Search results for: nonlinear ordinary differential equations

Authors: Mohammadreza Akbari, Leila Abdollahpour, Sara Akbari, Pooya Soleimani

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Transferring thermo at the field of solid materials for instance tube-shaped structures, causing dynamical vibration at them. Majority of thermal and fluid processes are done engineering science at solid materials, for example, thermo-transferred pipes, fluids, chemical and nuclear reactors, include thermal processes, so, they need to consider the moment solid-fundamental structural strength unto these thermal interactions. Fluid and thermo retentive materials in front of external force to it like thermodynamical force, hydrodynamical force and static force continuously according to a function of time vibrated, and this action causes relative displacement of the structural materials elements, as a result, the moment resistance analysis preservation materials in thermal processes, the most important parameters for design are discussed. Including structural substrate holder temperature and fluid of the administrative and industrial center, is a cylindrical tube that for vibration analysis of cylindrical cells with heat and fluid transfer requires the use of vibration differential equations governing the structure of a tubular and thermal differential equations as the vibrating motive force at double-glazed cylinders.

Keywords: heat transfer, elements in cylindrical coordinates, analytical solving the governing equations, structural vibration

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Authors: P. Selyshchev

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Construction materials for nuclear facilities are operated under extreme thermal and radiation conditions. First of all, they are nuclear fuel, fuel assemblies, and reactor vessel. It places high demands on the control of their state, stability of their state, and their operating conditions. An irradiated material is a typical example of an open non-equilibrium system with nonlinear feedbacks between its elements. Fluxes of energy, matter and entropy maintain states which are far away from thermal equilibrium. The links that arise under irradiation are inherently nonlinear. They form the mechanisms of feed-backs that can lead to instability. Due to this instability the temperature of the sample, heat transfer, and the defect density can exceed the steady-state value in several times. This can lead to change of typical operation and an accident. Therefore, it is necessary to take into account the thermal instability to avoid the emergency situation. The point is that non-thermal energy can be accumulated in materials because irradiation produces defects (first of all these are vacancies and interstitial atoms), which are metastable. The stored energy is about energy of defect formation. Thus, an annealing of the defects is accompanied by releasing of non-thermal stored energy into thermal one. Temperature of the material grows. Increase of temperature results in acceleration of defect annealing. Density of the defects drops and temperature grows more and more quickly. The positive feed-back is formed and self-reinforcing annealing of radiation defects develops. To describe these phenomena a theoretical approach to thermal instability is developed via formalism of complex systems. We consider system of nonlinear differential equations for different components of microstructure and temperature. The qualitative analysis of this non-linear dynamical system is carried out. Conditions for development of instability have been obtained. Points of bifurcation have been found. Convenient way to represent obtained results is a set of phase portraits. It has been shown that different regimes of material state under irradiation can develop. Thus degradation of irradiated material can be limited by means of choice appropriate kind of evolution of materials under irradiation.

Keywords: irradiation, material, non-equilibrium state, nonlinear feed-back, thermal instability

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Authors: Anthony R. Hassan, Jacob A. Gbadeyan

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In this paper, the analysis of a reactive hydromagnetic Poiseuille fluid flow under each of sensitized, Arrhenius and bimolecular chemical kinetics through a channel in the presence of heat source is carried out. An exothermic reaction is assumed while the concentration of the material is neglected. Adomian Decomposition Method (ADM) together with Pade Approximation is used to obtain the solutions of the governing nonlinear non – dimensional differential equations. Effects of various physical parameters on the velocity and temperature fields of the fluid flow are investigated. The entropy generation analysis and the conditions for thermal criticality are also presented.

