Search results for: the modified Korteweg-de Vries (KdV) equation

Authors: Naila Nasreen, Dianchen Lu

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This paper explores the dynamical behavior of the (2+1)-dimensional Boussinesq equation, which is a nonlinear water wave equation and is used to model wave packets in dispersive media with weak nonlinearity. This equation depicts how long wave made in shallow water propagates due to the influence of gravity. The (2+1)- dimensional Boussinesq equation combines the two-way propagation of the classical Boussinesq equation with the dependence on a second spatial variable, as that occurs in the two-dimensional Kadomstev- Petviashvili equation. This equation provides a description of head- on collision of oblique waves and it possesses some interesting properties. The governing model is discussed by the assistance of Ricatti equation mapping method, a relatively integration tool. The solutions have been extracted in different forms the solitary wave solutions as well as hyperbolic and periodic solutions. Moreover, the sensitivity analysis is demonstrated for the designed dynamical structural system’s wave profiles, where the soliton wave velocity and wave number parameters regulate the water wave singularity. In addition to being helpful for elucidating nonlinear partial differential equations, the method in use gives previously extracted solutions and extracts fresh exact solutions. Assuming the right values for the parameters, various graph in different shapes are sketched to provide information about the visual format of the earned results. This paper’s findings support the efficacy of the approach taken in enhancing nonlinear dynamical behavior. We believe this research will be of interest to a wide variety of engineers that work with engineering models. Findings show the effectiveness simplicity, and generalizability of the chosen computational approach, even when applied to complicated systems in a variety of fields, especially in ocean engineering.

Keywords: (2+1)-dimensional Boussinesq equation, solitary wave solutions, Ricatti equation mapping approach, nonlinear phenomena

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Authors: Yaping Zhao

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In the present study, the exact solutions for the steady response of quasi-linear systems under non-white wide-band random excitation are considered by means of the stochastic averaging method. The non linearity of the systems contains the power-law damping and the cross-product term of the power-law damping and displacement. The drift and diffusion coefficients of the Fokker-Planck-Kolmogorov (FPK) equation after averaging are obtained by a succinct approach. After solving the averaged FPK equation, the joint probability density function and the marginal probability density function in steady state are attained. In the process of resolving, the eigenvalue problem of ordinary differential equation is handled by integral equation method. Some new results are acquired and the novel method to deal with the problems in nonlinear random vibration is proposed.

Keywords: random vibration, stochastic averaging method, FPK equation, transition probability density

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Authors: Sumit Kumar Vishwakarma

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The aim of the paper is to investigate the influence of inhomogeneity associated with the elastic constants and density of the orthotropic medium. The inhomogeneity is considered as exponential function of depth. The impact of gravity had been discussed. Using the concept of separation of variables, the system of a partial differential equation (equation of motion) has been converted into ordinary differential equation, which is coupled in nature. It further reduces to a biquadratic equation whose roots were found by using MATLAB. A suitable boundary condition is employed to derive the dispersion equation in a closed-form. Numerical simulations had been performed to show the influence of the inhomogeneity parameter. It was observed that as the numerical values of increases, the phase velocity of Rayleigh waves decreases at a particular wavenumber. Graphical illustrations were drawn to visualize the effect of the increasing and decreasing values of the inhomogeneity parameter. It can be concluded that it has a remarkable bearing on the phase velocity as well as damping velocity.

Keywords: Rayleigh waves, orthotropic medium, gravity field, inhomogeneity

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Authors: Fahrudin Nugroho, Halim Hamadi, Yusril Yusuf, Pekik Nurwantoro, Ari Setiawan, Yoshiki Hidaka

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We investigate the Nikolaevskiy equation numerically using exponential time differencing method and pseudo-spectral method. This equation develops a long-wavelength modulation that behaves as a Nambu–Goldstone mode, and short-wavelength instability and exhibit turbulence. Using the autocorrelation analysis, the statistical properties of the turbulence governed by the equation are investigated. The autocorrelation then has been fitted with The Kohlrausch– Williams–Watts (KWW) expression. By varying the control parameter, we show a transition from compressed to stretched exponential for the auto-correlation function of Nikolaevskiy turbulence. The compressed exponential is an indicator of the existence of dynamical heterogeneity while the stretched indicates aging process. Thereby, we revealed the existence of dynamical heterogeneity and aging in the turbulence governed by Nikolaevskiy equation.

