Search results for: fractional differential equation

Authors: Tomotaka Aoki, Isao Tomita

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We examined the on-off ratio and frequency components of output signals from an electron-interference device made of GaAs/AlₓGa₁₋ₓAs by solving the time-dependent Schrödinger's equation on conducting electrons in the channel waveguide of the device. For electron-wave modulation, a periodic voltage of frequency f was applied to the channel. Furthermore, we examined the voltage-amplitude dependence of the signals in time and frequency domains and found that large applied voltage deformed the output-signal waveform and created additional side modes (frequencies) near the modulation frequency f and that there was a trade-off between on-off ratio and side-mode creation.

Keywords: electrical conduction, electron interference, frequency spectrum, on-off ratio

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Authors: Chandni Laddha

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Tourism was earlier considered as an activity performed by people only for the purpose of entertainment. However, the present era demand for adding something more to the concept of tourism. Nowadays, people are more protected towards environment, so this paper focuses on the significance of ecotourism for the attainment of sustainable development. Ecotourism is a way of sustainable growth of tourist spots maintaining their natural and actual status quo. The ecotourism in India becomes all the more important because India is famous on world map. Ecotourism believe that there should be sustainable equation between tourist and tourist place. Various aspects related to environmental tourism will be highlighted in this paper. Government efforts for the promotion of ecotourism will be discussed by explaining the tourism policy of India, some acts, rules etc. will also be discussed. The study comes up with some strategies to be adopted and which will lead in promoting the concept of ecotourism for an ecologically sustainable environment.

Keywords: tourism, eco-tourism, sustainable development, tourism policy, sustainable environment

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Authors: N. F. M. Mokhtar, N. Z. A. Hamid

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This paper reports an analytical investigation of the stability and thermal convection in a horizontal anisotropic porous medium in the presence of Coriolis force and magnetic field. The Darcy model is used in the momentum equation and Boussinesq approximation is considered for the density variation of the porous medium. The upper and lower boundaries of the porous medium are assumed to be conducting to temperature perturbation and we used first order Chebyshev polynomial Tau method to solve the resulting eigenvalue problem. Analytical solution is obtained for the case of stationary convection. It is found that the porous layer system becomes unstable when the mechanical anisotropy parameter elevated and increasing the Coriolis force and magnetic field help to stabilize the anisotropy porous medium.

Keywords: anisotropic, Chebyshev tau method, Coriolis force, Magnetic field

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Authors: N. M. Arifin, S. P. M. Isa, R. Nazar, N. Bachok, F. M. Ali, I. Pop

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In this paper, the steady forced convection boundary layer flow of a Casson fluid past a moving permeable semi-infinite flat plate beneath a uniform free stream is investigated. The mathematical problem reduces to a pair of noncoupled ordinary differential equations by similarity transformation, which is then solved numerically using the shooting method. Both the cases when the plate moves into or out of the origin are considered. Effects of the non-Newtonian (Casson) parameter, moving parameter, suction or injection parameter and Eckert number on the flow and heat transfer characteristics are thoroughly examined. Dual solutions are found to exist for each value of the governing parameters.

Keywords: forced convection, Casson fluids, moving flat plate, boundary layer

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Authors: Mohammed A. Abutalib

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Papillary thyroid carcinoma (PTC) accounts for the most common type of thyroid cancer, a well-differentiated type. PTC is featured by biologically low-grade and less aggressive tumors with a survival rate of 10 years in most of the diagnosed cases. PTC can be presented with the involvement of cervical lymph nodes in about 50% of the patients, yet the distant spread is very uncommon. Herein, we discussed an early 50-year-old male patient with a history of PTC that presented to the emergency department complaining of shortness of breath and a radiological finding of hydrothorax. Cytologic examination, together with immune-histochemical staining and molecular studies of pleural effusion aspiration, concluded the definitive diagnosis of metastatic papillary thyroid carcinoma in the pleural space. PTC seldom causes metastatic niches in the pleural space, and this is a rare clinical presentation; nevertheless, a differential diagnosis of thyroid metastasis needs to be excluded.