Keywords: chemical kinetics, entropy generation, thermal criticality, adomian decomposition method (ADM) and pade approximation

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Authors: Salihah Alghamdi, Surajit Ray

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Space-time data can be observed over irregularly shaped manifolds, which might have complex boundaries or interior gaps. Most of the existing methods do not consider the shape of the data, and as a result, it is difficult to model irregularly shaped data accommodating the complex domain. We used a method that can deal with space-time data that are distributed over non-planner shaped regions. The method is based on partial differential equations and finite element analysis. The model can be estimated using a penalized least squares approach with a regularization term that controls the over-fitting. The model is regularized using two roughness penalties, which consider the spatial and temporal regularities separately. The integrated square of the second derivative of the basis function is used as temporal penalty. While the spatial penalty consists of the integrated square of Laplace operator, which is integrated exclusively over the domain of interest that is determined using finite element technique. In this paper, we applied a spatio-temporal regression model with partial differential equations regularization (ST-PDE) approach to analyze a remote sensing data measuring the greenness of vegetation, measure by an index called enhanced vegetation index (EVI). The EVI data consist of measurements that take values between -1 and 1 reflecting the level of greenness of some region over a period of time. We applied (ST-PDE) approach to irregular shaped region of the EVI data. The approach efficiently accommodates the irregular shaped regions taking into account the complex boundaries rather than smoothing across the boundaries. Furthermore, the approach succeeds in capturing the temporal variation in the data.

Keywords: irregularly shaped domain, partial differential equations, finite element analysis, complex boundray

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Authors: Ahmed Elsayed Ahmed, Ashraf Hafez, A. N. Ouda, Hossam Eldin Hussein Ahmed, Hala Mohamed ABD-Elkader

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Unmanned Aircraft Systems (UAS) are playing increasingly prominent roles in defense programs and defense strategies around the world. Technology advancements have enabled the development of it to do many excellent jobs as reconnaissance, surveillance, battle fighters, and communications relays. Simulating a small unmanned aerial vehicle (SUAV) dynamics and analyzing its behavior at the preflight stage is too important and more efficient. The first step in the UAV design is the mathematical modeling of the nonlinear equations of motion. In this paper, a survey with a standard method to obtain the full non-linear equations of motion is utilized,and then the linearization of the equations according to a steady state flight condition (trimming) is derived. This modeling technique is applied to an Ultrastick-25e fixed wing UAV to obtain the valued linear longitudinal and lateral models. At the end, the model is checked by matching between the behavior of the states of the non-linear UAV and the resulted linear model with doublet at the control surfaces.

Keywords: UAV, equations of motion, modeling, linearization

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Authors: Rasaq Kareem, Jacob Gbadeyan

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In this study, analysis of the entropy generation of an unsteady reactive hydromagnetic generalized couette fluid flow of a two-step exothermic chemical reaction through a channel with isothermal wall temperature under the influence of different chemical kinetics namely: Sensitized, Arrhenius and Bimolecular kinetics was investigated. The modelled nonlinear dimensionless equations governing the fluid flow were simplified and solved using the combined Laplace Differential Transform Method (LDTM). The effects of fluid parameters associated with the problem on the fluid temperature, entropy generation rate and Bejan number were discussed and presented through graphs.

Keywords: couette, entropy, exothermic, unsteady

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Authors: Bououden Soraya

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This paper aims to study the existence of the change of coordinates which permits to transform a class of nonlinear dynamical systems into the so-called nonlinear observer canonical form (NOCF). Moreover, an algorithm to construct such a change of coordinates is given. Based on this form, we can design an observer with a linear error dynamic. This enables us to estimate the state of a nonlinear dynamical system. A concrete example (biological model) is provided to illustrate the feasibility of the proposed results.

Keywords: nonlinear observer canonical form, observer, design, gene regulation, gene expression

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Authors: D. S. Palimkar

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The FRIGDI (functional random integrodifferential inclusion) seems to be new and includes several known random differential inclusions already studied in the literature as special cases have been discussed in the literature for various aspects of the solutions. In this paper, we prove the existence result for FIGDI under the non-convex case of multi-valued function involved in it.Using random fixed point theorem of B. C. Dhage and caratheodory condition. This result is new to the theory of differential inclusion.

