Search results for: lumped spring-mass model

Authors: Vesna Bosilj Vuksic, Mirjana Pejic Bach, Tomislav Hernaus

Abstract:

The aim of this paper is to present a framework for empirical investigation of the effectiveness of simulation games for student learning of BPM concept. A future research methodology is explained and a normative model that extends the standard TAM model by introducing latent and mediating variables into the relationship between independent variables and dependent variable is developed. Future research propositions are defined in order to examine the benefits that can be achieved through the use of BPM simulation games in ERP courses.

Keywords: Business process management, simulation games, education, technology acceptance model.

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Authors: Kejun Zhuang, Zhaohui Wen

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This paper is concerned with a nonautonomous three species food chain model with Crowley–Martin type functional response and time delay. Using the Mawhin-s continuation theorem in theory of degree, sufficient conditions for existence of periodic solutions are obtained.

Keywords: Periodic solutions, coincidence degree, food chain model, Crowley–Martin functional response.

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Authors: Yoon- Ho Shin, Jin-Seung Choi, Dong-Won Kang, Jeong-Woo Seo, Joo-Hack Lee, Ju-Young Kim, Dae-Hyeok Kim, Seung-Tae Yang, Gye-Rae Tack

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It is difficult to study the effect of various variables on cycle fitting through actual experiment. To overcome such difficulty, the forward dynamics of a musculoskeletal model was applied to cycle fitting in this study. The measured EMG data weres compared with the muscle activities of the musculoskeletal model through forward dynamics. EMG data were measured from five cyclists who do not have musculoskeletal diseases during three minutes pedaling with a constant load (150 W) and cadence (90 RPM). The muscles used for the analysis were the Vastus Lateralis (VL), Tibialis Anterior (TA), Bicep Femoris (BF), and Gastrocnemius Medial (GM). Person’s correlation coefficients of the muscle activity patterns, the peak timing of the maximum muscle activities, and the total muscle activities were calculated and compared. BIKE3D model of AnyBody (Anybodytech, Denmark) was used for the musculoskeletal model simulation. The comparisons of the actual experiments with the simulation results showed significant correlations in the muscle activity patterns (VL: 0.789, TA: 0.503, BF: 0.468, GM: 0.670). The peak timings of the maximum muscle activities were distributed at particular phases. The total muscle activities were compared with the normalized muscle activities, and the comparison showed about 10% difference in the VL (+10%), TA (+9.7%), and BF (+10%), excluding the GM (+29.4%). Thus, it can be concluded that muscle activities of model & experiment showed similar results. The results of this study indicated that it was possible to apply the simulation of further improved musculoskeletal model to cycle fitting.

Keywords: Cycle fitting, EMG, Musculoskeletal modeling, Simulation.

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Authors: V.V. Lyahov, V.M. Neshchadim

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The structural stability of the model of a nonelectroneutral current sheath is investigated. The stationary model of a current sheath represents the system of four connected nonlinear differential first-order equations and thus they should manifest structural instability property, i.e. sensitivity to the infinitesimal changes of parameters and starting conditions. Domains of existence of the solutions of current sheath type are found. Those solutions of the current sheath type are realized only in some regions of sevendimensional space of parameters of the problem. The phase volume of those regions is small in comparison with the whole phase volume of the definition range of those parameters. It is shown that the offered model of a nonelectroneutral current sheath is applicable for theoretical interpretation of the bifurcational current sheaths observed in the magnetosphere.

Keywords: Distribution function, electromagnetic field, magnetoactive plasma, nonelectroneutral current sheath, structural instability, bifurcational current sheath.

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Authors: G. González-Silva, E. M. Matos, W. P. Martignoni, M. Mori

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The objective of this work is to show a procedure for mesh generation in a fluidized bed using large eddy simulations (LES) of a filtered two-fluid model. The experimental data were obtained by [1] in a laboratory fluidized bed. Results show that it is possible to use mesh with less cells as compared to RANS turbulence model with granular kinetic theory flow (KTGF). Also, the numerical results validate the experimental data near wall of the bed, which cannot be predicted by RANS.model.

