Search results for: limit equilibrium method

Authors: Taleb Hosni Abderrahmane, Berga Abdelmadjid

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The development of numerical analysis and its application to geomechanics problems have provided geotechnical engineers with extremely powerful tools. One of the most important problems in geotechnical engineering is the slope stability assessment. It is a very difficult task due to several aspects such the nature of the problem, experimental consideration, monitoring, controlling, and assessment. The main objective of this paper is to perform a comparative numerical study between the following methods: The Limit Equilibrium (LEM), Finite Element (FEM), Limit Analysis (LAM) and Distinct Element (DEM). The comparison is conducted in terms of the safety factors and the critical slip surfaces. Through the results, we see the feasibility to analyse slope stability by many methods.

Keywords: comparison, factor of safety, geomechanics, numerical methods, slope analysis, slip surfaces

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Authors: A.D. Susanti, W. B. Sediawan, S.K. Wirawan, Budhijanto, Ritmaleni

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Oryzanol content in rice bran oil (RBO) naturally has high antioxidant activity. Its reviewed has several health properties and high interested in pharmacy, cosmetics, and nutrition’s. Because of the low concentration of oryzanol in crude RBO (0.9-2.9%) then its need to be further processed for practical usage, such as via adsorption process. In this study, investigation and adjustment of adsorption equilibrium models were conducted through the kinetic data approachments. Mathematical modeling on kinetics of batch adsorption of oryzanol separation from RBO has been set-up and then applied for equilibrium results. The size of adsorbent particles used in this case are usually relatively small then the concentration in the adsorbent is assumed to be not different. Hence, the adsorption rate is controlled by the rate of oryzanol mass transfer from the bulk fluid of RBO to the surface of silica gel. In this approachments, the rate of mass transfer is assumed to be proportional to the concentration deviation from the equilibrium state. The equilibrium models applied were Langmuir, coefficient distribution, and Freundlich with the values of the parameters obtained from equilibrium results. It turned out that the models set-up can quantitatively describe the experimental kinetics data and the adjustment of the values of equilibrium isotherm parameters significantly improves the accuracy of the model. And then the value of mass transfer coefficient per unit adsorbent mass (kca) is obtained by curve fitting.

Keywords: adsorption equilibrium, adsorption kinetics, oryzanol, rice bran oil

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Authors: Majid Yazdandoust

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This study, tries to suggest a design method based on displacement using finite difference numerical modeling in reinforcing soil retaining wall with steel strip. In this case, dynamic loading characteristics such as duration, frequency, peak ground acceleration, geometrical characteristics of reinforced soil structure and type of the site are considered to correct the pseudo static method and finally introduce the pseudo static coefficient as a function of seismic performance level and peak ground acceleration. For this purpose, the influence of dynamic loading characteristics, reinforcement length, height of reinforced system and type of the site are investigated on seismic behavior of reinforcing soil retaining wall with steel strip. Numerical results illustrate that the seismic response of this type of wall is highly dependent to cumulative absolute velocity, maximum acceleration, and height and reinforcement length so that the reinforcement length can be introduced as the main factor in shape of failure. Considering the loading parameters, mechanically stabilized earth wall parameters and type of the site showed that the used method in this study leads to most efficient designs in comparison with other methods which are generally suggested in cods that are usually based on limit-equilibrium concept. The outputs show the over-estimation of equilibrium design methods in comparison with proposed displacement based methods here.

Keywords: pseudo static coefficient, seismic performance design, numerical modeling, steel strip reinforcement, retaining walls, cumulative absolute velocity, failure shape

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Authors: Kanshio Richard Tyokyaa, Jagadish Singh

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In this paper, we examined the location and stability of Out-Of-Plane Equilibrium points in the elliptic restricted three-body problem of an infinitesimal body when both primaries are taken as oblate spheroids with oblateness up to zonal harmonic J₄. The positions of the Equilibrium points L₆,₇ and their stability depend on the oblateness of the primaries and the eccentricity of their orbits. We explored the problem numerically to show the effects of parameters involved in the position and stability of the Out-Of-Plane Equilibrium points for the systems: HD188753 and Gliese 667. It is found that their positions are affected by the oblateness of the primaries, eccentricity and the semi-major axis of the orbits, but its stability behavior remains unchanged and is unstable.

