Search results for: integrated nested Laplace approximation

Authors: Kajingulu Malandala, Ranganai Edmore

Abstract:

The asymmetric Laplace distribution (ADL) is commonly used as the likelihood function of the Bayesian quantile regression, and it offers different families of likelihood method for quantile regression. Notwithstanding their popularity and practicality, ADL is not smooth and thus making it difficult to maximize its likelihood. Furthermore, Bayesian inference is time consuming and the selection of likelihood may mislead the inference, as the Bayes theorem does not automatically establish the posterior inference. Furthermore, ADL does not account for greater skewness and Kurtosis. This paper develops a new aspect of quantile regression approach for count data based on inverse of the cumulative density function of the Poisson, binomial and Delaporte distributions using the integrated nested Laplace Approximations. Our result validates the benefit of using the integrated nested Laplace Approximations and support the approach for count data.

Keywords: quantile regression, Delaporte distribution, count data, integrated nested Laplace approximation

Procedia PDF Downloads 130

Authors: Mustafa Aydın, Ali Murat Sunbul

Abstract:

Hierarchical or nested data structures usually are seen in many research areas. Especially, in the field of education, if we examine most of the studies, we can see the nested structures. Students in classes, classes in schools, schools in cities and cities in regions are similar nested structures. In a hierarchical structure, students being in the same class, sharing the same physical conditions and similar experiences and learning from the same teachers, they demonstrate similar behaviors between them rather than the students in other classes.

Keywords: hierarchical linear modeling, nested data, hierarchical structure, data structure

Procedia PDF Downloads 624

Authors: Abbas Ebrahimi, Mohammad Zandsalimy

Abstract:

The main purpose of this study is to investigate the feasibility of using FPGA (Field Programmable Gate Arrays) chips as alternatives for the conventional CPUs to accelerate the numerical solution of the Laplace equation. FPGA is an integrated circuit that contains an array of logic blocks, and its architecture can be reprogrammed and reconfigured after manufacturing. Complex circuits for various applications can be designed and implemented using FPGA hardware. The reconfigurable hardware used in this paper is an SoC (System on a Chip) FPGA type that integrates both microprocessor and FPGA architectures into a single device. In the present study the Laplace equation is implemented and solved numerically on both reconfigurable hardware and CPU. The precision of results and speedups of the calculations are compared together. The computational process on FPGA, is up to 20 times faster than a conventional CPU, with the same data precision. An analytical solution is used to validate the results.

Keywords: accelerating numerical solutions, CFD, FPGA, hardware definition language, numerical solutions, reconfigurable hardware

Procedia PDF Downloads 353

Authors: Zhenming Wang, Jun Zhu, Yuchen Yang, Ning Zhao

Abstract:

In the present paper, an alternative framework is proposed to construct a class of finite difference multi-resolution nested weighted essentially non-oscillatory (WENO) schemes with an increasingly higher order of accuracy for solving inviscid Euler equations. These WENO schemes firstly obtain a set of reconstruction polynomials by a hierarchy of nested central spatial stencils, and then recursively achieve a higher order approximation through the lower-order precision WENO schemes. The linear weights of such WENO schemes can be set as any positive numbers with a requirement that their sum equals one and they will not pollute the optimal order of accuracy in smooth regions and could simultaneously suppress spurious oscillations near discontinuities. Numerical results obtained indicate that these alternative finite-difference multi-resolution nested WENO schemes with different accuracies are very robust with low dissipation and use as few reconstruction stencils as possible while maintaining the same efficiency, achieving the high-resolution property without any equivalent multi-resolution representation. Besides, its finite volume form is easier to implement in unstructured grids.