Keywords: LES, Mesh, Gas-Solid, Fluidized bed

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Authors: Devdutt

Abstract:

In this paper, vibration control response of passenger seat in quarter car model having three degrees of freedom is studied. Three different control strategies are taken into account using Adaptive Neuro Fuzzy Inference System (ANFIS) controller. In first case, ANFIS controller is applied in main suspension of active quarter car model. In second case, passenger seat suspension is assembled with ANFIS controller. Finally, both main and passenger seat suspensions are integrated with ANFIS controller. Simulation work under random road excitations is performed using passive and controlled quarter car models for performance comparison of passenger ride comfort. Ride comfort analysis is also compared as per ISO 2631-1 criterion. The obtained simulation responses are compared taking passenger seat acceleration and displacement response in time and frequency domain for the selection of best control strategy in designed quarter car model.

Keywords: Active suspension system, ANFIS controller, passenger ride comfort, quarter car model.

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Authors: N. C. Sarkar, A. Bhaskar, Z. Zheng

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The driving behavior in area-based (i.e., non-lane based) traffic is induced by the presence of other individuals in the choice space from the driver’s visual perception area. The driving behavior of a subject vehicle is constrained by the potential leaders and leaders are frequently changed over time. This paper is to determine a stochastic model for a parameter of modified intelligent driver model (MIDM) in area-based traffic (as in developing countries). The parametric and non-parametric distributions are presented to fit the parameters of MIDM. The goodness of fit for each parameter is measured in two different ways such as graphically and statistically. The quantile-quantile (Q-Q) plot is used for a graphical representation of a theoretical distribution to model a parameter and the Kolmogorov-Smirnov (K-S) test is used for a statistical measure of fitness for a parameter with a theoretical distribution. The distributions are performed on a set of estimated parameters of MIDM. The parameters are estimated on the real vehicle trajectory data from India. The fitness of each parameter with a stochastic model is well represented. The results support the applicability of the proposed modeling for parameters of MIDM in area-based traffic flow simulation.

Keywords: Area-based traffic, car-following model, micro-simulation, stochastic modeling.

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Authors: Yalong Jiang, Zheru Chi

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In this paper, we study the factors which determine the capacity of a Convolutional Neural Network (CNN) model and propose the ways to evaluate and adjust the capacity of a CNN model for best matching to a specific pattern recognition task. Firstly, a scheme is proposed to adjust the number of independent functional units within a CNN model to make it be better fitted to a task. Secondly, the number of independent functional units in the capsule network is adjusted to fit it to the training dataset. Thirdly, a method based on Bayesian GAN is proposed to enrich the variances in the current dataset to increase its complexity. Experimental results on the PASCAL VOC 2010 Person Part dataset and the MNIST dataset show that, in both conventional CNN models and capsule networks, the number of independent functional units is an important factor that determines the capacity of a network model. By adjusting the number of functional units, the capacity of a model can better match the complexity of a dataset.

Keywords: CNN, capsule network, capacity optimization, character recognition, data augmentation; semantic segmentation.

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Authors: Seyed Ali Jafari, Mohammad Ghomi Avili, Emad Benhelal

Abstract:

In this study, a mathematical model was proposed and the accuracy of this model was assessed to predict the growth of Pseudomonas aeruginosa and rhamnolipid production under nitrogen limiting (sodium nitrate) fed-batch fermentation. All of the parameters used in this model were achieved individually without using any data from the literature. The overall growth kinetic of the strain was evaluated using a dual-parallel substrate Monod equation which was described by several batch experimental data. Fed-batch data under different glycerol (as the sole carbon source, C/N=10) concentrations and feed flow rates were used to describe the proposed fed-batch model and other parameters. In order to verify the accuracy of the proposed model several verification experiments were performed in a vast range of initial glycerol concentrations. While the results showed an acceptable prediction for rhamnolipid production (less than 10% error), in case of biomass prediction the errors were less than 23%. It was also found that the rhamnolipid production by P. aeruginosa was more sensitive at low glycerol concentrations. Based on the findings of this work, it was concluded that the proposed model could effectively be employed for rhamnolipid production by this strain under fed-batch fermentation on up to 80 g l- 1 glycerol.

Keywords: Fed-batch culture, glycerol, kinetic parameters, modelling, Pseudomonas aeruginosa, rhamnolipid.

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Authors: Dong-Young Yoo, Jong-Whoi Shin, Jin-Young Choi

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Social interest and demand on Home-Network has been increasing greatly. Although various services are being introduced to respond to such demands, they can cause serious security problems when linked to the open network such as Internet. This paper reviews the security requirements to protect the service users with assumption that the Home-Network environment is connected to Internet and then proposes the security model based on the requirement. The proposed security model can satisfy most of the requirements and further can be dynamically applied to the future ubiquitous Home-Networks.

