Search results for: interaction equation
5618 A Mathematical Equation to Calculate Stock Price of Different Growth Model
Authors: Weiping Liu
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This paper presents an equation to calculate stock prices of different growth model. This equation is mathematically derived by using discounted cash flow method. It has the advantages of being very easy to use and very accurate. It can still be used even when the first stage is lengthy. This equation is more generalized because it can be used for all the three popular stock price models. It can be programmed into financial calculator or electronic spreadsheets. In addition, it can be extended to a multistage model. It is more versatile and efficient than the traditional methods.Keywords: stock price, multistage model, different growth model, discounted cash flow method
Procedia PDF Downloads 3645617 Studies on Interaction between Anionic Polymer Sodium Carboxymethylcellulose with Cationic Gemini Surfactants
Authors: M. Kamil, Rahber Husain Khan
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In the present study, the Interaction of anionic polymer, sodium carboxymethylcellulose (NaCMC), with cationic gemini surfactants 2,2[(oxybis(ethane-1,2-diyl))bis(oxy)]bis(N-hexadecyl1-N,N-[di(E2)/tri(E3)]methyl1-2-oxoethanaminium)chloride (16-E2-16 and 16-E3-16) and conventional surfactant (CTAC) in aqueous solutions have been studied by surface tension measurement of binary mixtures (0.0- 0.5 wt% NaCMC and 1 mM gemini surfactant/10 mM CTAC solution). Surface tension measurements were used to determine critical aggregation concentration (CAC) and critical micelle concentration (CMC). The maximum surface excess concentration (Ґmax) at the air-water interface was evaluated by the Gibbs adsorption equation. The minimum area per surfactant molecule was evaluated, which indicates the surfactant-polymer Interaction in a mixed system. The effect of changing surfactant chain length on CAC and CMC values of mixed polymer-surfactant systems was examined. From the results, it was found that the gemini surfactant interacts strongly with NaCMC as compared to its corresponding monomeric counterpart CTAC. In these systems, electrostatic interactions predominate. The lowering of surface tension with an increase in the concentration of surfactants is higher in the case of gemini surfactants almost 10-15 times. The measurements indicated that the Interaction between NaCMC-CTAC resulted in complex formation. The volume of coacervate increases with an increase in CTAC concentration; however, above 0.1 wt. % concentration coacervate vanishes.Keywords: anionic polymer, gemni surfactants, tensiometer, CMC, interaction
Procedia PDF Downloads 585616 Energy Conservation and H-Theorem for the Enskog-Vlasov Equation
Authors: Eugene Benilov, Mikhail Benilov
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The Enskog-Vlasov (EV) equation is a widely used semi-phenomenological model of gas/liquid phase transitions. We show that it does not generally conserve energy, although there exists a restriction on its coefficients for which it does. Furthermore, if an energy-preserving version of the EV equation satisfies an H-theorem as well, it can be used to rigorously derive the so-called Maxwell construction which determines the parameters of liquid-vapor equilibria. Finally, we show that the EV model provides an accurate description of the thermodynamics of noble fluids, and there exists a version simple enough for use in applications.Keywords: Enskog collision integral, hard spheres, kinetic equation, phase transition
Procedia PDF Downloads 1195615 Numerical Solution of Manning's Equation in Rectangular Channels
Authors: Abdulrahman Abdulrahman
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When the Manning equation is used, a unique value of normal depth in the uniform flow exists for a given channel geometry, discharge, roughness, and slope. Depending on the value of normal depth relative to the critical depth, the flow type (supercritical or subcritical) for a given characteristic of channel conditions is determined whether or not flow is uniform. There is no general solution of Manning's equation for determining the flow depth for a given flow rate, because the area of cross section and the hydraulic radius produce a complicated function of depth. The familiar solution of normal depth for a rectangular channel involves 1) a trial-and-error solution; 2) constructing a non-dimensional graph; 3) preparing tables involving non-dimensional parameters. Author in this paper has derived semi-analytical solution to Manning's equation for determining the flow depth given the flow rate in rectangular open channel. The solution was derived by expressing Manning's equation in non-dimensional form, then expanding this form using Maclaurin's series. In order to simplify the solution, terms containing power up to 4 have been considered. The resulted equation is a quartic equation with a standard form, where its solution was obtained by resolving this into two quadratic factors. The proposed solution for Manning's equation is valid over a large range of parameters, and its maximum error is within -1.586%.Keywords: channel design, civil engineering, hydraulic engineering, open channel flow, Manning's equation, normal depth, uniform flow