Keywords: finite-difference, WENO schemes, high order, inviscid Euler equations, multi-resolution

Procedia PDF Downloads 115

Authors: Jayanta Pokharel, Gokarna Aryal, Netra Kanaal, Chris Tsokos

Abstract:

Investment in stocks and shares aims to seek potential gains while weighing the risk of future needs, such as retirement, children's education etc. Analysis of the behavior of the stock market returns and making prediction is important for investors to mitigate risk on investment. Historically, the normal variance models have been used to describe the behavior of stock market returns. However, the returns of the financial assets are actually skewed with higher kurtosis, heavier tails, and a higher center than the normal distribution. The Laplace distribution and its family are natural candidates for modeling stock returns. The Variance-Gamma (VG) distribution is the most sought-after distributions for modeling asset returns and has been extensively discussed in financial literatures. In this paper, it explore the other Laplace family, such as Asymmetric Laplace, Skewed Laplace, Kumaraswamy Laplace (KS) together with Variance-Gamma to model the weekly returns of the S&P 500 Index and it's eleven business sector indices. The method of maximum likelihood is employed to estimate the parameters of the distributions and our empirical inquiry shows that the Kumaraswamy Laplace distribution performs much better for stock returns modeling among the choice of distributions used in this study and in practice, KS can be used as a strong alternative to VG distribution.

Keywords: stock returns, variance-gamma, kumaraswamy laplace, maximum likelihood

Procedia PDF Downloads 37

Authors: Kankeyanathan Kannan

Abstract:

On approximation properties of group C* algebras is everywhere; it is powerful, important, backbone of countless breakthroughs. For a discrete group G, let A(G) denote its Fourier algebra, and let M₀A(G) denote the space of completely bounded Fourier multipliers on G. An approximate identity on G is a sequence (Φn) of finitely supported functions such that (Φn) uniformly converge to constant function 1 In this paper we prove that approximation property pass to free product.

Keywords: approximation property, weakly amenable, strong invariant approximation property, invariant approximation property

Procedia PDF Downloads 644

Authors: Carlos Gonzales, Zaida Quiroz, Marcos Prates

Abstract:

Several spatial variables collected at the same location that share a common spatial distribution can be modeled simultaneously through a multivariate geostatistical model that takes into account the correlation between these variables and the spatial autocorrelation. The main goal of this model is to perform spatial prediction of these variables in the region of study. Here we focus on a geostatistical multivariate formulation that relies on sharing common spatial random effect terms. In particular, the first response variable can be modeled by a mean that incorporates a shared random spatial effect, while the other response variables depend on this shared spatial term, in addition to specific random spatial effects. Each spatial random effect is defined through a Gaussian process with a valid covariance function, but in order to improve the computational efficiency when the data are large, each Gaussian process is approximated to a Gaussian random Markov field (GRMF), specifically to the block nearest neighbor Gaussian process (Block-NNGP). This approach involves dividing the spatial domain into several dependent blocks under certain constraints, where the cross blocks allow capturing the spatial dependence on a large scale, while each individual block captures the spatial dependence on a smaller scale. The multivariate geostatistical model belongs to the class of Latent Gaussian Models; thus, to achieve fast Bayesian inference, it is used the integrated nested Laplace approximation (INLA) method. The good performance of the proposed model is shown through simulations and applications for massive data.

Keywords: Block-NNGP, geostatistics, gaussian process, GRMF, INLA, multivariate models.

Procedia PDF Downloads 56

Authors: Najrullah Khan, Athar Ali Khan

Abstract:

The Topp-Leone distribution was introduced by Topp- Leone in 1955. In this paper, an attempt has been made to fit Topp-Leone Generalized exponential (TPGE) distribution. A real survival data set is used for illustrations. Implementation is done using R and JAGS and appropriate illustrations are made. R and JAGS codes have been provided to implement censoring mechanism using both optimization and simulation tools. The main aim of this paper is to describe and illustrate the Bayesian modelling approach to the analysis of survival data. Emphasis is placed on the modeling of data and the interpretation of the results. Crucial to this is an understanding of the nature of the incomplete or 'censored' data encountered. Analytic approximation and simulation tools are covered here, but most of the emphasis is on Markov chain based Monte Carlo method including independent Metropolis algorithm, which is currently the most popular technique. For analytic approximation, among various optimization algorithms and trust region method is found to be the best. In this paper, TPGE model is also used to analyze the lifetime data in Bayesian paradigm. Results are evaluated from the above mentioned real survival data set. The analytic approximation and simulation methods are implemented using some software packages. It is clear from our findings that simulation tools provide better results as compared to those obtained by asymptotic approximation.

