Search results for: differential equations
2797 Evaluation of Dynamic and Vibrational Analysis of the Double Chambered Cylinder along Thermal Interactions
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
Procedia PDF Downloads 3392796 Application of Regularized Spatio-Temporal Models to the Analysis of Remote Sensing Data
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
Procedia PDF Downloads 1362795 Existence Result of Third Order Functional Random Integro-Differential Inclusion
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
Procedia PDF Downloads 4592794 Comparison of Conventional Control and Robust Control on Double-Pipe Heat Exchanger
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
Procedia PDF Downloads 2152793 Geometric Nonlinear Dynamic Analysis of Cylindrical Composite Sandwich Shells Subjected to Underwater Blast Load
Authors: Mustafa Taskin, Ozgur Demir, M. Mert Serveren
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The precise study of the impact of underwater explosions on structures is of great importance in the design and engineering calculations of floating structures, especially those used for military purposes, as well as power generation facilities such as offshore platforms that can become a target in case of war. Considering that ship and submarine structures are mostly curved surfaces, it is extremely important and interesting to examine the destructive effects of underwater explosions on curvilinear surfaces. In this study, geometric nonlinear dynamic analysis of cylindrical composite sandwich shells subjected to instantaneous pressure load is performed. The instantaneous pressure load is defined as an underwater explosion and the effects of the liquid medium are taken into account. There are equations in the literature for pressure due to underwater explosions, but these equations have been obtained for flat plates. For this reason, the instantaneous pressure load equations are arranged to be suitable for curvilinear structures before proceeding with the analyses. Fluid-solid interaction is defined by using Taylor's Plate Theory. The lower and upper layers of the cylindrical composite sandwich shell are modeled as composite laminate and the middle layer consists of soft core. The geometric nonlinear dynamic equations of the shell are obtained by Hamilton's principle, taken into account the von Kàrmàn theory of large displacements. Then, time dependent geometric nonlinear equations of motion are solved with the help of generalized differential quadrature method (GDQM) and dynamic behavior of cylindrical composite sandwich shells exposed to underwater explosion is investigated. An algorithm that can work parametrically for the solution has been developed within the scope of the study.Keywords: cylindrical composite sandwich shells, generalized differential quadrature method, geometric nonlinear dynamic analysis, underwater explosion
Procedia PDF Downloads 1842792 The Improved Laplace Homotopy Perturbation Method for Solving Non-integrable PDEs
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
Procedia PDF Downloads 902791 Magneto-Convective Instability in a Horizontal Power-Law Nanofluid Saturated Porous Layer
Authors: Norazuwin Najihah Mat Tahir, Fuziyah Ishak, Seripah Awang Kechil
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The onset of the convective instability in the horizontal through flow of a power-law nanofluid saturated by porous layer heated from below under the influences of magnetic field are investigated in this study. The linear stability theory is used for the transformation of the partial differential equations to system of ordinary differential equations through infinitesimal perturbations, scaling, linearization and method of normal modes with two-dimensional periodic waves. The system is solved analytically for the closed form solution of the Rayleigh number by using the Galerkin-type weighted residuals method to investigate the onset of both traveling wave and oscillatory convection. The effects of the power-law index, Lewis number and Peclet number on the stability of the system were investigated. The Lewis number stabilizes while the power-law index and Peclet number destabilize the nanofluid system. The system in the presence of magnetic field is more stable than the system in the absence of magnetic field.Keywords: convection, instability, magnetic field, nanofluid, power-law
Procedia PDF Downloads 2622790 Parallel Multisplitting Methods for DAE’s
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
Procedia PDF Downloads 5412789 Modeling the Compound Interest Dynamics Using Fractional Differential Equations
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
Procedia PDF Downloads 1202788 Magnetohydrodynamic (MHD) Flow of Cu-Water Nanofluid Due to a Rotating Disk with Partial Slip
Authors: Tasawar Hayat, Madiha Rashid, Maria Imtiaz, Ahmed Alsaedi
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This problem is about the study of flow of viscous fluid due to rotating disk in nanofluid. Effects of magnetic field, slip boundary conditions and thermal radiations are encountered. An incompressible fluid soaked the porous medium. In this model, nanoparticles of Cu is considered with water as the base fluid. For Copper-water nanofluid, graphical results are presented to describe the influences of nanoparticles volume fraction (φ) on velocity and temperature fields for the slip boundary conditions. The governing differential equations are transformed to a system of nonlinear ordinary differential equations by suitable transformations. Convergent solution of the nonlinear system is developed. The obtained results are analyzed through graphical illustrations for different parameters. Moreover, the features of the flow and heat transfer characteristics are analyzed. It is found that the skin friction coefficient and heat transfer rate at the surface are highest in copper-water nanofluid.Keywords: MHD nanofluid, porous medium, rotating disk, slip effect