Keywords: Home-Network, Security, Vulnerability, Response, Countermeasure.

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Authors: K. A. Sumitra Devi, N. P. Banashree, Annamma Abraham

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Partitioning is a critical area of VLSI CAD. In order to build complex digital logic circuits its often essential to sub-divide multi -million transistor design into manageable Pieces. This paper looks at the various partitioning techniques aspects of VLSI CAD, targeted at various applications. We proposed an evolutionary time-series model and a statistical glitch prediction system using a neural network with selection of global feature by making use of clustering method model, for partitioning a circuit. For evolutionary time-series model, we made use of genetic, memetic & neuro-memetic techniques. Our work focused in use of clustering methods - K-means & EM methodology. A comparative study is provided for all techniques to solve the problem of circuit partitioning pertaining to VLSI design. The performance of all approaches is compared using benchmark data provided by MCNC standard cell placement benchmark net lists. Analysis of the investigational results proved that the Neuro-memetic model achieves greater performance then other model in recognizing sub-circuits with minimum amount of interconnections between them.

Keywords: VLSI, circuit partitioning, memetic algorithm, genetic algorithm.

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Authors: Ami Kim, Oubong Gwun, Juwhan Song

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In this paper, we proposed the distribution of mesh normal vector direction as a feature descriptor of a 3D model. A normal vector shows the entire shape of a model well. The distribution of normal vectors was sampled in proportion to each polygon's area so that the information on the surface with less surface area may be less reflected on composing a feature descriptor in order to enhance retrieval performance. At the analysis result of ANMRR, the enhancement of approx. 12.4%~34.7% compared to the existing method has also been indicated.

Keywords: Interpolated Normal Vector, Feature Descriptor, 3DModel Retrieval.

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Authors: M. R. AlRashidi, K. M. El-Naggar, M. F. AlHajri

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This paper presents Simulated Annealing based approach to estimate solar cell model parameters. Single diode solar cell model is used in this study to validate the proposed approach outcomes. The developed technique is used to estimate different model parameters such as generated photocurrent, saturation current, series resistance, shunt resistance, and ideality factor that govern the current-voltage relationship of a solar cell. A practical case study is used to test and verify the consistency of accurately estimating various parameters of single diode solar cell model. Comparative study among different parameter estimation techniques is presented to show the effectiveness of the developed approach.

Keywords: Simulated Annealing, Parameter Estimation, Solar Cell.

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Authors: Yaw-Juen Wang, Po-Chun Hsu

Abstract:

This paper presents an equivalent circuit model based on piecewise linear parallel branches (PLPB) to study solar cell modules which are partially shaded. The PLPB model can easily be used in circuit simulation software such as the ElectroMagnetic Transients Program (EMTP). This PLPB model allows the user to simulate several different configurations of solar cells, the influence of partial shadowing on a single or multiple cells, the influence of the number of solar cells protected by a bypass diode and the effect of the cell connection configuration on partial shadowing.

Keywords: Cell Connection Configurations, EMTP, Equivalent Circuit, Partial Shading, Photovoltaic Module

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Authors: V. Arabadzhi

Abstract:

We attempted investigate a boat model, based on the conversion of energy of surface wave into a sequence of unidirectional pulses of jet spurts, in other words - model of the boat, which is thrusting by the waves field on water surface. These pulses are forming some average reactive stream from the output nozzle on the stern of boat. The suggested model provides the conversion of its oscillatory motions (both pitching and rolling) into a jet flow. This becomes possible due to special construction of the boat and due to several details, sensitive to the local wave field. The boat model presents the uniflow jet engine without slow conversions of mechanical energy into intermediate forms and without any external sources of energy (besides surface waves). Motion of boat is characterized by fast jerks and average onward velocity, which exceeds the velocities of liquid particles in the wave.

Keywords: Flat-bottomed boat, Underwater wing, Input and output nozzles, Wave thrust, Conversion of wave into a jet stream, Oscillatory motion and onward motion, Squid-like pump, Hatch-like pump, The thrust due to lifting float, The thrust due to radiation reaction.