Keywords: out-of-plane, equilibrium points, stability, elliptic restricted three-body problem, oblateness, zonal harmonic

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Authors: Chand Pasha, Yasser Turki Alharbi, Krasamira Stancheva

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A simple spectrophotometric method for the determination of folic acid in pharmaceutical dosage samples was developed. The method is based on the diazotization reaction of thiourea with sodium nitrite in acidic medium yields diazonium compounds, which is then coupled with folic acid in basic medium yields yellow coloured azo dyes. Beer’s Lamberts law is observed in the range 0.5 – 16.2 μgmL-1 at a maximum wavelength of 416nm. The molar absorbtivity, sandells sensitivity, linear regression equation and detection limit and quantitation limit were found to be 5.695×104 L mol-1cm-1, 7.752×10-3 g cm-2, y= 0.092x - 0.018, 0.687 g mL-1 and 2.083 g mL-1. This method successfully determined Folate in Pharmaceutical formulations.

Keywords: folic acid determination, spectrophotometry, diazotization, thiourea, pharmaceutical dosage samples

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Authors: Khelifa Tarek, Benmebarek Sadok

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The 2D passive earth pressures acting on rigid retaining walls problem has been widely treated in the literature using different approaches (limit equilibrium, limit analysis, slip line and numerical computation), however, the 3D passive earth pressures problem has received less attention. This paper is concerned with the numerical study of 3D passive earth pressures induced by the translation of a rigid rough retaining wall for associated and non-associated soils. Using the explicit finite difference code FLAC3D, the increase of the passive earth pressures due to the decrease of the wall breadth is investigated. The results given by the present numerical analysis are compared with other investigation. The influence of the angle of dilation on the coefficients is also studied.

Keywords: numerical modeling, FLAC3D, retaining wall, passive earth pressures, angle of dilation

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Authors: H. C. Chinwenyi, H. D. Ibrahim, J. O. Adekunle

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The incubation period is defined as the time from infection with a microorganism to development of symptoms. In this research, two disease models: one with incubation period and another without incubation period were studied. The study involves the use of a  mathematical model with a single incubation period. The test for the existence and stability of the disease free and the endemic equilibrium states for both models were carried out. The fourth order Runge-Kutta method was used to solve both models numerically. Finally, a computer program in MATLAB was developed to run the numerical experiments. From the results, we are able to show that the endemic equilibrium state of the model with incubation period is locally asymptotically stable whereas the endemic equilibrium state of the model without incubation period is unstable under certain conditions on the given model parameters. It was also established that the disease free equilibrium states of the model with and without incubation period are locally asymptotically stable. Furthermore, results from numerical experiments using empirical data obtained from Nigeria Centre for Disease Control (NCDC) showed that the overall population of the infected people for the model with incubation period is higher than that without incubation period. We also established from the results obtained that as the transmission rate from susceptible to infected population increases, the peak values of the infected population for the model with incubation period decrease and are always less than those for the model without incubation period.

Keywords: asymptotic stability, Hartman-Grobman stability criterion, incubation period, Routh-Hurwitz criterion, Runge-Kutta method

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Authors: Reyhan Tekin Sitrava

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Teachers should have robust and comprehensive content knowledge for effective mathematics teaching. It was explained that content knowledge includes knowing the facts, truths, and concepts; explaining the reasons behind these facts, truths and concepts, and making relationship between the concepts and other disciplines. By virtue of its importance, it will be significant to explore teachers and prospective teachers’ content knowledge related to variety of topics in mathematics. From this point of view, the purpose of this study was to investigate prospective mathematics teachers’ content knowledge. Particularly, it was aimed to reveal the prospective teachers’ knowledge regarding the definition of limit and derivate. To achieve the purpose and to get in-depth understanding, a qualitative case study method was used. The data was collected from 34 prospective mathematics teachers through a questionnaire containing 2 questions. The first question required the prospective teachers to define the limit and the second one required to define the derivative. The data was analyzed using content analysis method. Based on the analysis of the data, although half of the prospective teachers (50%) could write the definition of the limit, nine prospective teachers (26.5%) could not define limit. However, eight prospective teachers’ definition was regarded as partially correct. On the other hand, twenty-seven prospective teachers (79.5%) could define derivative, but seven of them (20.5%) defined it partially. According to the findings, most of the prospective teachers have robust content knowledge on limit and derivative. This result is important because definitions have a virtual role in learning and teaching of mathematics. More specifically, definition is starting point to understand the meaning of a concept. From this point of view, prospective teachers should know the definitions of the concepts to be able to teach them correctly to the students. In addition, they should have knowledge about the relationship between limit and derivative so that they can explain these concepts conceptually. Otherwise, students may memorize the rules of calculating the derivative and the limit. In conclusion, the present study showed that most of the prospective mathematics teachers had enough knowledge about the definition of derivative and limit. However, the rest of them should learn their definition conceptually. The examples of correct, partially correct, and incorrect definition of both concepts will be presented and discussed based on participants’ statements. This study has some implications for instructors. Instructors should be careful about whether students learn the definition of these concepts or not. In order to this, the instructors may give prospective teachers opportunities to discuss the definition of these concepts and the relationship between the concepts.