Keywords: compressed exponential, dynamical heterogeneity, Nikolaevskiy equation, stretched exponential, turbulence

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Authors: Norhashidah Hj Mohd Ali, Teng Wai Ping

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In this paper, the formulation of a new group explicit method with a fourth order accuracy is described in solving the two-dimensional Helmholtz equation. The formulation is based on the nine-point fourth-order compact finite difference approximation formula. The complexity analysis of the developed scheme is also presented. Several numerical experiments were conducted to test the feasibility of the developed scheme. Comparisons with other existing schemes will be reported and discussed. Preliminary results indicate that this method is a viable alternative high accuracy solver to the Helmholtz equation.

Keywords: explicit group method, finite difference, Helmholtz equation, five-point formula, nine-point formula

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Authors: Aria Ratmandanu

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Boson stars can be viewed as zero temperature ground state, Bose-Einstein condensates, characterized by enormous occupation numbers. Time-dependent spherically symmetric spacetime can be a model of Boson Star. We use (3+1) split of Einstein equation (ADM formulation of general relativity) to solve Einstein field equation coupled to a complex scalar field (Einstein-Klein-Gordon Equation) on time-dependent spherically symmetric spacetime, We get the result that Boson stars are pulsating stars with the frequency of oscillation equal to its density. We search for interior solution of Boson stars and get the T.O.V. (Tollman-Oppenheimer-Volkoff) equation for Boson stars. Using T.O.V. equation, we get the equation of state and the relation between pressure and density, its total mass and along with its gravitational Mass. We found that the hypothetical particle Axion could form a Boson star with the size of a milky way galaxy and make it a candidate for a dark galaxy, (a galaxy that consists almost entirely of dark matter).

Keywords: axion, boson star, dark galaxy, time-dependent spherically symmetric spacetime

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Authors: Kitjapat Phuvoravan, Phattaraphong Ponsorn

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In the design of Castellated beams (CB), the web post buckling acted by horizontal shear force is one of the important failure modes that have to be considered. It is also a dominant governing mode when design following the AISC 31 design guideline which is just published. However, the equation of the web post buckling given by the guideline is still questionable for most of the engineers. So the purpose of this paper is to study and provide a proposed equation for design the web post buckling with more simplified and convenient to use. The study is also including the improper of the safety factor given by the guideline. The proposed design equation is acquired by regression method based on the results of finite element analysis. An amount of Cellular beam simulated to study is modelled by using shell element, analysis with both geometric and material nonlinearity. The results of the study show that the use of the proposed equation to design the web post buckling in Castellated beams is more simple and precise for computation than the equations provided from the guideline.

Keywords: castellated beam, web opening, web post buckling, design equation

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Authors: M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous movement disorder that often appears in the elderly. PD is induced by a loss of dopamine secretion. Some drugs increase the secretion of dopamine. In this paper, we will simply study the stability of PD models as a nonlinear delay differential equation. After a period of taking drugs, these act as positive feedback and increase the tremors of patients, and then, the differential equation has positive coefficients and the system is unstable under these conditions. We will present a set of suggested modifications to make the system more compatible with the biodynamic system. When giving a set of numerical examples, this research paper is concerned with the mathematical analysis, and no clinical data have been used.

Keywords: Parkinson's disease, stability, simulation, two delay differential equation

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Authors: Seyyed Ershad Moradi, Javad Khodaveisi, Atefeh Nasrollahpour

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In this study, the highly ordered mesoporous carbon molecular sieve with high surface area and pore volume have been synthesized and modified by TiO₂ doping. The titanium oxide modified mesoporous carbon (Ti-OMC) was characterized by scanning electron microscope (SEM), BET surface area, DRS also XRD analysis (low and wide angle). Degradation experiments were conducted in batch mode with the variables such as amount of contact time, initial solution concentration, and solution pH. The optimal conditions for the degradation of methyl red (MR) were 100 mg/L dye concentration, pH of 7, and 0.12 mg/L of TiO₂ modified mesoporous carbon photocatalyst dosage.