Keywords: Bayesian Inference, JAGS, Laplace Approximation, LaplacesDemon, posterior, R Software, simulation

Procedia PDF Downloads 498

Authors: Md. Fazlul Karim, Ahmad Izani Md. Ismail, Mohammed Ashaque Meah

Abstract:

This paper focuses on the development of a 2-D Boundary Fitted and Nested Grid (BFNG) model to compute the tsunami propagation of Indonesian tsunami 2004 along the coastal region of Penang in Peninsular Malaysia. In the presence of a curvilinear coastline, boundary fitted grids are suitable to represent the model boundaries accurately. On the other hand, when large gradient of velocity within a confined area is expected, the use of a nested grid system is appropriate to improve the numerical accuracy with the least grid numbers. This paper constructs a shallow water nested and orthogonal boundary fitted grid model and presents computational results of the tsunami impact on the Penang coast due to the Indonesian tsunami of 2004. The results of the numerical simulations are compared with available data.

Keywords: boundary fitted nested model, tsunami, Penang Island, 2004 Indonesian Tsunami

Procedia PDF Downloads 291

Authors: Shuo Liu, Dan Liu

Abstract:

In the field of named entity recognition, most of the research has been conducted around simple entities. However, for nested named entities, which still contain entities within entities, it has been difficult to identify them accurately due to their boundary ambiguity. In this paper, a hierarchical recognition model is constructed based on the grammatical structure and semantic features of Chinese text for boundary calculation based on lexical features. The analysis is carried out at different levels in terms of granularity, semantics, and lexicality, respectively, avoiding repetitive work to reduce computational effort and using the semantic features of words to calculate the boundaries of entities to improve the accuracy of the recognition work. The results of the experiments carried out on web-based microblogging data show that the model achieves an accuracy of 86.33% and an F1 value of 89.27% in recognizing nested named entities, making up for the shortcomings of some previous recognition models and improving the efficiency of recognition of nested named entities.

Keywords: coarse-grained, nested named entity, Chinese natural language processing, word embedding, T-SNE dimensionality reduction algorithm

Procedia PDF Downloads 96

Authors: Jack R. McKenzie, Peter A. Appleby, Thomas House, Neil Walton

Abstract:

Cold-start is a notoriously difficult problem which can occur in recommendation systems, and arises when there is insufficient information to draw inferences for users or items. To address this challenge, a contextual bandit algorithm – the Fast Approximate Bayesian Contextual Cold Start Learning algorithm (FAB-COST) – is proposed, which is designed to provide improved accuracy compared to the traditionally used Laplace approximation in the logistic contextual bandit, while controlling both algorithmic complexity and computational cost. To this end, FAB-COST uses a combination of two moment projection variational methods: Expectation Propagation (EP), which performs well at the cold start, but becomes slow as the amount of data increases; and Assumed Density Filtering (ADF), which has slower growth of computational cost with data size but requires more data to obtain an acceptable level of accuracy. By switching from EP to ADF when the dataset becomes large, it is able to exploit their complementary strengths. The empirical justification for FAB-COST is presented, and systematically compared to other approaches on simulated data. In a benchmark against the Laplace approximation on real data consisting of over 670, 000 impressions from autotrader.co.uk, FAB-COST demonstrates at one point increase of over 16% in user clicks. On the basis of these results, it is argued that FAB-COST is likely to be an attractive approach to cold-start recommendation systems in a variety of contexts.

Keywords: cold-start learning, expectation propagation, multi-armed bandits, Thompson Sampling, variational inference

Procedia PDF Downloads 80

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

Abstract:

In this paper, we propose a novel inference algorithm for the multi-class Gaussian process classification model that can be used in the field of human behavior recognition. This algorithm can drive simultaneously both a posterior distribution of a latent function and estimators of hyper-parameters in a Gaussian process classification model with multi-class. Our algorithm is based on the Laplace approximation (LA) technique and variational EM framework. This is performed in two steps: called expectation and maximization steps. First, in the expectation step, using the Bayesian formula and LA technique, we derive approximately the posterior distribution of the latent function indicating the possibility that each observation belongs to a certain class in the Gaussian process classification model. Second, in the maximization step, using a derived posterior distribution of latent function, we compute the maximum likelihood estimator for hyper-parameters of a covariance matrix necessary to define prior distribution for latent function. These two steps iteratively repeat until a convergence condition satisfies. Moreover, we apply the proposed algorithm with human action classification problem using a public database, namely, the KTH human action data set. Experimental results reveal that the proposed algorithm shows good performance on this data set.

