Search results for: elliptic equations

Authors: Alemayehu Mengesha, Solomon Belay

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We determine the general dispersion relation for the propagation of magnetohydrodynamic (MHD) waves in an astrophysical plasma by considering the effect of viscosity with an anisotropic pressure tensor. Basic MHD equations have been derived and linearized by the method of perturbation to develop the general form of the dispersion relation equation. Our result indicates that an astrophysical plasma with an anisotropic pressure tensor is stable in the presence of viscosity and a strong magnetic field at considerable wavelength. Currently, we are doing the numerical analysis of this work.

Keywords: astrophysical, magnetic field, instability, MHD, wavelength, viscosity

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Authors: Aliakbar Sayadi, Thomas Neitzert, Charles Clifton

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The hydration process of a green concrete with differences on fly ash and the poly-lactic acid ratio was investigated using electrical resistivity measurement. The results show that the hydration process of proposed concrete was significantly different with concrete containing petroleum aggregate. Moreover, a microstructure analysis corresponding to each hydration stage is conducted with scanning microscope for ploy-lactic acid and expanded polystyrene concrete. In addition, specific equations using the variables of this study were developed to understand and predict the relationship between setting time and resistivity development of proposed concrete containing eco-friendly aggregate.

Keywords: green concrete, SEM, hydration mechanism, eco-friendly aggregate

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Authors: Alexander I. Dovgyallo, Evgeniy A. Zinoviev, Svetlana O. Nekrasova

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The most of works applied for the pulse tube converters contain the workflow description implemented through the use of mathematical models on stationary modes. However, the study of the thermoacoustic systems unsteady behavior in the start, stop, and acoustic load changes modes is in the particular interest. The aim of the present study was to develop a mathematical thermal excitation model of acoustic oscillations in pulse tube engine (PTE) as a small-scale scheme of pulse tube engine operating at atmospheric air. Unlike some previous works this standing wave configuration is a fully closed system. The improvements over previous mathematical models are the following: the model allows specifying any values of porosity for regenerator, takes into account the piston weight and the friction in the cylinder and piston unit, and determines the operating frequency. The numerical method is based on the relation equations between the pressure and volume velocity variables at the ends of each element of PTE which is recorded through the appropriate transformation matrix. A solution demonstrates that the PTE operation frequency is the complex value, and it depends on the piston mass and the dynamic friction due to its movement in the cylinder. On the basis of the determined frequency thermoacoustically induced heat transport and generation of acoustic power equations were solved for channel with temperature gradient on its ends. The results of numerical simulation demonstrate the features of the initialization process of oscillation and show that that generated acoustic power more than power on the steady mode in a factor of 3…4. But doesn`t mean the possibility of its further continuous utilizing due to its existence only in transient mode which lasts only for a 30-40 sec. The experiments were carried out on small-scale PTE. The results shows that the value of acoustic power is in the range of 0.7..1.05 W for the defined frequency range f = 13..18 Hz and pressure amplitudes 11..12 kPa. These experimental data are satisfactorily correlated with the numerical modeling results. The mathematical model can be straightforwardly applied for the thermoacoustic devices with variable temperatures of thermal reservoirs and variable transduction loads which are expected to occur in practical implementations of portable thermoacoustic engines.

Keywords: nonlinear processes, pulse tube engine, thermal excitation, standing wave

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Authors: Zahra Neffah, Henda Kahalerras

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A numerical study is made in a parallel-plate porous channel subjected to an oscillating flow and an exothermic chemical reaction on its walls. The flow field in the porous region is modeled by the Darcy–Brinkman–Forchheimer model and the finite volume method is used to solve the governing equations. The effects of the modified Frank-Kamenetskii (FKm) and Damköhler (Dm) numbers, the amplitude of oscillation (A), and the Strouhal number (St) are examined. The main results show an increase of heat and mass transfer rates with A and St, and their decrease with FKm and Dm.