Procedia PDF Downloads 2522787 Parameter Estimation in Dynamical Systems Based on Latent Variables
Authors: Arcady Ponosov
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A novel mathematical approach is suggested, which facilitates a compressed representation and efficient validation of parameter-rich ordinary differential equation models describing the dynamics of complex, especially biology-related, systems and which is based on identification of the system's latent variables. In particular, an efficient parameter estimation method for the compressed non-linear dynamical systems is developed. The method is applied to the so-called 'power-law systems' being non-linear differential equations typically used in Biochemical System Theory.Keywords: generalized law of mass action, metamodels, principal components, synergetic systems
Procedia PDF Downloads 3492786 Second Order Analysis of Frames Using Modified Newmark Method
Authors: Seyed Amin Vakili, Sahar Sadat Vakili, Seyed Ehsan Vakili, Nader Abdoli Yazdi
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The main purpose of this paper is to present the Modified Newmark Method as a method of non-linear frame analysis by considering the effect of the axial load (second order analysis). The discussion will be restricted to plane frameworks containing a constant cross-section for each element. In addition, it is assumed that the frames are prevented from out-of-plane deflection. This part of the investigation is performed to generalize the established method for the assemblage structures such as frameworks. As explained, the governing differential equations are non-linear and cannot be formulated easily due to unknown axial load of the struts in the frame. By the assumption of constant axial load, the governing equations are changed to linear ones in most methods. Since the modeling and the solutions of the non-linear form of the governing equations are cumbersome, the linear form of the equations would be used in the established method. However, according to the ability of the method to reconsider the minor omitted parameters in modeling during the solution procedure, the axial load in the elements at each stage of the iteration can be computed and applied in the next stage. Therefore, the ability of the method to present an accurate approach to the solutions of non-linear equations will be demonstrated again in this paper.Keywords: nonlinear, stability, buckling, modified newmark method
Procedia PDF Downloads 4162785 Further Results on Modified Variational Iteration Method for the Analytical Solution of Nonlinear Advection Equations
Authors: A. W. Gbolagade, M. O. Olayiwola, K. O. Kareem
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In this paper, further to our result on recent paper on the solution of nonlinear advection equations, we present further results on the nonlinear nonhomogeneous advection equations using a modified variational iteration method.Keywords: lagrange multiplier, non-homogeneous equations, advection equations, mathematics
Procedia PDF Downloads 2912784 A Unified Fitting Method for the Set of Unified Constitutive Equations for Modelling Microstructure Evolution in Hot Deformation
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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
Procedia PDF Downloads 902783 Thermal Analysis for Darcy Forchheimer Effect with Hybrid Ferro Fluid Flow
Authors: Behzad Ali Khan, M. Zubair Akbar Qureshi
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The article analyzes the Darcy Forchheimer 2D Hybrid ferrofluid. The flow of a Hybrid ferrofluid is made due to an unsteady porous channel. The classical liquid water is treated as a based liquid. The flow in the permeable region is characterized by the Darcy-Forchheimer relation. Heat transfer phenomena are studied during the flow. The transformation of a partial differential set of equations into a strong ordinary differential frame is formed through appropriate variables. The numerical Shooting Method is executed for solving the simplified set of equations. In addition, a numerical analysis (ND-Solve) is utilized for the convergence of the applied technique. The influence of some flow model quantities like Pr (Prandtle number), r (porous medium parameter), F (Darcy-porous medium parameter), Re (Reynolds number), Pe (Peclet number) on velocity and temperature field are scrutinized and studied through sketches. Certain physical factors like f ''(η) (skin friction coefficient) and θ^'(η) (rate of heat transfer) are first derived and then presented through tables.Keywords: darcy forcheimer, hybrid ferro fluid, porous medium, porous channel
Procedia PDF Downloads 1692782 Classifying Time Independent Plane Symmetric Spacetime through Noether`s Approach
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
Procedia PDF Downloads 2262781 Nonlocal Beam Models for Free Vibration Analysis of Double-Walled Carbon Nanotubes with Various End Supports
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
Procedia PDF Downloads 2892780 New Insight into Fluid Mechanics of Lorenz Equations
Authors: Yu-Kai Ting, Jia-Ying Tu, Chung-Chun Hsiao
