Search results for: prediction equations

Authors: Hamdy M. Youssef, Eman A. Al-Lehaibi

Abstract:

This paper presents an iteration method for the numerical solutions of a one-dimensional problem of generalized thermoelasticity with one relaxation time under given initial and boundary conditions. The thermoelastic material with variable properties as a power functional graded has been considered. Adomian’s decomposition techniques have been applied to the governing equations. The numerical results have been calculated by using the iterations method with a certain algorithm. The numerical results have been represented in figures, and the figures affirm that Adomian’s decomposition method is a successful method for modeling thermoelastic problems. Moreover, the empirical parameter of the functional graded, and the lattice design parameter have significant effects on the temperature increment, the strain, the stress, the displacement.

Keywords: Adomian, decomposition method, generalized thermoelasticity, algorithm

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Authors: Jeon Chi-Ho, Lee Jae-Bin, Shim Chang-Su

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National bridge inventory in Korea shows that the number of old prestressed concrete (PSC) bridgeover 30 years of service life is rapidly increasing. Recently tendon corrosion is one of the most critical issues in the maintenance of PSC bridges. In this paper, mechanical properties of corroded strands, which were removed from old bridges, were evaluated using tensile test. In the result, the equations to express the mechanical behavior of corroded strand were derived and compared to existing equation. For the decision of tendon replacement, it is necessary to evaluate the effect of corrosion level on strength and ductility of the structure. Considerations on analysis of PSC girders were introduced, and decision making on tendon replacement was also proposed.

Keywords: prestressed concrete bridge, tendon, corrosion, strength, ductility

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Authors: Khaled M. El Naggar

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This paper introduces a digital method for fault section identification in transmission lines. The method uses digital set of the measured short circuit current to locate faults in electrical power systems. The digitized current is used to construct a set of overdetermined system of equations. The problem is then constructed and solved using the proposed digital optimization technique to find the fault distance. The proposed optimization methodology is an application of simulated annealing optimization technique. The method is tested using practical case study to evaluate the proposed method. The accurate results obtained show that the algorithm can be used as a powerful tool in the area of power system protection.

Keywords: optimization, estimation, faults, measurement, high voltage, simulated annealing

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Authors: K. Aravinth, C. T. Vignesh

Abstract:

The usage of pulse tube cryocoolers is significantly increased mainly due to the advantage of the absence of moving parts. The underlying idea of this project is to optimize the design of pulse tube, regenerator, a resonator in cryocooler and analyzing the thermo-acoustic oscillations with respect to the design parameters. Computational Fluid Dynamic (CFD) model with time-dependent validation is done to predict its performance. The continuity, momentum, and energy equations are solved for various porous media regions. The effect of changing the geometries and orientation will be validated and investigated in performance. The pressure, temperature and velocity fields in the regenerator and pulse tube are evaluated. This optimized design performance results will be compared with the existing pulse tube cryocooler design. The sinusoidal behavior of cryocooler in acoustic streaming patterns in pulse tube cryocooler will also be evaluated.

Keywords: acoustics, cryogenics, design, optimization

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Authors: Begum Koru, Isik Aybay, Demet Celik Ulusoy

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The discipline of law is quite complex and has its own terminology. Apart from written legal rules, there is also living law, which refers to legal practice. Basic legal rules aim at the happiness of individuals in social life and have different characteristics in different branches such as public or private law. On the other hand, law is a national phenomenon. The law of one nation and the legal system applied on the territory of another nation may be completely different. People who are experts in a particular field of law in one country may have insufficient expertise in the law of another country. Today, in addition to the local nature of law, international and even supranational law rules are applied in order to protect basic human values and ensure the protection of human rights around the world. Systems that offer algorithmic solutions to legal problems using artificial intelligence (AI) tools will perhaps serve to produce very meaningful results in terms of human rights. However, algorithms to be used should not be developed by only computer experts, but also need the contribution of people who are familiar with law, values, judicial decisions, and even the social and political culture of the society to which it will provide solutions. Otherwise, even if the algorithm works perfectly, it may not be compatible with the values of the society in which it is applied. The latest developments involving the use of AI techniques in legal systems indicate that artificial law will emerge as a new field in the discipline of law. More AI systems are already being applied in the field of law, with examples such as predicting judicial decisions, text summarization, decision support systems, and classification of documents. Algorithms for legal systems employing AI tools, especially in the field of prediction of judicial decisions and decision support systems, have the capacity to create automatic decisions instead of judges. When the judge is removed from this equation, artificial intelligence-made law created by an intelligent algorithm on its own emerges, whether the domain is national or international law. In this work, the aim is to make a general analysis of this new topic. Such an analysis needs both a literature survey and a perspective from computer experts' and lawyers' point of view. In some societies, the use of prediction or decision support systems may be useful to integrate international human rights safeguards. In this case, artificial law can serve to produce more comprehensive and human rights-protective results than written or living law. In non-democratic countries, it may even be thought that direct decisions and artificial intelligence-made law would be more protective instead of a decision "support" system. Since the values of law are directed towards "human happiness or well-being", it requires that the AI algorithms should always be capable of serving this purpose and based on the rule of law, the principle of justice and equality, and the protection of human rights.