Keywords: chemical reaction, heat and mass transfer, oscillating flow, porous channel

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Authors: Jagadish Rao Padubidri, Mehak Bhandary, Sowmya J. Rao

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Introduction: The significance of the human foot and its measurements in identifying an individual has been proved a lot of times by different studies in different geographical areas and its association to the stature and gender of the individual has been justified by many researches. In our study we have used different foot measurements including the length, width, malleol height and navicular height for establishing its association to stature and gender and to find out its accuracy. The purpose of this study is to show the relation of foot measurements with stature and gender, and to derive Multiple and Logistic regression equations for stature and gender estimation in South Indian population. Materials and Methods: The subjects for this study were 200 South Indian students out of which 100 were females and 100 were males, aged between 18 to 24 years. The data for the present study included the stature, foot length, foot breath, foot malleol height, foot navicular height of both right and left foot. Descriptive statistics, T-test and Pearson correlation coefficients were derived between stature, gender and foot measurements. The stature was estimated from right and left foot measurements for both male and female South Indian population using multiple regression analysis and logistic regression analysis for gender estimation. Results: The means, standard deviation, stature, right and left foot measurements and T-test in male population were higher than in females. LFL (Left foot length) is more than RFL (Right Foot length) in male groups, but in female groups the length of both foot are almost equal [RFL=226.6, LFL=227.1]. There is not much of difference in means of RFW (Right foot width) and LFW (Left foot width) in both the genders. Significant difference were seen in mean values of malleol and navicular height of right and left feet in male gender. No such difference was seen in female subjects. Conclusions: The study has successfully demonstrated the correlation of foot length in stature estimation in all the three study groups in both right and left foot. Next in parameters are Foot width and malleol height in estimating stature among male and female groups. Navicular height of both right and left foot showed poor relationship with stature estimation in both male and female groups. Multiple regression equations for both right and left foot measurements to estimate stature were derived with standard error ranging from 11-12 cm in males and 10-11 cm in females. The SEE was 5.8 when both male and female groups were pooled together. The logistic regression model which was derived to determine gender showed 85% accuracy and 92.5% accuracy using right and left foot measurements respectively. We believe that stature and gender can be estimated with foot measurements in South Indian population.

Keywords: foot length, gender, stature, South Indian

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Authors: Wesam Jasim, Dongbing Gu

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This paper presents an iterative linear quadratic regulator optimal control technique to solve the problem of quadrotors path tracking. The dynamic motion equations are represented based on unit quaternion representation and include some modelled aerodynamical effects as a nonlinear part. Simulation results prove the ability and effectiveness of iLQR to stabilize the quadrotor and successfully track different paths. It also shows that iLQR controller outperforms LQR controller in terms of fast convergence and tracking errors.

Keywords: iLQR controller, optimal control, path tracking, quadrotor UAVs

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Authors: A. A. Soliman

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The Modified Regularized Long Wave (MRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. The temporal evaluation of a Maxwellian initial pulse is then studied.

Keywords: collocation method, MRLW equation, Quartic B-splines, solitons

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Authors: Duplan Yves Jamont Junior

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The Diamond-Mortensen-Pissarides model widely used in labor economics is tailored to fishery. By this way, a fishing function is defined to depict the fishing technology, and Bellman equations are established to describe the behaviors of fishermen and conservationists. On this basis, a negotiation takes place as a Nash-bargaining over the upper limit of the fishing pressure between both political representative groups of fishermen and conservationists. The existence and uniqueness conditions of the Nash-bargained fishing pressure are established. Given the biomass evolution equation, the dynamics of the model variables (fishing pressure, biomass, fish need) is studied.

Keywords: conservation, fishery, fishing, Nash bargaining

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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: Moosa Mazloom, Morteza Mehrvand

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The goal of this study was to investigate the effects of silica fume and super plasticizer dosages on compressive and torsional properties of SCC. This work concentrated on concrete mixes having water/binder ratios of 0.45 and 0.35, which contained constant total binder contents of 400 kg/m3 and 500 kg/m3, respectively. The percentages of silica fume that replaced cement were 0 % and 10 %. The super plasticizer dosages utilized in the mixtures were 0.4%, 0.8%, 1.2 % and 1.6 % of the weight of cement. Prism dimensions used in this test were 10 × 10 × 40 cm3. The results of this research indicated that torsional strength of SCC prisms can be calculated using the equations presented in Canadian and American concrete building codes.

Keywords: self-compacting concrete, rectangular prism, torsional strength

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Authors: J. A. Gbadeyan, R. A. Kareem

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In this paper, we investigated the effects of unsteady internal heat generation of a two-step exothermic reactive hydromagnetic fluid flow under different chemical kinetics namely: Sensitized, Arrhenius and Bimolecular kinetics through an isothermal wall temperature channel. The resultant modeled nonlinear partial differential equations were simplified and solved using a combined Laplace-Differential Transform Method (LDTM). The solutions obtained were discussed and presented graphically to show the salient features of the fluid flow and heat transfer characteristics.

