Search results for: modulated differential scanning calorimetry (MDSC)

Authors: Benniche Omar

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We are concerned with abstract fully nonlinear differential equations having the form y’(t)=Ay(t)+f(t,y(t)) where A is an m—dissipative operator (possibly multi—valued) defined on a subset D(A) of a Banach space X with values in X and f is a given function defined on I×X with values in X. We consider a graph K in I×X. We recall that K is said to be viable with respect to the above abstract differential equation if for each initial data in K there exists at least one trajectory starting from that initial data and remaining in K at least for a short time. The viability problem has been studied by many authors by using various techniques and frames. If K is closed, it is shown that a tangency condition, which is mainly linked to the dynamic, is crucial for viability. In the case when X is infinite dimensional, compactness and convexity assumptions are needed. In this paper, we are concerned with the notion of near viability for a given graph K with respect to y’(t)=Ay(t)+f(t,y(t)). Roughly speaking, the graph K is said to be near viable with respect to y’(t)=Ay(t)+f(t,y(t)), if for each initial data in K there exists at least one trajectory remaining arbitrary close to K at least for short time. It is interesting to note that the near viability is equivalent to an appropriate tangency condition under mild assumptions on the dynamic. Adding natural convexity and compactness assumptions on the dynamic, we may recover the (exact) viability. Here we investigate near viability for a graph K in I×X with respect to y’(t)=Ay(t)+f(t,y(t)) where A and f are as above. We emphasis that the t—dependence on the perturbation f leads us to introduce a new tangency concept. In the base of a tangency conditions expressed in terms of that tangency concept, we formulate criteria for K to be near viable with respect to y’(t)=Ay(t)+f(t,y(t)). As application, an abstract null—controllability theorem is given.

Keywords: abstract differential equation, graph, tangency condition, viability

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

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

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

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Authors: Jian-Jun Shu

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

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

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Authors: Joon Ho Kim, Tae Kwon Ha

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Effect of aging treatment on microstructural aspects of interfacial layers of the Cu/Al clad sheet produced by Differential Speed Rolling (DSR) process were studied by Electron Back Scattered Diffraction (EBSD). Clad sheet of Al/Cu has been fabricated by using DSR, which caused severe shear deformation between Al and Cu plate to easily bond to each other. Rolling was carried out at 100°C with speed ratio of 2, in which the total thickness reduction was 45%. Interface layers of clad sheet were analyzed by EBSD after subsequent annealing at 400°C for 30 to 120 min. With increasing annealing time, thickness of interface layer and fraction of high angle grain boundary were increased and average grain size was decreased.

Keywords: aluminium/copper clad sheet, differential speed rolling, interface layer, microstructure, annealing, electron back scattered diffraction

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Authors: Y. J. Zhou, G. Lu

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In this paper, an analytical study is made for the dynamic behavior of human brain tissue under transient loading. In this analytical model the Mooney-Rivlin constitutive law is coupled with visco-elastic constitutive equations to take into account both the nonlinear and time-dependent mechanical behavior of brain tissue. Five ordinary differential equations representing the relationships of five main parameters (radial stress, circumferential stress, radial strain, circumferential strain, and particle velocity) are obtained by using the characteristic method to transform five partial differential equations (two continuity equations, one motion equation, and two constitutive equations). Analytical expressions of the attenuation properties for spherical wave in brain tissue are analytically derived. Numerical results are obtained based on the five ordinary differential equations. The mechanical responses (particle velocity and stress) of brain are compared at different radii including 5, 6, 10, 15 and 25 mm under four different input conditions. The results illustrate that loading curves types of the particle velocity significantly influences the stress in brain tissue. The understanding of the influence by the input loading cures can be used to reduce the potentially injury to brain under head impact by designing protective structures to control the loading curves types.