Keywords: AI and law, artificial law, protection of human rights, AI tools for legal systems

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Authors: B. Gepts, E. Meex, E. Nuyts, E. Knaepen, G. Verbeeck

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The importance of resource efficiency and environmental impact assessment has raised the interest in knowing the amount of materials used in buildings. If no BIM model or energy performance certificate is available, material quantities can be obtained through an estimation or time-consuming calculation. For the interior wall area, no validated estimation method exists. However, in the case of environmental impact assessment or evaluating the existing building stock as future material banks, knowledge of the material quantities used in interior walls is indispensable. This paper presents a validated method for the estimation of the interior wall area for dwellings based on easy-to-collect building characteristics. A database of 4963 residential buildings spread all over Belgium is used. The data are collected through onsite measurements of the buildings during the construction phase (between mid-2010 and mid-2017). The interior wall area refers to the area of all interior walls in the building, including the inner leaf of exterior (party) walls, minus the area of windows and doors, unless mentioned otherwise. The two predictive modelling techniques used are 1) a (stepwise) linear regression and 2) a decision tree. The best estimation method is selected based on the best R² k-fold (5) fit. The research shows that the building volume is by far the most important variable to estimate the interior wall area. A stepwise regression based on building volume per building, building typology, and type of house provides the best fit, with R² k-fold (5) = 0.88. Although the best R² k-fold value is obtained when the other parameters ‘building typology’ and ‘type of house’ are included, the contribution of these variables can be seen as statistically significant but practically irrelevant. Thus, if these parameters are not available, a simplified estimation method based on only the volume of the building can also be applied (R² k-fold = 0.87). The robustness and precision of the method (output) are validated three times. Firstly, the prediction of the interior wall area is checked by means of alternative calculations of the building volume and of the interior wall area; thus, other definitions are applied to the same data. Secondly, the output is tested on an extension of the database, so it has the same definitions but on other data. Thirdly, the output is checked on an unrelated database with other definitions and other data. The validation of the estimation methods demonstrates that the methods remain accurate when underlying data are changed. The method can support environmental as well as economic dimensions of impact assessment, as it can be used in early design. As it allows the prediction of the amount of interior wall materials to be produced in the future or that might become available after demolition, the presented estimation method can be part of material flow analyses on input and on output.

Keywords: buildings as material banks, building stock, estimation method, interior wall area

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Authors: Angga S. Fajar, A. Aminullah, J. Kiyono, R. A. Safitri

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This paper discusses about the application of ANN for optimizing of bridge structure design. ANN has been applied in various field of science concerning prediction and optimization. The structural optimization has several benefit including accelerate structural design process, saving the structural material, and minimize self-weight and mass of structure. In this paper, there are three types of bridge structure that being optimized including PSC I-girder superstructure, composite steel-concrete girder superstructure, and RC bridge pier. The different optimization strategy on each bridge structure implement back propagation method of ANN is conducted in this research. The optimal weight and easier design process of bridge structure with satisfied error are achieved.