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New physical insights into the nonlinear Lorenz equations related to flow resistance is discussed in this work. The chaotic dynamics related to Lorenz equations has been studied in many papers, which is due to the sensitivity of Lorenz equations to initial conditions and parameter uncertainties. However, the physical implication arising from Lorenz equations about convectional motion attracts little attention in the relevant literature. Therefore, as a first step to understand the related fluid mechanics of convectional motion, this paper derives the Lorenz equations again with different forced conditions in the model. Simulation work of the modified Lorenz equations without the viscosity or buoyancy force is discussed. The time-domain simulation results may imply that the states of the Lorenz equations are related to certain flow speed and flow resistance. The flow speed of the underlying fluid system increases as the flow resistance reduces. This observation would be helpful to analyze the coupling effects of different fluid parameters in a convectional model in future work.Keywords: Galerkin method, Lorenz equations, Navier-Stokes equations, convectional motion
Procedia PDF Downloads 3862779 Free Convection from a Perforated Spinning Cone with Heat Generation, Temperature-Dependent Viscosity and Partial Slip
Authors: Gilbert Makanda
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The problem of free convection from a perforated spinning cone with viscous dissipation, temperature-dependent viscosity, and partial slip was studied. The boundary layer velocity and temperature profiles were numerically computed for different values of the spin, viscosity variation, inertia drag force, Eckert, suction/blowing parameters. The partial differential equations were transformed into a system of ordinary differential equations which were solved using the fourth-order Runge-Kutta method. This paper considered the effect of partial slip and spin parameters on the swirling velocity profiles which are rarely reported in the literature. The results obtained by this method was compared to those in the literature and found to be in agreement. Increasing the viscosity variation parameter, spin, partial slip, Eckert number, Darcian drag force parameters reduce swirling velocity profiles.Keywords: free convection, suction/injection, partial slip, viscous dissipation
Procedia PDF Downloads 2402778 Thermal Buckling Response of Cylindrical Panels with Higher Order Shear Deformation Theory—a Case Study with Angle-Ply Laminations
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
Procedia PDF Downloads 3672777 Verification of Space System Dynamics Using the MATLAB Identification Toolbox in Space Qualification Test
Authors: Yuri V. Kim
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This article presents a new approach to the Functional Testing of Space Systems (SS). It can be considered as a generic test and used for a wide class of SS that from the point of view of System Dynamics and Control may be described by the ordinary differential equations. Suggested methodology is based on using semi-natural experiment- laboratory stand that doesn’t require complicated, precise and expensive technological control-verification equipment. However, it allows for testing system as a whole totally assembled unit during Assembling, Integration and Testing (AIT) activities, involving system hardware (HW) and software (SW). The test physically activates system input (sensors) and output (actuators) and requires recording their outputs in real time. The data is then inserted in laboratory PC where it is post-experiment processed by Matlab/Simulink Identification Toolbox. It allows for estimating system dynamics in form of estimation of system differential equations by the experimental way and comparing them with expected mathematical model prematurely verified by mathematical simulation during the design process.Keywords: system dynamics, space system ground tests and space qualification, system dynamics identification, satellite attitude control, assembling, integration and testing
Procedia PDF Downloads 1572776 Hybrid Equity Warrants Pricing Formulation under Stochastic Dynamics
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
Procedia PDF Downloads 1242775 Unsteady Reactive Hydromagnetic Fluid Flow of a Two-Step Exothermic Chemical Reaction through a Channel
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
Procedia PDF Downloads 4402774 Analysis of a Differential System to Get Insights on the Potential Establishment of Microsporidia MB in the Mosquito Population for Malaria Control
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
Procedia PDF Downloads 1022773 Data Centers’ Temperature Profile Simulation Optimized by Finite Elements and Discretization Methods
Authors: José Alberto García Fernández, Zhimin Du, Xinqiao Jin
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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
Procedia PDF Downloads 1592772 A Trapezoidal-Like Integrator for the Numerical Solution of One-Dimensional Time Dependent Schrödinger Equation
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
Procedia PDF Downloads 4112771 A Hybrid Block Multistep Method for Direct Numerical Integration of Fourth Order Initial Value Problems
Authors: Adamu S. Salawu, Ibrahim O. Isah
