Search results for: delay equations

Authors: Malika Elkyal

Abstract:

We consider an 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 does 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 to be substantial and unpredictable. Accordingly, we note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: parallel methods, asynchronous mode, multisplitting, differential algebraic equations

Procedia PDF Downloads 526

Authors: Ahmad Jawad Fardin

Abstract:

Over 60% of patients with breast cancer in Afghanistan present late with advanced stage III and IV, a major cause for the poor survival rate. The objectives of this study were to identify the contributing factors for the diagnosis and treatment delay and its outcome. This cross-sectional study was conducted on 318 patients with histologically confirmed breast cancer in the oncology department of Jamhoriat hospital, which is the first and only national cancer center in Afghanistan; data were collected from medical records and interviews conducted with women diagnosed with breast cancer, linear regression and logistic regression were used for analysis. Patient delay was defined as the time from first recognition of symptoms until first medical consultation and doctor form first consultation with a health care provider until histological confirmation of breast cancer. The mean age of patients was 49.2+_ 11.5years. The average time for the final diagnosis of breast cancer was 8.5 months; most patients had ductal carcinoma 260.7 (82%). Factors associated with delay were low education level 76% poor socioeconomic and cultural conditions 81% lack of cancer center 73% lack of screening 19%. The stage distribution was as follows stage IV 4 22% stage III 44.4% stage II 29.3% stage I 4.3%. Complex associated factors were identified to delayed the diagnosis of breast cancer and increased adverse outcomes consequently. Raising awareness and education in women, the establishment of cancer centers and providing accessible diagnosis service and screening, training of general practitioners; required to promote early detection, diagnosis and treatment.

Keywords: delayed diagnosis and poor outcome, breast cancer in Afghanistan, poor outcome of delayed breast cancer treatment, breast cancer delayed diagnosis and treatment in Afghanistan

Procedia PDF Downloads 152

Authors: Monika Foltyn-Zarychta

Abstract:

Climate change mitigation investment activities are inevitably extended in time extremely. The project cycle does not last for decades – sometimes it stretches out for hundreds of years and the project outcomes impact several generations. The longevity of those activities raises multiple problems in the appraisal procedure. One of the pivotal issues is the choice of the discount rate, which affect tremendously the net present value criterion. The paper aims at estimating the value of social discount rate for intergenerational investment projects in Poland based on individual intertemporal preferences. The analysis is based on questionnaire surveying Polish citizens and designed as contingent valuation method. The analysis aimed at answering two questions: 1) whether the value of the individual discount rate decline with increased time of delay, and 2) whether the value of the individual discount rate changes with increased spatial distance toward the gainers of the project. The valuation questions were designed to identify respondent’s indifference point between lives saved today and in the future due to hypothetical project mitigating climate changes. Several project effects’ delays (of 10, 30, 90 and 150 years) were used to test the decline in value with time. The variability in regard to distance was tested by asking respondents to estimate their indifference point separately for gainers in Poland and in Latvia. The results show that as the time delay increases, the average discount rate value decreases from 15,32% for 10-year delay to 2,75% for 150-year delay. Similar values were estimated for Latvian beneficiaries. There should be also noticed that the average volatility measured by standard deviation also decreased with time delay. However, the results did not show any statistically significant difference in discount rate values for Polish and Latvian gainers. The results showing the decline of the discount rate with time prove the possible economic efficiency of the intergenerational effect of climate change mitigation projects and may induce the assumption of the altruistic behavior of present generation toward future people. Furthermore, it can be backed up by the same discount rate level declared by Polish for distant in space Latvian gainers. The climate change activities usually need significant outlays and the payback period is extremely long. The more precise the variables in the appraisal are, the more trustworthy and rational the investment decision is. The discount rate estimations for Poland add to the vivid discussion concerning the issue of climate change and intergenerational justice.