Keywords: bridge structures, ANN, optimization, back propagation

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Authors: Khaled I. Nawafleh

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In this paper, it provide the canonical approach for studying dissipated oscillators based on the doubling of degrees of freedom. Clearly, expressions for Lagrangians of the elementary modes of the system are given, which ends with the familiar classical equations of motion for the dissipative oscillator. The equation for one variable is the time reversed of the motion of the second variable. it discuss in detail the extended Bateman Lagrangian specifically for a dual extended damped oscillator time-dependent. A Hamilton-Jacobi analysis showing the equivalence with the Lagrangian approach is also obtained. For that purpose, the techniques of separation of variables were applied, and the quantization process was achieved.

Keywords: doubling of degrees of freedom, dissipated harmonic oscillator, Hamilton-Jacobi, time-dependent lagrangians, quantization

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Authors: Tusar Kanti Dash, Ganapati Panda

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The evaluation of speech quality and intelligence is critical to the overall effectiveness of the Speech Enhancement Algorithms. Several intrusive and non-intrusive measures are employed to calculate these parameters. Non-Intrusive Evaluation is most challenging as, very often, the reference clean speech data is not available. In this paper, a novel non-intrusive speech evaluation measure is proposed using audio features derived from the Stockwell transform. These features are used with the Light Gradient Boosting Machine for the effective prediction of speech quality and intelligibility. The proposed model is analyzed using noisy and reverberant speech from four databases, and the results are compared with the standard Intrusive Evaluation Measures. It is observed from the comparative analysis that the proposed model is performing better than the standard Non-Intrusive models.

Keywords: non-Intrusive speech evaluation, S-transform, light GBM, speech quality, and intelligibility

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Authors: M. A. Ghebouli, A. Bouhemadou, H. Choutri, L. Louaila

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Some physical properties of the cubic perovskites CsXF3 (X = Sr, Ca, and Hg) have been investigated using pseudopotential plane–wave (PP-PW) method based on the density functional theory (DFT). The calculated lattice constants within GGA (PBE) and LDA (CA-PZ) agree reasonably with the available experiment data. The elastic constants and their pressure derivatives are predicted using the static finite strain technique. We derived the bulk and shear moduli, Young’s modulus, Poisson’s ratio and Lamé’s constants for ideal polycrystalline aggregates. The analysis of B/G ratio indicates that CsXF3 (X = Ca, Sr, and Hg) are ductile materials. The thermal effect on the volume, bulk modulus, heat capacities CV, CP, and Debye temperature was predicted.

Keywords: perovskite, PP-PW method, elastic constants, electronic band structure

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Authors: Galal Elkobrosy, Amr M. Abdelrazek, Bassuny M. Elsouhily, Mohamed E. Khidr

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Crank shaft length, connecting rod length, crank angle, engine rpm, cylinder bore, mass of piston and compression ratio are the inputs that can control the performance of the slider crank mechanism and then its efficiency. Several combinations of these seven inputs are used and compared. The throughput engine torque predicted by the simulation is analyzed through two different regression models, with and without interaction terms, developed according to multi-linear regression using LU decomposition to solve system of algebraic equations. These models are validated. A regression model in seven inputs including their interaction terms lowered the polynomial degree from 3^rd degree to 1^st degree and suggested valid predictions and stable explanations.

Keywords: design of experiments, regression analysis, SI engine, statistical modeling

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Authors: A. M. Byrne, E. Bonfiglio, C. Rigby, N. Edelstyn

