Search results for: Scalar wave equation

Authors: R. Haoui

Abstract:

The purpose of this work is to simulate the flow at the exit of Vulcan 1 engine of European launcher Ariane 5. The geometry of the propellant nozzle is already determined using the characteristics method. The pressure in the outlet section of the nozzle is less than atmospheric pressure on the ground, causing the existence of oblique and normal shock waves at the exit. During the rise of the launcher, the atmospheric pressure decreases and the shock wave disappears. The code allows the capture of shock wave at exit of nozzle. The numerical technique uses the Flux Vector Splitting method of Van Leer to ensure convergence and avoid the calculation instabilities. The Courant, Friedrichs and Lewy coefficient (CFL) and mesh size level are selected to ensure the numerical convergence. The nonlinear partial derivative equations system which governs this flow is solved by an explicit unsteady numerical scheme by the finite volume method. The accuracy of the solution depends on the size of the mesh and also the step of time used in the discretized equations. We have chosen in this study the mesh that gives us a stationary solution with good accuracy.

Keywords: Launchers, supersonic flow, finite volume, nozzles, shock wave.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 853

Authors: Minghui Wang, Juntao Zhang

Abstract:

An inversion-free iterative algorithm is presented for solving nonlinear matrix equation with a stepsize parameter t. The existence of the maximal solution is discussed in detail, and the method for finding it is proposed. Finally, two numerical examples are reported that show the efficiency of the method.

Keywords: Inversion-free method, Hermitian positive definite solution, Maximal solution, Convergence.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1579

Authors: M. Karami Khorramabadi, A. R. Nezamabadi

Abstract:

This paper studies free vibration of functionally graded beams Subjected to Axial Load that is simply supported at both ends lies on a continuous elastic foundation. The displacement field of beam is assumed based on Engesser-Timoshenko beam theory. The Young's modulus of beam is assumed to be graded continuously across the beam thickness. Applying the Hamilton's principle, the governing equation is established. Resulting equation is solved using the Euler's Equation. The effects of the constituent volume fractions and foundation coefficient on the vibration frequency are presented. To investigate the accuracy of the present analysis, a compression study is carried out with a known data.

Keywords: Functionally Graded Beam, Free Vibration, Elastic Foundation, Engesser-Timoshenko Beam Theory.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1902

Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for singular differential equation in Banach space, which improved and generalize the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1433

Authors: Huei-Fu Lu

Abstract:

This study links up the theories of social psychology, economics and sport management to assess the impact of sport participation on subjective well-being (SWB) and use a simple statistic method to estimate the relative monetary value that sport participation derives SWB for Taiwan-s college students. By constructing proper measurements on sport participation and SWB respectively, a structural equation model (SEM) is developed to perform a confirmatory factory analysis, and the causal relationship between sport participation and SWB as well as the effect of the demographic variables on these two concepts are also discussed.

Keywords: Demographics, Economic value, Sport participation, Structural equation modeling (SEM), Subjective well-being.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1630

Authors: Muthana A. M. Jameel Al-Jaboori

Abstract:

In this paper, we will present a mathematical model to design a system able to generate electricity from ocean-sea waves. We will use the basic principles of the transfer of the energy potential of waves in a chamber to force the air inside a vertical or inclined cylindrical column, which is topped by a wind turbine to rotate the electric generator. The present mathematical model included a high number of variables such as the wave, height, width, length, velocity, and frequency, as well as others for the energy cylindrical column, like varying diameters and heights, and the wave chamber shape diameter and height. While for the wells wind turbine the variables included the number of blades, length, width, and clearance, as well as the rotor and tip radius. Additionally, the turbine rotor and blades must be made from the light and strong material for a smooth blade surface. The variables were too vast and high in number. Then the program was run successfully within the MATLAB and presented very good modeling results.

Keywords: Water wave, model, wells turbine, MATLAB program, results.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1152

Authors: Fatma Ghangir, Andrzej F. Nowakowski, Franck C. G. A. Nicolleau, Thomas M. Michelitsch

Abstract:

The performance of high-resolution schemes is investigated for unsteady, inviscid and compressible multiphase flows. An Eulerian diffuse interface approach has been chosen for the simulation of multicomponent flow problems. The reduced fiveequation and seven equation models are used with HLL and HLLC approximation. The authors demonstrated the advantages and disadvantages of both seven equations and five equations models studying their performance with HLL and HLLC algorithms on simple test case. The seven equation model is based on two pressure, two velocity concept of Baer–Nunziato [10], while five equation model is based on the mixture velocity and pressure. The numerical evaluations of two variants of Riemann solvers have been conducted for the classical one-dimensional air-water shock tube and compared with analytical solution for error analysis.