Keywords: analytical method, mechanical responses, spherical wave propagation, traumatic brain injury

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Authors: Laura Amato, Paolo Mulatti, Fabrizio Montarsi, Matteo Mazzucato, Laura Gagliazzo, Michele Brichese, Manlio Palei, Gioia Capelli, Lebana Bonfanti

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West Nile virus (WNV) re-emerged in north-eastern Italy in 2008, after ten years from its first appearance in Tuscany. In 2009, a national surveillance programme was implemented, and re-modulated in north-eastern Italy in 2011. Hereby, we present the results of surveillance activities in 2008-2016 in the north-eastern Italian regions, with inferences on WNV epidemiological trend in the area. The re-modulated surveillance programmes aimed at early detecting WNV seasonal reactivation by searching IgM antibodies in horses. In 2013, the surveillance plans were further modified including a risk-based approach. Spatial analysis techniques, including Bernoulli space-time scan-statistics, were applied to the results of 2010–2012 surveillance on mosquitoes, equines, and humans to identify areas where WNV reactivation was more likely to occur. From 2008 to 2016, residential horses tested positive for anti-WNV antibodies on a yearly basis (503 cases), also in areas where WNV circulation was not detected in mosquito populations. Surveillance activities detected 26 syndromic cases in horses, 102 infected mosquito pools and WNV in 18 dead wild birds. Human cases were also recurrently detected in the study area during the surveillance period (68 cases of West Nile neuroinvasive disease). The recurrent identification of WNV in animals, mosquitoes, and humans indicates the virus has likely become endemic in the area. In 2016, findings of WNV positives in horses or mosquitoes were included as triggers for enhancing screening activities in humans. The evolution of the epidemiological situation prompts for continuous and accurate surveillance measures. The results of the 2013-2016 surveillance indicate that the risk-based approach was effective in early detecting seasonal reactivation of WNV, key factor of the integrated surveillance strategy in endemic areas.

Keywords: arboviruses, horses, Italy, surveillance, west nile virus, zoonoses

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Authors: Sufyan Muhammad

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Recently, in achieving highly efficient but at the same time highly accurate solutions has become the major target of numerical analyst community. The concept is termed as compact schemes and has gained great popularity and consequently, we construct compact schemes for fourth order parabolic differential equations used to study vibrations in structures. For the superiority of newly constructed schemes, we consider range of examples. We have achieved followings i.e. (a) numerical scheme utilizes minimum number of stencil points (which means new scheme is compact); (b) numerical scheme is highly accurate (which means new scheme is reliable) and (c) numerical scheme is highly efficient (which means new scheme is fast).

Keywords: central finite differences, compact schemes, Bernoulli's equations, finite differences

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Authors: Masek A., Zaborski M.

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In our studies, we propose the use of natural, pro-ecological substances such as polyphenols to protect polymers against ageing. In our studies, we plan to focus on the following compounds: polyphenols, gallic acid esters, flavonoides, carotenoids, curcumin and its derivatives, vitamin A, tocochromanoles, betalain. Phyto-compounds will be selected on the basis of available literature and our preliminary studies. So, we will select compounds with various contents of hydroxyl groups and colored substances capable of participating in color oxidation processes. The natural antioxidants which were added to ethylene-octene elastomer (polyolefin elastomer-Engage) and ethylene-nonbornene (TOPAS). Composites were then subjected to numerous ageing: weathering (climat of Floryda), UV (0,7 W/m2), thermo-oxidation ageing (1000C/10days) and thermal-shock (-600C/+1000C) as a function of the aging time. The efficiency of used anti-ageing agents was checked on the base of the changes after the degradation in deformation energy (tensile strength and elongation at the break), cross-link density, color (parameters L,a,b) and values of carbonyl index (based on the spectrum of infra red spectroscopy), OIT (induction oxygen time as performed in using differential scanning calorimeter -DSC) of the vulcanizates. Therefore polyphenols are considered to be the best stabilisers for polymeric composites against to oxidation processes.

Keywords: polymers, flavonoids, stabilization, ageing, oxidation

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Authors: Arcady Ponosov, Ramazan Kadiev

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Input-to-State Stability (ISS) is widely used in deterministic control theory but less known in the stochastic case. Roughly speaking, the theory explains when small perturbations of the right-hand sides of the system on the entire semiaxis cause only small changes in the solutions of the system, again on the entire semiaxis. This property is crucial in many applications. In the report, we explain how to define and study ISS for systems of linear stochastic differential equations with or without delays. The central result connects ISS with the property of Lyapunov stability. This relationship is well-known in the deterministic setting, but its stochastic version is new. As an application, a method of studying asymptotic Lyapunov stability for stochastic delay equations is described and justified. Several examples are provided that confirm the efficiency and simplicity of the framework.

