Search results for: Einstein's field equation

Authors: Sani Isa, Ali Musa

Abstract:

Burgers’ fluid with a fractional derivatives model in an annulus was analyzed. Combining appropriately the basic equations, with the fractionalized fractional Burger’s fluid model allow us to determine the velocity field, temperature and shear stress. The governing partial differential equation was solved using the combine Laplace transformation method and Riemann sum approximation to give velocity field, temperature and shear stress on the fluid flow. The influence of various parameters like fractional parameters, relaxation time and retardation time, are drawn. The results obtained are simulated using Mathcad software and presented graphically. From the graphical results, we observed that the relaxation time and time helps the flow pattern, on the other hand, other material constants resist the fluid flow while fractional parameters effect on fluid flow is opposite to each other.

Keywords: sani isa, Ali musaburger’s fluid, Laplace transform, fractional derivatives, annulus

Procedia PDF Downloads 10

Authors: Chao-Qing Dai

Abstract:

In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation.

Keywords: discrete sine-Gordon equation, variable coefficient Jacobian elliptic function method, exact solutions, equation

Procedia PDF Downloads 662

Authors: Surajit Chattopadhyay

Abstract:

Accelerated expansion of the current universe is well-established in the literature. Dark energy and modified gravity are two approaches to account for this accelerated expansion. In the present work, we consider scalar field models of dark energy, namely, tachyon and DBI essence in the framework of chameleon Brans-Dicke cosmology. The equation of state parameter is reconstructed and the subsequent cosmological implications are studied. We examined the stability for the obtained solutions of the crossing of the phantom divide under a quantum correction of massless conformally invariant fields and we have seen that quantum correction could be small when the phantom crossing occurs and the obtained solutions of the phantom crossing could be stable under the quantum correction. In the subsequent phase, we have established a correspondence between the NHDE model and the quintessence, the DBI-essence and the tachyon scalar field models in the framework of chameleon Brans–Dicke cosmology. We reconstruct the potentials and the dynamics for these three scalar field models we have considered. The reconstructed potentials are found to increase with the evolution of the universe and in a very late stage they are observed to decay.

Keywords: dark energy, holographic principle, modified gravity, reconstruction

Procedia PDF Downloads 401

Authors: Reza Mollapourasl, Majid Haghi

Abstract:

In this study, we develop local meshfree methods known as radial basis function-generated finite difference (RBF-FD) method and Hermite finite difference (RBF-HFD) method to design stencil weights and spatial discretization for Helmholtz equation. The convergence and stability of schemes are investigated numerically in three dimensions with irregular shaped domain. These localized meshless methods incorporate the advantages of the RBF method, finite difference and Hermite finite difference methods to handle the ill-conditioning issue that often destroys the convergence rate of global RBF methods. Moreover, numerical illustrations show that the proposed localized RBF type methods are efficient and applicable for problems with complex geometries. The convergence and accuracy of both schemes are compared by solving a test problem.

Keywords: radial basis functions, Hermite finite difference, Helmholtz equation, stability

Procedia PDF Downloads 95

Authors: Yanchun Zuo, Yingao Liu, Wei Liu, Le Yu, Run Huang, Lixin Guo

Abstract:

Electric field detection is important in many application scenarios. The traditional strategy is measuring the electric field with a man walking around in the area under test. This strategy cannot provide a satisfactory measurement accuracy. To solve the mentioned problem, an autopilot measurement system is divided. A mini-car is produced, which can travel in the area under test according to respect to the program within the CPU. The electric field measurement platform (EFMP) carries a central computer, two horn antennas, and a vector network analyzer. The mini-car stop at the sampling points according to the preset. When the car stops, the EFMP probes the electric field and stores data on the hard disk. After all the sampling points are traversed, an electric field map can be plotted. The proposed system can give an accurate field distribution description of the chamber.