Procedia PDF Downloads 1855614 Influence of an External Magnetic Field on the Acoustomagnetoelectric Field in a Rectangular Quantum Wire with an Infinite Potential by Using a Quantum Kinetic Equation
Authors: N. Q. Bau, N. V. Nghia
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The acoustomagnetoelectric (AME) field in a rectangular quantum wire with an infinite potential (RQWIP) is calculated in the presence of an external magnetic field (EMF) by using the quantum kinetic equation for the distribution function of electrons system interacting with external phonons and electrons scattering with internal acoustic phonon in a RQWIP. We obtained ananalytic expression for the AME field in the RQWIP in the presence of the EMF. The dependence of AME field on the frequency of external acoustic wave, the temperature T of system, the cyclotron frequency of the EMF and the intensity of the EMF is obtained. Theoretical results for the AME field are numerically evaluated, plotted and discussed for a specific RQWIP GaAs/GaAsAl. This result has shown that the dependence of the AME field on intensity of the EMF is nonlinearly and it is many distinct maxima in the quantized magnetic region. We also compared received fields with those for normal bulk semiconductors, quantum well and quantum wire to show the difference. The influence of an EMF on AME field in a RQWIP is newly developed.Keywords: rectangular quantum wire, acoustomagnetoelectric field, electron-phonon interaction, kinetic equation method
Procedia PDF Downloads 3045613 Exactly Fractional Solutions of Nonlinear Lattice Equation via Some Fractional Transformations
Authors: A. Zerarka, W. Djoudi
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We use some fractional transformations to obtain many types of new exact solutions of nonlinear lattice equation. These solutions include rational solutions, periodic wave solutions, and doubly periodic wave solutions.Keywords: fractional transformations, nonlinear equation, travelling wave solutions, lattice equation
Procedia PDF Downloads 6245612 Interaction of Local, Flexural-Torsional, and Flexural Buckling in Cold-Formed Steel Lipped-Angle Compression Members
Authors: K. C. Kalam Aswathy, M. V. Anil Kumar
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The possible failure modes of cold-formed steel (CFS) lipped angle (LA) compression members are yielding, local, flexural-torsional, or flexural buckling, and any possible interaction between these buckling modes. In general, the strength estimated by current design guidelines is conservative for these members when flexural-torsional buckling (FTB) is the first global buckling mode, as the post-buckling strength of this mode is not accounted for in the global buckling strength equations. The initial part of this paper reports the results of an experimental and numerical study of CFS-LA members undergoing independent FTB. The modifications are suggested to global buckling strength equations based on these results. Subsequently, the reduction in the ultimate strength from strength corresponding to independent buckling modes for LA members undergoing interaction between buckling modes such as local-flexural torsional, flexural-flexural torsional, local-flexural, and local-flexural torsional-flexural are studied systematically using finite element analysis results. A simple and more accurate interaction equation that accounts for the above interactions between buckling modes in CFS-LA compression members is proposed.Keywords: buckling interactions, cold-formed steel, flexural-torsional buckling, lipped angle
Procedia PDF Downloads 555611 Local Radial Basis Functions for Helmholtz Equation in Seismic Inversion
Authors: Hebert Montegranario, Mauricio Londoño
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Solutions of Helmholtz equation are essential in seismic imaging methods like full wave inversion, which needs to solve many times the wave equation. Traditional methods like Finite Element Method (FEM) or Finite Differences (FD) have sparse matrices but may suffer the so called pollution effect in the numerical solutions of Helmholtz equation for large values of the wave number. On the other side, global radial basis functions have a better accuracy but produce full matrices that become unstable. In this research we combine the virtues of both approaches to find numerical solutions of Helmholtz equation, by applying a meshless method that produce sparse matrices by local radial basis functions. We solve the equation with absorbing boundary conditions of the kind Clayton-Enquist and PML (Perfect Matched Layers) and compared with results in standard literature, showing a promising performance by tackling both the pollution effect and matrix instability.Keywords: Helmholtz equation, meshless methods, seismic imaging, wavefield inversion
Procedia PDF Downloads 5165610 Pressure Induced Phase Transition of Semiconducting Alloy TlxGa1-xAs
Authors: Madhu Sarwan, Ritu Dubey, Sadhna Singh
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We have investigated the structural phase transition from Zinc-Blende (ZB) to Rock-Salt (RS) structure of TlxGa1-xAs by using Interaction Potential Model (IPM). The IPM consists of Coulomb interaction, Three-Body Interaction (TBI), Van Der Wall (vdW) interaction and overlap repulsive short range interaction. The structural phase transition has been computed by using the vegard’s law. The volume collapse is also computed for this alloy. We have also investigated the second order elastic constants with composition for the alloy TlxGa1-xAs.Keywords: III-V alloy, elastic moduli, phase transition, semiconductors