Keywords: caratheodory condition, random differential inclusion, random solution, integro-differential inclusion

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Authors: Hanan Rizk

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A heat exchanger is a device used to mix liquids having different temperatures. In this case, the temperature control becomes a critical objective. This research work presents the temperature control of the double-pipe heat exchanger (multi-input multi-output (MIMO) system), which is modeled as first-order coupled hyperbolic partial differential equations (PDEs), using conventional and advanced control techniques and develops appropriate robust control strategy to meet stability requirements and performance objectives. We designed a PID controller and H-infinity controller for a heat exchanger (HE) system. Frequency characteristics of sensitivity functions and open-loop and closed-loop time responses are simulated using MATLAB software, and the stability of the system is analyzed using Kalman's test. The simulation results have demonstrated that the H-infinity controller is more efficient than PID in terms of robustness and performance.

Keywords: heat exchanger, multi-input multi-output system, MATLAB simulation, partial differential equations, PID controller, robust control

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Authors: Esther Cabezas-Rivas

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Ordinary differential equations (ODE) are a fundamental part of the curriculum for most engineering degrees, and students typically have difficulties in the subsequent abstract mathematical calculations. To enhance their motivation and profit that they are digital natives, we propose a teamwork project that includes the creation of a video. It should explain how to model mathematically a real-world problem transforming it into an ODE, which should then be solved using the tools learned in the lectures. This idea was indeed implemented with first-year students of a BSc in Engineering and Management during the period of online learning caused by the outbreak of COVID-19 in Spain. Each group of 4 students was assigned a different topic: model a hot water heater, search for the shortest path, design the quickest route for delivery, cooling a computer chip, the shape of the hanging cables of the Golden Gate, detecting land mines, rocket trajectories, etc. These topics should be worked out through two complementary channels: a written report describing the problem and a 10-15 min video on the subject. The report includes the following items: description of the problem to be modeled, detailed obtention of the ODE that models the problem, its complete solution, and interpretation in the context of the original problem. We report the outcomes of this teaching in context and active learning experience, including the feedback received by the students. They highlighted the encouragement of creativity and originality, which are skills that they do not typically relate to mathematics. Additionally, the video format (unlike a common presentation) has the advantage of allowing them to critically review and self-assess the recording, repeating some parts until the result is satisfactory. As a side effect, they felt more confident about their oral abilities. In short, students agreed that they had fun preparing the video. They recognized that it was tricky to combine deep mathematical contents with entertainment since, without the latter, it is impossible to engage people to view the video till the end. Despite this difficulty, after the activity, they claimed to understand better the material, and they enjoyed showing the videos to family and friends during and after the project.

Keywords: active learning, contextual teaching, models in differential equations, student-produced videos

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Authors: Noufe H. Aljahdaly

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The Laplace homotopy perturbation method (LHPM) is an approximate method that help to compute the approximate solution for partial differential equations. The method has been used for solving several problems in science. It requires the initial condition, so it solves the initial value problem. In physics, when some important terms are taken in account, we may obtain non-integrable partial differential equations that do not have analytical integrals. This type of PDEs do not have exact solution, therefore, we need to compute the solution without initial condition. In this work, we improved the LHPM to be able to solve non-integrable problem, especially the damped PDEs, which are the PDEs that include a damping term which makes the PDEs non-integrable. We improved the LHPM by setting a perturbation parameter and an embedding parameter as the damping parameter and using the initial condition for damped PDE as the initial condition for non-damped PDE.

Keywords: non-integrable PDEs, modified Kawahara equation;, laplace homotopy perturbation method, damping term

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Authors: Ahmed Machmoum, Malika El Kyal

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We consider iterative parallel multi-splitting method for differential algebraic equations. The main feature of the proposed idea is to use the asynchronous form. We prove that the multi-splitting technique can effectively accelerate the convergent performance of the iterative process. The main characteristic of an asynchronous mode is that the local algorithm not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays tobe substantial and unpredictable. Note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: computer, multi-splitting methods, asynchronous mode, differential algebraic systems

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Authors: Muath Awadalla, Maen Awadallah

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Banking sector covers different activities including lending money to customers. However, it is commonly known that customers pay money they have borrowed including an added amount called interest. Compound interest rate is an approach used in determining the interest to be paid. The instant compounded amount to be paid by a debtor is obtained through a differential equation whose main parameters are the rate and the time. The rate used by banks in a country is often defined by the government of the said country. In Switzerland, for instance, a negative rate was once applied. In this work, a new approach of modeling the compound interest is proposed using Hadamard fractional derivative. As a result, it appears that depending on the fraction value used in derivative the amount to be paid by a debtor might either be higher or lesser than the amount determined using the classical approach.