Keywords: thyroid cancer, malignant pleural effusion, cytology aspiration, papillary thyroid carcinoma

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Authors: K. R. Tshunza, A. Elvin, A. Gabremmeskel

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Final results of an extensive laboratory research program on “lapped gusset joints in compression” are presented. The investigation was carried out at the Heavy structures laboratory at the University of the Witwatersrand in Johannesburg, South Africa. A proposed, relatively easy to use analytical equation was found to be reasonably adequate in determining the global compressive capacity of lapped gussets joints under compressive load. A wide range of lapped mild steel plates of varying slenderness, welded on 219*10 and 127*6 Mild steel circular hollow sections of 1m length were tested in compression and the formula was validated with experimental results. The investigation show that the connection’s capacity is controlled by flexure due to the eccentricity between the plates that are connected side to side.

Keywords: compression, eccentricity, lapped gussets joints, moment resistance

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Authors: Yohanes Chekol Malede

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σ-phase has negative effects on the corrosion responses and the mechanical properties of steels. The growth of σ-phase in the austenite matrix of AISI 347H FG steel was simulated using DICTRA software using CALPHAD method. The simulation work included the influence of both volume diffusion and grain boundary diffusion. The simulation results showed a good agreement with the experimental findings. The simulation results revealed a Cr-depleted and a Ni-enriched σ-phase/austenite interface. Effects of temperature, grain size, and composition of alloying elements on the growth kinetics of σ-phase were assessed. The simulated results were fitted to the JMAK equation and a good correlation was obtained.

Keywords: AISI 347H FG austenitic steel, CALPHAD, sigma phase, microstructure evolution

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Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

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This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: interpolation, approximate solution, collocation, differential system, half step, converges, block method, efficiency

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Authors: Ishara Madusanka, So Morikawa

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Natural disasters, particularly floods, pose severe challenges globally, affecting both developed and developing countries. In many regions, especially Asia, riverine floods are prevalent and devastating. Integrated flood management incorporates structural and non-structural measures, with preventive relocation emerging as a cost-effective and proactive strategy for areas repeatedly impacted by severe flooding. However, preventive relocation is often hindered by economic, psychological, social, and institutional barriers. This study investigates the factors influencing resistance to preventive relocation and evaluates the role of flood risk information in shaping relocation decisions through risk perception. A conceptual model was developed, incorporating variables such as Flood Risk Information (FRI), Place Attachment (PA), Good Living Conditions (GLC), and Adaptation to Flooding (ATF), with Flood Risk Perception (FRP) serving as a mediating variable. The research was conducted in Welipitiya in the Polwatta river basin, Matara district, Sri Lanka, a region experiencing recurrent flood damage. For this study, an experimental design involving a structured questionnaire survey was utilized, with 185 households participating. The treatment group received flood risk information, including flood risk maps and historical data, while the control group did not. Data were collected in 2023 and analyzed using independent sample t-tests and Partial Least Squares Structural Equation Modeling (PLS-SEM). PLS-SEM was chosen for its ability to model latent variables, handle complex relationships, and suitability for exploratory research. Multi-group Analysis (MGA) assessed variations across different flood risk areas. Findings indicate that flood risk information had a limited impact on flood risk perception and relocation decisions, though its effect was significant in specific high-risk areas. Place attachment was a significant factor influencing relocation decisions across the sample. One potential reason for the limited impact of flood risk information on relocation decisions could be the lack of specificity in the information provided. The results suggest that while flood risk information alone may not significantly influence relocation decisions, it is crucial in specific contexts. Future studies and practitioners should focus on providing more detailed risk information and addressing psychological factors like place attachments to enhance preventive relocation efforts.