Keywords: climate change, social discount rate, investment appraisal, intergenerational justice

Procedia PDF Downloads 216

Authors: Mohamed Adnan Landolsi, Ali F. Almutairi

Abstract:

The paper addresses the problem of line-of-sight (LOS) vs. non-line-of-sight (NLOS) propagation link identification in ultra-wideband (UWB) wireless networks, which is necessary for improving the accuracy of radiolocation and positioning applications. A LOS/NLOS likelihood hypothesis testing approach is applied based on exploiting distinctive statistical features of the channel impulse response (CIR) using parameters related to the “skewness” of the CIR and its root mean square (RMS) delay spread. A log-normal fit is presented for the probability densities of the CIR parameters. Simulation results show that different environments (residential, office, outdoor, etc.) have measurable differences in their CIR parameters’ statistics, which is then exploited in determining the nature of the propagation channels. Correct LOS/NLOS channel identification rates exceeding 90% are shown to be achievable for most types of environments. Additional improvement is also obtained by combining both CIR skewness and RMS delay statistics.

Keywords: UWB, propagation, LOS, NLOS, identification

Procedia PDF Downloads 208

Authors: Mustafa Taskin, Ozgur Demir, M. Mert Serveren

Abstract:

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 162

Authors: Ahmad Forouzantabar, Mohammad Azadi

Abstract:

This paper presents sliding mode controller for bilateral teleoperation systems with robotic master and slave under constant communication delays. We extend the passivity-based coordination architecture to enhance position and force tracking in the presence of offset in initial conditions, environmental contacts and unknown parameters such as friction coefficient. To address these difficulties, a nonlinear sliding mode controller is designed to approximate the nonlinear dynamics of master and slave robots and improve both position and force tracking. Using the Lyapunov theory, the boundedness of master- slave tracking errors and the stability of the teleoperation system are also guaranteed. Numerical simulations show that proposed controller position and force tracking performances are superior to that of conventional coordination controller tracking performances.

Keywords: Lyapunov stability, teleoperation system, time delay, sliding mode controller

Procedia PDF Downloads 348

Authors: Hamdy M. Youssef, Eman A. Al-Lehaibi

Abstract:

Due to many applications and problems in the fields of plasma physics, geophysics, and other many topics, the interaction between the strain field and the magnetic field has to be considered. Adomian introduced the decomposition method for solving linear and nonlinear functional equations. This method leads to accurate, computable, approximately convergent solutions of linear and nonlinear partial and ordinary differential equations even the equations with variable coefficients. This paper is dealing with a mathematical model of generalized thermoelasticity of a half-space conducting medium. A magnetic field with constant intensity acts normal to the bounding plane has been assumed. Adomian’s decomposition method has been used to solve the model when the bounding plane is taken to be traction free and thermally loaded by harmonic heating. The numerical results for the temperature increment, the stress, the strain, the displacement, the induced magnetic, and the electric fields have been represented in figures. The magnetic field, the relaxation time, and the angular thermal load have significant effects on all the studied fields.

Keywords: Adomian’s decomposition method, magneto-thermoelasticity, finite conductivity, iteration method, thermal load

Procedia PDF Downloads 119

Authors: Mohammadreza Akbari, Pooya Soleimani Besheli, Reza Khalili, Davood Domiri Danji

Abstract:

In this conference, our aims are accuracy, capabilities and power at solving of the complicated non-linear partial differential. Our purpose is to enhance the ability to solve the mentioned nonlinear differential equations at basic science and engineering field and similar issues with a simple and innovative approach. As we know most of engineering system behavior in practical are nonlinear process (especially basic science and engineering field, etc.) and analytical solving (no numeric) these problems are difficult, complex, and sometimes impossible like (Fluids and Gas wave, these problems can't solve with numeric method, because of no have boundary condition) accordingly in this symposium we are going to exposure an innovative approach which we have named it Akbari-Ganji's Method or AGM in engineering, that can solve sets of coupled nonlinear differential equations (ODE, PDE) with high accuracy and simple solution and so this issue will emerge after comparing the achieved solutions by Numerical method (Runge-Kutta 4th). Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear partial differential equations, with help of that there is no difficulty for solving all nonlinear differential equations. Advantages and ability of this method (AGM) as follow: (a) Non-linear Differential equations (ODE, PDE) are directly solvable by this method. (b) In this method (AGM), most of the time, without any dimensionless procedure, we can solve equation(s) by any boundary or initial condition number. (c) AGM method always is convergent in boundary or initial condition. (d) Parameters of exponential, Trigonometric and Logarithmic of the existent in the non-linear differential equation with AGM method no needs Taylor expand which are caused high solve precision. (e) AGM method is very flexible in the coding system, and can solve easily varieties of the non-linear differential equation at high acceptable accuracy. (f) One of the important advantages of this method is analytical solving with high accuracy such as partial differential equation in vibration in solids, waves in water and gas, with minimum initial and boundary condition capable to solve problem. (g) It is very important to present a general and simple approach for solving most problems of the differential equations with high non-linearity in engineering sciences especially at civil engineering, and compare output with numerical method (Runge-Kutta 4th) and Exact solutions.

Keywords: new approach, AGM, sets of coupled nonlinear differential equation, exact solutions, numerical

Procedia PDF Downloads 423

Authors: Pradeepa Teegala, Ramreddy Chetteti

Abstract:

This work emphasizes the effects of heat generation/absorption and Joule heating on chemically reacting micropolar fluid flow over a truncated cone with convective boundary condition. For this complex fluid flow problem, the similarity solution does not exist and hence using non-similarity transformations, the governing fluid flow equations along with related boundary conditions are transformed into a set of non-dimensional partial differential equations. Several authors have applied the spectral quasi-linearization method to solve the ordinary differential equations, but here the resulting nonlinear partial differential equations are solved for non-similarity solution by using a recently developed method called the spectral quasi-linearization method (SQLM). Comparison with previously published work on special cases of the problem is performed and found to be in excellent agreement. The influence of pertinent parameters namely Biot number, Joule heating, heat generation/absorption, chemical reaction, micropolar and magnetic field on physical quantities of the flow are displayed through graphs and the salient features are explored in detail. Further, the results are analyzed by comparing with two special cases, namely, vertical plate and full cone wherever possible.

Keywords: chemical reaction, convective boundary condition, joule heating, micropolar fluid, spectral quasilinearization method

Procedia PDF Downloads 322

Authors: Elmongi Elbellili, Ben Lauwens, Daan Huybrechs

Abstract:

The increasing complexity of modern engineering systems presents a challenge to the digital simulation of these systems which usually can be represented by differential equations. The Linearly Implicit Quantized State System (LIQSS) offers an alternative approach to traditional numerical integration techniques for solving Ordinary Differential Equations (ODEs). This method proved effective for handling discontinuous and large stiff systems. However, the inherent discrete nature of LIQSS may introduce oscillations that result in unnecessary computational steps. The current oscillation detection mechanism relies on a condition that checks the significance of the derivatives, but it could be further improved. This paper describes a different cycle detection mechanism and presents the outcomes using LIQSS order one in simulating the Advection Diffusion problem. The efficiency of this new cycle detection mechanism is verified by comparing the performance of the current solver against the new version as well as a reference solution using a Runge-Kutta method of order14.

Keywords: numerical integration, quantized state systems, ordinary differential equations, stiffness, cycle detection, simulation

Procedia PDF Downloads 26

Authors: Idowu Ibikunle Albert, Atilade Adesanya Oluwafemi, Okedeyi Abiodun Sikiru, Mustapha Rilwan Adewale

Abstract:

These present-day all areas of transport have experienced large advances characterized by increases in the speeds and weight of vehicles. As a result, this paper considered the Transverse Vibration of an Elastic Beam Resting on a Variable Elastic Foundation Subjected to a moving Load. The beam is presumed to be uniformly distributed and has simple support at both ends. The moving distributed moving mass is assumed to move with constant velocity. The governing equations, which are fourth-order partial differential equations, were reduced to second-order partial differential equations using an analytical method in terms of series solution and solved by a numerical method using mathematical software (Maple). Results show that an increase in the values of beam parameters, moving Mass M, and k-stiffness K, significantly reduces the deflection profile of the vibrating beam. In the results, it was equally found that moving mass is greater than moving force.