Keywords: compound interest, fractional differential equation, hadamard fractional derivative, optimization

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Authors: Hamed Djalal

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The thermal analysis of the mechanical draft wet cooling tower is performed in this study by the heat and mass transfer modelization in the packing zone. After combining the heat and mass transfer laws, the mass and energy balances and by involving the Merkel assumptions; firstly, an ordinary differential equations system is derived and solved numerically by the Runge-Kutta method to determine the water and air temperatures, the humidity, and also other properties variation along the packing zone. Secondly, by making some linear assumptions for the air saturation curve, an analytical solution is formed, which is developed for the air washer calculation, but in this study, it is applied for the cooling tower to express also the previous parameters mathematically as a function of the packing height. Finally, a good agreement with experimental data is achieved by both solutions, but the numerical one seems to be the more accurate for modeling the heat and mass transfer process in the wet cooling tower.

Keywords: evaporative cooling, cooling tower, air washer, humidification, moist air, heat, and mass transfer

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Authors: Shangerganesh Lingeshwaran

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In this presentation, we have performed numerical simulations for a reaction-diffusion equation with various nonlinear density-dependent diffusion operators and proliferation functions. The mathematical model represented by parabolic partial differential equation is considered to study the invasion of gliomas (the most common type of brain tumors) and to describe the growth of cancer cells and response to their treatment. The unknown quantity of the given reaction-diffusion equation is the density of cancer cells and the mathematical model based on the proliferation and migration of glioma cells. A standard Galerkin finite element method is used to perform the numerical simulations of the given model. Finally, important observations on the each of nonlinear diffusion functions and proliferation functions are presented with the help of computational results.

Keywords: glioma invasion, nonlinear diffusion, reaction-diffusion, finite eleament method

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Authors: Chi Zhang, Jun Jiang

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Constitutive equations are very important in finite element (FE) modeling, and the accuracy of the material constants in the equations have significant effects on the accuracy of the FE models. A wide range of constitutive equations are available; however, fitting the material constants in the constitutive equations could be complex and time-consuming due to the strong non-linearity and relationship between the constants. This work will focus on the development of a set of unified MATLAB programs for fitting the material constants in the constitutive equations efficiently. Users will only need to supply experimental data in the required format and run the program without modifying functions or precisely guessing the initial values, or finding the parameters in previous works and will be able to fit the material constants efficiently.

Keywords: constitutive equations, FE modelling, MATLAB program, non-linear curve fitting

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Authors: Nazish Iftikhar, Adil Jhangeer, Tayyaba Naz

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The universe is expanding at an accelerated rate. Symmetries are useful in understanding universe’s behavior. Emmy Noether reported the relation between symmetries and conservation laws. These symmetries are known as Noether symmetries which correspond to a conserved quantity. In differential equations, conservation laws play an important role. Noether symmetries are helpful in modified theories of gravity. Time independent plane symmetric spacetime was classified by Noether`s theorem. By using Noether`s theorem, set of linear partial differential equations was obtained having A(r), B(r) and F(r) as unknown radial functions. The Lagrangian corresponding to considered spacetime in the Noether equation was used to get Noether operators. Different possibilities of radial functions were considered. Firstly, all functions were same. All the functions were considered as non-zero constant, linear, reciprocal and exponential respectively. Secondly, two functions were proportional to each other keeping third function different. Second case has four subcases in which four different relationships between A(r), B(r) and F(r) were discussed. In all cases, we obtained nontrivial Noether operators including gauge term. Conserved quantities for each Noether operators were also presented.

