrum of pharmacological action. They have bactericidal, antiviral, fungicidal, antiprotozoal, anti-inflammatory, spasmolytic, sedative and other activities. They are expectorant, spasmolytic, sedative, hypotensive, secretion enhancing, antioxidant remedies. Based on preliminary pharmacological studies, we have developed a formulation called “Phytobiotic” containing essential oils, a feed additive for poultry as an alternative to antibiotics. Phytobiotic is a water-soluble powder containing a composition of essential oils of thyme, clary, monarda and auxiliary substances: dry extract of liquorice and inhalation lactose. On this stage of research, the goal was to study the chemical composition of provided phytobiotic, identify the main substances and determine their quantity, investigate the biological activity of phytobiotic through in vitro and in vivo studies. Using gas chromatography-mass spectrometry, 38 components were identified in phytobiotic, representing acyclic-, monocyclic-, bicyclic-, and sesquiterpenes. Together with identification of main active substances, their quantitative content was determined, including acyclic terpene alcohol β-linalool, acyclic terpene ketone linalyl acetate, monocyclic terpenes: D-limonene and γ-terpinene, monocyclic aromatic terpene thymol. Provided phytobiotic has pronounced and at the same time broad spectrum of antibacterial activity. In the cell model, phytobiotic showed weak antioxidant activity, and it was stronger in the ORAC (chemical model) tests. Meanwhile anti-inflammatory activity was also observed. When fowls were supplied feed enriched with phytobiotic, it was observed that gained weight of the chickens in the experimental group exceeded the same data for the control group during the entire period of the experiment. The survival rate of broilers in the experimental group during the growth period was 98% compared to -94% in the control group. As a result of conducted researches probable four different mechanisms which are important for the action of phytobiotics were identified: sensory, metabolic, antioxidant and antibacterial action. General toxic, possible local irritant and allergenic effects of phytobiotic were also investigated. Performed assays proved that formulation is safe.

Keywords: Clary, essential oils, monarda, phytobiotics, poultry, thyme.

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Authors: Badr M. Alshammari, Mohamed A. El-Kady

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The paper presents new results of a recent industry supported research and development study in which an efficient framework for evaluating practical and meaningful power system reliability and quality indices was applied. The system-wide integrated performance indices are capable of addressing and revealing areas of deficiencies and bottlenecks as well as redundancies in the composite generation-transmission-demand structure of large-scale power grids. The technique utilizes a linear programming formulation, which simulates practical operating actions and offers a general and comprehensive framework to assess the harmony and compatibility of generation, transmission and demand in a power system. Practical applications to a reduced system model as well as a portion of the Saudi power grid are also presented in the paper for demonstration purposes.

Keywords: Power systems, Linear programming, Quality assessment, Reliability.

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Authors: Muhammad Amjad Sohail, Rizwan Ullah

Abstract:

This research paper presents the CFD analysis of oscillating airfoil during pitch cycle. Unsteady subsonic flow is simulated for pitching airfoil at Mach number 0.283 and Reynolds number 3.45 millions. Turbulent effects are also considered for this study by using K-ω SST turbulent model. Two-dimensional unsteady compressible Navier-Stokes code including two-equation turbulence model and PISO pressure velocity coupling is used. Pressure based implicit solver with first order implicit unsteady formulation is used. The simulated pitch cycle results are compared with the available experimental data. The results have a good agreement with the experimental data. Aerodynamic characteristics during pitch cycles have been studied and validated.

Keywords: Angle of attack, Centre of pressure, subsonic flow, pitching moment coefficient, turbulence mode

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Authors: Mandhapati P. Raju, Siddhartha Khaitan

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In-core memory requirement is a bottleneck in solving large three dimensional Navier-Stokes finite element problem formulations using sparse direct solvers. Out-of-core solution strategy is a viable alternative to reduce the in-core memory requirements while solving large scale problems. This study evaluates the performance of various out-of-core sequential solvers based on multifrontal or supernodal techniques in the context of finite element formulations for three dimensional problems on a Windows platform. Here three different solvers, HSL_MA78, MUMPS and PARDISO are compared. The performance of these solvers is evaluated on a 64-bit machine with 16GB RAM for finite element formulation of flow through a rectangular channel. It is observed that using out-of-core PARDISO solver, relatively large problems can be solved. The implementation of Newton and modified Newton's iteration is also discussed.