Keywords: unsteady, reactive, hydromagnetic, couette ow, exothermi creactio

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Authors: Kwok W. Cheung

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A scientific interpretation of creation reconciling the beliefs of six literal days of creation and a 13.7-billion-year-old universe currently perceived by most modern cosmologists is proposed. We hypothesize that the reference timeframe of God’s creation is associated with some cosmic time different from the earth's time. We show that the scale factor of earth time to cosmic time can be determined by the solution of the Friedmann equations. Based on this scale factor and some basic assumptions, we derive a Cosmic Time Dilation model that harmonizes the literal meaning of creation days and scientific discoveries with remarkable accuracy.

Keywords: cosmological expansion, time dilation, creation, genesis, relativity, Big Bang, biblical hermeneutics

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Authors: Soheil Arash Moghadam, Abdol R. Kashani Nia, Ali Akrami Zade

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Considering numerous applications of Autonomous Underwater Vehicles in various industries, there has been plenty of researches and studies on the motion control of such vehicles. One of the useful aspects for studying is the guidance of these vehicles. In this paper, while presenting motion equations with six degrees of freedom for Autonomous Underwater Vehicles, Proportional Navigation Guidance Law and the first order sliding mode control for TAIPAN AUV was used to address its guidance for the purpose of collision with a moving target.

Keywords: Autonomous Underwater Vehicle (AUV), degree of freedom (DOF), hydrodynamic, line of sight(LOS), proportional navigation guidance(PNG), sliding mode control(SMC)

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Authors: Mohammedi Ferhate

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This paper deals with the generalized the notion of the function of wave a micro particle moving free, the concept of the linear operator in the representation function delta of Dirac which is a generalization of the symbol of Kronecker to the case of a continuous variation of the sizes concerned with the condition of orthonormation of the Eigen functions the use of linear operators and their Eigen functions in connection with the solution of given differential equations, it is of interest to study the properties of the operators themselves and determine which of them follow purely from the nature of the operators, without reference to specific forms of Eigen functions. The models simulation examples are also presented.

Keywords: function, operator, simulation, wave

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Authors: Aneri Mehta, Krunal Mehta

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The unpredictable and vacillating relationship between India and Pakistan since days of Independence struggle is known world over. And this instability has never lost its magnitude to decrease the tensions between the two countries. Since India aspires to run for the race of future superpower and Pakistan struggles to remove the tag of a highly fickle and under developed economy; ruined largely not by the outsiders, but its own people and systems; it becomes really important to gauge what steps would these neighbors take in years to come. The progress and stability of both countries heavily relies on the favorable equations between the two nations. Therefore the paper tries to trace some roots of their faltering relationship and attempts to predict their future in a multidimensional perspective.

Keywords: economy, faltering relationship, multidimensional perspective, international relations

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Authors: S. B. Provost, Hossein Zareamoghaddam

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A univariate density approximation technique whereby the derivative of the logarithm of a density function is assumed to be expressible as a rational function is introduced. This approach which extends Pearson’s curve system is solely based on the moments of a distribution up to a determinable order. Upon solving a system of linear equations, the coefficients of the polynomial ratio can readily be identified. An explicit solution to the integral representation of the resulting density approximant is then obtained. It will be explained that when utilised in conjunction with sample moments, this methodology lends itself to the modelling of ‘big data’. Applications to sets of univariate and bivariate observations will be presented.

Keywords: density estimation, log-density, moments, Pearson's curve system

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Authors: M. Ndaw, G. Mendy, S. Ouya

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Risk management in banking sector is a key issue linked to financial system stability and its importance has been elevated by technological developments and emergence of new financial instruments. In this paper, we improve the model previously defined for quantifying internal control impact on banking risks by automatizing the residual criticality estimation step of FMECA. For this, we defined three equations and a maturity coefficient to obtain a mathematical model which is tested on all banking processes and type of risks. The new model allows an optimal assessment of residual criticality and improves the correlation rate that has become 98%.