Keywords: asymptotic stability, delay equations, operator methods, stochastic perturbations

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Authors: Madhav Khadilkar

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Construction of a large standby reservoir was required to provide secure water supply. The new reservoir was required to be constructed at the same location of an abandoned old open pond due to space constraints. Some investigations were carried out earlier to improvise and re-commission the existing pond. But due to a lack of quantified risk of settlement from voids in the underlying limestone, the shallow foundations were not found feasible. Since the reservoir was resting on hard strata for about three-quarter of plan area and one quarter was resting on soil underlying with limestone and considerably low subgrade modulus. Further investigations were carried out to ascertain the locations and extent of voids within the limestone. It was concluded that the risk due to lime dissolution was acceptably low, and the site was found geotechnically feasible. The hazard posed by limestone dissolution was addressed through the integrated structural and geotechnical analysis and design approach. Finite Element Analysis was carried out to quantify the stresses and differential settlement due to various probable loads and soil-structure interaction. Walls behaving as cantilever under operational loads were found undergoing in-plane bending and tensile forces due to soil-structure interaction. Sensitivity analysis for varying soil subgrade modulus was carried out to check the variation in the response of the structure and magnitude of stresses developed. The base slab was additionally checked for the loss of soil contact due to lime pocket formations at random locations. The expansion and contraction joints were planned to receive minimal additional forces due to differential settlement. The reservoir was designed to sustain the actions corresponding to allowable deformation limits per code, and geotechnical measures were proposed to achieve the soil parameters set in structural analysis.

Keywords: differential settlement, limestone dissolution, reservoir, soil structure interaction

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Authors: Sai Sankalp Vemavarapu

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This paper discusses the application of machine learning in the field of transportation engineering for predicting engineering properties of pavement more accurately and efficiently. Predicting the elastic properties aid us in assessing the current road conditions and taking appropriate measures to avoid any inconvenience to commuters. This improves the longevity and sustainability of the pavement layer while reducing its overall life-cycle cost. As an example, we have implemented differential evolution (DE) in the back-calculation of the elastic modulus of multi-layered pavement. The proposed DE global optimization back-calculation approach is integrated with a forward response model. This approach treats back-calculation as a global optimization problem where the cost function to be minimized is defined as the root mean square error in measured and computed deflections. The optimal solution which is elastic modulus, in this case, is searched for in the solution space by the DE algorithm. The best DE parameter combinations and the most optimum value is predicted so that the results are reproducible whenever the need arises. The algorithm’s performance in varied scenarios was analyzed by changing the input parameters. The prediction was well within the permissible error, establishing the supremacy of DE.

Keywords: cost function, differential evolution, falling weight deflectometer, genetic algorithm, global optimization, metaheuristic algorithm, multilayered pavement, pavement condition assessment, pavement layer moduli back calculation

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Authors: Ifeyinwa Orakwe, Ngozi Nwogu, Edward Gobina

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This work presents experimental results relating to the structural characterization of a commercially available alumina membrane. A γ-alumina mesoporous tubular membrane has been used. Nitrogen adsorption-desorption, scanning electron microscopy and gas permeability test has been carried out on the alumina membrane to characterize its structural features. Scanning electron microscopy (SEM) was used to determine the pore size distribution of the membrane. Pore size, specific surface area and pore size distribution were also determined with the use of the Nitrogen adsorption-desorption instrument. Gas permeation tests were carried out on the membrane using a variety of single and mixed gases. The permeabilities at different pressure between 0.05-1 bar and temperature range of 25-200oC were used for the single and mixed gases: nitrogen (N2), helium (He), oxygen (O2), carbon dioxide (CO2), 14%CO₂/N₂, 60%CO₂/N₂, 30%CO₂/CH4 and 21%O₂/N₂. Plots of flow rate verses pressure were obtained. Results got showed the effect of temperature on the permeation rate of the various gases. At 0.5 bar for example, the flow rate for N2 was relatively constant before decreasing with an increase in temperature, while for O2, it continuously decreased with an increase in temperature. In the case of 30%CO₂/CH4 and 14%CO₂/N₂, the flow rate showed an increase then a decrease with increase in temperature. The effect of temperature on the membrane performance of the various gases is presented and the influence of the trans membrane pressure drop will be discussed in this paper.

Keywords: alumina membrane, Nitrogen adsorption-desorption, scanning electron microscopy, gas permeation, temperature

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Authors: Beata Jackowska-Zduniak

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We formulate and analyze a mathematical model describing dynamics of cancer growth under the influence of radiation therapy. The effect of this type of therapy is considered as an additional equation of discussed model. Numerical simulations show that delay, which is added to ordinary differential equations and represent time needed for transformation from one type of cells to the other one, affects the behavior of the system. The validation and verification of proposed model is based on medical data. Analytical results are illustrated by numerical examples of the model dynamics. The model is able to reconstruct dynamics of treatment of cancer and may be used to determine the most effective treatment regimen based on the study of the behavior of individual treatment protocols.