Keywords: Out-of-core, PARDISO, MUMPS, Newton.

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Authors: T. R. Alencar, P. T. Leite

Abstract:

Several optimization algorithms specifically applied to the problem of Operation Planning of Hydrothermal Power Systems have been developed and are used. Although providing solutions to various problems encountered, these algorithms have some weaknesses, difficulties in convergence, simplification of the original formulation of the problem, or owing to the complexity of the objective function. Thus, this paper presents the development of a computational tool for solving optimization problem identified and to provide the User an easy handling. Adopted as intelligent optimization technique, Genetic Algorithms and programming language Java. First made the modeling of the chromosomes, then implemented the function assessment of the problem and the operators involved, and finally the drafting of the graphical interfaces for access to the User. The program has managed to relate a coherent performance in problem resolution without the need for simplification of the calculations together with the ease of manipulating the parameters of simulation and visualization of output results.

Keywords: Energy, Optimization, Hydrothermal Power Systemsand Genetic Algorithms

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Authors: Iliana Marinova, Valentin Mateev

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For investigations of electromagnetic field distributions in biological structures by Finite Element Method (FEM), a method for automatic 3D model building of human anatomical objects is developed. Models are made by meshed structures and specific electromagnetic material properties for each tissue type. Mesh is built according to specific FEM criteria for achieving good solution accuracy. Several FEM models of anatomical objects are built. Formulation using magnetic vector potential and scalar electric potential (A-V, A) is used for modeling of electromagnetic fields in human tissue objects. The developed models are suitable for investigations of electromagnetic field distributions in human tissues exposed in external fields during magnetic stimulation, defibrillation, impedance tomography etc.

Keywords: electromagnetic field, finite element method, humantissue.

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Authors: Bahareh Hajirostamloo

Abstract:

Recent research has shown that milk proteins can yield bioactive peptides with opioid, mineral binding, cytomodulatory, antihypertensive, immunostimulating, antimicrobial and antioxidative activity in the human body. Bioactive peptides are encrypted in milk proteins and are only released by enzymatic hydrolysis in vivo during gastrointestinal digestion, food processing or by microbial enzymes in fermented products. At present significant research is being undertaken on the health effects of bioactive peptides. A variety of naturally formed bioactive peptides have been found in fermented dairy products, such as yoghurt, sour milk and cheese. In particular, antihypertensive peptides have been identified in fermented milks, whey and ripened cheese. Some of these peptides have been commercialized in the form of fermented milks. Bioactive peptides have the potential to be used in the formulation of health-enhancing nutraceuticals, and as potent drugs with well defined pharmacological effects.

Keywords: Milk protein, Bioactive peptides, Health effects, Dairy product.

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Authors: Sheila Marie G. Hocson

Abstract:

One of the vital developmental tasks that an individual faces during adolescence is choosing a career. Arriving at a career decision is difficult and anxious for many adolescents in the tertiary level. The main purpose of this study is to determine the factors relating to career indecision among freshmen college students as basis for the formulation of a comprehensive career counseling program for the psychological well-being of freshmen university students. The subjects were purposively selected. The Slovin-s formula was used in determining the sample size, using a 0.05 margin of error in getting the total number of samples per college and per major. The researcher made use of descriptive correlational study in determining significant factors relating to career indecision. Multiple Regression Analysis indicated that career thoughts, career decisions and vocational identity as factors related to career indecision.