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Authors: A. Kospach, A. Mladek, M. Waltenberger, F. Schilling

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In this work, a coupled 1D/3D simulation approach for thermal protection and optimization of a trailer refrigeration power pack unit was developed. With the developed 1D/3D simulation approach thermal critical scenarios, such as summer, high-load scenarios are investigated. The 1D thermal model was built up consisting of the thermal network, which includes different point masses and associated heat transfers, the coolant and oil circuits, as well as the fan unit. The 3D computational fluid dynamics (CFD) model was developed to model the air flow through the power pack unit considering convective heat transfer effects. In the 1D thermal model the temperatures of the individual point masses were calculated, which served as input variables for the 3D CFD model. For the calculation of the point mass temperatures in the 1D thermal model, the convective heat transfer rates from the 3D CFD model were required as input variables. These two variables (point mass temperatures and convective heat transfer rates) were the main couple variables for the coupled 1D/3D simulation model. The coupled 1D/3D model was validated with measurements under normal operating conditions. Coupled simulations for summer high-load case were than performed and compared with a reference case under normal operation conditions. Hot temperature regions and components could be identified. Due to the detailed information about the flow field, temperatures and heat fluxes, it was possible to directly derive improvement suggestions for the cooling design of the transport refrigeration power pack unit.

Keywords: Coupled thermal simulation, thermal analysis, transport refrigeration unit, 3D computational fluid dynamics, 1D thermal modelling, thermal management systems.

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Authors: Shashank.B. Thakre, L.B. Bhuyar, Samir.J. Deshmukh

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The value of overall oxygen transfer Coefficient (KLa), which is the best measure of oxygen transfer in water through aeration, is obtained by a simple approach, which sufficiently explains the utility of the method to eliminate the discrepancies due to inaccurate assumption of saturation dissolved oxygen concentration. The rate of oxygen transfer depends on number of factors like intensity of turbulence, which in turns depends on the speed of rotation, size, and number of blades, diameter and immersion depth of the rotor, and size and shape of aeration tank, as well as on physical, chemical, and biological characteristic of water. An attempt is made in this paper to correlate the overall oxygen transfer Coefficient (KLa), as an independent parameter with other influencing parameters mentioned above. It has been estimated that the simulation equation developed predicts the values of KLa and power with an average standard error of estimation of 0.0164 and 7.66 respectively and with R2 values of 0.979 and 0.989 respectively, when compared with experimentally determined values. The comparison of this model is done with the model generated using Computational fluid dynamics (CFD) and both the models were found to be in good agreement with each other.

Keywords: CFD Model, Overall oxygen transfer coefficient, Power, Mathematical Model, Validation.

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Authors: S. K. Pillai, M. K. Jeyakumar

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Estimation of model parameters is necessary to predict the behavior of a system. Model parameters are estimated using optimization criteria. Most algorithms use historical data to estimate model parameters. The known target values (actual) and the output produced by the model are compared. The differences between the two form the basis to estimate the parameters. In order to compare different models developed using the same data different criteria are used. The data obtained for short scale projects are used here. We consider software effort estimation problem using radial basis function network. The accuracy comparison is made using various existing criteria for one and two predictors. Then, we propose a new criterion based on linear least squares for evaluation and compared the results of one and two predictors. We have considered another data set and evaluated prediction accuracy using the new criterion. The new criterion is easy to comprehend compared to single statistic. Although software effort estimation is considered, this method is applicable for any modeling and prediction.

Keywords: Software effort estimation, accuracy, Radial Basis Function, linear least squares.

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Authors: U. K. Vishwakarma , A. Dvivedi, P. Kumar

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Metal matrix composites (MMC) are generating extensive interest in diverse fields like defense, aerospace, electronics and automotive industries. In this present investigation, material removal rate (MRR) modeling has been carried out using an axisymmetric model of Al-SiC composite during electrical discharge machining (EDM). A FEA model of single spark EDM was developed to calculate the temperature distribution.Further, single spark model was extended to simulate the second discharge. For multi-discharge machining material removal was calculated by calculating the number of pulses. Validation of model has been done by comparing the experimental results obtained under the same process parameters with the analytical results. A good agreement was found between the experimental results and the theoretical value.