Keywords: flood risk communication, flood risk perception, place attachment, preventive relocation, structural equation modeling

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Authors: R. I. You, C. L. Ho, M. S. Dai, H. M. Hung, S. F. Yen, C. S. Chen, T. Y. Chao

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Neutrophils are the most abundant innate immune cells to against invading microorganisms. Numerous data shown neutrophils have plasticity in response to physiological and pathological conditions. Tumor-associated neutrophils (TAN) exist in distinct types of tumor and play an important role in cancer biology. Different transcriptomic profiles of neutrophils in tumor and non-tumor samples have been identified. Several miRNAs have been recognized as regulators of gene expression in neutrophil, which may have key roles in neutrophil activation. However, the miRNAs expression patterns in TAN are not well known. To address this question, magnetic bead isolated neutrophils from tumor-bearing mice were used in this study. We analyzed production of reactive oxygen species (ROS) by luminol-dependent chemiluminescence assay. The expression of miRNAs targeting NADPH oxidase, ROS generation and autophagy was explored using quantitative real-time polymerase chain reaction. Our data suggest that tumor environment influence neutrophil develop to differential states of activation via miRNAs regulation.

Keywords: tumor-associated neutrophil, miRNAs, neutrophil, ROS

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Authors: Benjamin Castillo, Luis Pastenes, Fernando Cordova

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The pathogen growth in animal source foods is a common problem in the food industry, causing monetary losses due to the spoiling of products or food intoxication outbreaks in the community. In this sense, the quality of the product is reflected by the population of deteriorating agents present in it, which are mainly bacteria. The factors which are likely associated with freshness in animal source foods are temperature and processing, storage, and transport times. However, the level of deterioration of products depends, in turn, on the characteristics of the bacterial population, causing the decomposition or spoiling, such as pH level and toxins. Knowing the growth dynamics of the agents that are involved in product contamination allows the monitoring for more efficient processing. This means better quality and reasonable costs, along with a better estimation of necessary time and temperature intervals for transport and storage in order to preserve product quality. The objective of this project is to design a secondary model that allows measuring the impact on temperature bacterial growth and the competition for pH adequacy and release of bacteriocins in order to describe such phenomenon and, thus, estimate food product half-life with the least possible risk of deterioration or spoiling. In order to achieve this objective, the authors propose an analysis of a three-dimensional ordinary differential which includes; logistic bacterial growth extended by the inhibitory action of bacteriocins including the effect of the medium pH; change in the medium pH levels through an adaptation of the Luedeking-Piret kinetic model; Bacteriocin concentration modeled similarly to pH levels. These three dimensions are being influenced by the temperature at all times. Then, this differential system is expanded, taking into consideration the variable temperature and the concentration of pulsed bacteriocins, which represent characteristics inherent of the modeling, such as transport and storage, as well as the incorporation of substances that inhibit bacterial growth. The main results lead to the fact that temperature changes in an early stage of transport increased the bacterial population significantly more than if it had increased during the final stage. On the other hand, the incorporation of bacteriocins, as in other investigations, proved to be efficient in the short and medium-term since, although the population of bacteria decreased, once the bacteriocins were depleted or degraded over time, the bacteria eventually returned to their regular growth rate. The efficacy of the bacteriocins at low temperatures decreased slightly, which equates with the fact that their natural degradation rate also decreased. In summary, the implementation of the mathematical model allowed the simulation of a set of possible bacteria present in animal based products, along with their properties, in various transport and storage situations, which led us to state that for inhibiting bacterial growth, the optimum is complementary low constant temperatures and the initial use of bacteriocins.

Keywords: bacterial growth, bacteriocins, mathematical modelling, temperature

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Authors: Arezoo Sadrinezhad, Kallol Sett, S. I. Hariharan

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In this paper, a probabilistic framework based on Fokker-Planck-Kolmogorov (FPK) approach has been applied to simulate triaxial cyclic constitutive behavior of uncertain soils. The framework builds upon previous work of the writers, and it has been extended for cyclic probabilistic simulation of triaxial undrained behavior of soils. von Mises elastic-perfectly plastic material model is considered. It is shown that by using probabilistic framework, some of the most important aspects of soil behavior under cyclic loading can be captured even with a simple elastic-perfectly plastic constitutive model.