Keywords: autopilot mini-car measurement system, electric field detection, field map, static zone measurement

Procedia PDF Downloads 96

Authors: Pius W. Molo Chin

Abstract:

Real life problems such as the Huxley equation are always modeled as nonlinear differential equations. These problems need accurate and reliable methods for their solutions. In this paper, we propose a nonstandard finite difference method in time and the Galerkin combined with the compactness method in the space variables. This coupled method, is used to analyze a two dimensional Huxley equation for the existence and uniqueness of the continuous solution of the problem in appropriate spaces to be defined. We proceed to design a numerical scheme consisting of the aforementioned method and show that the scheme is stable. We further show that the stable scheme converges with the rate which is optimal in both the L2 as well as the H1-norms. Furthermore, we show that the scheme replicates the decaying qualities of the exact solution. Numerical experiments are presented with the help of an example to justify the validity of the designed scheme.

Keywords: Huxley equations, non-standard finite difference method, Galerkin method, optimal rate of convergence

Procedia PDF Downloads 209

Authors: Maryam Khazaei Pool, Lori Lewis

Abstract:

This is a summary of articles based on higher order B-splines methods and the variation of B-spline methods such as Quadratic B-spline Finite Elements Method, Exponential Cubic B-Spline Method, Septic B-spline Technique, Quintic B-spline Galerkin Method, and B-spline Galerkin Method based on the Quadratic B-spline Galerkin method (QBGM) and Cubic B-spline Galerkin method (CBGM). In this paper, we study the B-spline methods and variations of B-spline techniques to find a numerical solution to the Burgers’ equation. A set of fundamental definitions, including Burgers equation, spline functions, and B-spline functions, are provided. For each method, the main technique is discussed as well as the discretization and stability analysis. A summary of the numerical results is provided, and the efficiency of each method presented is discussed. A general conclusion is provided where we look at a comparison between the computational results of all the presented schemes. We describe the effectiveness and advantages of these methods.

Keywords: Burgers’ equation, Septic B-spline, modified cubic B-spline differential quadrature method, exponential cubic B-spline technique, B-spline Galerkin method, quintic B-spline Galerkin method

Procedia PDF Downloads 117

Authors: D. Ravinder

Abstract:

Nickel ferrites and Ni doped Lithium nano ferrites [Li0.5Fe0.5]1-xNixFe2O4 with x= 0.8 and 1.0 synthesized by citrate-gel auto combustion method. The broad peaks in the X-ray diffraction pattern (XRD) indicate a crystalline behavior of the prepared samples. Low temperature magnetization studies i,e Field Cooled (FC) and Zero Field Cooled (ZFC) magnetic studies of the investigated samples are measured by using vibrating sample magnetometer (VSM). The magnetization of the prepared samples as a function of an applied magnetic field 10 T was measured at two different temperatures 5 K and 310 K. Field Cooled (FC) and Zero Field Cooled (ZFC) magnetization measurements under an applied field of 100 Oe and 1000 Oe in the temperature range of 5–375 K were carried out.

Keywords: ferro-spinels, field cooled (FC), Zero Field Cooled (ZFC) and blocking temperature, superpara magnetism, drug delivery applications

Procedia PDF Downloads 547

Authors: Aleksandar Dedic, Dusko Salemovic, Milorad Danilovic, Radomir Kuzmanovic

Abstract:

This paper takes into consideration the influence of bonding energy of water on energy demand of vacuum wood drying using the specific method of obtaining sorption isotherms. The experiment was carried out on oak wood at vacuum pressures of: 0.7 bar, 0.5bar and 0.3bar. The experimental work was done to determine a mathematical equation between the moisture content and energy of water-bonding. This equation helps in finding the average amount of energy of water-bonding necessary in calculation of energy consumption by use of the equation of heat balance in real drying chambers. It is concluded that the energy of water-bonding is large enough to be included into consideration. This energy increases at lower values of moisture content, when drying process approaches to the end, and its average values are lower on lower pressure.