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Introduction: Neuromarketing employs numerous methodologies when investigating products and advertisement effectiveness. Electroencephalography (EEG), a non-invasive measure of electrical activity from the brain, is commonly used in neuromarketing. EEG data can be considered using time-frequency (TF) analysis, where changes in the frequency of brainwaves are calculated to infer participant’s mental states, or event-related potential (ERP) analysis, where changes in amplitude are observed in direct response to a stimulus. This presentation discusses the findings of a systematic review of EEG measures in neuromarketing. A systematic review summarises evidence on a research question, using explicit measures to identify, select, and critically appraise relevant research papers. Thissystematic review identifies which EEG measures are the most robust predictor of customer preference and purchase intention. Methods: Search terms identified174 papers that used EEG in combination with marketing-related stimuli. Publications were excluded if they were written in a language other than English or were not published as journal articles (e.g., book chapters). The review investigated which TF effect (e.g., theta-band power) and ERP component (e.g., N400) most consistently reflected preference and purchase intention. Machine-learning prediction was also investigated, along with the use of EEG combined with physiological measures such as eye-tracking. Results: Frontal alpha asymmetry was the most reliable TF signal, where an increase in activity over the left side of the frontal lobe indexed a positive response to marketing stimuli, while an increase in activity over the right side indexed a negative response. The late positive potential, a positive amplitude increase around 600 ms after stimulus presentation, was the most reliable ERP component, reflecting the conscious emotional evaluation of marketing stimuli. However, each measure showed mixed results when related to preference and purchase behaviour. Predictive accuracy was greatly improved through machine-learning algorithms such as deep neural networks, especially when combined with eye-tracking or facial expression analyses. Discussion: This systematic review provides a novel catalogue of the most effective use of each EEG measure commonly used in neuromarketing. Exciting findings to emerge are the identification of the frontal alpha asymmetry and late positive potential as markers of preferential responses to marketing stimuli. Predictive accuracy using machine-learning algorithms achieved predictive accuracies as high as 97%, and future research should therefore focus on machine-learning prediction when using EEG measures in neuromarketing.

Keywords: EEG, ERP, neuromarketing, machine-learning, systematic review, time-frequency

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Authors: Xu Runzhang, Yang Yanbing, Niu Yi, Zhang Mingyou, Liu Yu

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For a class of semilinear parabolic equations with linear dynamical boundary conditions in a bounded domain, we obtain both global solutions and finite time blow-up solutions when the initial data varies in the phase space H1(Ω). Our main tools are the comparison principle, the potential well method and the concavity method. In particular, we discuss the behavior of the solutions with the initial data at critical and high energy level.

Keywords: high energy level, critical energy level, linear dynamical boundary condition, semilinear parabolic equation

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Authors: Jialin Wu, Zhiwei Lian, Jieyu Tang, Jingyun Shen

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Tornado is a serious and unpredictable natural disaster, which has an important impact on people's production and life. The probability of being hit by tornadoes in China was analyzed considering the principles of tornado formation. Then some suggestions on layout and shapes for newly-built buildings were provided combined with the characteristics of tornado wind fields. Fuzzy clustering and inverse closeness methods were used to evaluate the probability levels of tornado risks in various provinces based on classification and ranking. GIS was adopted to display the results. Finally, wind field single-vortex tornado was studied to discuss the optimized design of rural low-rise houses in Yancheng, Jiangsu as an example. This paper may provide enough data to support building and urban design in some specific regions.

Keywords: tornado probability, computational fluid dynamics, fuzzy mathematics, optimal design

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Authors: O. W. Lawal, L. O. Ahmed, Y. K. Ali

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The unsteady MHD Poiseuille flow of a third grade fluid between two parallel horizontal nonconducting porous plates is studied with heat transfer. The two plates are fixed but maintained at different constant temperature with the Joule and viscous dissipation taken into consideration. The fluid motion is produced by a sudden uniform exponential decaying pressure gradient and external uniform magnetic field that is perpendicular to the plates. The momentum and energy equations governing the flow are solved numerically using Maple program. The effects of magnetic field and third grade fluid parameters on velocity and temperature profile are examined through several graphs.

Keywords: exponential decaying pressure gradient, MHD flow, Poiseuille flow, third grade fluid

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Authors: Mohammad Asadpour, Maryam Sadeghi, Mahmoud Jafari

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The transformation of carbon dioxide into fuels and commodity chemicals is considered one of the most attractive methods to meet energy demands and reduce atmospheric CO₂ levels. Cobalt complexes have previously shown high faradaic efficiency in the reduction of CO₂ to CO. In this study, a nanostructure, referred to as a porphyrin-like buckyball, is simulated and analyzed for its electrical properties. The investigation aims to understand the unique characteristics of this material and its potential applications in electronic devices. Through computational simulations and analysis, the electrocatalytic reduction of CO₂ to CO by Cobalt-porphyrin-like buckyball is explored. The findings of this study offer valuable insights into the electrocatalytic properties of this predicted structure, paving the way for further research and development in the field of nanotechnology.