Keywords: elasto-plasticity, uncertainty, soils, fokker-planck equation, fourier spectral method, finite difference method

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Authors: Rogelio Luck, Yucheng Liu

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This paper proposes the continuous-time singular value decomposition (SVD) for the impulse response function, a special kind of Green’s functions e⁻⁽ᵗ⁻ ᵀ⁾, in order to find a set of singular functions and singular values so that the convolutions of such function with the set of singular functions on a specified domain are the solutions to the inhomogeneous differential equations for those singular functions. A numerical example was illustrated to verify the proposed method. Besides the continuous-time SVD, a discrete-time SVD is also presented for the impulse response function, which is modeled using a Toeplitz matrix in the discrete system. The proposed method has broad applications in signal processing, dynamic system analysis, acoustic analysis, thermal analysis, as well as macroeconomic modeling.

Keywords: singular value decomposition, impulse response function, Green’s function , Toeplitz matrix , Hankel matrix

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Authors: Daniel S. Brox

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Starting from earthquake fault dynamic equations, a correspondence between earthquake occurrence statistics in a seismic region before a major earthquake and eigenvalue statistics of a differential operator whose bound state eigenfunctions characterize the distribution of stress in the seismic region is derived. Modeling these eigenvalue statistics with a 2D Coulomb gas statistical physics model, previously reported deviation of seismic activation earthquake occurrence statistics from Gutenberg-Richter statistics in time intervals preceding the major earthquake is derived. It also explains how statistical physics modeling predicts a finite-dimensional nonlinear dynamic system that describes real-time velocity model evolution in the region undergoing seismic activation and how this prediction can be tested experimentally.

Keywords: seismic activation, statistical physics, geodynamics, signal processing

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Authors: Ibnorachid Zakaria, El Bikri Khalid, Benamar Rhali, Farah Abdoun

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The aim of the present work is to study the linear free symmetric vibration of three-layer sandwich beam using the energy method. The zigzag model is used to describe the displacement field. The theoretical model is based on the top and bottom layers behave like Euler-Bernoulli beams while the core layer like a Timoshenko beam. Based on Hamilton’s principle, the governing equation of motion sandwich beam is obtained in order to calculate the linear frequency parameters for a clamped-clamped and simple supported-simple-supported beams. The effects of material properties and geometric parameters on the natural frequencies are also investigated.

Keywords: linear vibration, sandwich, shear deformation, Timoshenko zig-zag model

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Authors: Mohammad Zamani, Ramin Mansouri

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Spillways are one of the most important hydraulic structures of dams that provide the stability of the dam and downstream areas at the time of flood. A circular vertical spillway with various inlet forms is very effective when there is not enough space for the other spillway. Hydraulic flow in a vertical circular spillway is divided into three groups: free, orifice, and under pressure (submerged). In this research, the hydraulic flow characteristics of a Circular Vertical Spillway are investigated with the CFD model. Two-dimensional unsteady RANS equations were solved numerically using Finite Volume Method. The PISO scheme was applied for the velocity-pressure coupling. The mostly used two-equation turbulence models, k-ε and k-ω, were chosen to model Reynolds shear stress term. The power law scheme was used for the discretization of momentum, k, ε, and ω equations. The VOF method (geometrically reconstruction algorithm) was adopted for interface simulation. In this study, three types of computational grids (coarse, intermediate, and fine) were used to discriminate the simulation environment. In order to simulate the flow, the k-ε (Standard, RNG, Realizable) and k-ω (standard and SST) models were used. Also, in order to find the best wall function, two types, standard wall, and non-equilibrium wall function, were investigated. The laminar model did not produce satisfactory flow depth and velocity along the Morning-Glory spillway. The results of the most commonly used two-equation turbulence models (k-ε and k-ω) were identical. Furthermore, the standard wall function produced better results compared to the non-equilibrium wall function. Thus, for other simulations, the standard k-ε with the standard wall function was preferred. The comparison criterion in this study is also the trajectory profile of jet water. The results show that the fine computational grid, the input speed condition for the flow input boundary, and the output pressure for the boundaries that are in contact with the air provide the best possible results. Also, the standard wall function is chosen for the effect of the wall function, and the turbulent model k-ε (Standard) has the most consistent results with experimental results. When the jet gets closer to the end of the basin, the computational results increase with the numerical results of their differences. The mesh with 10602 nodes, turbulent model k-ε standard and the standard wall function, provide the best results for modeling the flow in a vertical circular Spillway. There was a good agreement between numerical and experimental results in the upper and lower nappe profiles. In the study of water level over crest and discharge, in low water levels, the results of numerical modeling are good agreement with the experimental, but with the increasing water level, the difference between the numerical and experimental discharge is more. In the study of the flow coefficient, by decreasing in P/R ratio, the difference between the numerical and experimental result increases.