Keywords: Multiphase flow, gas-liquid flow, Godunov schems, Riemann solvers, HLL scheme, HLLC scheme.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2572

Authors: Ali Göksenli, Barlas Eryürek

Abstract:

In this study, failure analysis of pipe system at a micro hydroelectric power plant is investigated. Failure occurred at the pipe system in the powerhouse during shut down operation of the water flow by a valve. This locking had caused a sudden shock wave, also called “Water-hammer effect”, resulting in noise and inside pressure increase. After visual investigation of the effect of the shock wave on the system, a circumference crack was observed at the pipe flange weld region. To establish the reason for crack formation, calculations of pressure and stress values at pipe, flange and welding seams were carried out and concluded that safety factor was high (2.2), indicating that no faulty design existed. By further analysis, pipe system and hydroelectric power plant was examined. After observations it is determined that the plant did not include a ventilation nozzle (air trap), that prevents the system of sudden pressure increase inside the pipes which is caused by water-hammer effect. Analyses were carried out to identify the influence of water-hammer effect on inside pressure increase and it was concluded that, according Jowkowsky’s equation, shut down time is effective on inside pressure increase. The valve closing time was uncertain but by a shut down time of even one minute, inside pressure would increase by 7.6 bar (working pressure was 34.6 bar). Detailed investigations were also carried out on the assembly of the pipe-flange system by considering technical drawings. It was concluded that the pipe-flange system was not installed according to the instructions. Two of five weld seams were not applied and one weld was carried out faulty. This incorrect and inadequate weld seams resulted in; insufficient connection of the pipe to the flange constituting a strong notch effect at weld seam regions, increase in stress values and the decrease of strength and safety factor.

Keywords: Failure analysis, hydroelectric plant, water-hammer, crack, welding seam.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2705

Authors: A.Roshandel, N.Hedayat, H.kiamanesh

Abstract:

The one of most important objects in implementation of damage analysis observations is manner of dam break wave propagation. In this paper velocity and wave height due dam break in with and without tailwater states for appointment hazardous lands and flood radius are investigate. In order to modeling above phenomenon finite volume method of Roe type for solving shallow water equations is used. Results indicated that in the dry bed state risk radius due to dam break is too high. While in the wet bed risk radius has a less wide. Therefore in the first state constructions and storage facilities are encountered with destruction risk. Further velocity due to dam break in the second state is more comparing to the first state. Hence erosion and scour the river bed in the dry bed is too more compare to the wet bed.

Keywords: Dam break, finite volume method, tailwater, risk radius, scour

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1591

Authors: Evgeniy Burlutskiy

Abstract:

The paper presents a one-dimensional transient mathematical model of compressible thermal multi-component gas mixture flows in pipes. The set of the mass, momentum and enthalpy conservation equations for gas phase is solved. Thermo-physical properties of multi-component gas mixture are calculated by solving the Equation of State (EOS) model. The Soave-Redlich-Kwong (SRK-EOS) model is chosen. Gas mixture viscosity is calculated on the basis of the Lee-Gonzales-Eakin (LGE) correlation. Numerical analysis on rapid decompression in conventional dry gases is performed by using the proposed mathematical model. The model is validated on measured values of the decompression wave speed in dry natural gas mixtures. All predictions show excellent agreement with the experimental data at high and low pressure. The presented model predicts the decompression in dry natural gas mixtures much better than GASDECOM and OLGA codes, which are the most frequently-used codes in oil and gas pipeline transport service.

Keywords: Mathematical model, Rapid Gas Decompression

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2964

Authors: Fathi Alwafie

Abstract:

This paper presents a ray tracing simulation technique for characterize the radiowave propagation inside building. The implementation of an algorithm capable of enumerating a large number of propagation paths in interactive time for the special case of 2.5D. The effective dielectric constants of the building structure in the simulations are indicated. The study describes an efficient 2.5D model of ray tracing algorithm were compared with 3D model. The result of the first investigations is that the environment of the indoor wave significantly changes as we change the electric parameters of material constructions. A detailed analysis of the dependence of the indoor wave on the wideband characteristics of the channel: root mean square (RMS) delay spread characteristics and Mean excess delay, is also investigated.