Keywords: mathematical modeling, numerical simulation, ordinary differential equations, radiation therapy

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Authors: Jiajia Yao, Guanlin Wu, Fang Liu, Junshuai Xue, Yue Hao

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This study reports on the epitaxial growth of a GaN-based resonant tunneling diode (RTD) structure with stable and repeatable double negative differential resistance (NDR) characteristics at room temperature on a c-plane GaN-on-sapphire template using plasma-assisted molecular beam epitaxy (PA-MBE) technology. In this structure, two independent AlN/GaN RTDs are epitaxially connected in series in the vertical growth direction through a silicon-doped GaN layer. As the collector electrode bias voltage increases, the two RTDs respectively align the ground state energy level in the quantum well with the 2DEG energy level in the emitter accumulation well to achieve quantum resonant tunneling and then reach the negative differential resistance (NDR) region. The two NDR regions exhibit similar peak current densities and peak-to-valley current ratios, which are 230 kA/cm² and 249 kA/cm², 1.33 and 1.38, respectively, for a device with a collector electrode mesa diameter of 1 µm. The consistency of the NDR is much higher than the results of on-chip discrete RTD device interconnection, resulting from the smaller chip area, fewer interconnect parasitic parameters, and less process complexity. The methods and results presented in this paper show the brilliant prospects of GaN RTDs in the development of multi-value logic digital circuits.

Keywords: MBE, AlN/GaN, RTDs, double NDR

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Authors: Mario J. Meco-Gutierrez, Francisco Perez-Hidalgo, Juan R. Heredia-Larrubia, Antonio Ruiz-Gonzalez, Francisco Vargas-Merino

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More and more applications power inverters connected to transformers, for example, the connection facilities to the power grid renewable generation. It is well known that the quality of signal power inverters it is not a pure sine. The harmonic content produced negative effects, one of which is the heating of electrical machines and therefore, affects the life of the machines. The decrease of life of transformers can be calculated by Arrhenius or Montsinger equation. Analyzing this expression any (long-term) decrease of a transformer temperature for 6º C - 7º C means doubles its life-expectancy. Methodologies: This work presents the technique of pulse width modulation (PWM) with an injection of harmonic and triangular frequency carrier modulated in frequency. This technique is used to improve the quality of the output voltage signal of the power inverters controlled PWM. The proposed technique increases in the fundamental term and a significant reduction in low order harmonics with the same commutations per time that control sine PWM. To achieve this, the modulating wave is compared to a triangular carrier with variable frequency over the period of the modulator. Therefore, it is, advantageous for the modulating signal to have a large amount of sinusoidal “information” in the areas of greater sampling. A triangular signal with a frequency that varies over the modulator’s period is used as a carrier, for obtaining more samples in the area with the greatest slope. A power inverter controlled by PWM proposed technique is connected to a transformer. Results: In order to verify the derived thermal parameters under different operation conditions, another ambient and loading scenario is involved for a further verification, which was sampled from the same power transformer. Temperatures of different parts of the transformer will be exposed for each PWM control technique analyzed. An assessment of the temperature be done with different techniques PWM control and hence the life of the transformer is calculated for each technique. Conclusion: This paper analyzes such as transformer heating produced by this technique and compared with other forms of PWM control. In it can be seen as a reduction the harmonic content produces less heat transformer and therefore, an increase in the life of the transformer.

Keywords: heating, power-inverter, PWM, transformer

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Authors: Tomáš Dyk, Stanislav Procházka, Martin Drahanský

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The article proposes a new algorithm for detecting damaged areas of the tank barrel based on the image of the inner surface of the tank barrel. Damage position is calculated using image processing techniques such as edge detection, discrete wavelet transformation and image segmentation for accurate contour detection. The algorithm can detect surface damage in smoothbore and even in rifled tank barrels. The algorithm also calculates the volume of the detected damage from the depth map generated, for example, from the distance measurement unit. The proposed method was tested on data obtained by a tank barrel scanning device, which generates both surface image data and depth map. The article also discusses tank barrel scanning devices and how damaged surface impacts material resistance.

