Search results for: Bernstein polynomial approximation

Authors: Shangdong Zhu, Yunzhou Zhang, Jie Zhang, Hang Hu, Yazhou Zhang

Abstract:

Image stitching is a very important branch in the field of computer vision, especially for panoramic map. In order to eliminate shape distortion, a novel stitching method is proposed based on gradually changing matrix when images are horizontal. For images captured horizontally, this paper assumes that there is only translational operation in image stitching. By analyzing each parameter of the homography matrix, the global homography matrix is gradually transferred to translation matrix so as to eliminate the effects of scaling, rotation, etc. in the image transformation. This paper adopts matrix approximation to get the minimum value of the energy function so that the shape distortion at those regions corresponding to the homography can be minimized. The proposed method can avoid multiple horizontal images stitching failure caused by accumulated shape distortion. At the same time, it can be combined with As-Projective-As-Possible algorithm to ensure precise alignment of overlapping area.

Keywords: image stitching, gradually changing matrix, horizontal direction, matrix approximation, homography matrix

Procedia PDF Downloads 319

Authors: Anoop Kumar Suraj

Abstract:

Dr Rammanohar Lohia (1910-67), a radical Indian socialist thinker, left an unfinished and critical oeuvre of works on ‘Social Revolution’, argued for the necessity of fundamentally reordering our social structures and offered the ideological framework for such a radical change. An alternative kind of democratic political action called Saat Krantiya, or ‘seven revolutions’, sought to establish socialism with a strong cultural and historical foundation in Indian society. Lohia cautiously adopted civil disobedience [a Gandhian tool] as a means of seven revolutions as a mode of revolution. He saw Indian youth as the vanguard of the social revolution and claimed that the ideas of ‘constructive militancy’ and ‘militant construction’ were at the core of such a revolution. This paper demonstrates that Lohia presented a unique short theoretical paradigm to interpret history and revolution, and Sapta Kranti was a normative framework to arrive at an egalitarian society.

Keywords: Rammanohar Lohia, Sapt Kranti, matter and spirit, caste-class, human approximation

Procedia PDF Downloads 54

Authors: Wanhyun Cho, Soonja Kang, Sanggoon Kim, Soonyoung Park

Abstract:

We present probabilistic multinomial Dirichlet classification model for multidimensional data and Gaussian process priors. Here, we have considered an efficient computational method that can be used to obtain the approximate posteriors for latent variables and parameters needed to define the multiclass Gaussian process classification model. We first investigated the process of inducing a posterior distribution for various parameters and latent function by using the variational Bayesian approximations and important sampling method, and next we derived a predictive distribution of latent function needed to classify new samples. The proposed model is applied to classify the synthetic multivariate dataset in order to verify the performance of our model. Experiment result shows that our model is more accurate than the other approximation methods.

Keywords: multinomial dirichlet classification model, Gaussian process priors, variational Bayesian approximation, importance sampling, approximate posterior distribution, marginal likelihood evidence

Procedia PDF Downloads 444

Authors: Arun Goel

Abstract:

The present paper attempts to investigate the prediction of air entrainment rate and aeration efficiency of a free over-fall jets issuing from a triangular sharp crested weir by using regression based modelling. The empirical equations, support vector machine (polynomial and radial basis function) models and the linear regression techniques were applied on the triangular sharp crested weirs relating the air entrainment rate and the aeration efficiency to the input parameters namely drop height, discharge, and vertex angle. It was observed that there exists a good agreement between the measured values and the values obtained using empirical equations, support vector machine (Polynomial and rbf) models, and the linear regression techniques. The test results demonstrated that the SVM based (Poly & rbf) model also provided acceptable prediction of the measured values with reasonable accuracy along with empirical equations and linear regression techniques in modelling the air entrainment rate and the aeration efficiency of a free over-fall jets issuing from triangular sharp crested weir. Further sensitivity analysis has also been performed to study the impact of input parameter on the output in terms of air entrainment rate and aeration efficiency.