Keywords: career decisions, career guidance program, career thoughts, vocational identity

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Authors: A. A. Hossam-Eldin, E. N. Abdallah, M. S. El-Nozahy

Abstract:

Power system state estimation is the process of calculating a reliable estimate of the power system state vector composed of bus voltages' angles and magnitudes from telemetered measurements on the system. This estimate of the state vector provides the description of the system necessary for the operation and security monitoring. Many methods are described in the literature for solving the state estimation problem, the most important of which are the classical weighted least squares method and the nondeterministic genetic based method; however both showed drawbacks. In this paper a modified version of the genetic algorithm power system state estimation is introduced, Sensitivity of the proposed algorithm to genetic operators is discussed, the algorithm is applied to case studies and finally it is compared with the classical weighted least squares method formulation.

Keywords: Genetic algorithms, ill-conditioning, state estimation, weighted least squares.

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Authors: S. Levitsky, R. Bergman

Abstract:

Fluid rheology may have essential impact on sound propagation in a liquid-filled pipe, especially, in a low frequency range. Rheological parameters of liquid are temperature-sensitive, which ultimately results in a temperature dependence of the wave speed and attenuation in the waveguide. The study is devoted to modeling of this effect at sound propagation in an elastic pipe with polymeric liquid, described by generalized Maxwell model with non-zero high-frequency viscosity. It is assumed that relaxation spectrum is distributed according to the Spriggs law; temperature impact on the liquid rheology is described on the basis of the temperature-superposition principle and activation theory. The dispersion equation for the waveguide, considered as a thin-walled tube with polymeric solution, is obtained within a quasi-one-dimensional formulation. Results of the study illustrate the influence of temperature on sound propagation in the system.

Keywords: Elastic tube, sound propagation, temperature effect, viscoelastic liquid.

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Authors: Arpa Petchsomrit, Namfa Sermkaew, Ruedeekorn Wiwattanapatapee

Abstract:

Oil entrapped floating alginate beads of curcumin were developed and characterized. Cremophor EL, Cremophor RH and Tween 80 were utilized to improve the solubility of the drug. The oil-loaded floating gel beads prepared by emulsion gelation method contained sodium alginate, mineral oil and surfactant. The drug content and % encapsulation declined as the ratio of surfactant was increased. The release of curcumin from 1% alginate beads was significantly more than for the 2% alginate beads. The drug released from the beads containing 25% of Tween 80 was about 70% while a higher drug release was observed with the beads containing Cremophor EL or Cremohor RH (approximately 90%). The developed floating beads of curcumin powder with surfactant provided a superior drug release than those without surfactant. Floating beads based on oil entrapment containing the drug solubilized in surfactants is a new delivery system to enhance the dissolution of poorly soluble drugs.

Keywords: Alginate, curcumin, floating drug delivery, oil entrapped bead.

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Authors: Badr M. Alshammari, T. Guesmi

Abstract:

This study presents a modified version of the artificial bee colony (ABC) algorithm by including a local search technique for solving the non-convex economic power dispatch problem. The local search step is incorporated at the end of each iteration. Total system losses, valve-point loading effects and prohibited operating zones have been incorporated in the problem formulation. Thus, the problem becomes highly nonlinear and with discontinuous objective function. The proposed technique is validated using an IEEE benchmark system with ten thermal units. Simulation results demonstrate that the proposed optimization algorithm has better convergence characteristics in comparison with the original ABC algorithm.

Keywords: Economic power dispatch, artificial bee colony, valve-point loading effects, prohibited operating zones.

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Authors: E. Zippelius

Abstract:

Urban design aims to provide a stage for public life that, when once brought to life, is right away subject to subtle but continuous transformation. This paper explores such transformations and searches for ways how public life can be reinforced in the case of a housing settlement for the displaced in Nicosia, Cyprus. First, a sound basis of theoretical knowledge is established through literature review, notably the theory of the Production of Space by Henri Lefebvre, exploring its potential and defining key criteria for the following empirical analysis. The analysis is pinpointing the differences between spatial practice, representation of space and spaces of representation as well as their interaction, alliance, or even conflict. In doing so uncertainties, chances and challenges are unraveled that will be consequently linked to practice and action and lead to the formulation of a design strategy. A strategy, though, that does not long for achieving an absolute, finite certainty but understands the three dimensions of space formulated by Lefebvre as equal and space as continuously produced, hence, unfinished.

Keywords: Production of space, public space, urban life, urban transformation.