Keywords: circular vertical, spillway, numerical model, boundary conditions

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Authors: Jafar Khodagholizadeh

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In this talk, we study the tensor mode equation of perturbation in the presence of nonzero $-\Lambda$ as dark energy, whose dynamic nature depends on the Hubble parameter $ H$ and/or its time derivative. Dark energy, according to the total vacuum contribution, has little effect during the radiation-dominated era, but it reduces the squared amplitude of gravitational waves (GWs) up to $60\%$ for the wavelengths that enter the horizon during the matter-dominated era. Moreover, the observations bound on dark energy models, such as running vacuum model (RVM), generalized running vacuum model (GRVM), and generalized running vacuum subcase (GRVS), are effective in reducing the GWs’ amplitude. Although this effect is less for the wavelengths that enter the horizon at later times, this reduction is stable and permanent.

Keywords: gravitational waves, dark energy, GW's amplitude, all stage universe

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Authors: Akintayo Emmanuel Temitope, Akintayo Cecilia Olufunke, Ziegler Thomas

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Bio-polyols are important components in polyurethane industries. The preliminary studies into the synthesis of bio-polyol products (epoxy-polyol and epoxyl-polyurethanes) from Jatropha curcas were investigated. The reactions were followed by both infrared and nuclear magnetic resonance. Physico-chemical characterisation of the samples for iodine value (IV), acid value (AV), saponification value (SV) and hydroxyl value (HV) were carried out. Thermal transitions of the products were studied by heating 5 mg of the sample from 20ºC to 800ºC and then cooling down to -500ºC on a differential scanning calorimeter (DSC). The preparation of epoxylpolyol and polyurethane from Jatropha curcas oil was smooth and efficient. Results of film and solubility properties revealed that coatings of Jatropha curcas epoxy-polyurethanes performed better with increased loading of toluylene 2, 4-diisocyanate (TDI) up to 2 wt% while their solvent resistance decreased beyond a TDI loading of 1.2 wt%. DSC analysis shows the epoxy-polyurethane to be less stable compared to the epoxy-polyol.

Keywords: synthesis, epoxy-polyol, epoxy-polyurethane, jatropha curcas oil

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Authors: Pratik Gandhi, Kavitha Chandra, Charles Thompson

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A computational model of the acoustic room impulse response between transmitters and receivers located in an enclosed cavity under the influence of frequency-dependent reflection coefficients of the walls is presented. The characteristic features of the impulse responses that differentiate these results from frequency-independent reflecting surfaces are discussed. The image-source model is derived from the first principle solution to Green's function of the acoustic wave equation. The post-processing of the computed impulse response with a band-pass filter to better represents the response of a loud-speaker is demonstrated.

Keywords: acoustic room impulse response, frequency dependent reflection coefficients, Green's function, image model

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Authors: Farid M. Abdel-Rahim

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In this study, Se90Te7Cu3 chalcogenide glass was prepared using the melt quenching technique. The amorphous nature of the as prepared samples was confirmed by scanning electron microscope (SEM). Result of differential scanning calorimetric (DSC) under nonisothermal condition on composition bulk materials are reported and discussed. It shows that these glasses exhibit a single-stage glass transition and a single-stage crystallization on heating rates. The glass transition temperature (Tg), the onset crystallization (Tc), the crystallization temperature (Tp), were found by dependent on the composition and heating rates. Activation energy for glass transition (Et), activation energy of the amorphous –crystalline transformation (Ec), crystallization reaction rate constant (Kp), (n) and (m) are constants related to crystallization mechanism of the bulk samples have been determined by different formulations.