Keywords: air entrainment rate, dissolved oxygen, weir, SVM, regression

Procedia PDF Downloads 436

Authors: Ranjan Banerjee, W. D. Gunawardana

Abstract:

The free vibration and flutter analysis plays a major part in aircraft design which is indeed, a mandatory requirement. In particular, high aspect ratio transport airliner wings are prone to free vibration and flutter problems that must be addressed during the design process as demanded by the airworthiness authorities. The purpose of this paper is to carry out a detailed free vibration and flutter analysis for a wide range of high aspect ratio aircraft wings and generate design curves to provide useful visions and understandings of aircraft design from an aeroelastic perspective. In the initial stage of the investigation, the bending and torsional stiffnesses of a number of transport aircraft wings are looked at and critically examined to see whether it is possible to express the stiffness distributions in polynomial form, but in a sufficiently accurate manner. A similar attempt is made for mass and mass moment of inertia distributions of the wing. Once the choice of stiffness and mass distributions in polynomial form is made, the high aspect ratio wing is idealised by a series of bending-torsion coupled beams from a structural standpoint. Then the dynamic stiffness method is applied to compute the natural frequencies and mode shape of the wing. Next the wing is idealised aerodynamically and to this end, unsteady aerodynamic of Theodorsen type is employed to represent the harmonically oscillating wing. Following this step, a normal mode method through the use of generalised coordinates is applied to formulate the flutter problem. In essence, the generalised mass, stiffness and aerodynamic matrices are combined to obtain the flutter matrix which is subsequently solved in the complex domain to determine the flutter speed and flutter frequency. In the final stage of the investigation, an exhaustive parametric study is carried out by varying significant wing parameters to generate design curves which help to predict the free vibration and flutter behaviour of high aspect ratio transport aircraft wings in a generic manner. It is in the aeroelastic context of aircraft design where the results are expected to be most useful.

Keywords: high-aspect ratio wing, flutter, dynamic stiffness method, free vibration, aeroelasticity

Procedia PDF Downloads 285

Authors: B. Bouadjemi, S. Bentata, T. Lantri, A. Abbad, W. Benstaali, A. Zitouni, S. Cherid

Abstract:

We investigate the electronic structure, magnetic and optical properties of the orthorhombic NdMnO3 through density-functional-theory (DFT) calculations using both generalized gradient approximation GGA and GGA+U approaches, the exchange and correlation effects are taken into account by an orbital independent modified Becke Johnson (MBJ). The predicted band gaps using the MBJ exchange approximation show a significant improvement over previous theoretical work with the common GGA and GGA+U very closer to the experimental results. Band gap dependent optical parameters like dielectric constant, index of refraction, absorption coefficient, reflectivity and conductivity are calculated and analyzed. We find that when using MBJ we have obtained better results for band gap of NdMnO3 than in the case of GGA and GGA+U. The values of band gap founded in this work by MBJ are in a very good agreement with corresponding experimental values compared to other calculations. This comprehensive theoretical study of the optoelectronic properties predicts that this material can be effectively used in optical devices.

Keywords: DFT, optical properties, absorption coefficient, strong correlation, MBJ, orthorhombic NdMnO3, optoelectronic

Procedia PDF Downloads 909

Authors: Meriem Harmel, Houari Khachai

Abstract:

We have investigated the structural, electronic and optical properties of a compound perovskite CsSrF3 using the full-potential linearized augmented plane wave (FP-LAPW) method within density functional theory (DFT). In this approach, both the local density approximation (LDA) and the generalized gradient approximation (GGA) were used for exchange-correlation potential calculation. The ground state properties such as lattice parameter, bulk modulus and its pressure derivative were calculated and the results are compared whit experimental and theoretical data. Electronic and bonding properties are discussed from the calculations of band structure, density of states and electron charge density, where the fundamental energy gap is direct under ambient conditions. The contribution of the different bands was analyzed from the total and partial density of states curves. The optical properties (namely: the real and the imaginary parts of the dielectric function ε(ω), the refractive index n(ω) and the extinction coefficient k(ω)) were calculated for radiation up to 35.0 eV. This is the first quantitative theoretical prediction of the optical properties for the investigated compound and still awaits experimental confirmations.

Keywords: DFT, fluoroperovskite, electronic structure, optical properties

Procedia PDF Downloads 477

Authors: M. Saadi, S. E. H. Abaidia, M. Y. Mokeddem.

Abstract:

We present the results of a systematic and comparative study of the bulk, the structural properties, and phonon calculations of aluminum alloys using several exchange–correlations functional theory (DFT) with different plane-wave basis pseudo potential techniques. Density functional theory implemented by the Vienna Ab Initio Simulation Package (VASP) technique is applied to calculate the bulk and the structural properties of several structures. The calculations were performed for within several exchange–correlation functional and pseudo pententials available in this code (local density approximation (LDA), generalized gradient approximation (GGA), projector augmented wave (PAW)). The lattice dynamic code “PHON” developed by Dario Alfè was used to calculate some thermodynamics properties and phonon dispersion relation frequency distribution of Aluminium alloys using the VASP LDA PAW and GGA PAW results. The bulk and structural properties of the calculated structures were compared to different experimental and calculated works.