Keywords: Noether gauge symmetries, radial function, Noether operator, conserved quantities

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Authors: Babak Safaei, Ahmad Ghanbari, Arash Rahmani

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In the present study, the free vibration characteristics of double-walled carbon nanotubes (DWCNTs) are investigated. The small-scale effects are taken into account using the Eringen’s nonlocal elasticity theory. The nonlocal elasticity equations are implemented into the different classical beam theories namely as Euler-Bernoulli beam theory (EBT), Timoshenko beam theory (TBT), Reddy beam theory (RBT), and Levinson beam theory (LBT) to analyze the free vibrations of DWCNTs in which each wall of the nanotubes is considered as individual beam with van der Waals interaction forces. Generalized differential quadrature (GDQ) method is utilized to discretize the governing differential equations of each nonlocal beam model along with four commonly used boundary conditions. Then molecular dynamics (MD) simulation is performed for a series of armchair and zigzag DWCNTs with different aspect ratios and boundary conditions, the results of which are matched with those of nonlocal beam models to extract the appropriate values of the nonlocal parameter corresponding to each type of chirality, nonlocal beam model and boundary condition. It is found that the present nonlocal beam models with their proposed correct values of nonlocal parameter have good capability to predict the vibrational behavior of DWCNTs, especially for higher aspect ratios.

Keywords: double-walled carbon nanotubes, nonlocal continuum elasticity, free vibrations, molecular dynamics simulation, generalized differential quadrature method

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Authors: Abdullah Eqal Al Mazrooei

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Kalman filter is a famous algorithm that utilizes to estimate the state in the linear systems. It has numerous applications in technology and science. Since of the most of applications in real life can be described by nonlinear systems. So, Kalman filter does not work with the nonlinear systems because it is suitable to linear systems only. In this work, a nonlinear filtering algorithm is presented which is suitable to use with the special kinds of nonlinear systems. This filter generalizes the Kalman filter. This means that this filter also can be used for the linear systems. Our algorithm depends on a special linearization of the second degree. We introduced the nonlinear algorithm with a bilinear state-space model. A simulation example is presented to illustrate the efficiency of the algorithm.

Keywords: Kalman filter, filtering algorithm, nonlinear systems, state-space model

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Authors: Evln Ranga Charyulu, S. P. Venu Madhavarao, S. Udaya kumar, S. V. S. S. N. V. G. Krishna Murthy

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With the advent of new nanometer process technologies, it is possible to integrate billion transistors on a single substrate. When more and more functionality included there is the possibility of multi-million transistors switching simultaneously consuming more power and dissipating more power along with more leakage of current into the substrate of porous silicon or germanium material. These results in substrate heating and thermal noise generation coupled to signals of interest. The heating process is represented by coupled nonlinear partial differential equations in porous silicon and germanium. By identifying heat sources and heat fluxes may results in designing of ultra-low power circuits. The PDEs are solved by finite difference scheme assuming that boundary layer equations in porous silicon and germanium. Local heat fluxes along the vertical isothermal surface immersed in porous SI/Ge are considered. The parameters considered for optimization are thermal diffusivity, thermal expansion coefficient, thermal diffusion ratio, permeability, specific heat at constant temperatures, Rayleigh number, amplitude of wavy surface, mass expansion coefficient. The diffusion of heat was caused by the concentration gradient. Thermal physical properties are homogeneous and isotropic. By using L8, TAGUCHI method the parameters are optimized.

Keywords: heat transfer, pde, taguchi optimization, SI/Ge

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Authors: Ana M. Korol, Bibiana Riquelme, Osvaldo A. Rosso

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Since erythrocyte deformability analysis is mostly qualitative, the development of quantitative nonlinear methods is crucial for restricting subjectivity in the study of cell behaviour. An electro-optic mechanic system called erythrodeformeter has been developed and constructed in our laboratory in order to evaluate the erythrocytes' viscoelasticity. A numerical method formulated on the basis of fractal approximation for ordinary (OBM) and fractionary Brownian motion (FBM), as well as wavelet transform analysis, are proposed to distinguish chaos from noise based on the assumption that diffractometric data involves both deterministic and stochastic components, so it could be modelled as a system of bounded correlated random walk. Here we report studies on 25 donors: 4 alpha thalassaemic patients, 11 beta thalassaemic patients, and 10 healthy controls non-alcoholic and non-smoker individuals. The Correlation Coefficient, a nonlinear parameter, showed evidence of the changes in the erythrocyte deformability; the Wavelet Entropy could quantify those differences which are detected by the light diffraction patterns. Such quantifiers allow a good deal of promise and the possibility of a better understanding of the rheological erythrocytes aspects and also could help in clinical diagnosis.