Keywords: barrel, barrel diagnostic, image processing, surface damage detection, tank

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Authors: Y. A. Yahaya, Ahmad Tijjani Asabe

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This paper focuses on the formulation of 3-step hybrid Adams type method for the solution of first order differential equation (ODE). The methods which was derived on both grid and off grid points using multistep collocation schemes and also evaluated at some points to produced Block Adams type method and Adams moulton method respectively. The method with the highest order was selected to serve as the corrector. The convergence was valid and efficient. The numerical experiments were carried out and reveal that hybrid Adams type methods performed better than the conventional Adams moulton method.

Keywords: adam-moulton type (amt), corrector method, off-grid, block method, convergence analysis

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Authors: Alpana Agarwal, Akhil Sharma

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This work presents a fully differential CMOS amplifier consisting of two self-biased gain boosted inverter stages, that provides an alternative to the power hungry operational amplifier. The self-biasing avoids the use of external biasing circuitry, thus reduces the die area, design efforts, and power consumption. In the present work, regulated cascode technique has been employed for gain boosting. The Miller compensation is also applied to enhance the phase margin. The circuit has been designed and simulated in 1.8 V 0.18 µm CMOS technology. The simulation results show a high DC gain of 100.7 dB, Unity-Gain Bandwidth of 107.8 MHz, and Phase Margin of 66.7^o with a power dissipation of 286 μW and makes it suitable candidate for the high resolution pipelined ADCs.

Keywords: CMOS amplifier, gain boosting, inverter-based amplifier, self-biased inverter

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Authors: Andriy Didenko, Zanin Kavazovic

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Engineering students often have certain difficulties in mastering major theoretical concepts in mathematical courses such as differential equations. Student projects were proposed to motivate students’ learning and can be used as a tool to promote students’ interest in the material. Authors propose a student project that includes the use of Microsoft Excel. This instructional tool is often overlooked by both educators and students. An integral component of the experimental part of such a project is the exploration of an interactive spreadsheet. The aim is to assist engineering students in better understanding of Euler’s method. This method is employed to numerically solve first order differential equations. At first, students are invited to select classic equations from a list presented in a form of a drop-down menu. For each of these equations, students can select and modify certain key parameters and observe the influence of initial condition on the solution. This will give students an insight into the behavior of the method in different configurations as solutions to equations are given in numerical and graphical forms. Further, students could also create their own equations by providing functions of their own choice and a variety of initial conditions. Moreover, they can visualize and explore the impact of the length of the time step on the convergence of a sequence of numerical solutions to the exact solution of the equation. As a final stage of the project, students are encouraged to develop their own spreadsheets for other numerical methods and other types of equations. Such projects promote students’ interest in mathematical applications and further improve their mathematical and programming skills.

Keywords: student project, Euler's method, spreadsheet, engineering education

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Authors: Ladan Maijama’a, Jibril D. Jiya, Ejike C. Anene

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This paper presents Differential Evolution Algorithm (DEA) based Variable Structure Position Control (VSPC) of Laboratory DC servomotor (LDCSM). DEA is employed for the optimal tuning of Variable Structure Control (VSC) parameters for position control of a DC servomotor. The VSC combines the techniques of Sliding Mode Control (SMC) that gives the advantages of small overshoot, improved step response characteristics, faster dynamic response and adaptability to plant parameter variations, suppressed influences of disturbances and uncertainties in system behavior. The results of the simulation responses of the VSC parameters adjustment by DEA were performed in Matlab Version 2010a platform and yield better dynamic performance compared with the untuned VSC designed.

Keywords: differential evolution algorithm, laboratory DC servomotor, sliding mode control, variable structure control

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Authors: Olga V. Kharchenko

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Applicability of a KTA crystal-based laser system with optical parametric oscillators (OPO) generation to lidar sounding of the atmosphere in the spectral range 3–4 µm is studied in this work. A technique based on differential absorption lidar (DIAL) method and differential optical absorption spectroscopy (DOAS) is developed for lidar sounding of trace atmospheric gases (TAG). The DIAL-DOAS technique is tested to estimate its efficiency for lidar sounding of atmospheric trace gases.