Keywords: DFT, exchange-correlation functional, LDA, GGA, pseudopotential, PAW, VASP, PHON, phonon dispersion

Procedia PDF Downloads 485

Authors: A. Chateauneuf, M. Mostoufi, D. Vyncke

Abstract:

Monte Carlo (MC) simulation is a technique that provides approximate solutions to a broad range of mathematical problems. A drawback of the method is its high computational cost, especially in a high-dimensional setting, such as estimating the Tail Value-at-Risk for large portfolios or pricing basket options and Asian options. For these types of problems, one can construct an upper bound in the convex order by replacing the copula by the comonotonic copula. This comonotonic upper bound can be computed very quickly, but it gives only a rough approximation. In this paper we introduce the Comonotonic Monte Carlo (CoMC) simulation, by using the comonotonic approximation as a control variate. The CoMC is of broad applicability and numerical results show a remarkable speed improvement. We illustrate the method for estimating Tail Value-at-Risk and pricing basket options and Asian options when the logreturns follow a Black-Scholes model or a variance gamma model.

Keywords: control variate Monte Carlo, comonotonicity, option pricing, scientific computing

Procedia PDF Downloads 515

Authors: E. Marušić-Paloka, I. Pažanin, M. Prša

Abstract:

Subject of this study is the stationary heat conduction problem through a pipe filled with incompressible viscous fluid. In previous work, we observed the existence and uniqueness theorems for the corresponding boundary-value problem and within we have taken into account the effects of the pipe's dilatation due to the temperature of the fluid inside of the pipe. The main difficulty comes from the fact that flow domain changes depending on the solution of the observed heat equation leading to a non-standard coupled governing problem. The goal of this work is to find solution estimate since the exact solution of the studied problem is not possible to determine. We use an asymptotic expansion in order of a small parameter which is presented as a heat expansion coefficient of the pipe's material. Furthermore, an error estimate is provided for the mentioned asymptotic approximation of the solution for inner area of the pipe. Close to the boundary, problem becomes more complex so different approaches are observed, mainly Theory of Perturbations and Separations of Variables. In view of that, error estimate for the whole approximation will be provided with additional software simulations of gotten situation.

Keywords: asymptotic analysis, dilated pipe, error estimate, heat conduction

Procedia PDF Downloads 236

Authors: Y. Benmalem , A. Abbad, W. Benstaali, T. Lantri

Abstract:

Density functional theory is used to investigate the.the structural, electronic, and magnetic properties of the cubic anti-perovskites InNNi3 and ZnNNi3. The structure of antiperovskite also called (perovskite-inverse) identical to the perovskite structure of the general formula ABX3, where A is a main group (III–V) element or a metallic element, B is carbon or nitrogen, and X is a transition metal, displays a wide range of interesting physical properties, such as giant magnetoresistance. Elastic and electronic properties were determined using generalized gradient approximation (GGA), and local spin density approximation (LSDA) approaches, ), as implemented in the Wien2k computer package. The results show that the two compounds are strong ductile and satisfy the Born-Huang criteria, so they are mechanically stable at normal conditions. Electronic properties show that the two compounds studied are metallic and non-magnetic. The studies of these compounds have confirmed the effectiveness of the two approximations and the ground-state properties are in good agreement with experimental data and theoretical results available.

Keywords: anti-perovskites, elastic anisotropy, electronic band structure, first-principles calculations

Procedia PDF Downloads 285

Authors: Chukwuemeka Daniel Ezeliora, Chukwuebuka Lawrence Ezeliora

Abstract:

The research focused on the appraisal of impact strength on mild steel cladding weld metal geometry. Over the years, poor welding has resulted in failures in engineering components, poor material quality, the collapse of welded materials, and failures in material strength. This is as a result of poor selection and combination of welding input process parameters. The application of the Tungsten Inert Gas (TIG) welding method with weld specimen of length 60; width 40, and thickness of 10 was used for the experiment. A butt joint method was prepared for the welding, and tungsten inert gas welding process was used to perform the twenty (20) experimental runs. A response surface methodology was used to model and to analyze the system. For an adequate polynomial approximation, the experimental design was used to collect the data. The key parameters considered in this work are welding current, gas flow rate, welding speed, and voltage. The range of the input process parameters was selected from the literature and the design. The steps followed to achieve the experimental design and results is the use of response surface method (RSM) implemented in central composite design (CCD) to generate the design matrix, to obtain quadratic model, and evaluate the interactions in the factors as well as optimizing the factors and the response. The result expresses that the best impact strength of the mild steel cladding weld metal geometry is 115.419 Joules. However, it was observed that the result of the input factors is; current 180.4 amp, voltage 23.99 volt, welding speed 142.7 mm.s and gas flow rate 10.8 lit/min as the optimum of the input process parameters. The optimal solution gives a guide for optimal impact strength of the weldment when welding with tungsten inert gas (TIG) under study.