Keywords: chalcogenides, heat treatment, DSC, SEM, glass transition, thermal analysis

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Authors: Shohel Ahmed, Md. Abdul Alim, Sumaiya Rahman

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Optimal control can be helpful to test and compare different vaccination strategies of a certain disease. The mathematical model of HIV we consider here is a set of ordinary differential equations (ODEs) describing the interactions of CD4+T cells of the immune system with the human immunodeficiency virus (HIV). As an early treatment setting, we investigate an optimal chemotherapy strategy where control represents the percentage of effect the chemotherapy has on the system. The aim is to obtain a new optimal chemotherapeutic strategy where an isoperimetric constraint on the chemotherapy supply plays a crucial role. We outline the steps in formulating an optimal control problem, derive optimality conditions and demonstrate numerical results of an optimal control for the model. Numerical results illustrate how such a constraint alters the optimal vaccination schedule and its effect on cell-virus interactions.

Keywords: chemotherapy of HIV, optimal control involving ODEs, optimality conditions, Pontryagin’s maximum principle

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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: Nasser Mohamed Ramli, Mohamad Syafiq Mohamad

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Many types of controllers were applied on the continuous stirred tank reactor (CSTR) unit to control the temperature. In this research paper, Proportional-Integral-Derivative (PID) controller are compared with Fuzzy Logic controller for temperature control of CSTR. The control system for temperature non-isothermal of a CSTR will produce a stable response curve to its set point temperature. A mathematical model of a CSTR using the most general operating condition was developed through a set of differential equations into S-function using MATLAB. The reactor model and S-function are developed using m.file. After developing the S-function of CSTR model, User-Defined functions are used to link to SIMULINK file. Results that are obtained from simulation and temperature control were better when using Fuzzy logic control compared to PID control.

Keywords: CSTR, temperature, PID, fuzzy logic

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Authors: Abdelrahman Elsehsah, Hany Madkour, Khalid Farah

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This article presents a 3-D modified non-linear elastic model in the strain space. The Helmholtz free energy function is introduced with the existence of a dissipation potential surface in the space of thermodynamic conjugate forces. The constitutive equation and the damage evolution were derived as well. The modified damage has been examined to model the nonlinear behavior of reinforced concrete (RC) slabs with an opening. A parametric study with RC was carried out to investigate the impact of different factors on the behavior of RC slabs. These factors are the opening area, the opening shape, the place of opening, and the thickness of the slabs. And the numerical results have been compared with the experimental data from literature. Finally, the model showed its ability to be applied to the structural analysis of RC slabs.

Keywords: damage mechanics, 3-D numerical analysis, RC, slab with opening

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Authors: Aynur Aker, Hasan Kaya

Abstract:

Al-12.6wt.%Si-2wt.%Cu ternary alloy of near eutectic composition was directionally solidified upward at a constant temperature gradient in a wide range of growth rates (V=8.25-165.41 µm/s). The microstructures (λ), microhardness (HV), tensile stress (σ) and electrical resistivity (ρ) were measured from directionally solidified samples. The dependence of microstructures, microhardness and electrical resistivity on growth rate (V) was also determined by statistical analysis. According to these results, it has been found that for increasing values of V, the values of HV, σ and ρ increase. Variations of electrical resistivity for casting Al-Si-Cu alloy were also measured at the temperature in range 300-500 K. The enthalpy (ΔH) and the specific heat (Cp) for the Al-Si-Cu alloy were determined by differential scanning calorimeter (DSC) from heating trace during the transformation from solid to liquid. The results obtained in this work were compared with the similar experimental results in the literature.