Keywords: atmosphere, lidar sounding, DIAL, DOAS, trace gases, nonlinear crystal

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Authors: Motahar Reza, Rajni Chahal, Neha Sharma

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This article addresses the boundary layer flow and heat transfer of Casson fluid over a nonlinearly permeable stretching surface with chemical reaction in the presence of variable magnetic field. The effect of thermal radiation is considered to control the rate of heat transfer at the surface. Using similarity transformations, the governing partial differential equations of this problem are reduced into a set of non-linear ordinary differential equations which are solved by finite difference method. It is observed that the velocity at fixed point decreases with increasing the nonlinear stretching parameter but the temperature increases with nonlinear stretching parameter.

Keywords: boundary layer flow, nonlinear stretching, Casson fluid, heat transfer, radiation

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Authors: H. R. Kelidari, M. Saeedi, J. Akbari, K. Morteza-Semnani, H. Valizadeh

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Spironolactoe (SP) a synthetic steroid diuretic is a poorly water-soluble drug with a low and variable oral bioavailability. Regarding to the good solubility of SP in lipid materials, SP loaded Solid lipid nanoparticles (SP-SLNs) and nanostructured lipid carrier (SP-SLNs) were thus prepared in this work for accelerating dissolution of this drug. The SP loaded NLC with stearic acid (SA) as solid lipid and different Oleic Acid (OA) as liquid lipid content and SLN without OA were prepared by probe ultrasonication method. With increasing the percentage of OA from 0 to 30 wt% in SLN/NLC, the average size and zeta potential of nanoparticles felled down and entrapment efficiency (EE %) rose dramatically. The obtained micrograph particles showed pronounced spherical shape. Differential Scanning Calorimeter (DSC) measurements indicated that the presence of OA reduced the melting temperature and melting enthalpy of solid lipid in NLC structure. The results reflected good long-term stability of the nanoparticles and the measurements show that the particle size remains lower in NLC compare to SLN formulations, 6 months after production. Dissolution of SP-SLN and SP-NLC was about 5.1 and 7.2 times faster than raw drugs in 120 min respectively. These results indicated that the SP loaded NLC containing 70:30 solid lipid to liquid lipid ratio is a suitable carrier of SP with improved drug EE and steady drug release properties.

Keywords: drug release, lipid nanoparticles, spironolactone, stability

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Authors: Divij Gupta

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Pendular systems have a range of both mathematical and engineering applications, ranging from modelling the behaviour of a continuous mass-density rope to utilisation as Tuned Mass Dampers (TMD). Thus, it is of interest to study the differential equations governing the motion of such systems. Here we attempt to generalise these equations of motion for the plane compound pendulum with a finite number of N point masses. A Lagrangian approach is taken, and we attempt to find the generalised form for the Euler-Lagrange equations of motion for the i-th bob of the N -bob pendulum. The co-ordinates are parameterized as angular quantities to reduce the number of degrees of freedom from 2N to N to simplify the form of the equations. We analyse the form of these equations up to N = 4 to determine the general form of the equation. We also develop a MATLAB program to compute a solution to the system for a given input value of N and a given set of initial conditions.

Keywords: classical mechanics, differential equation, lagrangian analysis, pendulum

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Authors: Yuhanis Ibrahim, Sung-Pil Lee

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This study attempts to address factors that contribute to outline public art factors assessment, memorial monument specifically. Memorial monuments hold significant and rich message whether the intention of the art is to mark and commemorate important event or to inform younger generation about the past. Public monument should relate to the public and raise awareness about the significant issue. Therefore, by investigating the impact of the existing public memorial art will hopefully shed some lights to the upcoming public art projects’ stakeholders to ensure the lucid memorial message is delivered to the public directly. Public is the main actor as public is the fundamental purpose that the art was created. Perception is framed as one of the reliable evaluation tools to assess the public art impact factors. The Malaysia National Monument was selected to be the case study for the investigation. The public’s perceptions were gathered using a questionnaire that involved (n-115) participants to attain keywords, and next Semantical Differential Methodology (SDM) was adopted to evaluate the perceptions about the memorial monument. These perceptions were then measured with Reliability Factor and then were factorised using Factor Analysis of Principal Component Analysis (PCA) method to acquire concise factors for the monument assessment. The result revealed that there are four factors that influence public’s perception on the monument which are aesthetic, audience, topology, and public reception. The study concludes by proposing the factors for public memorial art assessment for the next future public memorial projects especially in Malaysia.