Keywords: bayesian rule, gaussian process classification model with multiclass, gaussian process prior, human action classification, laplace approximation, variational EM algorithm

Procedia PDF Downloads 300

Authors: Khaled Moaddy

Abstract:

In this paper, we present a fast and accurate numerical scheme for the solution of a Laplace equation with Dirichlet boundary conditions. The non-standard finite difference scheme (NSFD) is applied to construct the numerical solutions of a Laplace equation with two different Dirichlet boundary conditions. The solutions obtained using NSFD are compared with the solutions obtained using the standard finite difference scheme (SFD). The NSFD scheme is demonstrated to be reliable and efficient.

Keywords: standard finite difference schemes, non-standard schemes, Laplace equation, Dirichlet boundary conditions

Procedia PDF Downloads 103

Authors: Sofia M. Karadimitriou, Kostas Triantafyllopoulos, Timothy Heaton

Abstract:

Reduced dimension Dynamic Spatio-Temporal Models (DSTMs) jointly describe the spatial and temporal evolution of a function observed subject to noise. A basic state space model is adopted for the discrete temporal variation, while a continuous autoregressive structure describes the continuous spatial evolution. Application of such a DSTM relies upon the pre-selection of a suitable reduced set of basic functions and this can present a challenge in practice. In this talk, we propose an online estimation method for high dimensional spatio-temporal data based upon DSTM and we attempt to resolve this issue by allowing the basis to adapt to the observed data. Specifically, we present a wavelet decomposition in order to obtain a parsimonious approximation of the spatial continuous process. This parsimony can be achieved by placing a Laplace prior distribution on the wavelet coefficients. The aim of using the Laplace prior, is to filter wavelet coefficients with low contribution, and thus achieve the dimension reduction with significant computation savings. We then propose a Hierarchical Bayesian State Space model, for the estimation of which we offer an appropriate particle filter algorithm. The proposed methodology is illustrated using real environmental data.

Keywords: multidimensional Laplace prior, particle filtering, spatio-temporal modelling, wavelets

Procedia PDF Downloads 396

Authors: Hamdy M. Youssef, Mowffaq Oreijah, Hunaydi S. Alsharif

Abstract:

In this paper, a three-dimensional model of the generalized thermoelasticity with one relaxation time and variable thermal conductivity has been constructed. The resulting non-dimensional governing equations together with the Laplace and double Fourier transforms techniques have been applied to a three-dimensional half-space subjected to thermal loading with rectangular pulse and traction free in the directions of the principle co-ordinates. The inverses of double Fourier transforms, and Laplace transforms have been obtained numerically. Numerical results for the temperature increment, the invariant stress, the invariant strain, and the displacement are represented graphically. The variability of the thermal conductivity has significant effects on the thermal and the mechanical waves.

Keywords: thermoelasticity, thermal conductivity, Laplace transforms, Fourier transforms

Procedia PDF Downloads 193

Authors: Hamdy M. Youssef

Abstract:

In this work, the usual Euler–Bernoulli nanobeam has been modeled in the context of Lord-Shulman thermoelastic theorem, which contains non-Fourier heat conduction law. The nanobeam has been subjected to a constant magnetic field and ramp-type thermal loading. The Laplace transform definition has been applied to the governing equations, and the solutions have been obtained by using a direct approach. The inversions of the Laplace transform have been calculated numerically by using Tzou approximation method. The solutions have been applied to a nanobeam made of silicon nitride. The distributions of the temperature increment, lateral deflection, strain, stress, and strain-energy density have been represented in figures with different values of the magnetic field intensity and ramp-time heat parameter. The value of the magnetic field intensity and ramp-time heat parameter have significant effects on all the studied functions, and they could be used as tuners to control the energy which has been generated through the nanobeam.