Keywords: bonding energy, drying, isosters, oak, vacuum

Procedia PDF Downloads 265

Authors: Suprit Pradhan, Sushil Pradhan

Abstract:

Photosynthesis is a physiological process where green plants prepare their food from carbon dioxide from the atmosphere and water being absorbed from the soil in presence of sun light and chlorophyll. From this definition it is clear that four reactants (Carbon Dioxide, Water, Light and Chlorophyll) are essential for the process to proceed and the product is a sugar or carbohydrate ultimately stored as starch. The entire process has “Light Reaction” (Photochemical) and “Dark Reaction” (Biochemical). Biochemical reactions are very much complicated being catalysed by various enzymes and the path of carbon is known as “Calvin Cycle” according to the name of its discover. The overall reaction which is now universally accepted can be explained like this. Six molecules of carbon dioxide react with twelve molecules of water in presence of chlorophyll and sun light to give only one molecule of sugar (Carbohydrate) six molecules of water and six molecules of oxygen is being evolved in gaseous form. This is the accepted equation and also chemically balanced. However while teaching the subject the author came across a new balanced equation from among the students who happened to be the daughter of the author. In the new balanced equation in place of twelve water molecules in the reactant side seven molecules can be expressed and accordingly in place of six molecules of water in the product side only one molecule of water is produced. The energetics of the photosynthesis as related to the environment and the newly reported balanced chemical equation has been discussed in detail in the present research paper presentation in this international conference on energy, environmental and chemical engineering.

Keywords: biochemistry, enzyme , isotope, photosynthesis

Procedia PDF Downloads 506

Authors: Piyarat Parklug, Busaba Supawattanaobodee, Penpat Pinyowattanasilp

Abstract:

The radioactive iodine thyroid uptake (RAIU) has been widely used to differentiate the cause of thyrotoxicosis and treatment. Twenty-four hours RAIU is routinely used to calculate the dose of radioactive iodine (RAI) therapy; however, 2 days protocol is required. This study aims to evaluate the modification of Penpat Pinyowattanasilp equation application by the exclusion of outlier data, 3 hours RAIU less than 20% and more than 80%, to improve prediction of 24-hour uptake. The equation is predicted 24 hours RAIU (P24RAIU) = 32.5+0.702 (3 hours RAIU). Then calculating separation first and second therapeutic doses in Graves’ disease patients. Methods; This study was a retrospective study at Faculty of Medicine Vajira Hospital in Bangkok, Thailand. Inclusion were Graves’ disease patients who visited RAI clinic between January 2014-March 2019. We divided subjects into 2 groups according to first and second therapeutic doses. Results; Our study had a total of 151 patients. The study was done in 115 patients with first RAI dose and 36 patients with second RAI dose. The P24RAIU are highly correlated with actual 24-hour RAIU in first and second therapeutic doses (r = 0.913, 95% CI = 0.876 to 0.939 and r = 0.806, 95% CI = 0.649 to 0.897). Bland-Altman plot shows that mean differences between predictive and actual 24 hours RAI in the first dose and second dose were 2.14% (95%CI 0.83-3.46) and 1.37% (95%CI -1.41-4.14). The mean first actual and predictive therapeutic doses are 8.33 ± 4.93 and 7.38 ± 3.43 milliCuries (mCi) respectively. The mean second actual and predictive therapeutic doses are 6.51 ± 3.96 and 6.01 ± 3.11 mCi respectively. The predictive therapeutic doses are highly correlated with the actual dose in first and second therapeutic doses (r = 0.907, 95% CI = 0.868 to 0.935 and r = 0.953, 95% CI = 0.909 to 0.976). Bland-Altman plot shows that mean difference between predictive and actual P24RAIU in the first dose and second dose were less than 1 mCi (-0.94 and -0.5 mCi). This modification equation application is simply used in clinical practice especially patient with 3 hours RAIU in range of 20-80% in a Thai population. Before use, this equation for other population should be tested for the correlation.