Keywords: risk, control, banking, FMECA, criticality

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Authors: Liliana O. Martínez, Juan E. González, Manuel Ramírez-Aranda, Ana Cervantes-Herrera

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In this work, the use of a collection of mathematical challenges and puzzles aimed at students who are starting in algebra is proposed. The selected challenges and puzzles are intended to arouse students' interest in this area of mathematics, in addition to facilitating the teaching-learning process through challenges such as riddles, crossword puzzles, and board games, all in everyday situations that allow them to build themselves the learning. For this, it is proposed to carry out a "Math Rally: algebra" divided into four sections: mathematical reasoning, a hierarchy of operations, fractions, and algebraic equations.

Keywords: algebra, algebraic challenge, algebraic puzzle, math rally

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Authors: Johnson Oladele Fatokun, I. P. Akpan

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In this paper, the one-dimensional time dependent Schrödinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff ordinary differential equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10-4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable.

Keywords: Schrodinger’s equation, partial differential equations, method of lines (MOL), stiff ODE, trapezoidal-like integrator

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Authors: M. Ndaw, G. Mendy, S. Ouya

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Information system risk management helps to reduce or eliminate risk by implementing appropriate controls. In this paper, we propose a quantification model of controls impact on information system risks by automatizing the residual criticality estimation step of FMECA which is based on a inductive reasoning. For this, we defined three equations based on type and maturity of controls. For testing, the values obtained with the model were compared to estimated values given by interlocutors during different working sessions and the result is satisfactory. This model allows an optimal assessment of controls maturity and facilitates risk analysis of information system.

Keywords: information system, risk, control, FMECA method

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Authors: Derrouazin Mohammed Redhouane, Souakri Mohammed Lotfi, Henini Ghania

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This work consists, first of all, of mastering one of the powerful process simulation tools currently used in the industrial processes, which is the HYSYS sizing software, and second, of simulating a petroleum distillation column. This study is divided into two parts; where the first one consists of a dimensioning of the column with a fast approximating method using state equations, iterative calculations, and then a precise simulation method with the HYSYS software. The second part of this study is a hydrodynamic study in order to verify by obtained results the proper functioning of the plates.

Keywords: industry process engineering, water distillation, environment, HYSYS simulation tool

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Authors: R. S. Hassani, S. Chikh, L. Tadrist, S. Radev

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A bubbly flow in a vertical miniature tube is analyzed theoretically. The liquid and gas phase are co-current flowing upward. The gas phase is injected via a nozzle whose inner diameter is 0.11mm and it is placed on the axis of the tube. A force balance is applied on the bubble at its detachment. The set of governing equations are solved by use of Mathematica software. The bubble diameter and the bubble generation frequency are determined for various inlet phase velocities represented by the inlet mass quality. The results show different behavior of bubble growth and detachment depending on the tube size.

Keywords: two phase flow, bubble growth, mini-channel, generation frequency

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Authors: Rahele Mosleh

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This paper gives a survey of results on global stability of extended Ross model for malaria by constructing some elegant Lyapunov functions for two cases of epidemic, including disease-free and endemic occasions. The model is a nonlinear seven-dimensional system of ordinary differential equations that simulates this phenomenon in a more realistic fashion. We discuss the existence of positive disease-free and endemic equilibrium points of the model. It is stated that extended Ross model possesses invariant solutions for human and mosquito in a specific domain of the system.

Keywords: global stability, invariant solutions, Lyapunov function, stationary points

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Authors: Sammani Danwawu Abdullahi

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Vertex Enumeration Algorithms explore the methods and procedures of generating the vertices of general polyhedra formed by system of equations or inequalities. These problems of enumerating the extreme points (vertices) of general polyhedra are shown to be NP-Hard. This lead to exploring how to count the vertices of general polyhedra without listing them. This is also shown to be #P-Complete. Some fully polynomial randomized approximation schemes (fpras) of counting the vertices of some special classes of polyhedra associated with Down-Sets, Independent Sets, 2-Knapsack problems and 2 x n transportation problems are presented together with some discovered open problems.

Keywords: counting with uncertainties, mathematical programming, optimization, vertex enumeration

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Authors: M. Y. Malik, Farzana Khan

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In this article, we discuss the behavior of viscous fluid near stagnation point over a stretching cylinder with variable thermal conductivity. The effects of slip conditions are also encountered. Thermal conductivity is considered as a linear function of temperature. By using homotopy analysis method and Fehlberg method we compare the graphical results for both momentum and energy equations. The effect of different parameters on velocity and temperature fields are shown graphically.