Keywords: content knowledge, derivative, limit, prospective mathematics teachers

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Authors: Nathaporn Areerachakul

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In this study, the adsorption capacity of GAC with metsulfuron methyl was evaluated by using adsorption equilibrium and a fixed bed. Mathematical modelling was also used to simulate the GAC adsorption behavior. Adsorption equilibrium experiment of GAC was conducted using a constant concentration of metsulfuron methyl of 10 mg/L. The purpose of this study was to find the single component equilibrium concentration of herbicide. The adsorption behavior was simulated using the Langmuir, Freundlich, and Sips isotherm. The Sips isotherm fitted the experimental data reasonably well with an error of 6.6 % compared with 15.72 % and 7.07% for the Langmuir isotherm and Freudrich isotherm. Modelling using GAC adsorption theory could not replicate the experimental results in fixed bed column of 10 and 15 cm bed depths after a period more than 10 days of operation. This phenomenon is attributed to the formation of micro-organism (BAC) on the surface of GAC in addition to GAC alone.

Keywords: isotherm, adsorption equilibrium, GAC, metsulfuron methyl

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Authors: Endang Lukitaningsih, Fathul Jannah, Arief R. Hakim, Ratna D. Puspita, Zullies Ikawati

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Rifampicin is a semisynthetic antibiotic derivative of rifamycin B produced by Streptomyces mediterranei. RIF has been used worldwide as first line drug-prescribed throughout tuberculosis therapy. This study aims to develop and to validate an HPLC method couple with a UV detection for determination of rifampicin in spiked human plasma and its application for bioequivalence study. The chromatographic separation was achieved on an RP-C18 column (LachromHitachi, 250 x 4.6 mm., 5μm), utilizing a mobile phase of phosphate buffer/acetonitrile (55:45, v/v, pH 6.8 ± 0.1) at a flow of 1.5 mL/min. Detection was carried out at 337 nm by using spectrophotometer. The developed method was statistically validated for the linearity, accuracy, limit of detection, limit of quantitation, precise and specifity. The specifity of the method was ascertained by comparing chromatograms of blank plasma and plasma containing rifampicin; the matrix and rifampicin were well separated. The limit of detection and limit of quantification were 0.7 µg/mL and 2.3 µg/mL, respectively. The regression curve of standard was linear (r > 0.999) over a range concentration of 20.0 – 100.0 µg/mL. The mean recovery of the method was 96.68 ± 8.06 %. Both intraday and interday precision data showed reproducibility (R.S.D. 2.98% and 1.13 %, respectively). Therefore, the method can be used for routine analysis of rifampicin in human plasma and in bioequivalence study. The validated method was successfully applied in pharmacokinetic and bioequivalence study of rifampicin tablet in a limited number of subjects (under an Ethical Clearance No. KE/FK/6201/EC/2015). The mean values of Cmax, Tmax, AUC(0-24) and AUC(o-∞) for the test formulation of rifampicin were 5.81 ± 0.88 µg/mL, 1.25 hour, 29.16 ± 4.05 µg/mL. h. and 29.41 ± 4.07 µg/mL. h., respectively. Meanwhile for the reference formulation, the values were 5.04 ± 0.54 µg/mL, 1.31 hour, 27.20 ± 3.98 µg/mL.h. and 27.49 ± 4.01 µg/mL.h. From bioequivalence study, the 90% CIs for the test formulation/reference formulation ratio for the logarithmic transformations of Cmax and AUC(0-24) were 97.96-129.48% and 99.13-120.02%, respectively. According to the bioequivamence test guidelines of the European Commission-European Medicines Agency, it can be concluded that the test formulation of rifampicin is bioequivalence with the reference formulation.