Procedia PDF Downloads 5045609 Stress Solitary Waves Generated by a Second-Order Polynomial Constitutive Equation
Authors: Tsun-Hui Huang, Shyue-Cheng Yang, Chiou-Fen Shieha
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In this paper, a nonlinear constitutive law and a curve fitting, two relationships between the stress-strain and the shear stress-strain for sandstone material were used to obtain a second-order polynomial constitutive equation. Based on the established polynomial constitutive equations and Newton’s second law, a mathematical model of the non-homogeneous nonlinear wave equation under an external pressure was derived. The external pressure can be assumed as an impulse function to simulate a real earthquake source. A displacement response under nonlinear two-dimensional wave equation was determined by a numerical method and computer-aided software. The results show that a suit pressure in the sandstone generates the phenomenon of stress solitary waves.Keywords: polynomial constitutive equation, solitary, stress solitary waves, nonlinear constitutive law
Procedia PDF Downloads 4655608 Analysis of a Generalized Sharma-Tasso-Olver Equation with Variable Coefficients
Authors: Fadi Awawdeh, O. Alsayyed, S. Al-Shará
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Considering the inhomogeneities of media, the variable-coefficient Sharma-Tasso-Olver (STO) equation is hereby investigated with the aid of symbolic computation. A newly developed simplified bilinear method is described for the solution of considered equation. Without any constraints on the coefficient functions, multiple kink solutions are obtained. Parametric analysis is carried out in order to analyze the effects of the coefficient functions on the stabilities and propagation characteristics of the solitonic waves.Keywords: Hirota bilinear method, multiple kink solution, Sharma-Tasso-Olver equation, inhomogeneity of media
Procedia PDF Downloads 4855607 Kernel Parallelization Equation for Identifying Structures under Unknown and Periodic Loads
Authors: Seyed Sadegh Naseralavi
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This paper presents a Kernel parallelization equation for damage identification in structures under unknown periodic excitations. Herein, the dynamic differential equation of the motion of structure is viewed as a mapping from displacements to external forces. Utilizing this viewpoint, a new method for damage detection in structures under periodic loads is presented. The developed method requires only two periods of load. The method detects the damages without finding the input loads. The method is based on the fact that structural displacements under free and forced vibrations are associated with two parallel subspaces in the displacement space. Considering the concept, kernel parallelization equation (KPE) is derived for damage detection under unknown periodic loads. The method is verified for a case study under periodic loads.Keywords: Kernel, unknown periodic load, damage detection, Kernel parallelization equation
Procedia PDF Downloads 2575606 A Trapezoidal-Like Integrator for the Numerical Solution of One-Dimensional Time Dependent Schrödinger Equation
Authors: Johnson Oladele Fatokun, I. P. Akpan
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In this paper, the one-dimensional time dependent Schrödinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff ordinary differential equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10-4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable.Keywords: Schrodinger’s equation, partial differential equations, method of lines (MOL), stiff ODE, trapezoidal-like integrator
Procedia PDF Downloads 3845605 Investigation of Chlorophylls a and b Interaction with Inner and Outer Surfaces of Single-Walled Carbon Nanotube Using Molecular Dynamics Simulation
Authors: M. Dehestani, M. Ghasemi-Kooch
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In this work, adsorption of chlorophylls a and b pigments in aqueous solution on the inner and outer surfaces of single-walled carbon nanotube (SWCNT) has been studied using molecular dynamics simulation. The linear interaction energy algorithm has been used to calculate the binding free energy. The results show that the adsorption of two pigments is fine on the both positions. Although there is the close similarity between these two pigments, their interaction with the nanotube is different. This result is useful to separate these pigments from one another. According to interaction energy between the pigments and carbon nanotube, interaction between these pigments-SWCNT on the inner surface is stronger than the outer surface. The interaction of SWCNT with chlorophylls phytol tail is stronger than the interaction of SWCNT with porphyrin ring of chlorophylls.Keywords: adsorption, chlorophyll, interaction, molecular dynamics simulation, nanotube
Procedia PDF Downloads 2065604 State Estimation Based on Unscented Kalman Filter for Burgers’ Equation
Authors: Takashi Shimizu, Tomoaki Hashimoto