Keywords: factor analysis, public art, public perception, semantical differential methodology

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Authors: Clarinda Vitorino Nhangumbe, Fredericks Ebrahim, Betuel Canhanga

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The price of an option weather derivatives can be approximated as a solution of the two-dimensional convection-diffusion dominant partial differential equation derived from the Ornstein-Uhlenbeck process, where one variable represents the weather dynamics and the other variable represent the underlying weather index. With appropriate financial boundary conditions, the solution of the pricing equation is approximated using a nonstandard finite difference method. It is shown that the proposed numerical scheme preserves positivity as well as stability and consistency. In order to illustrate the accuracy of the method, the numerical results are compared with other methods. The model is tested for real weather data.

Keywords: nonstandard finite differences, Ornstein-Uhlenbeck process, partial differential equations approach, weather derivatives

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Authors: A. P. Srivastava, D. Srivastava, D. J. Browne

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Relaxation dynamics of Zr44Cu40Al8Ag8 bulk metallic glass (BMG) has been probed using dynamic mechanical analyzer. The BMG sample was casted in the form of a plate of dimension 55 mm x 40 mm x 3 mm using tilt casting technique. X-ray diffraction and transmission electron microscope have been used for the microstructural characterization of as-cast BMG. For the mechanical spectroscopy study, samples in the form of a bar of size 55 mm X 2 mm X 3 mm were machined from the BMG plate. The mechanical spectroscopy was performed on dynamic mechanical analyzer (DMA) by 50 mm 3-point bending method in a nitrogen atmosphere. It was observed that two glass transition process were competing in supercooled liquid region around temperature 390°C and 430°C. The supercooled liquid state was completely characterized using DMA and differential scanning calorimeter (DSC). In addition to the main α-relaxation process, presence of β relaxation process around temperature 360°C; below the glass transition temperature was also observed. The β relaxation process could be described by Arrhenius law with the activation energy of 160 kJ/mole. The volume of the flow unit associated with this relaxation process has been estimated. The results from DMA study has been used to characterize the shear transformation zone in terms of activation volume and size. High fragility parameter value of 34 and higher activation volume indicates that this alloy could show good plasticity in supercooled liquid region. The possible mechanism for the relaxation processes has been discussed.

Keywords: DMA, glass transition, metallic glass, thermoplastic forming

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Authors: Edina Koch, Péter Hudacsek

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In railways transition zone is present at the boundaries of zones with different stiffness. When a train rides from an embankment onto a stiff structure, such as a bridge, tunnel or culvert, an abrupt change in the support stiffness occurs possibly inducing differential settlements. This in long term can yield to the degradation of the tracks and foundations in the transition zones. A number of techniques have been proposed or implemented to provide gradual stiffness transition at the problem zones, such as methods to ensure gradually changing pad stiffness, application of long sleepers or installation of auxiliary rails in the transition zone. Aim of the research presented in this paper is to analyze the 3D and the dynamic effects induced by the passing train over an area where significant difference in the support stiffness exists. The effects were analyzed for different arrangements associated with certain differential settlement mitigation strategies of the transition zones.

Keywords: culvert, dynamic load, HS small model, railway transition zone

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Authors: M. S. H. Chowdhury, Ishak Hashim

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In this paper, linear and non-linear stiff systems of ordinary differential equations are solved by the classical Adomian decomposition method (ADM) and the multi-stage Adomian decomposition method (MADM). The MADM is a technique adapted from the standard Adomian decomposition method (ADM) where standard ADM is converted into a hybrid numeric-analytic method called the multistage ADM (MADM). The MADM is tested for several examples. Comparisons with an explicit Runge-Kutta-type method (RK) and the classical ADM demonstrate the limitations of ADM and promising capability of the MADM for solving stiff initial value problems (IVPs).

Keywords: stiff system of ODEs, Runge-Kutta Type Method, Adomian decomposition method, Multistage ADM

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Authors: Hesham A. Elkaranshawy, Amr M. Abdelrazek, Hosam M. Ezzat

Abstract:

The system of ordinary nonlinear differential equations describing sliding velocity during impact with friction for a three-dimensional rigid-multibody system is developed. No analytical solutions have been obtained before for this highly nonlinear system. Hence, a power series solution is proposed. Since the validity of this solution is limited to its convergence zone, a suitable time step is chosen and at the end of it a new series solution is constructed. For a case study, the trajectory of the sliding velocity using the proposed method is built using 6 time steps, which coincides with a Runge-Kutta solution using 38 time steps.

Keywords: impact with friction, nonlinear ordinary differential equations, power series solutions, rough collision

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