Keywords: equation, Graves’disease, prediction, 24-hour uptake

Procedia PDF Downloads 135

Authors: Ismail Seçer

Abstract:

The purpose of this study is to analyze the relationship between school burnout and academic motivation in high school students. The working group of the study consists of 455 students from the high schools in Erzurum city center, selected with appropriate sampling method. School Burnout Scale and Academic Motivation Scale were used in the study to collect data. Correlation analysis and structural equation modeling were used in the analysis of the data collected through the study. As a result of the study, it was determined that there are significant and negative relations between school burnout and academic motivation, and the school burnout has direct and indirect significant effects on the getting over himself, using knowledge and exploration dimension through the latent variable of academic motivation. Lastly, it was determined that school burnout is a significant predictor of academic motivation.

Keywords: school burnout, motivation, structural equation modeling, university

Procedia PDF Downloads 313

Authors: Tarek M. Alguhane, Ayman H. Khalil, M. N. Fayed, Ayman M. Ismail

Abstract:

This paper deals with different modeling aspects of masonry infill: no infill model, Layered shell infill model, and strut infill model. These models consider the complicated behavior of the in-filled plane frames under lateral load similar to an earthquake load. Three strut infill models are used: NBCC (2005) strut infill model, ASCE/SEI 41-06 strut infill model and proposed strut infill model based on modification to Canadian, NBCC (2005) strut infill model. Pushover and modal analyses of a masonry infill concrete frame with a single storey and an existing 5-storey RC building have been carried out by using different models for masonry infill. The corresponding hinge status, the value of base shear at target displacement as well as their dynamic characteristics have been determined and compared. A validation of the structural numerical models for the existing 5-storey RC building has been achieved by comparing the experimentally measured and the analytically estimated natural frequencies and their mode shapes. This study shows that ASCE/SEI 41-06 equation underestimates the values for the equivalent properties of the diagonal strut while Canadian, NBCC (2005) equation gives realistic values for the equivalent properties. The results indicate that both ASCE/SEI 41-06 and Canadian, NBCC (2005) equations for strut infill model give over estimated values for dynamic characteristic of the building. Proposed modification to Canadian, NBCC (2005) equation shows that the fundamental dynamic characteristic values of the building are nearly similar to the corresponding values using layered shell elements as well as measured field results.

Keywords: masonry infill, framed structures, RC buildings, non-structural elements

Procedia PDF Downloads 271

Authors: P. W. Chen, C. T. Chang, Y. Peng, J. Y. Wu, D. J. Jan, Md. Manirul Ali

Abstract:

In the last decade, the nature of cathode spot splitting and the current per spot depended on an oblique magnetic field was investigated. This model for cathode current splitting is developed that we have investigated with relationship the magnetic pressures produced by kinetic pressure, self-magnetic pressure, and changed with an external magnetic field. We propose a theoretical model that has been established to an external magnetic field with components normal and tangential to the cathode surface influenced on magnetic pressure strength. We mainly focus on developed to understand the current per spot influenced with the tangential magnetic field strength and normal magnetic field strength.

Keywords: cathode spot, vacuum arc discharge, oblique magnetic field, tangential magnetic field

Procedia PDF Downloads 316

Authors: Merouane Salhi, Toufik Zebbiche, Omar Abada

Abstract:

When the stagnation pressure of perfect gas increases, the specific heat and their ratio do not remain constant anymore and start to vary with this pressure. The gas does not remain perfect. Its state equation change and it becomes a real gas. In this case, the effects of molecular size and inter molecular attraction forces intervene to correct the state equation. The aim of this work is to show and discuss the effect of stagnation pressure on supersonic thermo dynamical, physical and geometrical flow parameters, to find a general case for real gas. With the assumptions that Berthelot’s state equation accounts for molecular size and inter molecular force effects, expressions are developed for analyzing supersonic flow for thermally and calorically imperfect gas lower than the dissociation molecules threshold. The designs parameters for supersonic nozzle like thrust coefficient depend directly on stagnation parameters of the combustion chamber. The application is for air. A computation of error is made in this case to give a limit of perfect gas model compared to real gas model.