Keywords: elastic beam, moving load, response of structure, variable elastic foundation

Procedia PDF Downloads 84

Authors: Anton V. Bourdine, Vladimir A. Burdin, Oleg R. Delmukhametov

Abstract:

This work presents a fast and simple method for the design of large core silica optical fibers with differential mode delay (DMD) management. Some results are reported concerned with refractive index profile optimization for 42 µm core 16-LP-mode optical fiber for next-generation optical networks. Here special refractive index profile form provides total DMD reducing over all mode staff under desired enhanced mode effective area. Method for the simulation of 'real manufactured' few-mode optical fiber (FMF) core geometry differing from the desired optimized structure by core non-symmetrical ellipticity and refractive index profile deviation including local fluctuations is proposed. Results of the following analysis of optimized FMF with inserted geometry distortions performed by earlier on developed modification of rigorous mixed finite-element method showed strong DMD degradation that requires additional higher-order mode management. In addition, this work also presents a method for design mode division multiplexer channel precision spatial positioning scheme at FMF core end that provides one of the potentiality solutions of described DMD degradation problem concerned with 'distorted' core geometry due to features of optical fiber manufacturing techniques.

Keywords: differential mode delay, few-mode optical fibers, nonlinear Shannon limit, optical fiber non-circularity, ‘real manufactured’ optical fiber core geometry simulation, refractive index profile optimization

Procedia PDF Downloads 125

Authors: Omojokun Gabriel Aju

Abstract:

Communication network is a process of exchanging data between two or more devices via some forms of transmission medium using communication protocols. The data could be in form of text, images, audio, video or numbers which can be grouped into FTP, Email, HTTP, VOIP or Video applications. The effectiveness of such data exchange will be proved if they are accurately delivered within specified time. While some senders will not really mind when the data is actually received by the receiving device, inasmuch as it is acknowledged to have been received by the receiver. The time a data takes to get to a receiver could be very important to another sender, as any delay could cause serious problem or even in some cases rendered the data useless. The validity or invalidity of a data after delay will therefore definitely depend on the type of data (information). It is therefore imperative for the network device (such as router) to be able to differentiate among the packets which are time sensitive and those that are not, when they are passing through the same network. So, here is where the queuing disciplines comes to play, to handle network resources when such network is designed to service widely varying types of traffics and manage the available resources according to the configured policies. Therefore, as part of the resources allocation mechanisms, a router within the network must implement some queuing discipline that governs how packets (data) are buffered while waiting to be transmitted. The implementation of the queuing discipline will regulate how the packets are buffered while waiting to be transmitted. In achieving this, various queuing disciplines are being used to control the transmission of these packets, by determining which of the packets get the highest priority, less priority and which packets are dropped. The queuing discipline will therefore control the packets latency by determining how long a packet can wait to be transmitted or dropped. The common queuing disciplines are first-in-first-out queuing, Priority queuing and Weighted-fair queuing (FIFO, PQ and WFQ). This paper critically evaluates and analyse through the use of Optimized Network Evaluation Tool (OPNET) Modeller, Version 14.5 the effects of three queuing disciplines (FIFO, PQ and WFQ) on the performance of 5 different applications (FTP, HTTP, E-Mail, Voice and Video) within specified parameters using packets sent, packets received and transmission delay as performance metrics. The paper finally suggests some ways in which networks can be designed to provide better transmission performance while using these queuing disciplines.

Keywords: applications, first-in-first-out queuing (FIFO), optimised network evaluation tool (OPNET), packets, priority queuing (PQ), queuing discipline, weighted-fair queuing (WFQ)

Procedia PDF Downloads 323

Authors: Kushakov Kholmurodjon, Muhammadjonov Akbarshox

Abstract:

This present paper is devoted to a system of second-order nonlinear differential equations with a special right-hand side, exactly, the linear part and a third-order polynomial of a special form. It is shown that for some relations between the parameters, there is a second-order curve in which trajectories leaving the points of this curve remain in the same place. Thus, the curve is invariant with respect to the given system. Moreover, this system is invariant under a non-degenerate linear transformation of variables. The form of this curve, depending on the relations between the parameters and the eigenvalues of the matrix, is proved. All solutions of this system of differential equations are shown analytically.