Keywords: porphyrin-like buckyball, DFT, nanomaterials, CO₂ to CO

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Authors: Pacharaporn Lekyan

Abstract:

The purpose of this study is to explore the conflict management affecting the workplace and analyze the ability of the prediction of leadership of the headman and the methods to handle the conflict in an organization. The quantitative research and developed the questionnaire in order to collect information from the respondents from 200 samples from leader or manager who worked in frozen food factories in Thailand. The result analysis shows about the problem of the relationship between conflict management factors, leadership, and the confliction in organization. The emotion of the leader in the organization is not the only factor that can affect conflict management but also the emotion of surrounding people which this factor can happen all the time and shows that four out of five factors of interpersonal conflict management have affected on emotion intelligence and also shows that the behaviors of leadership have an influence on conflict management.

Keywords: conflict management, emotional intelligence, leadership, factories' employee

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Authors: Marc Sader, Michiel Stock, Bernard De Baets

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Considering a large amount of adsorption data of adsorbate gases on adsorbent materials in literature, it is interesting to predict such adsorption data without experimentation. A quantitative structure-activity relationship (QSAR) is developed to correlate molecular characteristics of gases and existing knowledge of materials with their respective adsorption properties. The application of Random Forest, a machine learning method, on a set of adsorption isotherms at a wide range of partial pressures and concentrations is studied. The predicted adsorption isotherms are fitted to several adsorption equations to estimate the adsorption properties. To impute the adsorption properties of desired gases on desired materials, leave-one-out cross-validation is employed. Extensive experimental results for a range of settings are reported.

Keywords: adsorption, predictive modeling, QSAR, random forest

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Authors: S. Aizikovich, L. Krenev, Y. Tokovyy, Y. C. Wang

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An approximate analytical-numerical solution to the axisymmetric problem on thermo-mechanical indentation of a flat cylindrical punch into an arbitrarily non-homogeneous elastic half-space is constructed by making use of the bilateral asymptotic method. The key point of this method lies in evaluation of the ker¬nels in the obtained integral equations by making use of a numerical technique. Once the structure of the kernel is defined, it then is approximated by an analytical expression of special kind so that the solution of the integral equation can be achieved analytically. This fact allows for construction of the solution in an analytical form, which is convenient for analysis of the mechanical effects concerned with arbitrarily presumed non-homogeneity of the material.

Keywords: contact problem, circular punch, arbitrarily-nonhomogeneous halfspace

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Authors: Hariti Rafika, Fekih Malika, Saighi Mohamed

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Heat transfer by natural convection in storage tanks for LNG is extremely related to heat gains through the walls with thermal insulation is not perfectly efficient. In this paper, we present the study of natural convection in the unsteady regime for natural gas in aware phase using the fluent software. The gas is just on the surface of the liquid phase. The CFD numerical method used to solve the system of equations is based on the finite volume method. This numerical simulation allowed us to determine the temperature profiles, the stream function, the velocity vectors and the variation of the heat flux density in the vapor phase in the LNG storage tank volume. The results obtained for a general configuration, by numerical simulation were compared to those found in the literature.

Keywords: numerical simulation, natural convection, heat gains, storage tank, liquefied natural gas

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Authors: M. O. Durojaye, J. T. Agee

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This paper is on the one-dimensional, positive temperature coefficient (PTC) thermistor model with a hyperbolic tangent function approximation for the electrical conductivity. The method of asymptotic expansion was adopted to obtain the steady state solution and the unsteady-state response was obtained using the method of lines (MOL) which is a well-established numerical technique. The approach is to reduce the partial differential equation to a vector system of ordinary differential equations and solve numerically. Our analysis shows that the hyperbolic tangent approximation introduced is well suitable for the electrical conductivity. Numerical solutions obtained also exhibit correct physical characteristics of the thermistor and are in good agreement with the exact steady state solutions.

Keywords: electrical conductivity, hyperbolic tangent function, PTC thermistor, method of lines

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Authors: Yeliz Ekinci, Melis Koyuncu

Abstract:

Successful planning of solid waste management systems requires successful prediction of the amount of solid waste generated in an area. Waste management planning can protect the environment and human health, hence it is tremendously important for countries. The lack of information in waste generation can cause many environmental and health problems. Turkey is a country that plans to join European Union, hence, solid waste management is one of the most significant criteria that should be handled in order to be a part of this community. Solid waste management system requires a good forecast of solid waste generation. Thus, this study aims to forecast solid waste generation in Turkey. Artificial Neural Network and Linear Regression models will be used for this aim. Many models will be run and the best one will be selected based on some predetermined performance measures.