Keywords: mild steel, impact strength, response surface, bead geometry, welding

Procedia PDF Downloads 119

Authors: Yeliz Karaca, Carlo Cattani

Abstract:

This study focuses on the local Holder exponent as a measure of the function regularity for time series related to finance data. In this study, the attributes of the finance dataset belonging to 13 countries (India, China, Japan, Sweden, France, Germany, Italy, Australia, Mexico, United Kingdom, Argentina, Brazil, USA) located in 5 different continents (Asia, Europe, Australia, North America and South America) have been examined.These countries are the ones mostly affected by the attributes with regard to financial development, covering a period from 2012 to 2017. Our study is concerned with the most important attributes that have impact on the development of finance for the countries identified. Our method is comprised of the following stages: (a) among the multi fractal methods and Brownian motion Holder regularity functions (polynomial, exponential), significant and self-similar attributes have been identified (b) The significant and self-similar attributes have been applied to the Artificial Neuronal Network (ANN) algorithms (Feed Forward Back Propagation (FFBP) and Cascade Forward Back Propagation (CFBP)) (c) the outcomes of classification accuracy have been compared concerning the attributes that have impact on the attributes which affect the countries’ financial development. This study has enabled to reveal, through the application of ANN algorithms, how the most significant attributes are identified within the relevant dataset via the Holder functions (polynomial and exponential function).

Keywords: artificial neural networks, finance data, Holder regularity, multifractals

Procedia PDF Downloads 246

Authors: Min Kyung An

Abstract:

In this paper, we study the data collection problem in Wireless Sensor Networks (WSNs) adopting the two interference models: The graph model and the more realistic physical interference model known as Signal-to-Interference-Noise-Ratio (SINR). The main issue of the problem is to compute schedules with the minimum number of timeslots, that is, to compute the minimum latency schedules, such that data from every node can be collected without any collision or interference to a sink node. While existing works studied the problem with unit-sized and unbounded-sized message models, we investigate the problem with the bounded-sized message model, and introduce a constant factor approximation algorithm. To the best known of our knowledge, our result is the first result of the data collection problem with bounded-sized model in both interference models.

Keywords: data collection, collision-free, interference-free, physical interference model, SINR, approximation, bounded-sized message model, wireless sensor networks

Procedia PDF Downloads 221

Authors: Armel Asongu Nkembi, Ahmad Fawad

Abstract:

The aim of this paper is to determine in a concise way the transfer function that characterizes a DC electrical motor with a helix. In practice it can be obtained by applying a particular input to the system and then, based on the observation of its output, determine an approximation to the transfer function of the system. In our case, we use a step input and find the transfer function parameters that give the simulated first-order time response. The simulation of the system is done using MATLAB/Simulink. In order to determine the parameters, we assume a first order system and use the Broida approximation to determine the parameters and then its Mean Square Error (MSE). Furthermore, we design a PID controller for the control process first in the continuous time domain and tune it using the Ziegler-Nichols open loop process. We then digitize the controller to obtain a digital controller since most systems are implemented using computers, which are digital in nature.

Keywords: transfer function, step input, MATLAB, Simulink, DC electrical motor, PID controller, open-loop process, mean square process, digital controller, Ziegler-Nichols

Procedia PDF Downloads 55

Authors: Julien Romieux, Fabio Verdicchio

Abstract:

Wireless Sensor Networks (WSNs), which sense environmental data with battery-powered nodes, require multi-hop communication. This power-demanding task adds an extra workload that is unfairly distributed across the network. As a result, nodes run out of battery at different times: this requires an impractical individual node maintenance scheme. Therefore we investigate a new Cooperative Sensing approach that extends the WSN operational life and allows a more practical network maintenance scheme (where all nodes deplete their batteries almost at the same time). We propose a novel cooperative algorithm that derives a piecewise representation of the sensed signal while controlling approximation accuracy. Simulations show that our algorithm increases WSN operational life and spreads communication workload evenly. Results convey a counterintuitive conclusion: distributing workload fairly amongst nodes may not decrease the network power consumption and yet extend the WSN operational life. This is achieved as our cooperative approach decreases the workload of the most burdened cluster in the network.