Keywords: dynamic system, ellipse, hyperbola, Hess system, polar coordinate system

Procedia PDF Downloads 162

Authors: Muhammad Faraz, Talat Rafique, Jang Min Park

Abstract:

In this article, rotational flow above a permeable surface with a variable free stream angular velocity is considered. Main interest is to solve the associated heat/mass transport equations under different situations. Firstly, heat transport phenomena occurring in generalized vortex flow are analyzed under two altered heating processes, namely, the (i) prescribed surface temperature and (ii) prescribed heat flux. The vortex motion imposed at infinity is assumed to follow a power-law form 〖(r/r_0)〗^((2n-1)) where r denotes the radial coordinate, r_0 the disk radius, and n is a power-law parameter. Assuming a similar solution, the governing Navier-Stokes equations transform into a set of coupled ODEs which are treated numerically for the aforementioned thermal conditions. Secondly, mass transport phenomena accompanied by activation energy are incorporated into the generalized vortex flow situation. After finding self-similar equations, a numerical solution is furnished by using MATLAB's built-in function bvp4c.

Keywords: bödewadt flow, vortex flow, rotating flows, prescribed heat flux, permeable surface, activation energy

Procedia PDF Downloads 76

Authors: Vandana N. Purav

Abstract:

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 467

Authors: Yiming Jin, Yuanhao Gao

Abstract:

In this paper, using the method of multiple scales, the second sub-harmonic resonance in vortex-induced vibrations (VIV) of a marine pipeline close to the seabed is investigated based on a developed wake oscillator model. The amplitude-frequency equations are also derived. It is found that the oscillation will increase all the time when both discriminants of the amplitude-frequency equations are positive while the oscillation will decay when the discriminants are negative.

Keywords: vortex-induced vibrations, marine pipeline, seabed, sub-harmonic resonance

Procedia PDF Downloads 296

Authors: Maryam Mosleh, Mahmood Otadi

Abstract:

The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example.

Keywords: Fuzzy number, parametric form of a fuzzy number, fuzzy integrodifferential equation, homotopy analysis method

Procedia PDF Downloads 513

Authors: N. Senu, I. A. Kasim, F. Ismail, N. Bachok

Abstract:

In this paper zero-dissipative explicit Runge-Kutta method is derived for solving second-order ordinary differential equations with periodical solutions. The phase-lag and dissipation properties for Runge-Kutta (RK) method are also discussed. The new method has algebraic order three with dissipation of order infinity. The numerical results for the new method are compared with existing method when solving the second-order differential equations with periodic solutions using constant step size.

Keywords: dissipation, oscillatory solutions, phase-lag, Runge-Kutta methods

Procedia PDF Downloads 377

Authors: Parshanth Maroju, Ramandeep Behl, Sandile S. Motsa

Abstract:

In this study, we proposed a simple and interesting family of fourth-order multi-point methods without memory for obtaining simple roots. This family requires only three functional evaluations (viz. two of functions f(xn), f(yn) and third one of its first-order derivative f'(xn)) per iteration. Moreover, the accuracy and validity of new schemes is tested by a number of numerical examples are also proposed to illustrate their accuracy by comparing them with the new existing optimal fourth-order methods available in the literature. It is found that they are very useful in high precision computations. Further, the dynamic study of these methods also supports the theoretical aspect.