Keywords: supersonic flow, real gas model, Berthelot’s state equation, Simpson’s method, condensation function, stagnation pressure

Procedia PDF Downloads 507

Authors: Alouaoui Redha, Ferhat Samira, Bouaziz Mohamed Najib

Abstract:

In this work, we examine the thermal radiation effect on heat and mass transfer in steady laminar boundary layer flow of an incompressible viscous micropolar fluid over a vertical plate, with the presence of a magnetic field. Rosseland approximation is applied to describe the radiative heat flux in the energy equation. The resulting similarity equations are solved numerically. Many results are obtained and representative set is displayed graphically to illustrate the influence of the various parameters on different profiles. The conclusion is drawn that the flow field, temperature, concentration and microrotation as well as the skin friction coefficient and the both local Nusselt and local Sherwood numbers are significantly influenced by Magnetic parameter, material parameter and thermal radiation parameter.

Keywords: MHD, micropolar fluid, thermal radiation, heat and mass transfer, boundary layer

Procedia PDF Downloads 445

Authors: Tatyana Rybitskaya, Alexandr Starostenko, Kseniya Ryabchenko

Abstract:

Collector ring (CR) of FAIR project is a large acceptance storage ring and field quality plays a major role in the magnet design. The CR will use normal conducting dipole magnets. There will be 24 H-type sector magnets with a maximum field value of 1.6 T. The integrated over the length of the magnet field quality as a function of radius is ∆B.l/B.l = ±1x10⁻⁴. Below 1.6 T the value ∆B.l/B.l can be higher with a linear approximation up to ±2.5x10⁻⁴ at the field level of 0.8 T. An iron-dominated magnet with required field quality is produced with standard technology as the quality is dominated by the yoke geometry.

Keywords: conventional magnet, iron yoke dipole, harmonic terms, particle accelerators

Procedia PDF Downloads 139

Authors: Mohammad Reza Shahnazari, Reza Kazemi, Ali Saberi

Abstract:

Most of the engineering problems are in nonlinear forms. Nonlinear boundary layer problems defined in infinite intervals contain specific complexities, especially in boundary layer condition conformance. As an example of these nonlinear complex problems, the well-known Blasius equation can be mentioned, which itself is one of the classic boundary layer problems. No analytical solution has been proposed yet for the Blasius equation due to its complexity. In this paper, an analytical method, namely the Kourosh method, based on the singularity perturbation method and the Liao homotopy analysis is utilized to solve the Blasius problem. In this method, an inner solution is developed in the [0,1] interval to expedite the solution convergence. The magnitude of the f ˝(0), as an essential quantity for determining the physical parameters, is directly calculated from the solution of the boundary condition problem. The advantages of this solution are that it does not need any numerical solution, it has a closed form and that its validation is shown in the entire [0,∞] interval. Furthermore, all of the desirable parameters could be extracted through a series of simple analytical operations from the final solution. This solution also satisfies the continuity conditions, which is one of the main contributions of this paper in comparison with most of the other proposed analytical solutions available in the literature. Comparison with numerical solutions reveals that the proposed method is highly accurate and convenient for application.

Keywords: Blasius equation, boundary layer, Kourosh method, analytical solution

Procedia PDF Downloads 384

Authors: Alexander Aurell

Abstract:

One of the latest trends in the modeling of human crowds is the mean-field game approach. In the mean-field game approach, the motion of a human crowd is described by a nonstandard stochastic optimal control problem. It is nonstandard since congestion is considered, introduced through a dependence in the performance functional on the distribution of the crowd. This study extends the class of mean-field pedestrian crowd models to allow for non-local congestion and arbitrary, but finitely, many interacting crowds. The new congestion feature grants pedestrians a 'personal space' where crowding is undesirable. The model is treated as a mean-field type game which is derived from a particle picture. This, in contrast to a mean-field game, better describes a situation where the crowd can be controlled by a central planner. The latter is suitable for decentralized situations. Solutions to the mean-field type game are characterized via a Pontryagin-type Maximum Principle.