Keywords: validation, HPLC, plasma, bioequivalence

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Authors: J. Jena, Monica Saxena

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In this paper, the propagation of weak nonlinear waves in non-equilibrium flow has been studied in detail using the perturbation method. The expansive action of receding piston undergoing infinite acceleration has been discussed. Central expansion fan, compression waves and shock fronts have been discussed and the solutions up to the first order in the characteristic plane and physical plane have been obtained.

Keywords: Characteristic wave front, weak non-linear waves, central expansion fan, compression waves

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Authors: Nisha Budhwar, Sunita Daniel

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In this paper, we analyse the stability of the SEIR model of malaria with infective immigrants which was recently formulated by the authors. The model consists of an SEIR model for the human population and SI Model for the mosquitoes. Susceptible humans become infected after they are bitten by infectious mosquitoes and move on to the Exposed, Infected and Recovered classes respectively. The susceptible mosquito becomes infected after biting an infected person and remains infected till death. We calculate the reproduction number R0 using the next generation method and then discuss about the stability of the equilibrium points. We use the Lyapunov function to show the global stability of the equilibrium points.

Keywords: equilibrium points, exposed, global stability, infective immigrants, Lyapunov function, recovered, reproduction number, susceptible

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Authors: Emad A. M. Osman, Ahmed M. Abu-Bakr

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Compacted granular fill under shallow foundation is one of the oldest, cheapest, and easiest techniques to improve the soil characteristics to increase the bearing capacity and decrease settlement under footing. There are three main factors affecting the design of soil replacement to gain these advantages. These factors are the type of replaced soil, characteristics, and thickness. The first two factors can be easily determined by laboratory and field control. This paper emphasizes on how to determine the thickness accurately for footing under centric axial load by limit state design method. The advantages of the method are the way of determining the thickness (independent of experience) and it takes into account the replaced and original or underneath soil characteristics and reaches the goals of replaced soils economically.

Keywords: design of soil replacement, LSD method, soil replacement, soil improvement

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Authors: Zhipeng Feng, Huanhuan Qi, Pingchuan Shen, Fenggang Zang, Yixiong Zhang

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Numerical simulations of vortex-induced vibration of a three-dimensional flexible tube under uniform turbulent flow are calculated when Reynolds number is 1.35×10⁴. In order to achieve the vortex-induced vibration, the three-dimensional unsteady, viscous, incompressible Navier-Stokes equation and LES turbulence model are solved with the finite volume approach, the tube is discretized according to the finite element theory, and its dynamic equilibrium equations are solved by the Newmark method. The fluid-tube interaction is realized by utilizing the diffusion-based smooth dynamic mesh method. Considering the vortex-induced vibration system, the variety trends of lift coefficient, drag coefficient, displacement, vertex shedding frequency, phase difference angle of tube are analyzed under different frequency ratios. The nonlinear phenomena of locked-in, phase-switch are captured successfully. Meanwhile, the limit cycle and bifurcation of lift coefficient and displacement are analyzed by using trajectory, phase portrait, and Poincaré sections. The results reveal that: when drag coefficient reaches its minimum value, the transverse amplitude reaches its maximum, and the “lock-in” begins simultaneously. In the range of lock-in, amplitude decreases gradually with increasing of frequency ratio. When lift coefficient reaches its minimum value, the phase difference undergoes a suddenly change from the “out-of-phase” to the “in-phase” mode.