Keywords: basins of attraction, nonlinear equations, simple roots, Newton's method

Procedia PDF Downloads 290

Authors: Ziying Wu, Danfeng Yan

Abstract:

Multi-Access Edge Computing (MEC) is one of the key technologies of the future 5G network. By deploying edge computing centers at the edge of wireless access network, the computation tasks can be offloaded to edge servers rather than the remote cloud server to meet the requirements of 5G low-latency and high-reliability application scenarios. Meanwhile, with the development of IOV (Internet of Vehicles) technology, various delay-sensitive and compute-intensive in-vehicle applications continue to appear. Compared with traditional internet business, these computation tasks have higher processing priority and lower delay requirements. In this paper, we design a 5G-based Vehicle-Aware Multi-Access Edge Computing Network (VAMECN) and propose a joint optimization problem of minimizing total system cost. In view of the problem, a deep reinforcement learning-based joint computation offloading and task migration optimization (JCOTM) algorithm is proposed, considering the influences of multiple factors such as concurrent multiple computation tasks, system computing resources distribution, and network communication bandwidth. And, the mixed integer nonlinear programming problem is described as a Markov Decision Process. Experiments show that our proposed algorithm can effectively reduce task processing delay and equipment energy consumption, optimize computing offloading and resource allocation schemes, and improve system resource utilization, compared with other computing offloading policies.

Keywords: multi-access edge computing, computation offloading, 5th generation, vehicle-aware, deep reinforcement learning, deep q-network

Procedia PDF Downloads 78

Authors: Amir Aziz, Martin Tuner, Sebastian Verhelst, Oivind Andersson

Abstract:

Partially Premixed Combustion (PPC) is a combustion concept which aims to simultaneously achieve high efficiency and low engine-out emissions. Extending the ignition delay to promote the premixing, has been recognized as one of the key factor to achieve PPC. Fuels with high octane number have been proven to be a good candidates to extend the ignition delay. In this work, E85 (85% ethanol) has been used as a PPC fuel. The aim of this work was to investigate a suitable injection strategy for PPC combustion fueled with E85 in a single-cylinder heavy-duty engine. Single and double injection strategy were applied with different injection timing and the ratio between different injection pulses was varied. The performance and emission were investigated at low load. The results show that the double injection strategy should be preferred for PPC fueled with E85 due to low emissions and high efficiency, while keeping the pressure raise rate at very low levels.

Keywords: E85, partially premixed combustion, injection strategy, performance and emission

Procedia PDF Downloads 155

Authors: Abdelhafid Zenati, Mohamed Tadjine

Abstract:

The mathematical formulation of biomedical problems is an important phase to understand and predict the dynamic of the controlled population. In this paper we perform a stability analysis of a coupled model for healthy and cancerous cells dynamics in Acute Myeloid Leukemia, this represents our first aim. Second, we illustrate the effect of the interconnection between healthy and cancer cells. The PDE-based model is transformed to a nonlinear distributed state space model (delay system). For an equilibrium point of interest, necessary and sufficient conditions of global asymptotic stability are given. Thus, we came up to give necessary and sufficient conditions of global asymptotic stability of the origin and the healthy situation and control of the dynamics of normal hematopoietic stem cells and cancerous during myelode Acute leukemia. Simulation studies are given to illustrate the developed results.

Keywords: distributed delay, global stability, modelling, nonlinear models, PDE, state space

Procedia PDF Downloads 233

Authors: Raphael de Oliveira Garcia, Samuel Rocha de Oliveira

Abstract:

We have developed a new computer program in Fortran 90, in order to obtain numerical solutions of a system of Relativistic Magnetohydrodynamics partial differential equations with predetermined gravitation (GRMHD), capable of simulating the formation of relativistic jets from the accretion disk of matter up to his ejection. Initially we carried out a study on numerical methods of unidimensional Finite Volume, namely Lax-Friedrichs, Lax-Wendroff, Nessyahu-Tadmor method and Godunov methods dependent on Riemann problems, applied to equations Euler in order to verify their main features and make comparisons among those methods. It was then implemented the method of Finite Volume Centered of Nessyahu-Tadmor, a numerical schemes that has a formulation free and without dimensional separation of Riemann problem solvers, even in two or more spatial dimensions, at this point, already applied in equations GRMHD. Finally, the Nessyahu-Tadmor method was possible to obtain stable numerical solutions - without spurious oscillations or excessive dissipation - from the magnetized accretion disk process in rotation with respect to a central black hole (BH) Schwarzschild and immersed in a magnetosphere, for the ejection of matter in the form of jet over a distance of fourteen times the radius of the BH, a record in terms of astrophysical simulation of this kind. Also in our simulations, we managed to get substructures jets. A great advantage obtained was that, with the our code, we got simulate GRMHD equations in a simple personal computer.