Keywords: forecast, solid waste generation, solid waste management, Turkey

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Authors: Jian-Jun Shu

Abstract:

It is common knowledge that many physical problems (such as non-linear shallow-water waves and wave motion in plasmas) can be described by the Korteweg-de Vries (KdV) equation, which possesses certain special solutions, known as solitary waves or solitons. As a marriage of the KdV equation and the classical Burgers (KdVB) equation, the Korteweg-de Vries-Burgers (KdVB) equation is a mathematical model of waves on shallow water surfaces in the presence of viscous dissipation. Asymptotic analysis is a method of describing limiting behavior and is a key tool for exploring the differential equations which arise in the mathematical modeling of real-world phenomena. By using variable transformations, the asymptotic expansion of the KdVB equation is presented in this paper. The asymptotic expansion may provide a good gauge on the validation of the corresponding numerical scheme.

Keywords: asymptotic expansion, differential equation, Korteweg-de Vries-Burgers (KdVB) equation, soliton

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Authors: Ruixia Liu

Abstract:

Qinghai-Tibet Plateau has an important influence on the precipitation of its lower reaches. Data from remote sensing has itself advantage and numerical prediction model which assimilates RS data will be better than other. We got the assimilation data of MHS and terrestrial and sounding from GSI, and introduced the result into WRF, then got the result of RH and precipitation forecast. We found that assimilating MHS and terrestrial and sounding made the forecast on precipitation, area and the center of the precipitation more accurate by comparing the result of 1h,6h,12h, and 24h. Analyzing the difference of the initial field, we knew that the data assimilating about Qinghai-Tibet Plateau influence its lower reaches forecast by affecting on initial temperature and RH.

Keywords: Qinghai-Tibet Plateau, precipitation, data assimilation, GSI

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Authors: Hussam Elias, Ninovic Perez, Holger Hirsch

Abstract:

The completion of the EMC regulations worldwide is growing steadily as the usage of electronics in our daily lives is increasing more than ever. In this paper, we introduce a novel method to perform the final phase of Electromagnetic compatibility (EMC) measurement and to reduce the required test time according to the norm EN 55032 by using a developed tool and the conventional neural network(CNN). The neural network was trained using real EMC measurements, which were performed in the Semi Anechoic Chamber (SAC) by CETECOM GmbH in Essen, Germany. To implement our proposed method, we wrote software to perform the radiated electromagnetic interference (EMI) measurements and use the CNN to predict and determine the position of the turntable that meets the maximum radiation value.

Keywords: conventional neural network, electromagnetic compatibility measurement, mean absolute error, position error

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Authors: Yang Zhong, Meijie Xu

Abstract:

The explicit solutions for the natural frequencies and mode shapes of the orthotropic rectangular plate with four clamped edges are presented by the double finite cosine integral transform method. In the analysis procedure, the classical orthotropic rectangular thin plate is considered. Because only are the basic dynamic elasticity equations of the orthotropic thin plate adopted, it is not need prior to select the deformation function arbitrarily. Therefore, the solution developed by this paper is reasonable and theoretical. Finally, an illustrative example is given and the results are compared with those reported earlier. This method is found to be easier and effective. The results show reasonable agreement with other available results, but with a simpler and practical approach.

Keywords: rectangular orthotropic plate, four clamped edges, natural frequencies and mode shapes, finite integral transform

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Authors: Ahmed Guerine, Ali El Hafidi, Bruno Martin, Philippe Leclaire

Abstract:

This paper investigates the nonlinear dynamic response of a mechanical torque limiter which is used to protect drive parts from overload (helical transmission gears). The system is driven by four excitations: two external excitations (aerodynamics torque and force) and two internal excitations (two mesh stiffness fluctuations). In this work, we develop a dynamic model with lumped components and 28 degrees of freedom. We use the Runge Kutta step-by-step time integration numerical algorithm to solve the equations of motion obtained by Lagrange formalism. The numerical results have allowed us to identify the sources of vibration in the wind turbine. Also, they are useful to help the designer to make the right design and correctly choose the times for maintenance.