Keywords: mesoporous carbon, photodegradation, surface modification, titanium oxide

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Authors: Hati̇ce Bi̇rtane, Asli Beyler Çi̇ği̇l, Memet Vezi̇r Kahraman

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Polyimide (PI) is one of the most important super-engineering materials because of its mechanical properties and its thermal stability. Electronic industry is the typical extensive applications of polyimides including interlayer insulation films, buffer coating, films, alpha-ray shielding films, and alignment films for liquid crystal displays. The mechanical and thermal properties of polymers are generally improved by the addition of inorganic additives. The challenges in this area of high-performance organic/inorganic hybrid materials are to obtain significant improvements in the interfacial adhesion between the polymer matrix and the reinforcing material since the organic matrix is relatively incompatible with the inorganic phase. In this study, modified nanodiamond was prepared from the reaction of nanodiamond and (3-Mercaptopropyl)trimethoxysilane. Poly(amic acid) was prepared from the reaction of 3,3',4,4'-Benzophenonetetracarboxylic dianhydride (BTDA) and 4,4'-Oxydianiline (ODA). Polyimide/modified nanodiamond hybrids were prepared by blending of poly(amic acid) and organically modified nanodiamond. The morphology of the Polyimide/ modified nanodiamond hybrids was characterized by scanning electron microscopy (SEM). Chemical structure of polyimide and Polyimide/modified nanodiamond hybrids was characterized by FTIR. FTIR results showed that the Polyimide/modified nanodiamond hybrids were successfully prepared. A thermal property of the Polyimide/modified nanodiamond hybrids was characterized by thermogravimetric analysis (TGA).

Keywords: hybrid materials, nanodiamond, polyimide, polymer

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Authors: Elvis Adam Alhassan, Kaiyu Tian, Akos Konadu, Ernest Zamanah, Michael Jackson Adjabui, Ibrahim Justice Musah, Esther Agyeiwaa Owusu, Emmanuel K. A. Agyeman

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In this paper, how to solve simultaneous equations using the Elvis improved method is shown. The Elvis improved method says; to make one variable in the first equation the subject; make the same variable in the second equation the subject; equate the results and simplify to obtain the value of the unknown variable; put the value of the variable found into one equation from the first or second steps and simplify for the remaining unknown variable. The difference between our Elvis improved method and the substitution method is that: with Elvis improved method, the same variable is made the subject in both equations, and the two resulting equations equated, unlike the substitution method where one variable is made the subject of only one equation and substituted into the other equation. After describing the Elvis improved method, findings from 100 secondary students and the views of 5 secondary tutors to demonstrate the effectiveness of the method are presented. The study's purpose is proved by hypothetical examples.

Keywords: simultaneous equations, substitution method, elimination method, graphical method, Elvis improved method

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Authors: Yemane Hailu Fissuh, Zhongzhan Zhang

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a systematic observation from a defined time of origin up to certain failure or censor is known as survival data. Survival analysis is a major area of interest in biostatistics and biomedical researches. At the heart of understanding, the most scientific and medical research inquiries lie for a causality analysis. Thus, the main concern of this study is to investigate the causal effect of treatment on survival time conditional to the possibly time-varying covariates. The theory of causality often differs from the simple association between the response variable and predictors. A causal estimation is a scientific concept to compare a pragmatic effect between two or more experimental arms. To evaluate an average treatment effect on survival outcome, the estimating equation was adjusted for time-varying covariates under the semi-parametric transformation models. The proposed model intuitively obtained the consistent estimators for unknown parameters and unspecified monotone transformation functions. In this article, the proposed method estimated an unbiased average causal effect of treatment on survival time of interest. The modified estimating equations of semiparametric transformation models have the advantage to include the time-varying effect in the model. Finally, the finite sample performance characteristics of the estimators proved through the simulation and Stanford heart transplant real data. To this end, the average effect of a treatment on survival time estimated after adjusting for biases raised due to the high correlation of the left-truncation and possibly time-varying covariates. The bias in covariates was restored, by estimating density function for left-truncation. Besides, to relax the independence assumption between failure time and truncation time, the model incorporated the left-truncation variable as a covariate. Moreover, the expectation-maximization (EM) algorithm iteratively obtained unknown parameters and unspecified monotone transformation functions. To summarize idea, the ratio of cumulative hazards functions between the treated and untreated experimental group has a sense of the average causal effect for the entire population.