Keywords: finite volume methods, central schemes, fortran 90, relativistic astrophysics, jet

Procedia PDF Downloads 418

Authors: Kwan-u Kim, Jin-Sim, Ryong-Jin Jang, Sung-Duk Kim

Abstract:

106 years have passed since a great number of physicists explained astronomical and physical phenomena by solving geodesic equations in Schwarzschild metric. However, when solving the geodesic equations in Schwarzschild metric, they did not solve correctly one branch of the component of space among spatial and temporal components of four-dimensional force and did not come up with physical laws correctly by means of physical analysis from the results obtained by solving the geodesic equations. In addition to it, they did not treat the astronomical and physical phenomena in a physical way based on the exact physical laws obtained from the solution of the geodesic equations in Schwarzschild metric, so some former scholars mentioned that Einstein’s theoretical basis of general theory of relativity was obscure and incorrect, but they have not given a correct physical solution to the problems. Furthermore, because general theory of relativity has not given a quantitative solution to the obscure and incorrect problems, generalization of gravitational theory although the former scholars thought of it and tried to do it. In order to solve the problems it is necessary to explore theobscure and incorrect problems in general theory of relativity based on the physical laws and to find out the methodology of solving the problems. Therefore, first of all, as the first sarytep for achieving the purpose, the correct solution of the geodesic equation in Schwarzschild metric has been presented. Next, the correct physical laws found by making a physical analysis of the results has been presented, the obscure and incorrect problems have been showed and an analysis of them has been made on the basis of the physical laws. In addition, the experimental verification of the physical laws found by us has been made.

Keywords: equivalence principle, general relativity, geometrodynamics, Schwarzschild

Procedia PDF Downloads 27

Authors: Roslinda Nazar, Amin Noor, Khamisah Jafar, Ioan Pop

Abstract:

In this paper, the steady laminar three-dimensional boundary layer flow and heat transfer of a copper (Cu)-water nanofluid in the vicinity of a permeable shrinking flat surface in an otherwise quiescent fluid is studied. The nanofluid mathematical model in which the effect of the nanoparticle volume fraction is taken into account is considered. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using a similarity transformation which is then solved numerically using the function bvp4c from Matlab. Dual solutions (upper and lower branch solutions) are found for the similarity boundary layer equations for a certain range of the suction parameter. A stability analysis has been performed to show which branch solutions are stable and physically realizable. The numerical results for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are obtained, presented and discussed in detail for a range of various governing parameters.

Keywords: heat transfer, nanofluid, shrinking surface, stability analysis, three-dimensional flow

Procedia PDF Downloads 258

Authors: Arash Ghahraman, Gyula Bene

Abstract:

The object of this study is to investigate the effect of viscosity on the propagation of free-surface waves in an incompressible viscous fluid layer of arbitrary depth. While we provide a more detailed study of properties of linear surface waves, the description of fully nonlinear waves in terms of KdV-like (Korteweg-de Vries) equations is discussed. In the linear case, we find that in shallow enough fluids, no surface waves can propagate. Even in any thicker fluid layers, propagation of very short and very long waves is forbidden. When wave propagation is possible, only a single propagating mode exists for any given horizontal wave number. The numerical results show that there can be two types of non-propagating modes. One type is always present, and there exist still infinitely many of such modes at the same parameters. In contrast, there can be zero, one or two modes belonging to the other type. Another significant feature is that KdV-like equations. They describe propagating nonlinear viscous surface waves. Since viscosity gives rise to a new wavenumber that cannot be small at the same time as the original one, these equations may not exist. Nonetheless, we propose a reasonable nonlinear description in terms of 1+1 variate functions that make possible successive approximations.