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Authors: Ram N. Singh, Abraham K. George, Dawood N. Al-Namaani

Abstract:

The Euler-s equation of motion is extended to include the viscosity stress tensor leading to the formulation of Navier– Stokes type equation. The latter is linearized and applied to investigate the rotational motion or vorticity in a viscous fluid. Relations for the velocity of viscous waves and attenuation parameter are obtained in terms of viscosity (μ) and the density (¤ü) of the fluid. μ and ¤ü are measured experimentally as a function of temperature for two different samples of light and heavy crude oil. These data facilitated to determine the activation energy, velocity of viscous wave and the attenuation parameter. Shear wave velocity in heavy oil is found to be much larger than the light oil, whereas the attenuation parameter in heavy oil is quite low in comparison to light one. The activation energy of heavy oil is three times larger than light oil.

Keywords: Activation Energy, Attenuation, Crude Oil, Navier- Stokes Equation, Viscosity.

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Authors: E. T. L. Cöuras Ford, V. A. C.Vale, J. U. L Mendes

Abstract:

The sun is an inexhaustible source and harness its potential both for heating and power generation is one of the most promising and necessary alternatives, mainly due to environmental issues. However, it should be noted that this has always been present in the generation of energy on earth, only indirectly, since it is responsible for virtually all other energy sources, such as generating source of evaporation of the water cycle, allowing the impoundment and the consequent generation of electricity (hydroelectric power); winds are caused by atmospheric induction caused by large scale solar radiation; petroleum, coal and natural gas were generated from waste plants and animals that originally derived energy required for their development of solar radiation. This paper presents a study on the feasibility of using solar energy for water heating in homes. A simplified methodology developed for formulation of solar heating operation model of water in alternative systems of solar energy in Brazil, and compared it to that in the international market. Across this research, it was possible to create new paradigms for alternative applications to the use of solar energy.

Keywords: Solar energy, solar heating, solar project.

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Authors: Quoc Khanh Dang, Thomas Bourdeaud’huy, Khaled Mesghouni, Armand Toguy´eni

Abstract:

This paper studies a train routing and scheduling problem for busy railway stations. Our objective is to allow trains to be routed in dense areas that are reaching saturation. Unlike traditional methods that allocate all resources to setup a route for a train and until the route is freed, our work focuses on the use of resources as trains progress through the railway node. This technique allows a larger number of trains to be routed simultaneously in a railway node and thus reduces their current saturation. To deal with this problem, this study proposes an abstract model and a mixed-integer linear programming formulation to solve it. The applicability of our method is illustrated on a didactic example.

Keywords: Busy railway stations, mixed-integer linear programming, offline railway station management, train platforming, train routing, train scheduling.

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Authors: Gang Liu, Huimin Song, Can Wang, Runnan Zhang, Lu Fang

Abstract:

Currently, resource sharing and system security are critical issues. This paper proposes a POL module composed of PRIV ILEGE attribute (PA), obligation and log which improves attribute based access control (ABAC) model in dynamically granting authorizations and revoking authorizations. The following describes the new model termed PABAC in terms of the POL module structure, attribute definitions, policy formulation and authorization architecture, which demonstrate the advantages of it. The POL module addresses the problems which are not predicted before and not described by access control policy. It can be one of the subject attributes or resource attributes according to the practical application, which enhances the flexibility of the model compared with ABAC. A scenario that illustrates how this model is applied to the real world is provided.

Keywords: Access control, attribute based access control, granting authorizations, privilege, revoking authorizations, system security.

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Authors: N. Winya, S. Chankapoe, C. Kiriratnikom

Abstract:

In this study, an ablation, mechanical and thermal properties of a rocket motor insulation from phenolic/ fiber matrix composites forming a laminate with different fiber between fiberglass and locally available synthetic fibers. The phenolic/ fiber matrix composites was mechanics and thermal properties by means of tensile strength, ablation, TGA and DSC. The design of thermal insulation involves several factors.Determined the mechanical properties according to MIL-I-24768: Density >1.3 g/cm3, Tensile strength >103 MPa and Ablation <0.14 mm/s to optimization formulation of phenolic binder, fiber glass reinforcement and other ingredients were conducted after that the insulation prototype was formed and cured. It was found that the density of phenolic/fiberglass composites and phenolic/ synthetic fiber composite was 1.66 and 1.41 g/cm3 respectively. The ablative of phenolic/fiberglass composites and phenolic/ synthetic fiber composite was 0.13 and 0.06 mm/s respectively.