Keywords: congestion, crowd dynamics, interacting populations, mean-field approximation, optimal control

Procedia PDF Downloads 437

Authors: Mostafa Shahriari, Theophile Chaumont-Frelet, David Pardo

Abstract:

Resistivity measurements are used to characterize the Earth’s subsurface. They are categorized into two different groups: (a) those acquired on the Earth’s surface, for instance, controlled source electromagnetic (CSEM) and Magnetotellurics (MT), and (b) those recorded with borehole logging instruments such as Logging-While-Drilling (LWD) devices. LWD instruments are mostly used for geo-steering purposes, i.e., to adjust dip and azimuthal angles of a well trajectory to drill along a particular geological target. Modern LWD tools measure all nine components of the magnetic field corresponding to three orthogonal transmitter and receiver orientations. In order to map the Earth’s subsurface and perform geo-steering, we invert measurements using a gradient-based method that utilizes the derivatives of the recorded measurements with respect to the inversion variables. For resistivity measurements, these inversion variables are usually the constant resistivity value of each layer and the bed boundary positions. It is well-known how to compute derivatives with respect to the constant resistivity value of each layer using semi-analytic or numerical methods. However, similar formulas for computing the derivatives with respect to bed boundary positions are unavailable. The main contribution of this work is to provide an adjoint-based formulation for computing derivatives with respect to the bed boundary positions. The key idea to obtain the aforementioned adjoint state formulations for the derivatives is to separate the tangential and normal components of the field and treat them differently. This formulation allows us to compute the derivatives faster and more accurately than with traditional finite differences approximations. In the presentation, we shall first derive a formula for computing the derivatives with respect to the bed boundary positions for the potential equation. Then, we shall extend our formulation to 3D Maxwell’s equations. Finally, by considering a 1D domain and reducing the dimensionality of the problem, which is a common practice in the inversion of resistivity measurements, we shall derive a formulation to compute the derivatives of the measurements with respect to the bed boundary positions using a 1.5D variational formulation. Then, we shall illustrate the accuracy and convergence properties of our formulations by comparing numerical results with the analytical derivatives for the potential equation. For the 1.5D Maxwell’s system, we shall compare our numerical results based on the proposed adjoint-based formulation vs those obtained with a traditional finite difference approach. Numerical results shall show that our proposed adjoint-based technique produces enhanced accuracy solutions while its cost is negligible, as opposed to the finite difference approach that requires the solution of one additional problem per derivative.

Keywords: inverse problem, bed boundary positions, electromagnetism, potential equation

Procedia PDF Downloads 172

Authors: N. Messai, A. Boumali

Abstract:

In this work, we aim to solve the two dimensional Kemmer equation including Dirac oscillator interaction term, in the background space-time generated by a cosmic string which is submitted to an uniform magnetic field. Eigenfunctions and eigenvalues of our problem have been found and the influence of the cosmic string space-time on the energy spectrum has been analyzed.

Keywords: Kemmer oscillator, cosmic string, Dirac oscillator, eigenfunctions

Procedia PDF Downloads 579

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

Abstract:

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

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

Procedia PDF Downloads 327

Authors: Phuoc Si Nguyen

Abstract:

Infinite impulse response (IIR) filters can be designed from an analogue low pass prototype by using frequency transformation in the s-domain and bilinear z-transformation with pre-warping frequency; this method is known as frequency transformation from the s-domain to the z-domain. This paper will introduce a new method to transform an IIR digital filter to another type of IIR digital filter (low pass, high pass, band pass, band stop or narrow band) using a technique based on inverse bilinear z-transformation and inverse matrices. First, a matrix equation is derived from inverse bilinear z-transformation and Pascal’s triangle. This Low Pass Digital to Digital Filter Pascal Matrix Equation is used to transform a low pass digital filter to other digital filter types. From this equation and the inverse matrix, a Digital to Digital Filter Pascal Matrix Equation can be derived that is able to transform any IIR digital filter. This paper will also introduce some specific matrices to replace the inverse matrix, which is difficult to determine due to the larger size of the matrix in the current method. This will make computing and hand calculation easier when transforming from one IIR digital filter to another in the digital domain.