Keywords: free surface wave, water waves, KdV equation, viscosity

Procedia PDF Downloads 124

Authors: Syukri Himran, Erwin Eka Putra, Nanang Roni

Abstract:

This study explains the natural convection of viscous fluid flowing on semi-infinite vertical plate. A set of the governing equations describing the continuity, momentum and energy, have been reduced to dimensionless forms by introducing the references variables. To solve the problems, the equations are formulated by explicit finite-difference in time dependent form and computations are performed by Fortran program. The results describe velocity, temperature profiles both in transient and steady state conditions. An approximate value of heat transfer coefficient and the effects of Pr on convection flow are also presented.

Keywords: natural convection, vertical plate, velocity and temperature profiles, steady and unsteady

Procedia PDF Downloads 464

Authors: Ahmed Alghurabi, Mysara Mohyaldinn, Shiferaw Jufar, Obai Younis, Abdullah Abduljabbar

Abstract:

Erosion modeling equations were typically acquired from regulated experimental trials for solid particles entrained in single-phase or multi-phase flows. Evidently, those equations were later employed to predict the erosion damage caused by the continuous impacts of solid particles entrained in streamflow. It is also well-known that the particle impact angle and velocity do not change drastically in gas-sand flow erosion prediction; hence an accurate prediction of erosion can be projected. On the contrary, high-density fluid flows, such as water flow, through complex geometries, such as sand screens, greatly affect the sand particles’ trajectories/tracks and consequently impact the erosion rate predictions. Particle tracking models and erosion equations are frequently applied simultaneously as a method to improve erosion visualization and estimation. In the present work, computational fluid dynamic (CFD)-based erosion modeling was performed using a commercially available software; ANSYS Fluent. The continuous phase (water flow) behavior was simulated using the realizable K-epsilon model, and the secondary phase (solid particles), having a 5% flow concentration, was tracked with the help of the discrete phase model (DPM). To accomplish a successful erosion modeling, three erosion equations from the literature were utilized and introduced to the ANSYS Fluent software to predict the screen wire-slot velocity surge and estimate the maximum erosion rates on the screen surface. Results of turbulent kinetic energy, turbulence intensity, dissipation rate, the total pressure on the screen, screen wall shear stress, and flow velocity vectors were presented and discussed. Moreover, the particle tracks and path-lines were also demonstrated based on their residence time, velocity magnitude, and flow turbulence. On one hand, results from the utilized erosion equations have shown similarities in screen erosion patterns, locations, and DPM concentrations. On the other hand, the model equations estimated slightly different values of maximum erosion rates of the wire-wrapped screen. This is solely based on the fact that the utilized erosion equations were developed with some assumptions that are controlled by the experimental lab conditions.

Keywords: CFD simulation, erosion rate prediction, material loss due to erosion, water-sand flow

Procedia PDF Downloads 130

Authors: X. Wang, J. S. Kuang

Abstract:

The Fixed-angle Softened Truss Model with Tension-stiffening (FASTMT) has a superior performance in predicting the shear behaviour of reinforced concrete (RC) membrane elements, especially for the post-cracking behaviour. Nevertheless, massive computational work is inevitable due to the multiple transcendental equations involved in the stress-strain relationship. In this paper, an iterative root-finding technique is introduced to FASTMT for solving quickly the transcendental equations of the tension-stiffening effect of RC membrane elements. This fast FASTMT, which performs in MATLAB, uses the bisection method to calculate the tensile stress of the membranes. By adopting the simplification, the elapsed time of each loop is reduced significantly and the transcendental equations can be solved accurately. Owing to the high efficiency and good accuracy as compared with FASTMT, the fast FASTMT can be further applied in quick prediction of shear behaviour of complex large-scale RC structures.

Keywords: bisection method, FASTMT, iterative root-finding technique, reinforced concrete membrane

Procedia PDF Downloads 247