Keywords: Phenolic Resin, Ablation, Rocket Motor, Insulation

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Authors: Alexandra Leukauf, Alexander Schirrer, Emir Talic

Abstract:

Numerical computation of wave propagation in a large domain usually requires significant computational effort. Hence, the considered domain must be truncated to a smaller domain of interest. In addition, special boundary conditions, which absorb the outward travelling waves, need to be implemented in order to describe the system domains correctly. In this work, the linear one dimensional wave equation is approximated by utilizing the Fourier Galerkin approach. Furthermore, the artificial boundaries are realized with absorbing boundary conditions. Within this work, a systematic work flow for setting up the wave problem, including the absorbing boundary conditions, is proposed. As a result, a convenient modal system description with an effective absorbing boundary formulation is established. Moreover, the truncated model shows high accuracy compared to the global domain.

Keywords: Absorbing boundary conditions, boundary control, Fourier Galerkin approach, modal approach, wave equation.

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Authors: Y. Abdelrazig

Abstract:

Evolutionary optimization methods such as genetic algorithms have been used extensively for the construction site layout problem. More recently, ant colony optimization algorithms, which are evolutionary methods based on the foraging behavior of ants, have been successfully applied to benchmark combinatorial optimization problems. This paper proposes a formulation of the site layout problem in terms of a sequencing problem that is suitable for solution using an ant colony optimization algorithm. In the construction industry, site layout is a very important planning problem. The objective of site layout is to position temporary facilities both geographically and at the correct time such that the construction work can be performed satisfactorily with minimal costs and improved safety and working environment. During the last decade, evolutionary methods such as genetic algorithms have been used extensively for the construction site layout problem. This paper proposes an ant colony optimization model for construction site layout. A simple case study for a highway project is utilized to illustrate the application of the model.

Keywords: Construction site layout, optimization, ant colony.

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Authors: Shuenn-Yih Chang, Chiu-Li Huang

Abstract:

Three structure-dependent integration methods have been developed for solving equations of motion, which are second-order ordinary differential equations, for structural dynamics and earthquake engineering applications. Although they generally have the same numerical properties, such as explicit formulation, unconditional stability and second-order accuracy, a different performance is found in solving the free vibration response to either linear elastic or nonlinear systems with high frequency modes. The root cause of this different performance in the free vibration responses is analytically explored herein. As a result, it is verified that a weak instability is responsible for the different performance of the integration methods. In general, a weak instability will result in an inaccurate solution or even numerical instability in the free vibration responses of high frequency modes. As a result, a weak instability must be prohibited for time integration methods.

Keywords: Dynamic analysis, high frequency, integration method, overshoot, weak instability.

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Authors: A. Maghari, V. H. Maleki

Abstract:

In this paper, we present a quantum statistical mechanical formulation from our recently analytical expressions for partial-wave transition matrix of a three-particle system. We report the quantum reactive cross sections for three-body scattering processes 1+(2,3)→1+(2,3) as well as recombination 1+(2,3)→1+(3,1) between one atom and a weakly-bound dimer. The analytical expressions of three-particle transition matrices and their corresponding cross-sections were obtained from the threedimensional Faddeev equations subjected to the rank-two non-local separable potentials of the generalized Yamaguchi form. The equilibrium quantum statistical mechanical properties such partition function and equation of state as well as non-equilibrium quantum statistical properties such as transport cross-sections and their corresponding transport collision integrals were formulated analytically. This leads to obtain the transport properties, such as viscosity and diffusion coefficient of a moderate dense gas.

Keywords: Statistical mechanics, Nonlocal separable potential, three-body interaction, Faddeev equations.

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