Keywords: a modified estimation equation, causal effect, semiparametric transformation models, survival analysis, time-varying covariate

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Authors: Ali Dehgan Moroozeh, B. Farhadi Bansouleh

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Evapotranspiration is one of the most important components of the hydrological cycle. Evapotranspiration (ETo) is an important variable in water and energy balances on the earth’s surface, and knowledge of the distribution of ET is a key factor in hydrology, climatology, agronomy and ecology studies. Many researchers have a valid relationship, which is a function of climate factors, to estimate the potential evapotranspiration presented to the plant water stress or water loss, prevent. The FAO-Penman method (PM) had been recommended as a standard method. This method requires many data and these data are not available in every area of world. So, other methods should be evaluated for these conditions. When sufficient or reliable data to solve the PM equation are not available then Hargreaves equation can be used. The Hargreaves equation (HG) requires only daily mean, maximum and minimum air temperature extraterrestrial radiation .In this study, Hargreaves method (HG) were evaluated in 12 stations in the North West region of Iran. Results of HG and M.HG methods were compared with results of PM method. Statistical analysis of this comparison showed that calibration process has had significant effect on efficiency of Hargreaves method.

Keywords: evapotranspiration, hargreaves, equation, FAO-Penman method

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Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi

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Differential equations are of fundamental importance in engineering and applied mathematics, since many physical laws and relations appear mathematically in the form of such equations. The equilibrium state of structures consisting of one-dimensional elements can be described by an ordinary differential equation. The response of these kinds of structures under the loading, namely relationship between the displacement field and loading field, can be predicted by the solution of these differential equations and on satisfying the given boundary conditions. When the effect of change of geometry under loading is taken into account in modeling of equilibrium state, then these differential equations are partially integrable in quartered. They also exhibit instability characteristics when the structures are loaded compressively. The purpose of this paper is to represent the ability of the Modified Newmark Method in analyzing flexural-torsional instability of struts for both bifurcation and non-bifurcation structural systems. The results are shown to be very accurate with only a small number of iterations. The method is easily programmed, and has the advantages of simplicity and speeds of convergence and easily is extended to treat material and geometric nonlinearity including no prismatic members and linear and nonlinear spring restraints that would be encountered in frames. In this paper, these abilities of the method will be extended to the system of linear differential equations that govern strut flexural torsional stability.

Keywords: instability, torsion, flexural, buckling, modified newmark method stability

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Authors: A. Zerarka, W. Djoudi

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The method developed in this work uses a generalised coth and csch funtions method to construct new exact travelling solutions to the nonlinear lattice equation. The technique of the homogeneous balance method is used to handle the appropriated solutions.

Keywords: coth functions, csch functions, nonlinear partial differential equation, travelling wave solutions

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Authors: Itissam Abuiziah

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In several hydraulic systems, it is necessary to calculate the head losses which depend on the resistance flow friction factor in Darcy equation. Computing the resistance friction is based on implicit Colebrook-White equation which is considered as the standard for the friction calculation, but it needs high computational cost, therefore; several explicit approximation methods are used for solving an implicit equation to overcome this issue. It follows that the relative error is used to determine the most accurate method among the approximated used ones. Steel, cast iron and polyethylene pipe materials investigated with practical diameters ranged from 0.1m to 2.5m and velocities between 0.6m/s to 3m/s. In short, the results obtained show that the suitable method for some cases may not be accurate for other cases. For example, when using steel pipe materials, Zigrang and Silvester's method has revealed as the most precise in terms of low velocities 0.6 m/s to 1.3m/s. Comparatively, Halland method showed a less relative error with the gradual increase in velocity. Accordingly, the simulation results of this study might be employed by the hydraulic engineers, so they can take advantage to decide which is the most applicable method according to their practical pipe system expectations.