Keywords: Al-Si-Cu alloy, microstructures, micro-hardness, tensile stress electrical resistivity, enthalpy

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Authors: Jovanca Smith, Derek Gay

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All universities possess a standard by which students are assessed and administered into their programs. This paper considers the effect of the educational history of students, as measured by specific subject grades in Caribbean examinations, on overall performance in introductory engineering math and mechanics courses. Results reflect a correlation between the highest grade in the Caribbean examinations with a higher probability of successful advancement in the university courses. Alternatively, lower entrance grades are commensurate with underperformance in the university courses. Results also demonstrate that students matriculating with the Caribbean examinations will not necessarily possess a significant advantage over students entering through an alternative route, and while previous educational background of students is a significant indicator of tentative performance in the University level math and mechanics courses, it is not the sole factor.

Keywords: bimodal distribution, differential learning, engineering education, entrance qualification

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Authors: M. A. Khanday, Aasma Rafiq, Khalid Nazir

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This paper is an attempt to establish the mathematical models to understand the distribution of drug administration in the human body through oral and intravenous routes. Three models were formulated based on diffusion process using Fick’s principle and the law of mass action. The rate constants governing the law of mass action were used on the basis of the drug efficacy at different interfaces. The Laplace transform and eigenvalue methods were used to obtain the solution of the ordinary differential equations concerning the rate of change of concentration in different compartments viz. blood and tissue medium. The drug concentration in the different compartments has been computed using numerical parameters. The results illustrate the variation of drug concentration with respect to time using MATLAB software. It has been observed from the results that the drug concentration decreases in the first compartment and gradually increases in other subsequent compartments.

Keywords: Laplace transform, diffusion, eigenvalue method, mathematical model

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

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In this paper, we propose a method for the dynamic response of multi-storey structures with uncertain-but-bounded parameters. The effectiveness of the proposed method is demonstrated by a numerical example of three-storey structures. This equation is integrated numerically using Newmark’s method. The numerical results are obtained by the proposed method. The simulation accounting the interval analysis method results are compared with a probabilistic approach results. The interval analysis method provides a mean curve that is between an upper and lower bound obtained from the probabilistic approach.

Keywords: multi-storey structure, dynamic response, interval analysis method, random parameters

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Authors: Sung-Sik Park, Han Chang, Kyung-Hun Chae, Sae-Byeok Lee

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In this study, a three-dimensional (3D) Particle method without using grid was developed for analyzing large deformation of soils instead of using ordinary finite element method (FEM) or finite difference method (FDM). In the 3D Particle method, the governing equations were discretized by various particle interaction models corresponding to differential operators such as gradient, divergence, and Laplacian. The Mohr-Coulomb failure criterion was incorporated into the 3D Particle method to determine soil failure. The yielding and hardening behavior of soil before failure was also considered by varying viscosity of soil. First of all, an unconfined compression test was carried out and the large deformation following soil yielding or failure was simulated by the developed 3D Particle method. The results were also compared with those of a commercial FEM software PLAXIS 3D. The developed 3D Particle method was able to simulate the 3D large deformation of soils due to soil yielding and calculate the variation of normal and shear stresses following clay deformation.

Keywords: particle method, large deformation, soil column, confined compressive stress

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Authors: Faruk Firat Çalim, Nurullah Karaca, Hakan Tacettin Türker

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In this study, out-of-plane free vibrations of a circular rods is investigated theoretically. The governing equations for naturally twisted and curved spatial rods are obtained using Timoshenko beam theory and rewritten for circular rods. Effects of the axial and shear deformations are considered in the formulations. Ordinary differential equations in scalar form are solved analytically by using transfer matrix method. The circular rods of the mass matrix are obtained by using straight rod of consistent mass matrix. Free vibrations frequencies obtained by solving eigenvalue problem. A computer program coded in MATHEMATICA language is prepared. Circular beams are analyzed through various examples for free vibrations analysis. Results are compared with ANSYS results based on finite element method and available in the literature.

Keywords: circular rod, out-of-plane free vibration analysis, transfer matrix method

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