Keywords: red blood cells, deformability, nonlinear dynamics, chaos theory, wavelet trannsform

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Authors: Humayun R. H. Kabir

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An analytical solution before used for static and free-vibration response has been extended for thermal buckling response on cylindrical panel with anti-symmetric laminations. The partial differential equations that govern kinematic behavior of shells produce five coupled differential equations. The basic displacement and rotational unknowns are similar to first order shear deformation theory---three displacement in spatial space, and two rotations about in-plane axes. No drilling degree of freedom is considered. Boundary conditions are considered as complete hinge in all edges so that the panel respond on thermal inductions. Two sets of double Fourier series are considered in the analytical solution process. The sets are selected that satisfy mixed type of natural boundary conditions. Numerical results are presented for the first 10 eigenvalues, and first 10 mode shapes for Ux, Uy, and Uz components. The numerical results are compared with a finite element based solution.

Keywords: higher order shear deformation, composite, thermal buckling, angle-ply laminations

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Authors: Alireza Lohrasbi, Alireza Lavaei, Mohammadali M. Shahlaei

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The liquid flow and the free surface shape during the initial stage of dam breaking are investigated. A numerical scheme is developed to predict the wave of an unsteady, incompressible viscous flow with free surface. The method involves a two dimensional finite element (2D), in a vertical plan. The Naiver-Stokes equations for conservation of momentum and mass for Newtonian fluids, continuity equation, and full nonlinear kinematic free-surface equation were used as the governing equations. The mapping developed to solve highly deformed free surface problems common in waves formed during wave propagation, transforms the run up model from the physical domain to a computational domain with Arbitrary Lagrangian Eulerian (ALE) finite element modeling technique.

Keywords: dam break, Naiver-Stokes equations, free-surface flows, Arbitrary Lagrangian-Eulerian

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Authors: M. G. Murtaza, E. E. Tzirtzilakis, M. Ferdows

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Biomagnetic fluid dynamics is an interdisciplinary field comprising engineering, medicine, and biology. Bio fluid dynamics is directed towards finding and developing the solutions to some of the human body related diseases and disorders. This article describes the flow and heat transfer of two dimensional, steady, laminar, viscous and incompressible biomagnetic fluid over a non-linear stretching sheet in the presence of magnetic dipole. Our model is consistent with blood fluid namely biomagnetic fluid dynamics (BFD). This model based on the principles of ferrohydrodynamic (FHD). The temperature at the stretching surface is assumed to follow a power law variation, and stretching velocity is assumed to have a nonlinear form with signum function or sign function. The governing boundary layer equations with boundary conditions are simplified to couple higher order equations using usual transformations. Numerical solutions for the governing momentum and energy equations are obtained by efficient numerical techniques based on the common finite difference method with central differencing, on a tridiagonal matrix manipulation and on an iterative procedure. Computations are performed for a wide range of the governing parameters such as magnetic field parameter, power law exponent temperature parameter, and other involved parameters and the effect of these parameters on the velocity and temperature field is presented. It is observed that for different values of the magnetic parameter, the velocity distribution decreases while temperature distribution increases. Besides, the finite difference solutions results for skin-friction coefficient and rate of heat transfer are discussed. This study will have an important bearing on a high targeting efficiency, a high magnetic field is required in the targeted body compartment.