Keywords: Colebrook–White, explicit equation, friction factor, hydraulic resistance, implicit equation, Reynolds numbers

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Authors: Manisha Kankarej

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The purpose of this paper is to show a relation between CR structure and F-structure satisfying polynomial equation. In this paper, we have checked the significance of CR structure and F-structure on Integrability conditions and Nijenhuis tensor. It was proved that all the properties of Integrability conditions and Nijenhuis tensor are satisfied by CR structures and F-structure satisfying polynomial equation.

Keywords: CR-submainfolds, CR-structure, integrability condition, Nijenhuis tensor

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Authors: Matheus Fernando Pereira, Varese Salvador Timoteo

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In this work, we have solved the two-dimensional advection-diffusion equation numerically for a spatially dependent solute dispersion along non-uniform flow with a pulse type source in order to make a systematic study on the influence of medium heterogeneity, initial flow velocity, and initial dispersion coefficient parameters on the solutions of the equation. The behavior of the solutions is then investigated as we change the three parameters independently. Our results show that even though the parameters represent different physical features of the system, the effect on their variation is very similar. We also observe that the effects caused by the parameters on the concentration depend on the distance from the source. Finally, our numerical results are in good agreement with the exact solutions for all values of the parameters we used in our analysis.

Keywords: advection-diffusion equation, dispersion, numerical methods, pulse-type source

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Authors: Ted Silva

Abstract:

Dietrich de Velsa's Équation à un inconnu / Equation to an Unknown hybridizes art cinema style with the sexually explicit aesthetics of pornography to envision a uniquely queer world unmoored by heteronormative influence. This stylization evokes the memory of a queer history that once approximated such a prospect. With this historical and political context in mind, this paper utilizes formal analysis to assess how the film frames queer sexual encounters as tender acts of care, sometimes literally mending physical wounds. However, Equation to Unknown also highlights the transience of these sexual exchanges. By emphasizing the homogeneity of the protagonist’s sexual conquests, the film reveals that these practices have a darker meaning when the men reject the individualized connection to pursue purely visceral gratification. Given the lack of diversity or even recognizable identifying factors, the men become more anonymous to each other the more they pair up. Ultimately, Equation to an Unknown both celebrates and problematizes its vision of a queer utopia, highlighting areas in the community wherein intimacy and care flourish and locating those spots in which they are neglected.

Keywords: pornography studies, queer cinema, French cinema, history

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Authors: Khairil Iskandar Othman, Nadhirah Kamal, Zarina Bibi Ibrahim

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Block methods for solving stiff systems of ordinary differential equations (ODEs) are based on backward differential formulas (BDF) with PE(CE)2 and Newton method. In this paper, we introduce Modified Newton as a new strategy to get more efficient result. The derivation of BBDF using modified block Newton method is presented. This new block method with predictor-corrector gives more accurate result when compared to the existing BBDF.

Keywords: modified Newton, stiff, BBDF, Jacobian matrix

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Authors: Tomoaki Hashimoto

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Recent technological advance has prompted significant interest in developing the control theory of quantum systems. Following the increasing interest in the control of quantum dynamics, this paper examines the control problem of Schrödinger equation because quantum dynamics is basically governed by Schrödinger equation. From the practical point of view, stochastic disturbances cannot be avoided in the implementation of control method for quantum systems. Thus, we consider here the robust stabilization problem of Schrödinger equation against stochastic disturbances. In this paper, we adopt model predictive control method in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. The objective of this study is to derive the stability criterion for model predictive control of Schrödinger equation under stochastic disturbances.