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Controlling the flow of fluids is a challenging problem that arises in many fields. Burgers’ equation is a fundamental equation for several flow phenomena such as traffic, shock waves, and turbulence. The optimal feedback control method, so-called model predictive control, has been proposed for Burgers’ equation. However, the model predictive control method is inapplicable to systems whose all state variables are not exactly known. In practical point of view, it is unusual that all the state variables of systems are exactly known, because the state variables of systems are measured through output sensors and limited parts of them can be only available. In fact, it is usual that flow velocities of fluid systems cannot be measured for all spatial domains. Hence, any practical feedback controller for fluid systems must incorporate some type of state estimator. To apply the model predictive control to the fluid systems described by Burgers’ equation, it is needed to establish a state estimation method for Burgers’ equation with limited measurable state variables. To this purpose, we apply unscented Kalman filter for estimating the state variables of fluid systems described by Burgers’ equation. The objective of this study is to establish a state estimation method based on unscented Kalman filter for Burgers’ equation. The effectiveness of the proposed method is verified by numerical simulations.Keywords: observer systems, unscented Kalman filter, nonlinear systems, Burgers' equation
Procedia PDF Downloads 1225603 How Social Capital Mediates the Relationships between Interpersonal Interaction and Health: Location-Based Augmented Reality Games
Authors: Chechen Liao, Pui-Lai To, Yi-Hui Wang
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Recently location-based augmented reality games (LBS+AR) have become increasingly popular as a major form of entertainment. Location-based augmented reality games have provided a lot of opportunities for face-to-face interaction among players. Prior studies also indicate that the social side of location-based augmented reality games are one of the major reasons for players to engage in the games. However, the impact of the usage of location-based augmented reality games has not been well explored. The study examines how interpersonal interaction affects social capital and health through playing location-based augmented reality games. The study also investigates how social capital mediates the relationships between interpersonal interaction and health. The study uses survey method to collect data. Six-hundred forty-seven questionnaires are collected. Structural equation modeling is used to investigate the relationships among variables. The causal relationships between variables in the research model are tested. The results of the study indicated that four interpersonal attraction attributes, including ability, proximity, similarity, and familiarity, are identified by ways of factor analysis. Interpersonal attraction is important for location-based augmented reality game-players to develop bonding and bridging social capital. Bonding and bridging social capital have a positive impact on the mental and social health of game-players. The results of the study provide academic and practical implications for future growth of location-based augmented reality games.Keywords: health, interpersonal interaction, location-based augmented reality games, social capital
Procedia PDF Downloads 2305602 Study on the Central Differencing Scheme with the Staggered Version (STG) for Solving the Hyperbolic Partial Differential Equations
Authors: Narumol Chintaganun
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In this paper we present the second-order central differencing scheme with the staggered version (STG) for solving the advection equation and Burger's equation. This scheme based on staggered evolution of the re-constructed cell averages. This scheme results in the second-order central differencing scheme, an extension along the lines of the first-order central scheme of Lax-Friedrichs (LxF) scheme. All numerical simulations presented in this paper are obtained by finite difference method (FDM) and STG. Numerical results are shown that the STG gives very good results and higher accuracy.Keywords: central differencing scheme, STG, advection equation, burgers equation
Procedia PDF Downloads 5335601 The Application on Interactivity of Light in New Media Art
Authors: Yansong Chen
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In the age of media convergence, new media technology is constantly impacting, changing, and even reshaping the limits of Art. From the technological ontology of the new media art, the concept of interaction design has always been dominated by I/O (Input/Output) systems through the ages, which ignores the content of systems and kills the aura of art. Light, as a fusion media, basically comes from the extension of some human feelings and can be the content of the input or the effect of output. In this paper, firstly, on the basis of literature review, the interaction characteristics research was conducted on light. Secondly, starting from discourse patterns of people and machines, people and people, people, and imagining things, we propose three light modes: object-oriented interaction, Immersion interaction, Tele-Presence interaction. Finally, this paper explains how to regain the aura of art through light elements in new media art and understand multiple levels of 'Interaction design'. In addition, the new media art, especially the light-based interaction art, enriches the language patterns and motivates emerging art forms to be more widespread and popular, which achieves its aesthetics growth.Keywords: new media art, interaction design, light art, immersion