Keywords: nanobeam, vibration, constant magnetic field, ramp-type thermal loading, non-Fourier heat conduction law

Procedia PDF Downloads 86

Authors: Yinwei Lin, Cha'o-Kuang Chen

Abstract:

In this article, the Laplace Adomian transform method (LADM) and double decomposition method (DDM) are used to solve the annular hyperbolic profile fins with variable thermal conductivity. As the thermal conductivity parameter ε is relatively large, the numerical solution using DDM become incorrect. Moreover, when the terms of DDM are more than seven, the numerical solution using DDM is very complicated. However, the present method can be easily calculated as terms are over seven and has more precisely numerical solutions. As the thermal conductivity parameter ε is relatively large, LADM also has better accuracy than DDM.

Keywords: fins, thermal conductivity, Laplace transform, Adomian, nonlinear

Procedia PDF Downloads 305

Authors: N. Guruprasad

Abstract:

This paper presents a modification of approximation method for transportation problems. The initial basic feasible solution can be computed using either Russel's or Vogel's approximation methods. Russell’s approximation method provides another excellent criterion that is still quick to implement on a computer (not manually) In most cases Russel's method yields a better initial solution, though it takes longer than Vogel's method (finding the next entering variable in Russel's method is in O(n1*n2), and in O(n1+n2) for Vogel's method). However, Russel's method normally has a lesser total running time because less pivots are required to reach the optimum for all but small problem sizes (n1+n2=~20). With this motivation behind we have incorporated a variation of the same – what we have proposed it has TMC (Total Modified Cost) to obtain fast and efficient solutions.

Keywords: computation, efficiency, modified cost, Russell’s approximation method, transportation, Vogel’s approximation method

Procedia PDF Downloads 494

Authors: Chaghoub Soraya, Zhang Xiaoyan

Abstract:

This research presents the first constant approximation algorithm to the p-median network design problem with multiple cable types. This problem was addressed with a single cable type and there is a bifactor approximation algorithm for the problem. To the best of our knowledge, the algorithm proposed in this paper is the first constant approximation algorithm for the p-median network design with multiple cable types. The addressed problem is a combination of two well studied problems which are p-median problem and network design problem. The introduced algorithm is a random sampling approximation algorithm of constant factor which is conceived by using some random sampling techniques form the literature. It is based on a redistribution Lemma from the literature and a steiner tree problem as a subproblem. This algorithm is simple, and it relies on the notions of random sampling and probability. The proposed approach gives an approximation solution with one constant ratio without violating any of the constraints, in contrast to the one proposed in the literature. This paper provides a (21 + 2)-approximation algorithm for the p-median network design problem with multiple cable types using random sampling techniques.

Keywords: approximation algorithms, buy-at-bulk, combinatorial optimization, network design, p-median

Procedia PDF Downloads 164

Authors: Valeria Bondarenko

Abstract:

In this paper, we propose two problems related to fractal Brownian motion. First problem is simultaneous estimation of two parameters, Hurst exponent and the volatility, that describe this random process. Numerical tests for the simulated fBm provided an efficient method. Second problem is approximation of the increments of the observed time series by a power function by increments from the fractional Brownian motion. Approximation and estimation are shown on the example of real data, daily deposit interest rates.

Keywords: fractional Brownian motion, Gausssian processes, approximation, time series, estimation of properties of the model

Procedia PDF Downloads 341

Authors: Smita Sonker, Uaday Singh

Abstract:

Various investigators have determined the degree of approximation of functions belonging to the classes W(L r , ξ(t)), Lip(ξ(t), r), Lip(α, r), and Lipα using different summability methods with monotonocity conditions. Recently, Lal has determined the degree of approximation of the functions belonging to Lipα and W(L r , ξ(t)) classes by using Ces`aro-N¨orlund (C 1 .Np)- summability with non-increasing weights {pn}. In this paper, we shall determine the degree of approximation of 2π - periodic functions f belonging to the function classes Lipα and W(L r , ξ(t)) by C 1 .T - means of Fourier series of f. Our theorems generalize the results of Lal and we also improve these results in the light off. From our results, we also derive some corollaries.