Keywords: Picrocellular, Propagation, Ray tracing

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1585

Authors: Azizollah Khormali, Seyyed Shahab Tabatabaee Moradi, Dmitry Petrakov

Abstract:

One of the most important parameters in petroleum reservoirs is the pressure distribution along the reservoir, as the pressure varies with the time and location. A popular method to determine the pressure distribution in a reservoir in the unsteady state regime of flow is applying Darcy’s equation and solving this equation numerically. The numerical simulation of reservoirs is based on these numerical solutions of different partial differential equations (PDEs) representing the multiphase flow of fluids. Pressure profile has obtained in a one dimensional system solving Darcy’s equation explicitly. Changes of pressure profile in three situations are investigated in this work. These situations include section length changes, step time changes and time approach to infinity. The effects of these changes in pressure profile are shown and discussed in the paper.

Keywords: Explicit solution, Numerical simulation, Petroleum reservoir, Pressure distribution.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 4166

Authors: F. Soleymani, M. Sharifi

Abstract:

Most of the nonlinear equation solvers do not converge always or they use the derivatives of the function to approximate the root of such equations. Here, we give a derivative-free algorithm that guarantees the convergence. The proposed two-step method, which is to some extent like the secant method, is accompanied with some numerical examples. The illustrative instances manifest that the rate of convergence in proposed algorithm is more than the quadratically iterative schemes.

Keywords: Non-linear equation, iterative methods, derivative-free, convergence.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1746

Authors: A.Tajaddini

Abstract:

In this paper, two matrix iterative methods are presented to solve the matrix equation A1X1B1 + A2X2B2 + ... + AlXlBl = C the minimum residual problem l i=1 AiXiBi−CF = minXi∈BRni×ni l i=1 AiXiBi−CF and the matrix nearness problem [X1, X2, ..., Xl] = min[X1,X2,...,Xl]∈SE [X1,X2, ...,Xl] − [X1, X2, ..., Xl]F , where BRni×ni is the set of bisymmetric matrices, and SE is the solution set of above matrix equation or minimum residual problem. These matrix iterative methods have faster convergence rate and higher accuracy than former methods. Paige’s algorithms are used as the frame method for deriving these matrix iterative methods. The numerical example is used to illustrate the efficiency of these new methods.

Keywords: Bisymmetric matrices, Paige’s algorithms, Least square.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1365

Authors: Kaoutar Lamrini Uahabi, Mohamed Atounti

Abstract:

In the present work, we consider one category of curves denoted by L(p, k, r, n). These curves are continuous arcs which are trajectories of roots of the trinomial equation zn = αzk + (1 − α), where z is a complex number, n and k are two integers such that 1 ≤ k ≤ n − 1 and α is a real parameter greater than 1. Denoting by L the union of all trinomial curves L(p, k, r, n) and using the box counting dimension as fractal dimension, we will prove that the dimension of L is equal to 3/2.

Keywords: Feasible angles, fractal dimension, Minkowski sausage, trinomial curves, trinomial equation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 607

Authors: Lavanya Srinivasan

Abstract:

Biometric identification is to identify unique features in a person like fingerprints, iris, ear, and voice recognition that need the subject's permission and physical contact. Gait biometric is used to identify the unique gait of the person by extracting moving features. The main advantage of gait biometric to identify the gait of a person at a distance, without any physical contact. In this work, the gait biometric is used for person re-identification. The person walking naturally compared with the same person walking with bag, coat and case recorded using long wave infrared, short wave infrared, medium wave infrared and visible cameras. The videos are recorded in rural and in urban environments. The pre-processing technique includes human identified using You Only Look Once, background subtraction, silhouettes extraction and synthesis Gait Entropy Image by averaging the silhouettes. The moving features are extracted from the Gait Entropy Energy Image. The extracted features are dimensionality reduced by the Principal Component Analysis and recognized using different classifiers. The comparative results with the different classifier show that Linear Discriminant Analysis outperform other classifiers with 95.8% for visible in the rural dataset and 94.8% for longwave infrared in the urban dataset.