Procedia PDF Downloads 1985600 A Parametric Study on Lateral Torsional Buckling of European IPN and IPE Cantilevers
Authors: H. Ozbasaran
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IPN and IPE sections, which are commonly used European I shapes, are widely used in steel structures as cantilever beams to support overhangs. A considerable number of studies exist on calculating lateral torsional buckling load of I sections. However, most of them provide series solutions or complex closed-form equations. In this paper, a simple equation is presented to calculate lateral torsional buckling load of IPN and IPE section cantilever beams. First, differential equation of lateral torsional buckling is solved numerically for various loading cases. Then a parametric study is conducted on results to present an equation for lateral torsional buckling load of European IPN and IPE beams. Finally, results obtained by presented equation are compared to differential equation solutions and finite element model results. ABAQUS software is utilized to generate finite element models of beams. It is seen that the results obtained from presented equation coincide with differential equation solutions and ABAQUS software results. It can be suggested that presented formula can be safely used to calculate critical lateral torsional buckling load of European IPN and IPE section cantilevers.Keywords: cantilever, IPN, IPE, lateral torsional buckling
Procedia PDF Downloads 5175599 Self-Reliance Support and Environment Interaction in Long-Term Care
Authors: Chen-Yuan Hsu
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Introduction Elderly is growing and results to live in the long-term care (LTC) and then due to the routine of the facilities in Taiwan, also resulted to losing of those people with environment interaction, so, the self-reliance support (SRS) for those people to experience environment interaction is an essential. Methods This study was recruited samples of a LTC in the central of Taiwan. There was a following research on the SRS group with 20 samples collected and routine care group with 20 samples. A structured questionnaire as the Environment Interaction Dimension, as data collection included demographic information and the dimensions of environment interaction. Data analysis used SPSS 22.0 for Window 2000 to report the finding. Results The Environment Interaction Dimension for Taiwanese is a Chinese version of the containing 8 items. The result of t-test analysis found that environment interaction showed a significant difference between groups (p<.05), the result recommended that there was a higher score of environment interaction dimension on the SRS group (29.90±5.56) comparing with the routine care group (22.1±5.53). Conclusion This study showed that the SRS group was higher than the routine care group on the environment interaction dimension for Taiwanese elderly living in the LTC. The results can also provide the reference for LTC, to encourage those people to participate in SRS in LTC, and therefore also improving their environment interaction.Keywords: self-reliance support, environment interaction, long-term care, elderly
Procedia PDF Downloads 655598 Soliton Solutions of the Higher-Order Nonlinear Schrödinger Equation with Dispersion Effects
Authors: H. Triki, Y. Hamaizi, A. El-Akrmi
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We consider the higher order nonlinear Schrödinger equation model with fourth-order dispersion, cubic-quintic terms, and self-steepening. This equation governs the propagation of fem to second pulses in optical fibers. We present new bright and dark solitary wave type solutions for such a model under certain parametric conditions. This kind of solution may be useful to explain some physical phenomena related to wave propagation in a nonlinear optical fiber systems supporting high-order nonlinear and dispersive effects.Keywords: nonlinear Schrödinger equation, high-order effects, soliton solution
Procedia PDF Downloads 5995597 Analytical Solution of Non–Autonomous Discrete Non-Linear Schrodinger Equation With Saturable Non-Linearity
Authors: Mishu Gupta, Rama Gupta
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It has been elucidated here that non- autonomous discrete non-linear Schrödinger equation is associated with saturable non-linearity through photo-refractive media. We have investigated the localized solution of non-autonomous saturable discrete non-linear Schrödinger equations. The similarity transformation has been involved in converting non-autonomous saturable discrete non-linear Schrödinger equation to constant-coefficient saturable discrete non-linear Schrödinger equation (SDNLSE), whose exact solution is already known. By back substitution, the solution of the non-autonomous version has been obtained. We have analysed our solution for the hyperbolic and periodic form of gain/loss term, and interesting results have been obtained. The most important characteristic role is that it helps us to analyse the propagation of electromagnetic waves in glass fibres and other optical wave mediums. Also, the usage of SDNLSE has been seen in tight binding for Bose-Einstein condensates in optical mediums. Even the solutions are interrelated, and its properties are prominently used in various physical aspects like optical waveguides, Bose-Einstein (B-E) condensates in optical mediums, Non-linear optics in photonic crystals, and non-linear kerr–type non-linearity effect and photo refracting medium.Keywords: B-E-Bose-Einstein, DNLSE-Discrete non linear schrodinger equation, NLSE-non linear schrodinger equation, SDNLSE - saturable discrete non linear Schrodinger equation