Keywords: vortex induced vibration, limit cycle, LES, CFD, FEM

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Authors: Hee-Jae Suh, Kyung-Su Kim, Min-Ji Kim, Yeon-Seong Jeong, Ok-Hwan Lee, Jae-Wook Shin, Hyang-Sook Chun, Chan Lee

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Canthaxanthin is keto-carotenoid produced from beta-carotene and it has been approved to be used in many countries as a food coloring agent. Canthaxanthin has been analyzed using High Performance Liquid Chromatography (HPLC) system with various ways of pretreatment methods. Four official methods for verification of canthaxanthin at FSA (UK), AOAC (US), EFSA (EU) and MHLW (Japan) were compared to improve its analytical and the pretreatment method. The Linearity, the limit of detection (LOD), the limit of quantification (LOQ), the accuracy, the precision and the recovery ratio were determined from each method with modification in pretreatment method. All HPLC methods exhibited correlation coefficients of calibration curves for canthaxanthin as 0.9999. The analysis methods from FSA, AOAC, and MLHW showed the LOD of 0.395 ppm, 0.105 ppm, and 0.084 ppm, and the LOQ of 1.196 ppm, 0.318 ppm, 0.254 ppm, respectively. Among tested methods, HPLC method of MHLW with modification in pretreatments was finally selected for the analysis of canthaxanthin in lab, because it exhibited the resolution factor of 4.0 and the selectivity of 1.30. This analysis method showed a correlation coefficients value of 0.9999 and the lowest LOD and LOQ. Furthermore, the precision ratio was lower than 1 and the accuracy was almost 100%. The method presented the recovery ratio of 90-110% with modification in pretreatment method. The cross-validation of coefficient variation was 5 or less among tested three institutions in Korea.

Keywords: analytic method, canthaxanthin, food colorants, pretreatment method

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Authors: Larifah Mohd Sidik, Anuar Kasa

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In recent years, the demands for raw water are increasing along with the growth of the economy and population. Hence, the need for the construction and operation of dams is one of the solutions for the management of water resources problems. The stability of the embankment should be taken into consideration to evaluate the safety of retaining water. The safety of the dam is mostly based on numerous measurable components, for instance, seepage flowrate, pore water pressure and deformation of the embankment. Seepage and slope stability is the primary and most important reason to ascertain the overall safety behavior of the dams. This research study was conducted to evaluate static condition seepage and slope stability performances of Batu dam which is located in Kuala Lumpur capital city. The numerical solution Geostudio-2012 software was employed to analyse the seepage using finite element method, SEEP/W and slope stability using limit equilibrium method, SLOPE/W for three different cases of reservoir level operations; normal and flooded condition. Results of seepage analysis using SEEP/W were utilized as parental input for the analysis of SLOPE/W. Sensitivity analysis on hydraulic conductivity of material was done and calibrated to minimize the relative error of simulation SEEP/W, where the comparison observed field data and predicted value were also carried out. In seepage analysis, such as leakage flow rate, pore water distribution and location of a phreatic line are determined using the SEEP/W. The result of seepage analysis shows the clay core effectively lowered the phreatic surface and no piping failure is shown in the result. Hence, the total seepage flux was acceptable and within the permissible limit.

Keywords: earth dam, dam safety, seepage, slope stability, pore water pressure

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Authors: Ehsan Vaziri Goodarzi, Mahmood Houshmand, Omid Fatahi Valilai, Vahidreza Ghezavati, Shahrooz Bamdad

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One important paradigm of industry 4.0 is Cloud Manufacturing (CM). In CM everything is considered as a service, therefore, the CM platform should consider all service provider's capabilities and tries to integrate services in an equilibrium state. This research develops a framework for implementing manufacturing cloud service composition in the equilibrium state. The developed framework using well-known tools called axiomatic design (AD) and game theory. The research has investigated the factors for forming equilibrium for measures of the manufacturing cloud service composition. Functional requirements (FRs) represent the measures of manufacturing cloud service composition in the equilibrium state. These FRs satisfied by related Design Parameters (DPs). The FRs and DPs are defined by considering the game theory, QoS, consumer needs, parallel and cooperative services. Ultimately, four FRs and DPs represent the framework. To insure the validity of the framework, the authors have used the first AD’s independent axiom.

Keywords: axiomatic design, manufacturing cloud service composition, cloud manufacturing, industry 4.0

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Authors: Shahbaa F. Bdewi, Bakhtyar K. Aziz, Ayad A. R. Mutar

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Nano-materials show different surface properties due to their high surface area and active sites. This study investigates the feasibility of using nano-MgO (NMO) for removing Congo red (CR) dye from wastewater. NMO was prepared by molten salt method. Equilibrium experiments show the equilibrium was reached after 120 minutes and maximum adsorption efficiency was obtained in acidic media up to pH 6. Isotherm studies revealed the favorability of the adsorption process. The overall adsorption process was spontaneous and endothermic in nature with a maximum adsorption capacity of 1100 mg g-1 at 40°C as estimated from Langmuir isotherm. The adsorption kinetics was found to follow pseudo second-order rate equation. Relatively high activation energy (180.7 kJ mol-1) was obtained which is consistent with chemisorption mechanism for the adsorption process.