Keywords: biometric, gait, silhouettes, You Only Look Once

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 489

Authors: A. Maghari, V. H. Maleki

Abstract:

In this paper, we present a quantum statistical mechanical formulation from our recently analytical expressions for partial-wave transition matrix of a three-particle system. We report the quantum reactive cross sections for three-body scattering processes 1+(2,3)→1+(2,3) as well as recombination 1+(2,3)→1+(3,1) between one atom and a weakly-bound dimer. The analytical expressions of three-particle transition matrices and their corresponding cross-sections were obtained from the threedimensional Faddeev equations subjected to the rank-two non-local separable potentials of the generalized Yamaguchi form. The equilibrium quantum statistical mechanical properties such partition function and equation of state as well as non-equilibrium quantum statistical properties such as transport cross-sections and their corresponding transport collision integrals were formulated analytically. This leads to obtain the transport properties, such as viscosity and diffusion coefficient of a moderate dense gas.

Keywords: Statistical mechanics, Nonlocal separable potential, three-body interaction, Faddeev equations.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2093

Authors: Nopparat Pochai

Abstract:

Smoke discharging is a main reason of air pollution problem from industrial plants. The obstacle of a building has an affect with the air pollutant discharge. In this research, a mathematical model of the smoke dispersion from two sources and one source with a structural obstacle is considered. The governing equation of the model is an isothermal mass transfer model in a viscous fluid. The finite element method is used to approximate the solutions of the model. The triangular linear elements have been used for discretising the domain, and time integration has been carried out by semi-implicit finite difference method. The simulations of smoke dispersion in cases of one chimney and two chimneys are presented. The maximum calculated smoke concentration of both cases are compared. It is then used to make the decision for smoke discharging and air pollutant control problems on industrial area.

Keywords: Air pollution, Smoke dispersion, Finite element method, Stream function, Vorticity equation, Convection-diffusion equation, Semi-implicit method

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2077

Authors: Taiwo Olusoji Lawrence, Peace Mawo Aaron

Abstract:

Seismic analysis of bedforms has proven to be one of the best ways to study deepwater sedimentary features. Canyons are known to be sediment transportation conduit. Sediment wave are large-scale depositional bedforms in various parts of the world's oceans formed predominantly by suspended load transport. These undulating objects usually have tens of meters to a few kilometers in wavelength and a height of several meters. Cyclic steps have long long-wave upstream-migrating bedforms confined by internal hydraulic jumps. They usually occur in regions with high gradients and slope breaks. Cyclic steps and migrating sediment waves are the most common bedform on the seafloor. Cyclic steps and related sediment wave bedforms are significant to the morpho-dynamic evolution of deep-water depositional systems architectural elements, especially those located along tectonically active margins with high gradients and slope breaks that can promote internal hydraulic jumps in turbidity currents. This report examined sedimentary activities and sediment transportation in submarine canyons and provided distinctive insight into factors that created a complex seabed canyon system in the Ceara Fortaleza basin Brazilian Equatorial Margin (BEM). The growing importance of cyclic steps made it imperative to understand the parameters leading to their formation, migration, and architecture as well as their controls on sediment transport in canyon thalweg. We extracted the parameters of the observed bedforms and evaluated the aspect ratio and asymmetricity. We developed a relationship between the hydraulic jump magnitude, depth of the hydraulic fall and the length of the cyclic step therein. It was understood that an increase in the height of the cyclic step increases the magnitude of the hydraulic jump and thereby increases the rate of deposition on the preceding stoss side. An increase in the length of the cyclic steps reduces the magnitude of the hydraulic jump and reduces the rate of deposition at the stoss side. Therefore, flat stoss side was noticed at most preceding cyclic step and sediment wave.

Keywords: Ceara Fortaleza, sediment wave, cyclic steps, submarine canyons.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 757

Authors: H. Mirzabozorg, M. Varmazyari

Abstract:

In the present article, effect of non-uniform excitation of reservoir bottom on nonlinear response of concrete gravity dams is considered. Anisotropic damage mechanics approach is used to model nonlinear behavior of mass concrete in 2D space. The tallest monolith of Pine Flat dam is selected as a case study. The horizontal and vertical components of 1967 Koyna earthquake is used to excite the system. It is found that crest response and stresses within the dam body decrease significantly when the reservoir is excited nonuniformly. In addition, the crack profiles within the dam body and in vicinity of the neck decreases.