Procedia PDF Downloads 1225596 A Dynamic Equation for Downscaling Surface Air Temperature
Authors: Ch. Surawut, D. Sukawat
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In order to utilize results from global climate models, dynamical and statistical downscaling techniques have been developed. For dynamical downscaling, usually a limited area numerical model is used, with associated high computational cost. This research proposes dynamic equation for specific space-time regional climate downscaling from the Educational Global Climate Model (EdGCM) for Southeast Asia. The equation is for surface air temperature. These equations provide downscaling values of surface air temperature at any specific location and time without running a regional climate model. In the proposed equations, surface air temperature is approximated from ground temperature, sensible heat flux and 2m wind speed. Results from the application of the equation show that the errors from the proposed equations are less than the errors for direct interpolation from EdGCM.Keywords: dynamic equation, downscaling, inverse distance, weight interpolation
Procedia PDF Downloads 2755595 Linearization of Y-Force Equation of Rigid Body Equation of Motion and Behavior of Fighter Aircraft under Imbalance Weight on Wings during Combat
Authors: Jawad Zakir, Syed Irtiza Ali Shah, Rana Shaharyar, Sidra Mahmood
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Y-force equation comprises aerodynamic forces, drag and side force with side slip angle β and weight component along with the coupled roll (φ) and pitch angles (θ). This research deals with the linearization of Y-force equation using Small Disturbance theory assuming equilibrium flight conditions for different state variables of aircraft. By using assumptions of Small Disturbance theory in non-linear Y-force equation, finally reached at linearized lateral rigid body equation of motion; which says that in linearized Y-force equation, the lateral acceleration is dependent on the other different aerodynamic and propulsive forces like vertical tail, change in roll rate (Δp) from equilibrium, change in yaw rate (Δr) from equilibrium, change in lateral velocity due to side force, drag and side force components due to side slip, and the lateral equation from coupled rotating frame to decoupled rotating frame. This paper describes implementation of this lateral linearized equation for aircraft control systems. Another significant parameter considered on which y-force equation depends is ‘c’ which shows that any change bought in the weight of aircrafts wing will cause Δφ and cause lateral force i.e. Y_c. This simplification also leads to lateral static and dynamic stability. The linearization of equations is required because much of mathematics control system design for aircraft is based on linear equations. This technique is simple and eases the linearization of the rigid body equations of motion without using any high-speed computers.Keywords: Y-force linearization, small disturbance theory, side slip, aerodynamic force drag, lateral rigid body equation of motion
Procedia PDF Downloads 4595594 Fundamental Solutions for Discrete Dynamical Systems Involving the Fractional Laplacian
Authors: Jorge Gonzalez Camus, Valentin Keyantuo, Mahamadi Warma
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In this work, we obtain representation results for solutions of a time-fractional differential equation involving the discrete fractional Laplace operator in terms of generalized Wright functions. Such equations arise in the modeling of many physical systems, for example, chain processes in chemistry and radioactivity. The focus is on the linear problem of the simplified Moore - Gibson - Thompson equation, where the discrete fractional Laplacian and the Caputo fractional derivate of order on (0,2] are involved. As a particular case, we obtain the explicit solution for the discrete heat equation and discrete wave equation. Furthermore, we show the explicit solution for the equation involving the perturbed Laplacian by the identity operator. The main tool for obtaining the explicit solution are the Laplace and discrete Fourier transforms, and Stirling's formula. The methodology mainly is to apply both transforms in the equation, to find the inverse of each transform, and to prove that this solution is well defined, using Stirling´s formula.Keywords: discrete fractional Laplacian, explicit representation of solutions, fractional heat and wave equations, fundamental
Procedia PDF Downloads 1755593 The Role of Situational Factors in User Experience during Human-Robot Interaction
Authors: Da Tao, Tieyan Wang, Mingfu Qin