Keywords: bilinear z-transformation, frequency transformation, inverse bilinear z-transformation, IIR digital filters

Procedia PDF Downloads 412

Authors: Bing Gu

Abstract:

Abstract—Most of Conventional facial recognition systems are based on image features, such as LBP, SIFT. Recently some DBN-based 2D facial recognition systems have been proposed. However, we find there are few DBN-based 3D facial recognition system and relative researches. 3D facial images include all the individual biometric information. We can use these information to build more accurate features, So we present our DBN-based face recognition system using Light Field. We can see Light Field as another presentation of 3D image, and Light Field Camera show us a way to receive a Light Field. We use the commercially available Light Field Camera to act as the collector of our face recognition system, and the system receive a state-of-art performance as convenient as conventional 2D face recognition system.

Keywords: DBN, face recognition, light field, Lytro

Procedia PDF Downloads 458

Authors: Gautam Kumar Saharia, Sagardeep Talukdar, Riki Dutta, Sudipta Nandy

Abstract:

The physics informed neural network (PINN) method opens up an approach for numerically solving nonlinear partial differential equations leveraging fast calculating speed and high precession of modern computing systems. We construct the PINN based on strong universal approximation theorem and apply the initial-boundary value data and residual collocation points to weekly impose initial and boundary condition to the neural network and choose the optimization algorithms adaptive moment estimation (ADAM) and Limited-memory Broyden-Fletcher-Golfard-Shanno (L-BFGS) algorithm to optimize learnable parameter of the neural network. Next, we improve the PINN with a weighted loss function to obtain both the bright and dark soliton solutions of Fokas-Lenells equation (FLE). We find the proposed scheme of adjustable weight coefficients into PINN has a better convergence rate and generalizability than the basic PINN algorithm. We believe that the PINN approach to solve the partial differential equation appearing in nonlinear optics would be useful to study various optical phenomena.

Keywords: deep learning, optical Soliton, neural network, partial differential equation

Procedia PDF Downloads 119

Authors: Alexandra Leukauf, Alexander Schirrer, Emir Talic

Abstract:

Numerical computation of wave propagation in a large domain usually requires significant computational effort. Hence, the considered domain must be truncated to a smaller domain of interest. In addition, special boundary conditions, which absorb the outward travelling waves, need to be implemented in order to describe the system domains correctly. In this work, the linear one dimensional wave equation is approximated by utilizing the Fourier Galerkin approach. Furthermore, the artificial boundaries are realized with absorbing boundary conditions. Within this work, a systematic work flow for setting up the wave problem, including the absorbing boundary conditions, is proposed. As a result, a convenient modal system description with an effective absorbing boundary formulation is established. Moreover, the truncated model shows high accuracy compared to the global domain.

Keywords: absorbing boundary conditions, boundary control, Fourier Galerkin approach, modal approach, wave equation

Procedia PDF Downloads 389

Authors: Rahisham Abd Rahman

Abstract:

In this paper, a nonlinear pollution model has been proposed to compute electric field distribution over the polymeric insulator surface under wet contaminated conditions. A 2D axial-symmetric insulator geometry, energized with 11kV was developed and analysed using Finite Element Method (FEM). A field-dependent conductivity with simplified assumptions was established to characterize the electrical properties of the pollution layer. Comparative field studies showed that simulation of dynamic pollution model results in a more realistic field profile, offering better understanding on how the electric field behaves under wet polluted conditions.