Keywords: optimal control, stochastic systems, quantum systems, stabilization

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Authors: Seyed M. Khatami, H. Naderpour, R. Vahdani, R. C. Barros

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Many previous studies have been carried out to calculate the impact force and the dissipated energy between two neighboring buildings during seismic excitation, when they collide with each other. Numerical studies are an important part of impact, which several researchers have tried to simulate the impact by using different formulas. Estimation of the impact force and the dissipated energy depends significantly on some parameters of impact. Mass of bodies, stiffness of spring, coefficient of restitution, damping ratio of dashpot and impact velocity are some known and unknown parameters to simulate the impact and measure dissipated energy during collision. Collision is usually shown by force-displacement hysteresis curve. The enclosed area of the hysteresis loop explains the dissipated energy during impact. In this paper, the effect of using different types of impact models is investigated in order to calculate the impact force. To increase the accuracy of impact model and to optimize the results of simulations, a new damping equation is assumed and is validated to get the best results of impact force and dissipated energy, which can show the accuracy of suggested equation of motion in comparison with other formulas. This relation is called "n-m". Based on mathematical relation, an initial value is selected for the mentioned coefficients and kinetic energy loss is calculated. After each simulation, kinetic energy loss and energy dissipation are compared with each other. If they are equal, selected parameters are true and, if not, the constant of parameters are modified and a new analysis is performed. Finally, two unknown parameters are suggested to estimate the impact force and calculate the dissipated energy.

Keywords: impact force, dissipated energy, kinetic energy loss, damping relation

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Authors: Tanima Chowdhury, Sanjay Chattopadhaya, Narayan Ch. Saha

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Khoa is an indigenous heat desiccated milk product having very poor shelf life. At ambient condition, shelf-life of khoa is normally only 2 days. The aim of present study was to determine the effect of benzoic acid as preservative as well as modified atmosphere packaging (MAP) technology to enhance shelf life of khoa at 27±2°C and 65% RH. During storage, analysis of chemical, sensory as well as microbiological characteristics were taken into consideration to mark distinguishable changes between the package of modified atmosphere technology (MAP) and ordinarily packed khoa (with and without preservative) samples. The results indicated a significant decrease of moisture content, pH and sensory scores and increase in titratable acidity, standard plate count and yeast and mould count during storage, irrespective of the type of packaging conditions. However, the rate of changes in characteristics of product packed in modified atmosphere was found to be slow. The storage study indicated that the khoa packed in ordinary packaging, with and without preservative, was acceptable for 4 and 8 days, respectively, whereas for modified atmosphere packed samples, it was consumable up to 8 and 12 days, respectively.

Keywords: benzoic acid, khoa, modified atmosphere packaging, shelf life

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Authors: M. Ghasemi-Varnamkhasti, S. H. Yoosefian, A. Mohammad-Razdari

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This study investigated the effects of Ag nanoparticle polyethylene film and active modified atmosphere on the postharvest quality of tomatoes stored at 6 ºC. The atmosphere composition used in the packaging was 7% O₂ + 7% CO₂ + 86% N₂, and synthetic air (control). The variables measured were weight loss, firmness, color and respiration rate over 21 days. The results showed that the combination of Ag nanoparticle polyethylene film and modified atmosphere could extend the shelf life of tomatoes to 21 days and could influence the postharvest quality of tomatoes. Also, existence of Ag nanoparticles caused preventing from increasing weight loss, a*, b*, Chroma, Hue angle and reducing firmness and L*. As well as, tomatoes at Ag nanoparticle polyethylene films had lower respiration rate than Polyethylene and paper bags to 13.27% and 23.50%, respectively. The combination of Ag nanoparticle polyethylene film and active modified atmosphere was effective with regard to delaying maturity during the storage period, and preserving the quality of tomatoes.

Keywords: ag nanoparticles, modified atmosphere, polyethylene film, tomato

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Authors: Toufic Abd El-Latif Sadek

Abstract:

The Asphalt object represents the asphalted areas, like roads. The best original data of thermal images occurred at a specific time during the days of the year, by preventing the gaps in times which give the close and same brightness from different objects, using seven sample objects, asphalt, concrete, metal, rock, dry soil, vegetation, and water. It has been found in this study a general timing equation for capturing satellite thermal images at different locations, depends on a fixed time the sunrise and sunset; Capture Time= Tcap =(TM*TSR) ±TS.