Keywords: Lipschitz classes, product matrix operator, signals, trigonometric Fourier approximation

Procedia PDF Downloads 442

Authors: Fazlul Karim, Esa Al-Islam

Abstract:

Many problems in oceanography and environmental sciences require the solution of shallow water equations on physical domains having curvilinear coastlines and abrupt changes of ocean depth near the shore. Finite-difference technique for the shallow water equations representing the boundary as stair step may give inaccurate results near the coastline where results are of greatest interest for various applications. This suggests the use of methods which are capable of incorporating the irregular boundary in coastal belts. At the same time, large velocity gradient is expected near the beach and islands as water depth vary abruptly near the coast. A nested numerical scheme with fine resolution is the best resort to enhance the numerical accuracy with the least grid numbers for the region of interests where the velocity changes rapidly and which is unnecessary for the away of the region. This paper describes the development of a boundary fitted nested grid (BFNG) model to compute tsunami propagation of 2004 Indonesian tsunami in Southern Thailand coastal waters. In this paper, we develop a numerical model employing the shallow water nested model and an orthogonal boundary fitted grid to investigate the tsunami impact on the Southern Thailand due to the Indonesian tsunami of 2004. Comparisons of water surface elevation obtained from numerical simulations and field measurements are made.

Keywords: Indonesian tsunami of 2004, Boundary-fitted nested grid model, Southern Thailand, finite difference method

Procedia PDF Downloads 402

Authors: Ali Bagherpour

Abstract:

The aim of this study was to determinate the variety of Anaplasma species among cattle of Khuzestan province, Iran. From April 2013 to June 2013, a total of 200 blood samples were collected via the jugular vein from healthy cattle (100), randomly. The extracted DNA from blood cells were amplified by Anaplasma-all primers, which amplify an approximately 1468bp DNA fragment from region of 16S rRNA gene from various members of the genus Anaplasma. For raising the test sensivity, the PCR products were amplified with the primers, which were designed from the region flanked by the first primers. The amplified nested PCR product had an expected PCR product with 345 nucleotides in length. 44 out of 100 cattle blood samples were Anaplasma spp. positive by first PCR and nested PCR. All cattle positive samples were further analyzed for the presence of A. centrale, A. bovis and A. phagocytophilum by specific nested PCR. A.phagocytophilum was identified by specific nested PCR in 3% of cattle blood samples. The extracted DNA from positive Anaplasma spp. samples were amplified by Anaplasma marginale/ovis specific primers, which amplify an approximately 866bp DNA fragment from region of msp4 gene. 41 out of 100 cattle blood samples (41%) were positive for Anaplasma marginale and Anaplasma ovis, respectively.

Keywords: Iran, Khuzestan, Anaplasma species, Cattle, A. marginale, A. ovis, A. phagocytophilum, PCR

Procedia PDF Downloads 465

Authors: Farrukh Javed, Krzysztof Podgórski

Abstract:

We propose a new model that accounts for the asymmetric response of volatility to positive ('good news') and negative ('bad news') shocks in economic time series the so-called leverage effect. In the past, asymmetric powers of errors in the conditionally heteroskedastic models have been used to capture this effect. Our model is using the gamma difference representation of the generalized Laplace distributions that efficiently models the asymmetry. It has one additional natural parameter, the shape, that is used instead of power in the asymmetric power models to capture the strength of a long-lasting effect of shocks. Some fundamental properties of the model are provided including the formula for covariances and an explicit form for the conditional distribution of 'bad' and 'good' news processes given the past the property that is important for the statistical fitting of the model. Relevant features of volatility models are illustrated using S&P 500 historical data.

Keywords: heavy tails, volatility clustering, generalized asymmetric laplace distribution, leverage effect, conditional heteroskedasticity, asymmetric power volatility, GARCH models

Procedia PDF Downloads 355

Authors: J. Ranjbarn, A. Alibeigloo

Abstract:

In this paper, we present an analytical method for analysis of nano-scale spherical shell subjected to thermo-mechanical shocks based on nonlocal elasticity theory. Thermo-mechanical properties of nano shpere is assumed to be temperature dependent. Governing partial differential equation of motion is solved analytically by using Laplace transform for time domain and power series for spacial domain. The results in Laplace domain is transferred to time domain by employing the fast inverse Laplace transform (FLIT) method. Accuracy of present approach is assessed by comparing the the numerical results with the results of published work in literature. Furtheremore, the effects of non-local parameter and wall thickness on the dynamic characteristics of the nano-sphere are studied.