Keywords: two-stage helical gear, lumped model, dynamic response, torque-limiter

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Authors: Muhammad Sohail Khan, Rehan Ali Shah

Abstract:

The present paper applies the optimal homotopy perturbation method (OHPM) and the optimal homotopy asymptotic method (OHAM) introduced recently to obtain analytic approximations of the non-linear equations modeling the flow of polymer in case of wire coating of a corotational Maxwell fluid. Expression for the velocity field is obtained in non-dimensional form. Comparison of the results obtained by the two methods at different values of non-dimensional parameter l₁₀, reveal that the OHPM is more effective and easy to use. The OHPM solution can be improved even working in the same order of approximation depends on the choices of the auxiliary functions.

Keywords: corotational Maxwell model, optimal homotopy asymptotic method, optimal homotopy perturbation method, wire coating die

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Authors: Sadia Arshad, Ayesha Sohail, Sana Javed, Khadija Maqbool, Salma Kanwal

Abstract:

The dynamical study of the carriers play an essential role in the evolution and global transmission of infectious diseases and will be discussed in this study. To make this approach novel, we will consider the fractional order model which is generalization of integer order derivative to an arbitrary number. Since the integration involved is non local therefore this property of fractional operator is very useful to study epidemic model for infectious diseases. An extended numerical method (ODE solver) is implemented on the model equations and we will present the simulations of the model for different values of fractional order to study the effect of carriers on transmission dynamics. Global dynamics of fractional model are established by using the reproduction number.

Keywords: Fractional differential equation, Numerical simulations, epidemic model, transmission dynamics

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Authors: Jurriaan Gillissen

Abstract:

This work is concerned with stabilizing the numerical integration of the Navier-Stokes equation (NSE), backwards in time. Applications involve the detection of sources of, e.g., sound, heat, and pollutants. Stable reverse numerical integration of parabolic differential equations is also relevant for image de-blurring. While the literature addresses the reverse integration problem of the advection-diffusion equation, the problem of numerical reverse integration of the NSE has, to our knowledge, not yet been addressed. Owing to the presence of viscosity, the NSE is irreversible, i.e., when going backwards in time, the fluid behaves, as if it had a negative viscosity. As an effect, perturbations from the perfect solution, due to round off errors or discretization errors, grow exponentially in time, and reverse integration of the NSE is inherently unstable, regardless of using an implicit time integration scheme. Consequently, some sort of filtering is required, in order to achieve a stable, numerical, reversed integration. The challenge is to find a filter with a minimal adverse affect on the accuracy of the reversed integration. In the present work, we explore an adjoint gradient method (AGM) to achieve this goal, and we apply this technique to two-dimensional (2D), decaying turbulence. The AGM solves for the initial velocity field u0 at t = 0, that, when integrated forward in time, produces a final velocity field u1 at t = 1, that is as close as is feasibly possible to some specified target field v1. The initial field u0 defines a minimum of a cost-functional J, that measures the distance between u1 and v1. In the minimization procedure, the u0 is updated iteratively along the gradient of J w.r.t. u0, where the gradient is obtained by transporting J backwards in time from t = 1 to t = 0, using the adjoint NSE. The AGM thus effectively replaces the backward integration by multiple forward and backward adjoint integrations. Since the viscosity is negative in the adjoint NSE, each step of the AGM is numerically stable. Nevertheless, when applied to turbulence, the AGM develops instabilities, which limit the backward integration to small times. This is due to the exponential divergence of phase space trajectories in turbulent flow, which produces a multitude of local minima in J, when the integration time is large. As an effect, the AGM may select unphysical, noisy initial conditions. In order to improve this situation, we propose two remedies. First, we replace the integration by a sequence of smaller integrations, i.e., we divide the integration time into segments, where in each segment the target field v1 is taken as the initial field u0 from the previous segment. Second, we add an additional term (regularizer) to J, which is proportional to a high-order Laplacian of u0, and which dampens the gradients of u0. We show that suitable values for the segment size and for the regularizer, allow a stable reverse integration of 2D decaying turbulence, with accurate results for more then O(10) turbulent, integral time scales.

Keywords: time reversed integration, parabolic differential equations, adjoint gradient method, two dimensional turbulence

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