Keywords: asphalt, satellite, thermal images, timing equation

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Authors: Sagardeep Talukdar, Gautam Kumar Saharia, Riki Dutta, Sudipta Nandy

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In non-linear optics, the Fokas-Lenells equation (FLE) is a well-known integrable equation that describes how ultrashort pulses move across optical fiber. It admits localized wave solutions, just like any other integrable equation. We apply the Hirota bilinearization method to obtain the soliton solution of FLE. The proposed bilinearization makes use of an auxiliary function. We apply the method to FLE with a vanishing boundary condition, that is, to obtain bright soliton. We have obtained bright 1-soliton, 2-soliton solutions and propose the scheme for obtaining N-soliton solution. We have used an additional parameter which is responsible for the shift in the position of the soliton. Further analysis of the 2-soliton solution is done by asymptotic analysis. We discover that the suggested bilinearization approach, which makes use of the auxiliary function, greatly simplifies the process while still producing the desired outcome. We think that the current analysis will be helpful in understanding how FLE is used in nonlinear optics and other areas of physics.

Keywords: asymptotic analysis, fokas-lenells equation, hirota bilinearization method, soliton

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Authors: F. Onyango, Salim R. Wanjala, M. Ndege, L. Masu

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Asphalt concrete pavements have a short life cycle, failing mainly due to temperature changes, traffic loading and ageing. Modified asphalt mixtures provide the technology to produce a bituminous binder with improved viscoelastic properties which remain in balance over a wider temperature range and loading conditions. In this research, 60/70 penetration grade asphalt binder was modified by adding 2, 4, 6, 8, and 10 percent by weight of asphalt binder following the wet process and the mineral aggregate was modified by adding 1, 2, 3, 4, and 5 percent crumb rubber by volume of the mineral aggregate following the dry process. The LDPE modified asphalt binder Rheological properties were evaluated. The laboratory results showed an increase in viscosity, softening point and stiffness of the binder. The modified asphalt was then used in preparing asphalt mixtures by Marshall Mix design procedure. The Marshall stability values for mixes containing 2% crumb rubber and 4% LDPE were found to be 30% higher than the conventional asphalt concrete mix.

Keywords: crumb rubber, dry process, hot mix asphalt, wet process

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Authors: Z. N. Ali, O. A. Babatunde, S. Garba, H. M. S. Haruna

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The potency of modified and unmodified activated carbons prepared from shells of Cocos nucifera (coconut shell), straws of Pennisetum glaucum (millet) and Sorghum bicolor (sorghum) for adsorption of hydrogen sulphide gas were investigated using an adsorption apparatus (stainless steel cylinder) at constant temperature (ambient temperature). The adsorption equilibria states were obtained when the pressure indicated on the pressure gauge remained constant. After modification with nitric acid, results of the scanning electron microscopy of the unmodified and modified activated carbons showed that HNO3 greatly improved the formation of micropores and mesopores on the activated carbon surface. The adsorption of H2S gas was found to be highest in modified Cocos nucifera activated carbon with maximum monolayer coverage of 28.17 mg/g, and the adsorption processes were both physical and chemical with the physical process being predominant. The adsorption data were well fitted into the Langmuir isotherm model with the adsorption capacities of the activated carbons in the order modified Cocos nucifera > modified Pennisetum glaucum > modified Sorghum bicolor > unmodified Cocos nucifera > unmodified Pennisetum glaucum > unmodified Sorghum bicolour.

Keywords: activated carbon adsorption, hydrogen sulphide, nitric acid, modification, stainless steel cylinder

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Authors: Abdelati El Allaoui, Said Melliani, Lalla Saadia Chadli

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The objective of this paper is to study the existence and uniqueness of Mild solutions for a complex fuzzy evolution equation with nonlocal conditions that accommodates the notion of fuzzy sets defined by complex-valued membership functions. We first propose definition of complex fuzzy strongly continuous semigroups. We then give existence and uniqueness result relevant to the complex fuzzy evolution equation.

Keywords: Complex fuzzy evolution equations, nonlocal conditions, mild solution, complex fuzzy semigroups

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Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

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The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: collocation method, cubic trigonometric B-spline, finite difference, wave equation

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