Keywords: cooperative signal processing, signal representation and approximation, power management, wireless sensor networks

Procedia PDF Downloads 390

Authors: Md. Shams Razi Shopnil, Tanvir Imtiaz, Sabrina Mahjabin, Md. Sahadat Hossain

Abstract:

Saturated hydraulic conductivity is one of the most significant attributes of pavement base course. Determination of hydraulic conductivity is a routine procedure for regular aggregate base courses. However, in many cases, a cement-stabilized base course is used with compromised drainage ability. Traditional hydraulic conductivity testing procedure is a readily available option which leads to two consequential drawbacks, i.e., the time required for the specimen to be saturated and extruding the sample after completion of the laboratory test. To overcome these complications, this study aims at formulating an empirical approach to predicting hydraulic conductivity based on Unconfined Compressive Strength test results. To do so, this study comprises two separate experiments (Constant Head Permeability test and Unconfined Compressive Strength test) conducted concurrently on a specimen having the same physical credentials. Data obtained from the two experiments were then used to devise a correlation between hydraulic conductivity and unconfined compressive strength. This correlation in the form of a polynomial equation helps to predict the hydraulic conductivity of cement-treated pavement base course, bypassing the cumbrous process of traditional permeability and less commonly used horizontal permeability tests. The correlation was further corroborated by a different set of data, and it has been found that the derived polynomial equation is deemed to be a viable tool to predict hydraulic conductivity.

Keywords: hydraulic conductivity, unconfined compressive strength, recycled plastics, recycled concrete aggregates

Procedia PDF Downloads 90

Authors: Damir Latypov

Abstract:

A hybrid classical-quantum algorithm to solve boundary integral equations (BIE) arising in problems of electromagnetic and acoustic scattering is proposed. The quantum speed-up is due to a Quantum Linear System Algorithm (QLSA). The original QLSA of Harrow et al. provides an exponential speed-up over the best-known classical algorithms but only in the case of sparse systems. Due to the non-local nature of integral operators, matrices arising from discretization of BIEs, are, however, dense. A QLSA for dense matrices was introduced in 2017. Its runtime as function of the system's size N is bounded by O(√Npolylog(N)). The run time of the best-known classical algorithm for an arbitrary dense matrix scales as O(N².³⁷³). Instead of exponential as in case of sparse matrices, here we have only a polynomial speed-up. Nevertheless, sufficiently high power of this polynomial, ~4.7, should make QLSA an appealing alternative. Unfortunately for the QLSA, the asymptotic separability of the Green's function leads to high compressibility of the BIEs matrices. Classical fast algorithms such as Multilevel Fast Multipole Method (MLFMM) take advantage of this fact and reduce the runtime to O(Nlog(N)), i.e., the QLSA is only quadratically faster than the MLFMM. To be truly impactful for computational electromagnetics and acoustics engineers, QLSA must provide more substantial advantage than that. We propose a computational scheme which combines elements of the classical fast algorithms with the QLSA to achieve the required performance.

Keywords: quantum linear system algorithm, boundary integral equations, dense matrices, electromagnetic scattering theory

Procedia PDF Downloads 154

Authors: Petter Eklund, Jonathan Sjölund, Sandra Eriksson, Mats Leijon

Abstract:

The spoke type rotor can be used to obtain magnetic flux concentration in permanent magnet machines. This allows the air gap magnetic flux density to exceed the remanent flux density of the permanent magnets but gives problems with leakage fluxes in the magnetic circuit. The end leakage flux of one spoke type permanent magnet rotor design is studied through measurements and finite element simulations. The measurements are performed in the end regions of a 12 kW prototype generator for a vertical axis wind turbine. The simulations are made using three dimensional finite elements to calculate the magnetic field distribution in the end regions of the machine. Also two dimensional finite element simulations are performed and the impact of the two dimensional approximation is studied. It is found that the magnetic leakage flux in the end regions of the machine is equal to about 20% of the flux in the permanent magnets. The overestimation of the performance by the two dimensional approximation is quantified and a curve-fitted expression for its behavior is suggested.