Keywords: Concrete gravity dam, dam-reservoir-foundation interaction, traveling wave, damage mechanics.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1781

Authors: Kangkang Wu, Kaizhi Wang, Zhijun Yuan

Abstract:

This paper deals with a mini radar system aimed at detecting small targets at the low latitude. The radar operates at Ku-band in the frequency modulated continuous wave (FMCW) mode with two receiving channels. The radar system has the characteristics of compactness, mobility, and low power consumption. This paper focuses on the implementation of the radar system, and the Block least mean square (Block LMS) algorithm is applied to minimize the fortuitous distortion. It is validated from a series of experiments that the track of the unmanned aerial vehicle (UAV) can be easily distinguished with the radar system.

Keywords: Unmanned aerial vehicle, interference, block least mean square, frequency modulated continuous wave.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1064

Authors: Fatemeh Panjeh Ali Beik

Abstract:

In the present work, we propose a new method for solving the matrix equation AXB=F . The new method can be considered as a generalized form of the well-known global full orthogonalization method (Gl-FOM) for solving multiple linear systems. Hence, the method will be called extended Gl-FOM (EGl- FOM). For implementing EGl-FOM, generalized forms of block Krylov subspace and global Arnoldi process are presented. Finally, some numerical experiments are given to illustrate the efficiency of our new method.

Keywords: Matrix equations, Iterative methods, Block Krylovsubspace methods.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1950

Authors: Marziyeh Halimi, Roushanak Lotfikar, Simin Mansouri Borojeni

Abstract:

In this paper we considered the Neumann problem for the fourth order differential equation. First we define the weighted Sobolev space 2 Wα and generalized solution for this equation. Then we consider the existence and uniqueness of the generalized solution, as well as give the description of the spectrum and of the domain of definition of the corresponding operator.

Keywords: Neumann problem, weighted Sobolev spaces, generalized solution, spectrum of linear operators.2000 mathematic subject classification: 34A05, 34A30.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1399

Authors: H. Taheri Shahraiyni, B. Ataie Ashtiani

Abstract:

Flow movement in unsaturated soil can be expressed by a partial differential equation, named Richards equation. The objective of this study is the finding of an appropriate implicit numerical solution for head based Richards equation. Some of the well known finite difference schemes (fully implicit, Crank Nicolson and Runge-Kutta) have been utilized in this study. In addition, the effects of different approximations of moisture capacity function, convergence criteria and time stepping methods were evaluated. Two different infiltration problems were solved to investigate the performance of different schemes. These problems include of vertical water flow in a wet and very dry soils. The numerical solutions of two problems were compared using four evaluation criteria and the results of comparisons showed that fully implicit scheme is better than the other schemes. In addition, utilizing of standard chord slope method for approximation of moisture capacity function, automatic time stepping method and difference between two successive iterations as convergence criterion in the fully implicit scheme can lead to better and more reliable results for simulation of fluid movement in different unsaturated soils.

Keywords: Finite Difference methods, Richards equation, fullyimplicit, Crank-Nicolson, Runge-Kutta.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2344

Authors: Z. El Felsoufi, L. Azrar

Abstract:

This paper studies a mathematical model based on the integral equations for dynamic analyzes numerical investigations of a non-uniform or multi-material composite beam. The beam is subjected to a sub-tangential follower force and elastic foundation. The boundary conditions are represented by generalized parameterized fixations by the linear and rotary springs. A mathematical formula based on Euler-Bernoulli beam theory is presented for beams with variable cross-sections. The non-uniform section introduces non-uniformity in the rigidity and inertia of beams and consequently, more complicated equilibrium who governs the equation. Using the boundary element method and radial basis functions, the equation of motion is reduced to an algebro-differential system related to internal and boundary unknowns. A generalized formula for the deflection, the slope, the moment and the shear force are presented. The free vibration of non-uniform loaded beams is formulated in a compact matrix form and all needed matrices are explicitly given. The dynamic stability analysis of slender beam is illustrated numerically based on the coalescence criterion. A realistic case related to an industrial chimney is investigated.