Keywords: Electrical Discharge Machining, FEA, Metal matrix composites, Multi-discharge

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Authors: Mohd Yusri Ibrahim

Abstract:

Although it is known that interpersonal skills are essential for personal development, the debate however continues as to how to measure those skills, especially in youths. This study was conducted to develop a measurement model of interpersonal skills by suggesting three construct namely personal, skills and relationship; six function namely self, perception, listening, conversation, emotion and conflict management; and 30 behaviours as indicators. This cross-sectional survey by questionnaires was applied in east side of peninsula of Malaysia for 150 respondents, and analyzed by structural equation modelling (SEM) by AMOS. The suggested constructs, functions and indicators were consider accepted as measurement elements by observing on regression weight for standard loading, average variance extracted (AVE) for convergent validity, square root of AVE for discriminant validity, composite reliability (CR), and at least three fit indexes for model fitness. Finally, a measurement model of interpersonal skill for youth was successfully developed.

Keywords: Interpersonal communication, interpersonal skill, youth.

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Authors: A. Amar

Abstract:

Analysis of the elastic scattering of protons on ¹⁰B nuclei has been done in the framework of the optical model and single folding model at the beam energies up to 17 MeV. We could enhance the optical potential parameters using Esis88 Code, as well as SPI GENOA Code. Linear relationship between volume real potential (V₀) and proton energy (E_p) has been obtained. Also, surface imaginary potential W_D is proportional to the proton energy (E_p) in the range 0.400 and 17 MeV. The radiative reaction ¹⁰B(p,γ)¹¹C has been analyzed using potential model. A comparison between ¹⁰B(p,γ)¹¹C and ⁶Li(p,γ)⁷Be has been made. Good agreement has been found between theoretical and experimental results in the whole range of energy. The radiative resonance reaction ⁷Li(p,γ)⁸Be has been studied.

Keywords: Elastic scattering of protons on 10B nuclei, optical potential parameters, potential model, radiative reaction.

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Authors: Woo-Young Jung, Minho Kwon

Abstract:

Seismic design criteria based on performance of structures have recently been adopted by practicing engineers in response to destructive earthquakes. A simple but efficient structural-analysis tool capable of predicting both the strength and ductility is needed to analyze reinforced concrete (RC) structures under such event. A three-dimensional lattice model is developed in this study to analyze torsions in high-strength RC members. Optimization techniques for determining optimal variables in each lattice model are introduced. Pure torsion tests of RC members are performed to validate the proposed model. Correlation studies between the numerical and experimental results confirm that the proposed model is well capable of representing salient features of the experimental results.

Keywords: Torsion, non-linear analysis, three-dimensional lattice, high-strength concrete.

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Authors: A. Brahma

Abstract:

Drying is a phenomenon that accompanies the hardening of hydraulic materials. This study is concerned the modelling of drying shrinkage of the hydraulic materials and the prediction of the rate of spontaneous deformations of hydraulic materials during hardening. The model developed takes consideration of the main factors affecting drying shrinkage. There was agreement between drying shrinkage predicted by the developed model and experimental results. In last we show that developed model describe the evolution of the drying shrinkage of high performances concretes correctly.

Keywords: Drying, hydraulic concretes, shrinkage, modeling, prediction.

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Authors: Souhir Ben Amor, Heni Boubaker, Lotfi Belkacem

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This aims of this paper is to forecast the electricity spot prices. First, we focus on modeling the conditional mean of the series so we adopt a generalized fractional -factor Gegenbauer process (k-factor GARMA). Secondly, the residual from the -factor GARMA model has used as a proxy for the conditional variance; these residuals were predicted using two different approaches. In the first approach, a local linear wavelet neural network model (LLWNN) has developed to predict the conditional variance using the Back Propagation learning algorithms. In the second approach, the Gegenbauer generalized autoregressive conditional heteroscedasticity process (G-GARCH) has adopted, and the parameters of the k-factor GARMA-G-GARCH model has estimated using the wavelet methodology based on the discrete wavelet packet transform (DWPT) approach. The empirical results have shown that the k-factor GARMA-G-GARCH model outperform the hybrid k-factor GARMA-LLWNN model, and find it is more appropriate for forecasts.

Keywords: k-factor, GARMA, LLWNN, G-GARCH, electricity price, forecasting.