Keywords: adsorption, congo red, magnesium oxide, nanoparticles

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Authors: Anil P. Dewani, Alok S. Tripathi, Anil V. Chandewar

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Present manuscript reports the development and validation of a quantitative high performance liquid chromatography method for the pharmacokinetic evaluation of Glimepiride (GLM) and Ilaprazole (ILA) in rat plasma. The plasma samples were involved with Solid phase extraction process (SPE). The analytes were resolved on a Phenomenex C18 column (4.6 mm× 250 mm; 5 µm particle size) using a isocratic elution mode comprising methanol:water (80:20 % v/v) with pH of water modified to 3 using Formic acid, the total run time was 10 min at 225 nm as common wavelength, the flow rate throughout was 1ml/min. The method was validated over the concentration range from 10 to 600 ng/mL for GLM and ILA, in rat plasma. Metformin (MET) was used as Internal Standard. Validation data demonstrated the method to be selective, sensitive, accurate and precise. The limit of detection was 1.54 and 4.08 and limit of quantification was 5.15 and 13.62 for GLM and ILA respectively, the method demonstrated excellent linearity with correlation coefficients (r2) 0.999. The intra and inter-day precision (RSD%) values were < 2.0% for both ILA and GLM. The method was successfully applied in pharmacokinetic studies followed by oral administration in rats.

Keywords: pharmacokinetics, glimepiride, ilaprazole, HPLC, SPE

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Authors: M. Chen, S-Q. Zhang, X. Wang, D. Tate

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This paper presents a numerical solution, namely limit and shakedown analysis, to predict the safety state of smart structures made of heterogeneous materials under unknown cyclic loadings, for instance, the flexure hinge in the micro-positioning stage driven by piezoelectric actuator. In combination of homogenization theory and finite-element method (FEM), the safety evaluation problem is converted to a large-scale nonlinear optimization programming for an acceptable bounded loading as the design reference. Furthermore, a general numerical scheme integrated with the FEM and interior-point-algorithm based optimization tool is developed, which makes the practical application possible.

Keywords: limit state, shakedown analysis, homogenization, heterogeneous structure

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Authors: Dina Kon Mushid, Sage Ngoie, Tshimbalanga Madiba, Kabutakapua Kakanda

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Slope stability assessment is still the biggest challenge in mining activities and civil engineering structures. The slope in an opencast mine frequently reaches multiple weak layers that lead to the instability of the pit. Faults and soft layers throughout the rock would increase weathering and erosion rates. Therefore, it is essential to investigate the stability of the complex strata to figure out how stable they are. In the Dikuluwe-Mashamba (DIMA) area, the lithology of the stratum is a set of metamorphic rocks whose parent rocks are sedimentary rocks with a low degree of metamorphism. Thus, due to the composition and metamorphism of the parent rock, the rock formation is different in hardness and softness, which means that when the content of dolomitic and siliceous is high, the rock is hard. It is softer when the content of argillaceous and sandy is high. Therefore, from the vertical direction, it appears as a weak and hard layer, and from the horizontal direction, it seems like a smooth and hard layer in the same rock layer. From the structural point of view, the main structures in the mining area are the Dikuluwe dipping syncline and the Mashamba dipping anticline, and the occurrence of rock formations varies greatly. During the folding process of the rock formation, the stress will concentrate on the soft layer, causing the weak layer to be broken. At the same time, the phenomenon of interlayer dislocation occurs. This article aimed to evaluate the stability of metasedimentary rocks of the Dikuluwe-Mashamba (DIMA) open-pit mine using limit equilibrium and stereographic methods Based on the presence of statistical structural planes, the stereographic projection was used to study the slope's stability and examine the discontinuity orientation data to identify failure zones along the mine. The results revealed that the slope angle is too steep, and it is easy to induce landslides. The numerical method's sensitivity analysis showed that the slope angle and groundwater significantly impact the slope safety factor. The increase in the groundwater level substantially reduces the stability of the slope. Among the factors affecting the variation in the rate of the safety factor, the bulk density of soil is greater than that of rock mass, the cohesion of soil mass is smaller than that of rock mass, and the friction angle in the rock mass is much larger than that in the soil mass. The analysis showed that the rock mass structure types are mostly scattered and fragmented; the stratum changes considerably, and the variation of rock and soil mechanics parameters is significant.