Keywords: nano-scale spherical shell, nonlocal elasticity theory, thermomechanical shock, dynamic response

Procedia PDF Downloads 340

Authors: N. Lebga, Kh. Bouamama, K. Kassali

Abstract:

We report first-principles calculation results on the structural and elastic properties of ZnS x Se1−x alloy for which we employed the virtual crystal approximation provided with the ABINIT program. The calculations done using density functional theory within the local density approximation and employing the virtual-crystal approximation, we made a comparative study between the numerical results obtained from ab-initio calculation using ABINIT or Wien2k within the Density Functional Theory framework with either Local Density Approximation or Generalized Gradient approximation and the pseudo-potential plane-wave method with the Hartwigzen Goedecker Hutter scheme potentials. It is found that the lattice parameter, the phase transition pressure, and the elastic constants (and their derivative with respect to the pressure) follow a quadratic law in x. The variation of the elastic constants is also numerically studied and the phase transformations are discussed in relation to the mechanical stability criteria.

Keywords: density functional theory, elastic properties, ZnS, ZnSe,

Procedia PDF Downloads 545

Authors: Geeta Partap, Nitika Chugh

Abstract:

The present paper deals with the flexural vibrations of homogeneous, isotropic, generalized micropolar microstretch thermoelastic thin Euler-Bernoulli beam resonators, due to Exponential time varying load. Both the axial ends of the beam are assumed to be at simply supported conditions. The governing equations have been solved analytically by using Laplace transforms technique twice with respect to time and space variables respectively. The inversion of Laplace transform in time domain has been performed by using the calculus of residues to obtain deflection.The analytical results have been numerically analyzed with the help of MATLAB software for magnesium like material. The graphical representations and interpretations have been discussed for Deflection of beam under Simply Supported boundary condition and for distinct considered values of time and space as well. The obtained results are easy to implement for engineering analysis and designs of resonators (sensors), modulators, actuators.

Keywords: microstretch, deflection, exponential load, Laplace transforms, residue theorem, simply supported

Procedia PDF Downloads 281

Authors: Anusuya Ghosh, Vishnu Narayanan

Abstract:

The approximation of convex set by semidefinite representable set plays an important role in semidefinite programming, especially in modern convex optimization. To optimize a linear function over a convex set is a hard problem. But optimizing the linear function over the semidefinite representable set which approximates the convex set is easy to solve as there exists numerous efficient algorithms to solve semidefinite programming problems. So, our approximation technique is significant in optimization. We develop a technique to approximate any closed convex set, say K by compactly semidefinite representable set. Further we prove that there exists a sequence of compactly semidefinite representable sets which give tighter approximation of the closed convex set, K gradually. We discuss about the convergence of the sequence of compactly semidefinite representable sets to closed convex set K. The recession cone of K and the recession cone of the compactly semidefinite representable set are equal. So, we say that the sequence of compactly semidefinite representable sets converge strongly to the closed convex set. Thus, this approximation technique is very useful development in semidefinite programming.

Keywords: semidefinite programming, semidefinite representable set, compactly semidefinite representable set, approximation

Procedia PDF Downloads 352

Authors: Sen-Yung Lee, Li-Kuo Chou, Chao-Kuang Chen

Abstract:

In this study, the problem of temperature transient response of a spiral fin, with its end insulated, is analyzed with base end subjected to a variation of fluid temperature. The hybrid method of Laplace transforms/Adomian decomposed method-Padé, is applied to the temperature transient response of the fin, the result of the temperature distribution and the heat flux at the base of the spiral fin are obtained, show a good agreement in the physical phenomenon.

Keywords: Laplace transforms, Adomian decomposed method- Padé, transient response, heat transfer

Procedia PDF Downloads 392

Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

Abstract:

In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

Procedia PDF Downloads 505