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Direct solution to several forms of fourth-order ordinary differential equations is not easily obtained without first reducing them to a system of first-order equations. Thus, numerical methods are being developed with the underlying techniques in the literature, which seeks to approximate some classes of fourth-order initial value problems with admissible error bounds. Multistep methods present a great advantage of the ease of implementation but with a setback of several functions evaluation for every stage of implementation. However, hybrid methods conventionally show a slightly higher order of truncation for any k-step linear multistep method, with the possibility of obtaining solutions at off mesh points within the interval of solution. In the light of the foregoing, we propose the continuous form of a hybrid multistep method with Chebyshev polynomial as a basis function for the numerical integration of fourth-order initial value problems of ordinary differential equations. The basis function is interpolated and collocated at some points on the interval [0, 2] to yield a system of equations, which is solved to obtain the unknowns of the approximating polynomial. The continuous form obtained, its first and second derivatives are evaluated at carefully chosen points to obtain the proposed block method needed to directly approximate fourth-order initial value problems. The method is analyzed for convergence. Implementation of the method is done by conducting numerical experiments on some test problems. The outcome of the implementation of the method suggests that the method performs well on problems with oscillatory or trigonometric terms since the approximations at several points on the solution domain did not deviate too far from the theoretical solutions. The method also shows better performance compared with an existing hybrid method when implemented on a larger interval of solution.Keywords: Chebyshev polynomial, collocation, hybrid multistep method, initial value problems, interpolation
Procedia PDF Downloads 1202770 Dynamical Systems and Fibonacci Numbers
Authors: Vandana N. Purav
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The Dynamical systems concept is a mathematical formalization for any fixed rule that describes the time dependence of a points position in its ambient space. e.g. pendulum of a clock, the number of fish each spring in a lake, the number of rabbits spring in an enclosure, etc. The Dynamical system theory used to describe the complex nature that is dynamical systems with differential equations called continuous dynamical system or dynamical system with difference equations called discrete dynamical system. The concept of dynamical system has its origin in Newtonian mechanics.Keywords: dynamical systems, Fibonacci numbers, Newtonian mechanics, discrete dynamical system
Procedia PDF Downloads 4842769 MHD Stagnation-Point Flow over a Plate
Authors: H. Niranjan, S. Sivasankaran
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Heat and mass transfer near a steady stagnation point boundary layer flow of viscous incompressible fluid through porous media investigates along a vertical plate is thoroughly studied under the presence of magneto hydrodynamic (MHD) effects. The fluid flow is steady, laminar, incompressible and in two-dimensional. The nonlinear differential coupled parabolic partial differential equations of continuity, momentum, energy and specie diffusion are converted into the non-similar boundary layer equations using similarity transformation, which are then solved numerically using the Runge-Kutta method along with shooting method. The effects of the conjugate heat transfer parameter, the porous medium parameter, the permeability parameter, the mixed convection parameter, the magnetic parameter, and the thermal radiation on the velocity and temperature profiles as well as on the local skin friction and local heat transfer are presented and analyzed. The validity of the methodology and analysis is checked by comparing the results obtained for some specific cases with those available in the literature. The various parameters on local skin friction, heat and mass transfer rates are presented in tabular form.Keywords: MHD, porous medium, slip, convective boundary condition, stagnation point
Procedia PDF Downloads 2952768 Displacement Solution for a Static Vertical Rigid Movement of an Interior Circular Disc in a Transversely Isotropic Tri-Material Full-Space
Authors: D. Mehdizadeh, M. Rahimian, M. Eskandari-Ghadi
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This article is concerned with the determination of the static interaction of a vertically loaded rigid circular disc embedded at the interface of a horizontal layer sandwiched in between two different transversely isotropic half-spaces called as tri-material full-space. The axes of symmetry of different regions are assumed to be normal to the horizontal interfaces and parallel to the movement direction. With the use of a potential function method, and by implementing Hankel integral transforms in the radial direction, the government partial differential equation for the solely scalar potential function is transformed to an ordinary 4th order differential equation, and the mixed boundary conditions are transformed into a pair of integral equations called dual integral equations, which can be reduced to a Fredholm integral equation of the second kind, which is solved analytically. Then, the displacements and stresses are given in the form of improper line integrals, which is due to inverse Hankel integral transforms. It is shown that the present solutions are in exact agreement with the existing solutions for a homogeneous full-space with transversely isotropic material. To confirm the accuracy of the numerical evaluation of the integrals involved, the numerical results are compared with the solutions exists for the homogeneous full-space. Then, some different cases with different degrees of material anisotropy are compared to portray the effect of degree of anisotropy.Keywords: transversely isotropic, rigid disc, elasticity, dual integral equations, tri-material full-space
Procedia PDF Downloads 432