Keywords: biomagnetic fluid, FHD, MHD, nonlinear stretching sheet

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Authors: Teh Raihana Nazirah Roslan, Siti Zulaiha Ibrahim, Sharmila Karim

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A warrant is a financial contract that confers the right but not the obligation, to buy or sell a security at a certain price before expiration. The standard procedure to value equity warrants using call option pricing models such as the Black–Scholes model had been proven to contain many flaws, such as the assumption of constant interest rate and constant volatility. In fact, existing alternative models were found focusing more on demonstrating techniques for pricing, rather than empirical testing. Therefore, a mathematical model for pricing and analyzing equity warrants which comprises stochastic interest rate and stochastic volatility is essential to incorporate the dynamic relationships between the identified variables and illustrate the real market. Here, the aim is to develop dynamic pricing formulations for hybrid equity warrants by incorporating stochastic interest rates from the Cox-Ingersoll-Ross (CIR) model, along with stochastic volatility from the Heston model. The development of the model involves the derivations of stochastic differential equations that govern the model dynamics. The resulting equations which involve Cauchy problem and heat equations are then solved using partial differential equation approaches. The analytical pricing formulas obtained in this study comply with the form of analytical expressions embedded in the Black-Scholes model and other existing pricing models for equity warrants. This facilitates the practicality of this proposed formula for comparison purposes and further empirical study.

Keywords: Cox-Ingersoll-Ross model, equity warrants, Heston model, hybrid models, stochastic

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Authors: Charlene N. T. Mfangnia, Henri E. Z. Tonnang, Berge Tsanou, Jeremy Herren

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Microsporidia MB is a recently discovered symbiont capable of blocking the transmission of Plasmodium from mosquitoes to humans. The symbiont can spread both horizontally and vertically among the mosquito population. This dual transmission gives the symbiont the ability to invade the mosquito population. The replacement of the mosquito population by the population of symbiont-infected mosquitoes then appears as a promising strategy for malaria control. In this context, the present study uses differential equations to model the transmission dynamics of Microsporidia MB in the population of female Anopheles mosquitoes. Long-term propagation scenarios of the symbiont, such as extinction, persistence or total infection, are obtained through the determination of the target and basic reproduction numbers, the equilibria, and the study of their stability. The stability is illustrated numerically, and the contribution of vertical and horizontal transmission in the spread of the symbiont is assessed. Data obtained from laboratory experiments are then used to explain the low prevalence observed in nature. The study also shows that the male death rate, the mating rate and the attractiveness of MB-positive mosquitoes are the factors that most influence the transmission of the symbiont. In addition, the introduction of temperature and the study of bifurcations show the significant influence of the environmental condition in the propagation of Microsporidia MB. This finding proves the necessity of taking into account environmental variables for the potential establishment of the symbiont in a new area.

Keywords: differential equations, stability analysis, malaria, microsporidia MB, horizontal transmission, vertical transmission, numerical illustration

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Authors: Teng Li, Kamran Mohseni

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This paper presents an inviscid regularization technique for the incompressible two-phase flow simulations. This technique is known as observable method due to the understanding of observability that any feature smaller than the actual resolution (physical or numerical), i.e., the size of wire in hotwire anemometry or the grid size in numerical simulations, is not able to be captured or observed. Differ from most regularization techniques that applies on the numerical discretization, the observable method is employed at PDE level during the derivation of equations. Difficulties in the simulation and analysis of realistic fluid flow often result from discontinuities (or near-discontinuities) in the calculated fluid properties or state. Accurately capturing these discontinuities is especially crucial when simulating flows involving shocks, turbulence or sharp interfaces. Over the past several years, the properties of this new regularization technique have been investigated that show the capability of simultaneously regularizing shocks and turbulence. The observable method has been performed on the direct numerical simulations of shocks and turbulence where the discontinuities are successfully regularized and flow features are well captured. In the current paper, the observable method will be extended to two-phase interfacial flows. Multiphase flows share the similar features with shocks and turbulence that is the nonlinear irregularity caused by the nonlinear terms in the governing equations, namely, Euler equations. In the direct numerical simulation of two-phase flows, the interfaces are usually treated as the smooth transition of the properties from one fluid phase to the other. However, in high Reynolds number or low viscosity flows, the nonlinear terms will generate smaller scales which will sharpen the interface, causing discontinuities. Many numerical methods for two-phase flows fail at high Reynolds number case while some others depend on the numerical diffusion from spatial discretization. The observable method regularizes this nonlinear mechanism by filtering the convective terms and this process is inviscid. The filtering effect is controlled by an observable scale which is usually about a grid length. Single rising bubble and Rayleigh-Taylor instability are studied, in particular, to examine the performance of the observable method. A pseudo-spectral method is used for spatial discretization which will not introduce numerical diffusion, and a Total Variation Diminishing (TVD) Runge Kutta method is applied for time integration. The observable incompressible Euler equations are solved for these two problems. In rising bubble problem, the terminal velocity and shape of the bubble are particularly examined and compared with experiments and other numerical results. In the Rayleigh-Taylor instability, the shape of the interface are studied for different observable scale and the spike and bubble velocities, as well as positions (under a proper observable scale), are compared with other simulation results. The results indicate that this regularization technique can potentially regularize the sharp interface in the two-phase flow simulations