Keywords: slope stability, weak layer, safety factor, limit equilibrium method, stereography method

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Authors: Eti Dwi Wiraningsih, Folashade Agusto, Lina Aryati, Syamsuddin Toaha, Suzanne Lenhart, Widodo, Willy Govaerts

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This paper considers a deterministic model for the transmission dynamics of rabies virus in the wild dogs-domestic dogs-human zoonotic cycle. The effect of vaccination and culling in dogs is considered on the model, then the stability was analysed to get basic reproduction number. We use the next generation matrix method and Routh-Hurwitz test to analyze the stability of the Disease-Free Equilibrium and Endemic Equilibrium of this model.

Keywords: stability analysis, rabies model, vaccination effect, culling in dogs

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Authors: Qing Dai, Zhengkui Lin, Jiajia Zhang, Yi Qu

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Based on activity method, this paper focuses on morning commuting behavior when commuters travel with autonomous vehicles (AVs). Firstly, a net utility function of commuters is constructed by the activity utility of commuters at home, in car and at workplace, and the disutility of travel time cost and that of schedule delay cost. Then, this net utility function is applied to build an equilibrium model. Finally, under the assumption of constant marginal activity utility, the properties of equilibrium are analyzed. The results show that, in autonomous driving, the starting and ending time of morning peak and the number of commuters who arrive early and late at workplace are the same as those in manual driving. In automatic driving, however, the departure rate of arriving early at workplace is higher than that of manual driving, while the departure rate of arriving late is just the opposite. In addition, compared with manual driving, the departure time of arriving at workplace on time is earlier and the number of people queuing at the bottleneck is larger in automatic driving. However, the net utility of commuters and the total net utility of system in automatic driving are greater than those in manual driving.

Keywords: autonomous cars, bottleneck model, activity utility, user equilibrium

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Authors: Imad Eddine Charif, Sidi Mohamed Mekelleche, Didier Villemin

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The solvent effects on the keto-enol tautomeric equilibriums of acetylacetone and dimedone are theoretically investigated at the correlated Becke-3-parameter-Lee-Yang-Parr (B3LYP) and second-order Møller-Plesset (MP2) computational levels. The present study shows that the most stable keto tautomer of acetylacetone corresponds to the trans-diketo, E,Z form; while the most stable enol tautomer corresponds to the closed cis-enol,Z,Z form. The keto tautomer of dimedone prefers the trans diketo, E, E form; while the most stable enol tautomer corresponds to trans-enol form. The calculated free Gibbs enthalpies indicate that, in polar solvents, the keto-enol equilibrium of acetylacetone is shifted toward the keto tautomer; whereas the keto-enol equilibrium of dimedone is shifted towards the enol tautomer. The experimental trends of the change of equilibrium constants with respect to the change of solvent polarity are well reproduced by both B3LYP and MP2 calculations.

Keywords: acetylacetone, dimedone, solvent effects, keto-enol equilibrium, theoretical calculations

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Authors: Masoud Ghermezi

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Studying the sheet metals is one of the most important research areas in the field of metal forming due to their extensive applications in the aerospace industries. A useful method for determining the forming limit of these materials and consequently preventing the rupture of sheet metals during the forming process is the use of the forming limit curve (FLC). In addition to specifying the forming limit, this curve also delineates a boundary for the allowed values of strain in sheet metal forming; these characteristics of the FLC along with its accuracy of computation and wide range of applications have made this curve the basis of research in the present paper. This study presents a new model that not only agrees with the results obtained from the above mentioned theory, but also eliminates its shortcomings. In this theory, like in the M-K theory, a thin sheet with an inhomogeneity as a gradient thickness reduction with a sinusoidal function has been chosen and subjected to two-dimensional stress. Through analytical evaluation, ultimately, a governing differential equation has been obtained. The numerical solution of this equation for the range of positive strains (stretched region) yields the results that agree with the results obtained from M-K theory. Also the solution of this equation for the range of negative strains (tension region) completes the FLC curve. The findings obtained by applying this equation on two alloys with the hardening exponents of 0.4 and 0.24 indicate the validity of the presented equation.