Keywords: slip conditions, stretching cylinder, heat generation/absorption, stagnation point flow, variable thermal conductivity

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Authors: Natasha Sharma, Kulbhushan Agnihotri

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Cellular Automata are discrete dynamical systems which are based on local character and spatial disparateness of the spreading process. These factors are generally neglected by traditional models based on differential equations for epidemic spread. The aim of this work is to introduce an SEIR model based on cellular automata on graphs to imitate epidemic spreading. Distinctively, it is an SEIR-type model where the population is divided into susceptible, exposed, infected and recovered individuals. The results obtained from simulations are in accordance with the spreading behavior of a real time epidemics.

Keywords: cellular automata, epidemic spread, graph, susceptible

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Authors: Lele Zhang, Hui Leng Choo, Alexander Konyukhov, Shuguang Li

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Finite Element (FE) model of simplified e-bike structure was generated by main frame with two tiers, which consisted of pipe, mass, beam, and shell elements (pipe 289, beam188, shell 181, shell 281, combin14, link11, mass21). These elements would be introduced and demonstrated using mathematical formulas. Based on coupling theory, constrain equations was proposed. Exporting all the parameters obtained from theory part, the connection stiffness matrix of the whole e-bike structure between each of these elements was detected.

Keywords: coupling theory, stiffness matrix, e-bike, finite element model

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Authors: T. G. Kassem, A. K. Adunchezor, J. P. Chollom

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This paper describes a mathematical model developed to predict the dynamics of Hepatitis B virus (HBV) infection and to evaluate the potential impact of vaccination and treatment on its dynamics. We used a compartmental model expressed by a set of differential equations based on the characteristic of HBV transmission. With these, we find the threshold quantity R0, then find the local asymptotic stability of disease free equilibrium and endemic equilibrium. Furthermore, we find the global stability of the disease free and endemic equilibrium.

Keywords: hepatitis B virus, epidemiology, vaccination, mathematical model

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Authors: Y. Pala, M. O. Ertas

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In this paper, the general Riccati equation is analytically solved by a new transformation. By the method developed, looking at the transformed equation, whether or not an explicit solution can be obtained is readily determined. Since the present method does not require a proper solution for the general solution, it is especially suitable for equations whose proper solutions cannot be seen at first glance. Since the transformed second order linear equation obtained by the present transformation has the simplest form that it can have, it is immediately seen whether or not the original equation can be solved analytically. The present method is exemplified by several examples.

Keywords: Riccati equation, analytical solution, proper solution, nonlinear

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Authors: William Kelly, Sorelle Veigne, Xianhua Li, Zuyi Huang, Shyamsundar Subramanian, Eugene Schaefer

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The ambr15™ bioreactor is a single-use microbioreactor for cell line development and process optimization. The ambr system offers fully automatic liquid handling with the possibility of fed-batch operation and automatic control of pH and oxygen delivery. With operating conditions for large scale biopharmaceutical production properly scaled down, micro bioreactors such as the ambr15™ can potentially be used to predict the effect of process changes such as modified media or different cell lines. In this study, gassing rates and dilution rates were varied for a semi-continuous cell culture system in the ambr15™ bioreactor. The corresponding changes to metabolite production and consumption, as well as cell growth rate and therapeutic protein production were measured. Conditions were identified in the ambr15™ bioreactor that produced metabolic shifts and specific metabolic and protein production rates also seen in the corresponding larger (5 liter) scale perfusion process. A Dynamic Flux Balance model was employed to understand and predict the metabolic changes observed. The DFB model-predicted trends observed experimentally, including lower specific glucose consumption when CO₂ was maintained at higher levels (i.e. 100 mm Hg) in the broth. A Computational Fluid Dynamic (CFD) model of the ambr15™ was also developed, to understand transfer of O₂ and CO₂ to the liquid. This CFD model predicted gas-liquid flow in the bioreactor using the ANSYS software. The two-phase flow equations were solved via an Eulerian method, with population balance equations tracking the size of the gas bubbles resulting from breakage and coalescence. Reasonable results were obtained in that the Carbon Dioxide mass transfer coefficient (kLa) and the air hold up increased with higher gas flow rate. Volume-averaged kLa values at 500 RPM increased as the gas flow rate was doubled and matched experimentally determined values. These results form a solid basis for optimizing the ambr15™, using both CFD and FBA modelling approaches together, for use in microscale simulations of larger scale cell culture processes.

Keywords: cell culture, computational fluid dynamics, dynamic flux balance analysis, microbioreactor

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