Keywords: Chimney, BEM and integral equation formulation, non uniform cross section, vibration and Flutter.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1588

Authors: Sanjib Kr Pal, S. Bhattacharyya

Abstract:

Mixed convection of Cu-water nanofluid in an enclosure with thick wavy bottom wall has been investigated numerically. A co-ordinate transformation method is used to transform the computational domain into an orthogonal co-ordinate system. The governing equations in the computational domain are solved through a pressure correction based iterative algorithm. The fluid flow and heat transfer characteristics are analyzed for a wide range of Richardson number (0.1 ≤ Ri ≤ 5), nanoparticle volume concentration (0.0 ≤ ϕ ≤ 0.2), amplitude (0.0 ≤ α ≤ 0.1) of the wavy thick- bottom wall and the wave number (ω) at a fixed Reynolds number. Obtained results showed that heat transfer rate increases remarkably by adding the nanoparticles. Heat transfer rate is dependent on the wavy wall amplitude and wave number and decreases with increasing Richardson number for fixed amplitude and wave number. The Bejan number and the entropy generation are determined to analyze the thermodynamic optimization of the mixed convection.

Keywords: Entropy generation, mixed convection, conjugate heat transfer, numerical, nanofluid, wall waviness.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1021

Authors: Li Xiguang

Abstract:

In this paper, by constructing a special non-empty closed convex set and utilizing M¨onch fixed point theory, we investigate the existence of solution for a class of fourth-order singular differential equation in Banach space, which improved and generalized the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1652

Authors: Changqiao Wu, Guoqing Ding, Xin Chen

Abstract:

In this paper, ways of modeling dynamic measurement systems are discussed. Specially, for linear system with single-input single-output, it could be modeled with shallow neural network. Then, gradient based optimization algorithms are used for searching the proper coefficients. Besides, method with normal equation and second order gradient descent are proposed to accelerate the modeling process, and ways of better gradient estimation are discussed. It shows that the mathematical essence of the learning objective is maximum likelihood with noises under Gaussian distribution. For conventional gradient descent, the mini-batch learning and gradient with momentum contribute to faster convergence and enhance model ability. Lastly, experimental results proved the effectiveness of second order gradient descent algorithm, and indicated that optimization with normal equation was the most suitable for linear dynamic models.

Keywords: Dynamic system modeling, neural network, normal equation, second order gradient descent.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 750

Authors: Promise A. Azor, Avievie Igodo, Esabai M. Ase

Abstract:

The paper merged the return of premium clause and voluntary contributions to investigate retirees’ investment plan in a defined contributory (DC) pension scheme with a portfolio comprising of a risk-free asset and a risky asset whose price process is described by geometric Brownian motion (GBM). The paper considers additional voluntary contributions paid by members, charge on balance by pension fund administrators and the mortality risk of members of the scheme during the accumulation period by introducing return of premium clause. To achieve this, the Weilbull mortality force function is used to establish the mortality rate of members during accumulation phase. Furthermore, an optimization problem from the Hamilton Jacobi Bellman (HJB) equation is obtained using dynamic programming approach. Also, the Legendre transformation method is used to transform the HJB equation which is a nonlinear partial differential equation to a linear partial differential equation and solves the resultant equation for the value function and the optimal distribution plan under logarithm utility function. Finally, numerical simulations of the impact of some important parameters on the optimal distribution plan were obtained and it was observed that the optimal distribution plan is inversely proportional to the initial fund size, predetermined interest rate, additional voluntary contributions, charge on balance and instantaneous volatility.

Keywords: Legendre transform, logarithm utility, optimal distribution plan, return clause of premium, charge on balance, Weibull mortality function.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 159

Authors: Sameerah Jamal, Abdul Hamid Kara, Ashfaque H. Bokhari

Abstract:

Equations on curved manifolds display interesting properties in a number of ways. In particular, the symmetries and, therefore, the conservation laws reduce depending on how curved the manifold is. Of particular interest are the wave and Gordon-type equations; we study the symmetry properties and conservation laws of these equations on the Milne and Bianchi type III metrics. Properties of reduction procedures via symmetries, variational structures and conservation laws are more involved than on the well known flat (Minkowski) manifold.

Keywords: Bianchi metric, conservation laws, Milne metric, symmetries.

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1750