Keywords: electric field distributions, pollution layer, dynamic model, polymeric outdoor insulators, finite element method (FEM)

Procedia PDF Downloads 390

Authors: Avinash Nayak, Debopam Das

Abstract:

The current work implements the variational principle to find the optimum initial perturbation that provides maximum growth in an impulsively blocked channel flow. The conventional method for studying temporal stability has always been through modal analysis. In most of the transient flows, this modal analysis is still followed with the quasi-steady assumption, i.e. change in base flow is much slower compared to perturbation growth rate. There are other studies where transient analysis on time dependent flows is done by formulating the growth of perturbation as an initial value problem. But the perturbation growth is sensitive to the initial condition. This study intends to find the initial perturbation that provides the maximum growth at a later time. Here, the expression of base flow for blocked channel is derived and the formulation is based on the two dimensional perturbation with stream function representing the perturbation quantity. Hence, the governing equation becomes the Orr-Sommerfeld equation. In the current context, the cost functional is defined as the ratio of disturbance energy at a terminal time 'T' to the initial energy, i.e. G(T) = ||q(T)||2/||q(0)||2 where q is the perturbation and ||.|| defines the norm chosen. The above cost functional needs to be maximized against the initial perturbation distribution. It is achieved with the constraint that perturbation follows the basic governing equation, i.e. Orr-Sommerfeld equation. The corresponding adjoint equation is derived and is solved along with the basic governing equation in an iterative manner to provide the initial spatial shape of the perturbation that provides the maximum growth G (T). The growth rate is plotted against time showing the development of perturbation which achieves an asymptotic shape. The effects of various parameters, e.g. Reynolds number, are studied in the process. Thus, the study emphasizes on the usage of optimal perturbation and its growth to understand the stability characteristics of time dependent flows. The assumption of quasi-steady analysis can be verified against these results for the transient flows like impulsive blocked channel flow.

Keywords: blocked channel flow, calculus of variation, hydrodynamic stability, optimal perturbation

Procedia PDF Downloads 418

Authors: Mokhtar Labiod, Nabil Ikhlef, Keltoum Bouherine, Olivier Leroy

Abstract:

A numerical model for the radio-frequency (RF) Argon discharge chamber is developed to simulate the low pressure low temperature inductively coupled plasma. This model will be of fundamental importance in the design of the plasma magnetic control system. Electric and magnetic fields inside the discharge chamber are evaluated by solving a magnetic vector potential equation. To start with, the equations of the ideal magnetohydrodynamics theory will be presented describing the basic behaviour of magnetically confined plasma and equations are discretized with finite element method in cylindrical coordinates. The discharge chamber is assumed to be axially symmetric and the plasma is treated as a compressible gas. Plasma generation due to ionization is added to the continuity equation. Magnetic vector potential equation is solved for the electromagnetic fields. A strong dependence of the plasma properties on the discharge conditions and the gas temperature is obtained.

Keywords: direct-coupled model, magnetohydrodynamic, modelling, plasma torch simulation

Procedia PDF Downloads 426

Authors: S. S. Abas, Y. M. Yatim

Abstract:

In this paper the unsteady, slender, symmetric dry patch in an infinitely wide and thin liquid film of Newtonian fluid draining under gravity down an inclined plane in the presence of strong surface-tension effect is considered. A similarity transformation, named a travelling-wave similarity solution is used to reduce the governing partial differential equation into the ordinary differential equation which is then solved numerically using a shooting method. The introduction of surface-tension effect on the flow leads to a fourth-order ordinary differential equation. The solution obtained predicts that the dry patch has a quartic shape and the free surface has a capillary ridge near the contact line which decays in an oscillatory manner far from it.

Keywords: dry patch, Newtonian fluid, similarity solution, surface-tension effect, travelling-wave, unsteady thin-film flow

Procedia PDF Downloads 302