Keywords: end effects, end leakage flux, permanent magnet machine, spoke type rotor

Procedia PDF Downloads 332

Authors: H. Krarcha

Abstract:

The structural, elastic, vibrational and thermal properties of AHfO3 compounds with the cubic perovskites structure have been investigated, by employing a first principles method, using the plane wave pseudo potential calculations (PP-PW), based on the density functional theory (DFT), within the local density approximation (LDA). The optimized lattice parameters, independent elastic constants (C11, C12 and C44), bulk modulus (B), compressibility (b), shear modulus (G), Young’s modulus (Y ), Poisson’s ratio (n), Lame´’s coefficients (m, l), as well as band structure, density of states and electron density distributions are obtained and analyzed in comparison with the available theoretical and experimental data. For the first time the numerical estimates of elastic parameters of the polycrystalline AHfO3 ceramics (in framework of the VoigteReusseHill approximation) are performed. The quasi-harmonic Debye model, by means of total energy versus volume calculations obtained with the FP-LAPW method, is applied to study the thermal and vibrational effects. Predicted temperature and pressure effects on the structural parameters, thermal expansions, heat capacities, and Debye temperatures are determined from the non-equilibrium Gibbs functions.

Keywords: Hafnium, elastic propreties, first principles calculation, perovskite

Procedia PDF Downloads 381

Authors: N. H. Adenan, M. S. M. Noorani

Abstract:

River flow prediction is an essential to ensure proper management of water resources can be optimally distribute water to consumers. This study presents an analysis and prediction by using nonlinear prediction method involving monthly river flow data in Tanjung Tualang from 1976 to 2006. Nonlinear prediction method involves the reconstruction of phase space and local linear approximation approach. The phase space reconstruction involves the reconstruction of one-dimensional (the observed 287 months of data) in a multidimensional phase space to reveal the dynamics of the system. Revenue of phase space reconstruction is used to predict the next 72 months. A comparison of prediction performance based on correlation coefficient (CC) and root mean square error (RMSE) have been employed to compare prediction performance for nonlinear prediction method, ARIMA and SVM. Prediction performance comparisons show the prediction results using nonlinear prediction method is better than ARIMA and SVM. Therefore, the result of this study could be used to developed an efficient water management system to optimize the allocation water resources.

Keywords: river flow, nonlinear prediction method, phase space, local linear approximation

Procedia PDF Downloads 412

Authors: Edward Schwalb, Matthias Dehmer, Michael Schlenkrich, Farzaneh Taslimi, Ketron Mitchell-Wynne, Horen Kuecuekyan

Abstract:

We present a generalized feature extraction approach for supporting Machine Learning (ML) algorithms which perform tasks similar to Finite-Element Analysis (FEA). We report results for estimating the Head Injury Categorization (HIC) of vehicle engine compartments across various impact scenarios. Our experiments demonstrate that models learned using features derived with a simple discretization approach provide a reasonable approximation of a full simulation. We observe that Decision Trees could be as effective as Neural Networks for the HIC task. The simplicity and performance of the learned Decision Trees could offer a trade-off of a multiple order of magnitude increase in speed and cost improvement over full simulation for a reasonable approximation. When used as a complement to full simulation, the approach enables rapid approximate feedback to engineering teams before submission for full analysis. The approach produces mesh independent features and is further agnostic of the assembly structure.

Keywords: mechanical design validation, FEA, supervised decision tree, convolutional neural network.

Procedia PDF Downloads 139

Authors: A. Amar

Abstract:

The angular distributions of the nuclear systems under consideration have been analyzed in the framework of the optical model (OM), where the real part was taken in the crystal model form. A crystal model (CM) has been applied to deuteron elastically scattered by ⁶,⁷Li and ⁹Be. A crystal model (CM) + distorted-wave Born approximation (DWBA) + dynamic polarization potential (DPP) potential has been applied to deuteron elastically scattered by ⁶,⁷Li and 9Be. Also, a crystal model has been applied to ⁶Li elastically scattered by ¹⁶O and ²⁸Sn in addition to the ⁷Li+⁷Li system and the ¹²C(alpha,⁸Be) ⁸Be reaction. The continuum-discretized coupled-channels (CDCC) method has been applied to the ⁷Li+⁷Li system and agreement between the crystal model and the continuum-discretized coupled-channels (CDCC) method has been observed. In general, the models succeeded in reproducing the differential cross sections at the full angular range and for all the energies under consideration.