Keywords: sheet metal, metal forming, forming limit curve (FLC), M-K theory

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Authors: Nurudeen Oluwasola Lasisi

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The COVID-19 is an infection caused by coronavirus, which has been designated as a pandemic in the world. In this paper, we proposed a model to study the effect of distancing and wearing masks on the transmission of COVID-19 infection dynamics. The invariant region of the model is established. The COVID-19 free equilibrium and the reproduction number of the model were obtained. The local and global stability of the model is determined using the linearization technique method and Lyapunov method. It was found that COVID-19 free equilibrium state is locally asymptotically stable in feasible region Ω if R₀ < 1 and globally asymptomatically stable if R₀ < 1, otherwise unstable if R₀ > 1. More so, numerical analysis and simulations of the dynamics of the COVID-19 infection are presented.

Keywords: distancing, reproduction number, wearing of mask, local and global stability, modelling, transmission

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Authors: Jixiang Zhang

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A dynamic of Bertrand duopoly game is analyzed, where players use different production methods and choose their prices with bounded rationality. The equilibriums of the corresponding discrete dynamical systems are investigated. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability of Nash equilibrium, as some parameters of the model are varied, gives rise to complex dynamics such as cycles of higher order and chaos. On this basis, we discover that an increase of adjustment speed of bounded rational player can make Bertrand market sink into the chaotic state. Finally, the complex dynamics, bifurcations and chaos are displayed by numerical simulation.

Keywords: Bertrand duopoly model, discrete dynamical system, heterogeneous expectations, nash equilibrium

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Authors: G. Akgun, I. Algul, H. Kurtaran

Abstract:

In this paper geometrically nonlinear static behavior of laminated composite hollow super-elliptic beams is investigated using generalized differential quadrature method. Super-elliptic beam can have both oval and elliptic cross-sections by adjusting parameters in super-ellipse formulation (also known as Lamé curves). Equilibrium equations of super-elliptic beam are obtained using the virtual work principle. Geometric nonlinearity is taken into account using von-Kármán nonlinear strain-displacement relations. Spatial derivatives in strains are expressed with the generalized differential quadrature method. Transverse shear effect is considered through the first-order shear deformation theory. Static equilibrium equations are solved using Newton-Raphson method. Several composite super-elliptic beam problems are solved with the proposed method. Effects of layer orientations of composite material, boundary conditions, ovality and ellipticity on bending behavior are investigated.

Keywords: generalized differential quadrature, geometric nonlinearity, laminated composite, super-elliptic cross-section

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Authors: Jixiang Zhang, Yanhua Wang

Abstract:

A dynamic of Bertrand duopoly game is analyzed, where players use different production methods and choose their prices with bounded rationality. The equilibriums of the corresponding discrete dynamical systems are investigated. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability conditions of Nash equilibrium under a local adjustment process are studied. The stability of Nash equilibrium, as some parameters of the model are varied, gives rise to complex dynamics such as cycles of higher order and chaos. On this basis, we discover that an increase of adjustment speed of bounded rational player can make Bertrand market sink into the chaotic state. Finally, the complex dynamics, bifurcations and chaos are displayed by numerical simulation.

Keywords: Bertrand duopoly model, discrete dynamical system, heterogeneous expectations, nash equilibrium

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Authors: Saeed Mahjoub Moghadas, Farhad Asadi, Shahed Torkamandi, Hassan Moradi, Mahmood Purgamshidian

Abstract:

In this paper, we present real-time obstacle avoidance approach for both autonomous and non-autonomous DS-based controllers and also based on dynamical systems (DS) method. In this approach, we can modulate the original dynamics of the controller and it allows us to determine safety margin and different types of DS to increase the robot’s reactiveness in the face of uncertainty in the localization of the obstacle and especially when robot moves very fast in changeable complex environments. The method is validated in simulation and influence of different autonomous and non-autonomous DS such as limit cycles, and unstable DS on this algorithm and also the position of different obstacles in complex environment is explained. Finally, we describe how the avoidance trajectories can be verified through different parameters such as safety factor.

Keywords: limit cycles, nonlinear dynamical system, real time obstacle avoidance, DS-based controllers

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