Keywords: Euler equations, incompressible flow simulation, inviscid regularization technique, two-phase flow

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Authors: K. Karuppasamy

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In this paper analysis of an infinite beam resting on multilayer tensionless extensible geosynthetic reinforced granular fill - poor soil system overlying soft soil strata under moving the load with constant velocity is presented. The beam is subjected to a concentrated load moving with constant velocity. The upper reinforced granular bed is modeled by a rough membrane embedded in Pasternak shear layer overlying a series of compressible nonlinear Winkler springs representing the underlying the very poor soil. The multilayer tensionless extensible geosynthetic layer has been assumed to deform such that at the interface the geosynthetic and the soil have some deformation. Nonlinear behavior of granular fill and the very poor soil has been considered in the analysis by means of hyperbolic constitutive relationships. Governing differential equations of the soil foundation system have been obtained and solved with the help of appropriate boundary conditions. The solution has been obtained by employing finite difference method by means of Gauss-Siedel iterative scheme. Detailed parametric study has been conducted to study the influence of various parameters on the response of soil – foundation system under consideration by means of deflection and bending moment in the beam and tension mobilized in the geosynthetic layer. These parameters include the magnitude of applied load, the velocity of the load, damping, the ultimate resistance of the poor soil and granular fill layer. The range of values of parameters has been considered as per Indian Railways conditions. This study clearly observed that the comparisons of multilayer tensionless extensible geosynthetic reinforcement with poor foundation soil and magnitude of applied load, relative compressibility of granular fill and ultimate resistance of poor soil has significant influence on the response of soil – foundation system. However, for the considered range of velocity, the response has been found to be insensitive towards velocity. The ultimate resistance of granular fill layer has also been found to have no significant influence on the response of the system.

Keywords: infinite beams, multilayer tensionless extensible geosynthetic, granular layer, moving load and nonlinear behavior of poor soil

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Authors: José Alberto García Fernández, Zhimin Du, Xinqiao Jin

Abstract:

Nowadays, data center industry faces strong challenges for increasing the speed and data processing capacities while at the same time is trying to keep their devices a suitable working temperature without penalizing that capacity. Consequently, the cooling systems of this kind of facilities use a large amount of energy to dissipate the heat generated inside the servers, and developing new cooling techniques or perfecting those already existing would be a great advance in this type of industry. The installation of a temperature sensor matrix distributed in the structure of each server would provide the necessary information for collecting the required data for obtaining a temperature profile instantly inside them. However, the number of temperature probes required to obtain the temperature profiles with sufficient accuracy is very high and expensive. Therefore, other less intrusive techniques are employed where each point that characterizes the server temperature profile is obtained by solving differential equations through simulation methods, simplifying data collection techniques but increasing the time to obtain results. In order to reduce these calculation times, complicated and slow computational fluid dynamics simulations are replaced by simpler and faster finite element method simulations which solve the Burgers‘ equations by backward, forward and central discretization techniques after simplifying the energy and enthalpy conservation differential equations. The discretization methods employed for solving the first and second order derivatives of the obtained Burgers‘ equation after these simplifications are the key for obtaining results with greater or lesser accuracy regardless of the characteristic truncation error.

Keywords: Burgers' equations, CFD simulation, data center, discretization methods, FEM simulation, temperature profile

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Authors: Y. A. Yahaya, Ahmad Tijjani Asabe

Abstract:

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

Procedia PDF Downloads 594