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Authors: A. M. Tahsini

Abstract:

The Spalart and Allmaras turbulence model has been implemented in a numerical code to study the compressible turbulent flows, which the system of governing equations is solved with a finite volume approach using a structured grid. The AUSM+ scheme is used to calculate the inviscid fluxes. Different benchmark problems have been computed to validate the implementation and numerical results are shown. A special Attention is paid to wall jet applications. In this study, the jet is submitted to various wall boundary conditions (adiabatic or uniform heat flux) in forced convection regime and both two-dimensional and axisymmetric wall jets are considered. The comparison between the numerical results and experimental data has given the validity of this turbulence model to study the turbulent wall jets especially in engineering applications.

Keywords: Wall Jet, Heat transfer, Numerical Simulation, Spalart-Allmaras Turbulence model.

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Authors: Zhouhong Li, Jiming Yang

Abstract:

In this paper, a class of predator-prey-chain model with harvesting terms are studied. By using Mawhin-s continuation theorem of coincidence degree theory and some skills of inequalities, some sufficient conditions are established for the existence of eight positive periodic solutions. Finally, an example is presented to illustrate the feasibility and effectiveness of the results.

Keywords: Positive periodic solutions, Predator-prey-chain model, coincidence degree, harvesting term.

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Authors: S. Dhib, S. A. Addouche, T. Loukil, A. Elmhamedi

Abstract:

In this paper, a reverse supply chain network is investigated for a decision making. This decision is surrounded by complex flows of returned products, due to the increasing quantity, the type of returned products and the variety of recovery option products (reuse, recycling, and refurbishment). The most important problem in the reverse logistic network (RLN) is to orient returned products to the suitable type of recovery option. However, returned products orientations from collect sources to the recovery disposition have not well considered in performance model. In this study, we propose a performance model for designing a network configuration on reverse logistics. Conceptual and analytical models are developed with taking into account operational, economic and environmental factors on designing network.

Keywords: Reverse logistics, Network design, Performance model, Open loop configuration.

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Authors: Muhammad Zeeshan UlHaque, Peng Du, Leo K. Cheng, Marc D. Jacobs

Abstract:

Sensory nerves in the foot play an important part in the diagnosis of various neuropathydisorders, especially in diabetes mellitus.However, a detailed description of the anatomical distribution of the nerves is currently lacking. A computationalmodel of the afferent nerves inthe foot may bea useful tool for the study of diabetic neuropathy. In this study, we present the development of an anatomically-based model of various major sensory nerves of the sole and dorsal sidesof the foot. In addition, we presentan algorithm for generating synthetic somatosensory nerve networks in the big-toe region of a right foot model. The algorithm was based on a modified version of the Monte Carlo algorithm, with the capability of being able to vary the intra-epidermal nerve fiber density in differentregionsof the foot model. Preliminary results from the combinedmodel show the realistic anatomical structure of the major nerves as well as the smaller somatosensory nerves of the foot. The model may now be developed to investigate the functional outcomes of structural neuropathyindiabetic patients.

Keywords: Diabetic neuropathy, Finite element modeling, Monte Carlo Algorithm, Somatosensory nerve networks

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Authors: Rajendra K. Ray, Kim Dan Nguyen

Abstract:

An unstructured finite volume numerical model is presented here for simulating shallow-water flows with wetting and drying fronts. The model is based on the Green-s theorem in combination with Chorin-s projection method. A 2nd-order upwind scheme coupled with a Least Square technique is used to handle convection terms. An Wetting and drying treatment is used in the present model to ensures the total mass conservation. To test it-s capacity and reliability, the present model is used to solve the Parabolic Bowl problem. We compare our numerical solutions with the corresponding analytical and existing standard numerical results. Excellent agreements are found in all the cases.

Keywords: Finite volume method, Projection method, Shallow water, Unstructured grid, wetting/drying fronts.

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Authors: Mohammad Modarres, Shirin Aslani

Abstract:

The goal of this paper is to develop a model to integrate “pricing" and “advertisement" for short life cycle products, such as branded fashion clothing products. To achieve this goal, we apply the concept of “Dynamic Pricing". There are two classes of advertisements, for the brand (regardless of product) and for a particular product. Advertising the brand affects the demand and price of all the products. Thus, the model considers all these products in relation with each other. We develop two different methods to integrate both types of advertisement and pricing. The first model is developed within the framework of dynamic programming. However, due to the complexity of the model, this method cannot be applicable for large size problems. Therefore, we develop another method, called hieratical approach, which is capable of handling the real world problems. Finally, we show the accuracy of this method, both theoretically and also by simulation.

Keywords: Advertising, Dynamic programming, Dynamic pricing, Promotion.

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