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While social robots have been increasingly developed and rapidly applied in our daily life, how robots should interact with humans is still an urgent problem to be explored. Appropriate use of interactive behavior is likely to create a good user experience in human-robot interaction situations, which in turn can improve people’s acceptance of robots. This paper aimed to systematically and quantitatively examine the effects of several important situational factors (i.e., interaction distance, interaction posture, and feedback style) on user experience during human-robot interaction. A three-factor mixed designed experiment was adopted in this study, where subjects were asked to interact with a social robot in different interaction situations by combinations of varied interaction distance, interaction posture, and feedback style. A set of data on users’ behavioral performance, subjective perceptions, and eye movement measures were tracked and collected, and analyzed by repeated measures analysis of variance. The results showed that the three situational factors showed no effects on behavioral performance in tasks during human-robot interaction. Interaction distance and feedback style yielded significant main effects and interaction effects on the proportion of fixation times. The proportion of fixation times on the robot is higher for negative feedback compared with positive feedback style. While the proportion of fixation times on the robot generally decreased with the increase of the interaction distance, it decreased more under the positive feedback style than under the negative feedback style. In addition, there were significant interaction effects on pupil diameter between interaction distance and posture. As interaction distance increased, mean pupil diameter became smaller in side interaction, while it became larger in frontal interaction. Moreover, the three situation factors had significant interaction effects on user acceptance of the interaction mode. The findings are helpful in the underlying mechanism of user experience in human-robot interaction situations and provide important implications for the design of robot behavioral expression and for optimal strategies to improve user experience during human-robot interaction.Keywords: social robots, human-robot interaction, interaction posture, interaction distance, feedback style, user experience
Procedia PDF Downloads 925592 Modeling of Physico-Chemical Characteristics of Concrete for Filling Trenches in Radioactive Waste Management
Authors: Ilija Plecas, Dalibor Arbutina
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The leaching rate of 60Co from spent mix bead (anion and cation) exchange resins in a cement-bentonite matrix has been studied. Transport phenomena involved in the leaching of a radioactive material from a cement-bentonite matrix are investigated using three methods based on theoretical equations. These are: the diffusion equation for a plane source, an equation for diffusion coupled to a first order equation and an empirical method employing a polynomial equation. The results presented in this paper are from a 25-year mortar and concrete testing project that will influence the design choices for radioactive waste packaging for a future Serbian radioactive waste disposal center.Keywords: cement, concrete, immobilization, leaching, permeability, radioactivity, waste
Procedia PDF Downloads 2815591 Periodicity of Solutions of a Nonlinear Impulsive Differential Equation with Piecewise Constant Arguments
Authors: Mehtap Lafcı
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In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments
Procedia PDF Downloads 4825590 Prototype of an Interactive Toy from Lego Robotics Kits for Children with Autism
Authors: Ricardo A. Martins, Matheus S. da Silva, Gabriel H. F. Iarossi, Helen C. M. Senefonte, Cinthyan R. S. C. de Barbosa
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This paper is the development of a concept of the man/robot interaction. More accurately in developing of an autistic child that have more troubles with interaction, here offers an efficient solution, even though simple; however, less studied for this public. This concept is based on code applied thought out the Lego NXT kit, built for the interpretation of the robot, thereby can create this interaction in a constructive way for children suffering with Autism.Keywords: lego NXT, interaction, BricX, autismo, ANN (Artificial Neural Network), MLP back propagation, hidden layers
Procedia PDF Downloads 5365589 A Boundary Backstepping Control Design for 2-D, 3-D and N-D Heat Equation
Authors: Aziz Sezgin
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We consider the problem of stabilization of an unstable heat equation in a 2-D, 3-D and generally n-D domain by deriving a generalized backstepping boundary control design methodology. To stabilize the systems, we design boundary backstepping controllers inspired by the 1-D unstable heat equation stabilization procedure. We assume that one side of the boundary is hinged and the other side is controlled for each direction of the domain. Thus, controllers act on two boundaries for 2-D domain, three boundaries for 3-D domain and ”n” boundaries for n-D domain. The main idea of the design is to derive ”n” controllers for each of the dimensions by using ”n” kernel functions. Thus, we obtain ”n” controllers for the ”n” dimensional case. We use a transformation to change the system into an exponentially stable ”n” dimensional heat equation. The transformation used in this paper is a generalized Volterra/Fredholm type with ”n” kernel functions for n-D domain instead of the one kernel function of 1-D design.Keywords: backstepping, boundary control, 2-D, 3-D, n-D heat equation, distributed parameter systems
Procedia PDF Downloads 375