Keywords: optical model (OM), crystal model (CM), distorted-wave born approximation (DWBA), dynamic polarization potential (DPP), the continuum-discretized coupled-channels (CDCC) method, and deuteron elastically scattered by ⁶, ⁷Li and ⁹Be

Procedia PDF Downloads 79

Authors: Lawrence A. Farinola

Abstract:

Four point implicit schemes for the approximation of the first and pure second order derivatives for the solution of the Dirichlet problem for one dimensional Schrodinger equation with respect to the time variable t were constructed. Also, special four-point implicit difference boundary value problems are proposed for the first and pure second derivatives of the solution with respect to the spatial variable x. The Grid method is also applied to the mixed second derivative of the solution of the Linear Schrodinger time-dependent equation. It is assumed that the initial function belongs to the Holder space C⁸⁺ᵃ, 0 < α < 1, the Schrodinger wave function given in the Schrodinger equation is from the Holder space Cₓ,ₜ⁶⁺ᵃ, ³⁺ᵃ/², the boundary functions are from C⁴⁺ᵃ, and between the initial and the boundary functions the conjugation conditions of orders q = 0,1,2,3,4 are satisfied. It is proven that the solution of the proposed difference schemes converges uniformly on the grids of the order O(h²+ k) where h is the step size in x and k is the step size in time. Numerical experiments are illustrated to support the analysis made.

Keywords: approximation of derivatives, finite difference method, Schrödinger equation, uniform error

Procedia PDF Downloads 120

Authors: Gregor Kosec

Abstract:

Simple and robust numerical approach for solving flow problems is presented, where involved physical fields are represented through the local approximation functions, i.e., the considered field is approximated over a local support domain. The approximation functions are then used to evaluate the partial differential operators. The type of approximation, the size of support domain, and the type and number of basis function can be general. The solution procedure is formulated completely through local computational operations. Besides local numerical method also the pressure velocity is performed locally with retaining the correct temporal transient. The complete locality of the introduced numerical scheme has several beneficial effects. One of the most attractive is the simplicity since it could be understood as a generalized Finite Differences Method, however, much more powerful. Presented methodology offers many possibilities for treating challenging cases, e.g. nodal adaptivity to address regions with sharp discontinuities or p-adaptivity to treat obscure anomalies in physical field. The stability versus computation complexity and accuracy can be regulated by changing number of support nodes, etc. All these features can be controlled on the fly during the simulation. The presented methodology is relatively simple to understand and implement, which makes it potentially powerful tool for engineering simulations. Besides simplicity and straightforward implementation, there are many opportunities to fully exploit modern computer architectures through different parallel computing strategies. The performance of the method is presented on the lid driven cavity problem, backward facing step problem, de Vahl Davis natural convection test, extended also to low Prandtl fluid and Darcy porous flow. Results are presented in terms of velocity profiles, convergence plots, and stability analyses. Results of all cases are also compared against published data.

Keywords: fluid flow, meshless, low Pr problem, natural convection

Procedia PDF Downloads 233

Authors: Najwa Mimouni, Omar Rahli, Rachid Bennacer, Salah Chikh

Abstract:

In the present work 2D and 3D numerical simulations of double diffusion natural convection in an elongated enclosure filled with a binary fluid saturating a porous medium are carried out. In the formulation of the problem, the Boussinesq approximation is considered and cross Neumann boundary conditions are specified for heat and mass walls conditions. The numerical method is based on the control volume approach with the third order QUICK scheme. Full approximation storage (FAS) with full multigrid (FMG) method is used to solve the problem. For the explored large range of the controlling parameters, we clearly evidenced that the increase in the depth of the cavity i.e. the lateral aspect ratio has an important effect on the flow patterns. The 2D perfect parallel flows obtained for a small lateral aspect ratio are drastically destabilized by increasing the cavity lateral dimension. This yields a 3D fluid motion with a much more complicated flow pattern and the classically studied 2D parallel flows are impossible.

Keywords: bifurcation, natural convection, heat and mass transfer, parallel flow, porous media

Procedia PDF Downloads 473

Authors: Sung Duk Kim, Kwan U. Kim, Jin Sim, Ryong Jin Jang

Abstract:

The phenomenon of seasonal variations in the Earth’s rotation velocity was discovered in the 1930s when a crystal clock was developed and analyzed in a quantitative way for the first time between 1955 and 1968 when observation data of the seasonal variations was analyzed by an atomic clock. According to the previous investigation, atmospheric circulation is supposed to be a factor affecting the seasonal variations in the Earth’s rotation velocity in many cases, but the problem has not been solved yet. In order to solve the problem, it is necessary to apply dynamics to consider the Earth’s spatial motion, rotation, and change of shape of the Earth (movement of materials in and out of the Earth and change of the Earth’s figure) at the same time and in interrelation to the accuracy of post-Newtonian approximation regarding the Earth body as a system of mass points because the stability of the Earth’s rotation angular velocity is in the range of 10⁻⁸~10⁻⁹. For it, the equation was derived, which can consider the 3 kinds of motion above mentioned at the same time by taking the effect of the resultant external force on the Earth’s rotation into account in a relativistic way to the accuracy of post-Newtonian approximation. Therefore, the equation has been solved to obtain the theoretical values of periodic change in the Earth’s rotation velocity, and they have been compared with the astronomical observation data so to reveal the cause for the periodic change in the Earth’s rotation velocity.

Keywords: Earth rotation, moment function, periodic change, seasonal variation, relativistic change

Procedia PDF Downloads 73

Authors: Li Long, Thomas Ortlepp

Abstract:

A theoretical model for the optimization of thermopile sensor performance is developed for thermoelectric-based infrared radiation detection. It is shown that the performance of polycrystalline silicon film thermopile sensor can be optimized according to the thermoelectric quality factor, sensor layer structure factor, and sensor layout geometrical form factor. Based on the properties of electrons, phonons, grain boundaries, and their interactions, the thermoelectric quality factor of polycrystalline silicon is analyzed with the relaxation time approximation of the Boltzmann transport equation. The model includes the effect of grain structure, grain boundary trap properties, and doping concentration. The layer structure factor is analyzed with respect to the infrared absorption coefficient. The optimization of layout design is characterized by the form factor, which is calculated for different sensor designs. A double-layer polycrystalline silicon thermopile infrared sensor on a suspended membrane has been designed and fabricated with a CMOS-compatible process. The theoretical approach is confirmed by measurement results.

Keywords: polycrystalline silicon, relaxation time approximation, specific detectivity, thermal conductivity, thermopile infrared sensor

Procedia PDF Downloads 139

Authors: Apoorva Vinod, Archana Mathur, Snehanshu Saha

Abstract:

Though there exists a plethora of Activation Functions (AFs) used in single and multiple hidden layer Neural Networks (NN), their behavior always raised curiosity, whether used in combination or singly. The popular AFs –Sigmoid, ReLU, and Tanh–have performed prominently well for shallow and deep architectures. Most of the time, AFs are used singly in multi-layered NN, and, to the best of our knowledge, their performance is never studied and analyzed deeply when used in combination. In this manuscript, we experiment with multi-layered NN architecture (both on shallow and deep architectures; Convolutional NN and VGG16) and investigate how well the network responds to using two different AFs (Sigmoid-Tanh, Tanh-ReLU, ReLU-Sigmoid) used alternately against a traditional, single (Sigmoid-Sigmoid, Tanh-Tanh, ReLUReLU) combination. Our results show that using two different AFs, the network achieves better accuracy, substantially lower loss, and faster convergence on 4 computer vision (CV) and 15 Non-CV (NCV) datasets. When using different AFs, not only was the accuracy greater by 6-7%, but we also accomplished convergence twice as fast. We present a case study to investigate the probability of networks suffering vanishing and exploding gradients when using two different AFs. Additionally, we theoretically showed that a composition of two or more AFs satisfies Universal Approximation Theorem (UAT).

Keywords: activation function, universal approximation function, neural networks, convergence

Procedia PDF Downloads 158

Authors: Augustine Okolie, Johannes Müller, Mirjam Kretzchmar

Abstract:

We adopt a maximum-likelihood framework to estimate parameters of a stochastic susceptible-infected-recovered (SIR) model with contact tracing on a rooted random tree. Given the number of detectees per index case, our estimator allows to determine the degree distribution of the random tree as well as the tracing probability. Since we do not discover all infectees via contact tracing, this estimation is non-trivial. To keep things simple and stable, we develop an approximation suited for realistic situations (contract tracing probability small, or the probability for the detection of index cases small). In this approximation, the only epidemiological parameter entering the estimator is the basic reproduction number R0. The estimator is tested in a simulation study and applied to covid-19 contact tracing data from India. The simulation study underlines the efficiency of the method. For the empirical covid-19 data, we are able to compare different degree distributions and perform a sensitivity analysis. We find that particularly a power-law and a negative binomial degree distribution meet the data well and that the tracing probability is rather large. The sensitivity analysis shows no strong dependency on the reproduction number.

Keywords: stochastic SIR model on graph, contact tracing, branching process, parameter inference

Procedia PDF Downloads 77